2.1 Board gender diversity and foreign acquisition premium

The premium paid by the acquirer in foreign M&A deals can be explained by the premises of agency theory, as well as hubris theory. Agency theory suggests that managers tend to achieve their personal interests at the expense of shareholders' interest, that is, biased judgements are made in evaluating the target value (Abou-El-Sood, 2021; Fama & Jensen, 1983). Hubris hypothesis, formulated by Roll (1986), further highlights that managers overestimate their ability and over-evaluate target firms. Roll (1986) argues that higher premiums paid in acquisition deals are linked to managerialism or hubris-based M&A, where managers chase their own interests or overestimate the target's value. Overpayment occurs when acquirers are overconfident in their ability to manage the target and, thus, they over-price the target (e.g., Baker et al., 2012; Harford et al., 2012; Roll, 1986). The phenomenon of overconfidence (hubris) results in a higher acquisition premium payment, which is more related to male-dominated M&A (e.g., Barber & Odean, 2001). Previous studies (e.g., Huang & Kisgen, 2013; Levi et al., 2014) further support this phenomenon by showing that male directors present relatively higher overconfidence in corporate M&A investment decisions relative to female counterparts, affecting acquisition premium payments. Ragon (2011) suggests that male directors are more likely to pay a higher bid for targets than female counterparts. However, Ragon (2011) notes that diversified boards, with more female directors, are more inclined to pay lower bid premiums for targets compared with male directors since females are normally less overconfident (e.g., Beyer, 1990; Croson & Gneezy, 2009; Levi et al., 2014). Baker et al. (2012) indicate that female directors of acquiring firms can generate effective negotiations, which might lead to lower M&A premiums paid during M&A transactions.

Moreover, prior research suggests that female directors are more active in using monitoring functions, thereby mitigating conflict of interest between managers and shareholders. Adams and Ferreira (2009) show that female directors perform better monitoring roles, require extra audit efforts and provide better managerial accountability than their male counterparts. Furthermore, Francoeur et al. (2008) suggest that women in the boardroom often bring a fresh perspective to complex investment issues, and this can help correct informational biases associated with the estimation of foreign targets' value. Arnaboldi et al. (2021) and Karavitis et al. (2021) find that the presence of females in the boardroom is associated with a reduction in financial misconduct fines and cost of lending. Levi et al. (2014) suggest that a positive role of board gender diversity arises from the heterogeneity of personality traits between female and male directors. In particular, a significant strand of research suggests that female directors are more risk-averse in their financial decision-making than male counterparts (Eckel & Grossman, 2002; Jianakoplos & Bernasek, 1998). Thus, female risk-aversion traits are useful to alleviate risks resulting from overestimating acquisition synergies, and such traits are more pronounced in uncertain investments, for example, foreign M&A deals (Levi et al., 2014; Schubert et al., 1999). In this regard, Niessen and Ruenzi (2006) indicate that acquirers with more female directors on the board are associated with a lower level of unsystematic risk and more stable returns.

Overall, the above discussion drives us to postulate the first hypothesis as follows:

2.2 Board gender diversity and foreign M&A outcomes

Resource dependency theory posits that firms work in an open system in which their outcomes are dependent on external organizations and environmental contingencies (Pfeffer & Salancik, 2003). Such a context imposes challenges and uncertainties for firms, which can be mitigated by creating effective linkages between corporate boards and external entities to reduce dependency and obtain the needed resources (Hillman et al., 2007). In this regard, the literature provides evidence that gender diversity on boards facilitates more effective communication with external entities and swifter resolution of difficult issues (e.g., Ali et al., 2014). More specifically, women in the boardroom provide three important attributes to alleviate the dependencies and surrounding uncertainties: advice and counsel, legitimacy, and communication channels (Liu et al., 2014; Pfeffer & Salancik, 2003). The premises of resource dependence theory present several arguments to promote board gender diversity (e.g., Carter et al., 2010; García-Meca et al., 2015; Hillman & Dalziel, 2003; Isidro & Sobral, 2015; Nguyen et al., 2020; Reguera-Alvarado et al., 2017). For example, diversity on the board acts as a bridge to important constituencies in the external environment, resulting in greater access to more talent. Gender-diverse boards bring in unique information that can potentially improve the advisory function and, thence, help in better decision-making. Board diversity also sends important positive signals to the product and labour markets since ‘women often bring a fresh perspective on complex issues, and this can help correct informational biases in strategy formulation and problem-solving’ (Francoeur et al., 2008: 84). Collectively, this body of studies, grounded in resource dependence theory, suggests potential positive corporate outcomes (both immediately or in the short- and long-term) resulting from board gender diversity.¹

So far, only a handful of empirical research has examined the short-term market reaction to M&A deals with gender-diverse boards, particularly in China. Employing a sample of US firms, Huang and Kisgen (2013) document higher returns around acquisition announcements made by firms with female executives. Likewise, the market is likely to react positively around the announcement day of M&A by more diversified boards (Byrd & Hickman, 1992; Liu et al., 2015). This can be explained as the market expecting more heterogeneity on the board and, thus, the possibility of value creation to the acquirers (Hagendorff et al., 2008). Lee and James (2007) suggest that the market generally reacts more positively to the appointment of female directors compared to male directors. Interestingly, Kang et al. (2010) find that investor reaction is more favourable to the appointment of female outside directors followed by female appointments to non-CEO executive roles. Schmid and Urban (2016) show that the market reacts negatively to the death of female board members.²

Based on the previous discussion, we postulate the following hypothesis:

While examining short-term windows around corporate events is standard practice in our setting, prior market reaction research shows that market expectations, particularly about M&A outcomes in the short-term, are not necessarily reflecting the outcomes in the long-term (e.g., Ahmed & Elshandidy, 2021), and that these expectations can generally be biased (Eagly & Karau, 2002). More specifically, previous research (e.g., Loy & Rupertus, 2022) suggests that short-term market reactions would proxy for the expected, rather than actual, impact of female directors concerning shareholder value. Following an M&A deal, the market is expected to undergo an adjustment period, evaluating decision quality. Thus, it is plausible to expand the examination of the impact on corporate outcomes to the long-term (Gregory et al., 2013; Wolfers, 2006). It is argued that the (positive) effects of gender diversity are associated with long-term corporate outcomes (FRC, 2021; Wolfers, 2006). That said, it was a surprise to us to find that previous studies have overlooked examining the long-term outcomes of M&A deals in relation to female board representation.

In this regard, a strand of literature suggests that a greater presentation of female directors on the board enhances corporate outcomes (e.g., Liu et al., 2021; Lückerath-Rovers, 2013; Terjesen et al., 2016). This enhancement, due to gender diversity, is empowered by various perspectives (e.g., woman directors' board monitoring and advisory roles, and ethical and risk-aversion traits) that improve the decision-making process (Zalata et al., 2019). Specifically, for firms engaged in foreign acquisitions, gender diversified boards bring invaluable market-specific information and knowledge, perspectives, and views (e.g., Giannetti et al., 2015). Generally, previous studies (e.g., Boulouta, 2013; Brahma et al., 2021; Campbell & Mínguez-Vera, 2008; Carter et al., 2003; Erhardt et al., 2003; Low et al., 2015; Mahadeo et al., 2012; Terjesen et al., 2016) find a positive relationship between board gender diversity and firm performance and value (as captured by various measures including return on sales, return on equity, return on capital expenditure, ROA, and BHAR). Agyemang-Mintah and Schadewitz (2019) find a positive relationship between gender diversity and the value of financial institutions in the UK before and during the financial crisis, but not after. Farag and Mallin (2017) show that a critical mass of female representation on the board of directors can reduce European banks' vulnerability to financial crisis. Moreover, another branch of studies finds a positive relationship between gender diversity and other corporate aspects such as corporate social responsibility and innovation (e.g., Beji et al., 2020; Byron & Post, 2016; Nekhili et al., 2017; Torchia et al., 2011). Evidence by Arun et al. (2015) and Zalata et al. (2018) suggests that the presence of women directors on the corporate boards reduces earnings management practices.

On the other hand, another strand of the literature shows unfavourable, mixed, or inconclusive results with respect to board gender diversity and different corporate outcome variables (e.g., Adams & Ferreira, 2009; Ahern & Dittmar, 2012; Carter et al., 2010; De Cabo et al., 2012; Hassan & Marimuthu, 2016; Jeong & Harrison, 2017; Marinova et al., 2015; Matsa & Miller, 2013; Rose, 2007; Shehata et al., 2017; Smith et al., 2006). Engelen et al. (2012) further find a statistically insignificant relationship between gender diversity and Dutch firm performance during the financial crisis. Consistent with the social-psychological theory of minority position, Westphal and Milton (2000) suggest that female directors on the board are likely to reduce the inside board dynamics. Furthermore, gender diversity would result in conflicting viewpoints, divergent values and different experiences, making the decision-making process time-consuming and less effective (e.g., Campbell & Mínguez-Vera, 2008; Carter et al., 2010; Lau & Murnighan, 1998). In this regard, Cao et al. (2019, p. 1035) indicate that gender diversity can ‘lead to lengthier deliberations, disagreements among board members, and other communication breakdowns’. Consistent with this, Agrawal et al. (1992) suggest that acquirers experience a wealth loss over the 5-year post-merger period due to the negative influence of minority members such as less representative female directors.

This mixed evidence on the relationship between board gender diversity and corporate outcomes in the long-term leads us to formulate the following hypothesis:

3.1 Sample

Employing the GTA CSMAR (China Stock Market and Accounting Research) databases to compile the foreign M&A and financial data of all Chinese listed firms during 1998–2019,³ we downloaded the Chinese foreign M&A deals during 2000–2017 since our analyses require 2 years of pre- and post-merger performance data from the effective year of M&A deals. Consistent with prior research (e.g., Ahmed & Elshandidy, 2021; Alexandridis et al., 2013; Du et al., 2016; Elrazaz et al., 2021), the following procedures are adopted to reach our final sample. First, only Chinese-listed acquirers of completed foreign M&A deals are kept in our sample.⁴ Second, financial and utilities acquirers are excluded due to their distinct regulations, accounting practices and financial reporting systems. Third, targets must be listed firms.⁵ Fourth, acquirers should take over absolute control of more than 50% of the targets. Fifth, following prior research (e.g., Amewu & Alagidede, 2018; Chakrabarti et al., 2009; Liu et al., 2021; Liu & McConnell, 2013; Tao et al., 2017), we exclude multiple foreign M&A deals during a calendar year to ensure the accuracy of the acquirer's long-term operating performance and Buy and Hold Abnormal Return (BHAR) results. Thus, our analysis focuses on cases where the market can unambiguously identify the deal influences since including such multiple acquisitions would introduce confounding effects, making it challenging to disentangle the effects of individual acquisitions on acquirers' long-term outcomes. Sixth, the bid represents the first offer by a given acquirer for a given target to avoid overweighting-contested deals that may bias our t-statistics upwards (Du et al., 2016).⁶ Seventh, we exclude deals labelled as minority stake purchases, acquisitions of remaining interest, privatizations, leveraged buyouts, spinoffs, recapitalizations, self-tenders or exchange offers and repurchases (Alexandridis et al., 2013). Finally, our sample excludes acquirers without sufficient financial and market data available. This leaves us with a final sample of 292 foreign M&As by Chinese listed bidders.⁷

3.2 Empirical models

The acquisition premium is measured as the ratio of M&A deal value minus the target's pre-announcement market value to the target's market value 4 weeks before the announcement date (Laamanen, 2007). Following Ahern and Dittmar (2012) and Ahmed et al. (2022), we measure gender diversity as the percentage of female directors on the acquirer's board (%Female directors). C_i,t−1 is a vector of control variables. η_k,t controls for industry and year fixed effects.⁸

Long-term performance is captured by the change in ROA (∆ROA). Specifically, ∆ROA variable is the acquirer's return on assets 2 years after minus 2 years before the effective year of foreign acquisition. ROA is the ratio of the acquirer's average profit before tax and interest to total assets (Yang et al., 2019). C_i,t−1 is a vector of control variables. η_k,t controls for industry and year fixed effects.

Based on Levi et al. (2014), it is essential to separate the effect of different roles of female directors, namely, independent directors and executive directors. Thus, we run all the previous models (1–3) after replacing the %Female director variable with the proportion of independent female directors and the proportion of female executive directors variables on the acquirer board (Liu et al., 2014; Peni, 2014). Finally, following prior literature on gender diversity and M&A (e.g., Adams & Ferreira, 2009; Dezsö & Ross, 2012; Masulis et al., 2007; Uysal, 2011; Zalata et al., 2021), our set of control variables include board size, board independence, leverage, management size, sales growth, natural logarithm of cash, firm size, firm age, capital expenditure, and deal size. All independent variables employed in our regression models are lagged by 1 year relative to the dependent variable (e.g., Elsayed et al., 2023). We further use industry and year fixed effects to control for the inherently volatile industries and unobserved effects over the years, as well as robust standard errors that control for both serial correlation and heteroscedasticity. Additionally, we winsorize continuous variables on the 1% of both tails to mitigate the influence of outliers.¹⁰ The definitions and measures of these control variables are provided in detail in Appendix A.

4.1 Descriptive statistics

Table 1 reports descriptive statistics for our final sample of 292 foreign M&A by Chinese acquirers which shows that, on average, the proportion of female directors on the board of Chinese firms involved in foreign acquisitions is 6.8%. Furthermore, the proportion of female independent directors and female executive directors on acquirers' board is 1.9% and 1.3%, respectively.¹¹ Regarding our dependent variables, the mean acquisition premium is 1.108. The average 3-day (5-day) accumulative abnormal return around the M&A announcement is 0.6% and 0.5%, respectively. The mean value of ΔROA is −1.1%, suggesting that Chinese acquirers experience an average decrease in performance in the 2 years after, compared to the 2 years before foreign acquisition.

Moreover, our sample shows the following board characteristics of acquirers engaged in foreign M&A deals during the sample period. On average, the natural logarithm of the board size is 2.332; the percentage of board independence is 35.7%; the natural logarithm of the management size is 1.95; and 4.5% (2%) of CEO (chairperson) positions are represented by female directors. Approximately 96.6% (1%) of acquisition deals are made using cash (stock) payment, which is consistent with the fact that stock-for-stock is not a pervasive payment method in China or foreign M&A transactions (Gu & Reed, 2016).

4.2 Does board gender diversity associate with foreign acquisition premium?

Table 2 shows results related to testing H1, which addresses the influence of women in the boardroom on foreign acquisition premium. Column 1 of Table 2 shows a statistically negative coefficient on the %Female directors variable (t-statistic −4.00 at the 1% significance level).¹² This leads to not rejecting H1 that acquirers with more women in the boardroom are more likely to pay a lower premium on foreign M&A deals in China. This finding is consistent with the results of Huang and Kisgen (2013) and Levi et al. (2014), suggesting that females are normally less overconfident, which reduces the probability of earning overestimation for the target and, thereby, paying less premium.

Column 2 of Table 2 presents our results after distinguishing between female independent and non-independent directors. We find that the coefficients on Female independent (t-statistic −1.90 at the 10% significance level) and Female executive (t-statistic −1.84 at the 10% significance level) are negatively significant. Therefore, our previous finding on female directors can be attributable to both the monitoring and supervisory roles played by female directors. These results are in line with prior research supporting the supervisory (e.g., Rossi & Volpin, 2004; Sonenshine & Reynolds, 2014) and monitoring roles (e.g., Cotter et al., 1997; Davis et al., 1991; Hermalin & Weisbach, 1998; Shivdasani, 1993) played by female directors in the firm.

4.3 Does board gender diversity associate with the short-term market reaction around the announcement of foreign acquisition?

Columns 1 and 3 of Table 3 present the effects on acquirers' CAR3 and CAR5 around the announcement of foreign acquisitions. The coefficients on %Female directors suggest that the proportion of female directors on the board has a significantly positive impact on market reaction. Specifically, %Female directors is positively significant at the 1% significance level (t-statistics are 7.38 in CAR3 test and 6.34 CAR5 test). From the economic perspective, the percentage increase of female director representation on the bidder board increases the 3- and 5-day CAR by 0.335 and 0.391 basis points, respectively. Collectively, these results support our conjecture that acquirers with higher female representation on the board can benefit from positive short-term market reaction around the announcement of foreign acquisitions. These findings lead to not rejecting of H2a, that the market is likely to react positively to the announcement of foreign acquisitions by Chinese acquirers with more female members in the boardroom.

Columns 2 and 4 of Table 3 present our results after distinguishing between female independent and non-independent directors. We find significantly positive coefficients on the %Female Independent variable (t-statistic 5.50 at the 1% significance level) and %Female Executive variable (t-statistic 2.68 at the 1% significance level) in CAR3 tests. Furthermore, we find significantly positive coefficients on the %Female Independent variable (t-statistic 5.52 at the 1% significance level) and %Female Executive variable (t-statistic 2.48 at the 1% significance level) in CAR5 tests. This implies that the market appreciates both the monitoring and supervisory role played by female directors. These results are consistent with prior research that boards with higher outside female directors represent a positive corporate governance signal to the market (e.g., Shleifer & Vishny, 1997). These findings are also in line with Liu et al.'s (2015) view that higher independent members on the bidder's board experience significantly higher abnormal returns, since effective monitoring by female directors restrains loss-making projects, especially when their counterpart male directors are overconfident.

4.4 Does board gender diversity associate with the long-term performance of foreign acquisition?

Table 4 shows results of the association between women in the boardroom and the long-term operating synergies of acquirers after the completion of foreign M&A. Here, we test the impact of the change in the operating performance of acquirers in 2 years pre- to post- the effective year of acquisition as captured by changes in ROA.

Column 1 of Table 4 shows a positively significant female director coefficient (t-statistic 1.78 at the 10% significance level). Column 2 presents our results after distinguishing between independent and non-independent female directors. We find only a significantly positive coefficient on the %Female Independent variable (t-statistic 3.46 at the 1% significance level). This suggests that the long-term impact of women on the board is more pronounced in the monitoring role. This finding is consistent with agency theory premises that board diversity is an important mechanism to monitor the management and, hence, improve performance (i.e., Carter et al., 2010; Hillman & Dalziel, 2003). This is also in line with previous studies (i.e., Ossorio, 2020) that a higher percentage of independent female directors positively affects the decision-making process in reducing low-profit and high-risk foreign acquisitions. Collectively, our empirical findings support H2b that the percentage of female directors on the acquirers' board is associated with M&A long-term performance in China. Additionally, in line with prior research (i.e., Chen & Young, 2010; Liu et al., 2014), the results of Table 4 suggest that acquirers with a female chair experience significant improvement in long-term performance following foreign acquisitions.

Turning to control variables, Table 4 shows that firm size and capital expenditure variables have a significant positive effect on changes in ROA following foreign M&A deals. However, the deal size has a negative influence on post-foreign acquisition long-term performance.

5.1 Long-term outcomes using Buy and Hold Abnormal Return (BHAR) proxy

Table 5 presents the effect of board gender diversity and the BHAR of acquiring firms over 24 months. In line with our previous results in Section 4.4, it shows that Chinese acquirers with female directors on the board experience significantly positive BHAR 24-month post-foreign M&A deal at the 5% significance level, indicating that foreign acquisitions are valuable investments for acquirers with more females in the boardroom. Similarly, we observe that the percentage of independent female directors variable is positively related to acquirers' BHAR 24 months following the effective date of foreign acquisitions.¹³

5.2 Instrumental variables to address endogeneity (omitted variable bias)

Consistent with prior research (Adams et al., 2010; Farrell & Hersch, 2005; Hermalin & Weisbach, 1998), we employ a two-stage least squares (2SLS) statistical technique to address endogeneity concerns related to possible omitted variables. Following previous studies (e.g., Flabbi et al., 2019; Mekhaimer et al., 2022; Xing et al., 2021), we employ four instrumental variables: the regional trend in the percentage of female directors, the regional trend in the percentage of female executives, the multiplication of these two instruments, and province gross domestic product (GDP) growth. This procedure assumes that aggregate trends in the gender diversity on board at the regional level are unrelated to the time-varying firm-level heterogeneity that leads to endogeneity. Regional trends are expected to employ as valid instruments since the trends are correlated with the relevant gender diversity in each firm in the region (i.e., meet the relevance condition), but are not directly associated with acquisition premium or outcomes in a specific firm (i.e., meet the exogeneity condition). Likewise, the province's annual GDP growth is used since regional economic growth is likely to correlate with women's opportunities for empowerment and advancement.

We also run different specification tests to examine that our instruments are not weak and valid. Specifically, we run Cragg-Partial F statistic, Hansen J statistic (p-value), and Wald test of exogeneity (p-value). Collectively, these statistic estimates suggest that instrumental variables used in our analysis are valid and not weak (e.g., Larcker & Rusticus, 2010; Stock et al., 2002). Table 6 reports the 2SLS second stage (alongside the first stage) regressions results, which are all qualitatively consistent with our main findings. This implies that inferences driven by our analyses are not subject to endogeneity problems attributable to possible omitted variables.

5.3 Propensity score matching to address potential self-selection bias

Testing whether board diversity influences the premium and outcomes of foreign acquisitions using an OLS method can trigger self-selection bias. Specifically, a potential bias is that a firm's decision to recruit females in the boardroom is unlikely to be exogenous. To address this bias, we employ propensity score matching by establishing a treatment group (e.g., board with female directors) matched to a control group (e.g., board without female directors). First, we calculate each observation's propensity score using a logit model that predicts the likelihood of the presence of female directors as a function of board-level, firm-level and deal-level characteristics (Ln Board Size, % independent, leverage, Ln Assets, Ln Cash, Ln sales growth and deal size), all of which have been established as related to the presence of female directors on the board (Adams & Ferreira, 2009; Dezsö & Ross, 2012; Masulis et al., 2007; Yermack, 1996). Then, we apply the nearest neighbour matching approach without replacement, which means that each firm in the control group can only appear and match one firm in the treated group (Ge & Lennox, 2011). We also restrict the observations to being on the common support by excluding firms in the control group whose propensity lies above the maximum value or below the minimum value of propensity score among firms in the treated group and vice versa. This guarantees that we do not match firms concentrated at the extreme boundaries (Saunders & Steffen, 2011).¹⁴

Table 7 presents the effect of board gender diversity in the boardroom on foreign acquisitions' premium and outcomes after accounting for endogeneity concerns using PSM. It confirms that our previous empirical findings reported in Tables 2–5 are robust and not affected by the selection bias problem.

5.4 Heckman's two-step model to address endogeneity

In line with prior research (e.g., Zalata et al., 2021), we further address the possible endogeneity concerns by employing Heckman's (1979) two-step model. In the first step, we run probit regression of the likelihood of having a female director on the board of directors on the set of our control variables (e.g., Elsayed et al., 2022). The first-step model also includes our exogenous instruments mentioned above as suggested by prior research (Feng et al., 2009; Larcker & Rusticus, 2010). In the second-step, inverse Mill's ratio (IMR) estimated from the probit model in the first-step is included as an additional variable in our models.

Table 8 reports Heckman's second-stage regressions results, which are all qualitatively consistent with our main findings. This further assures that inferences driven by our analyses are not subject to endogeneity concerns.

5.5 Gender diversity and foreign acquisitions during the financial crisis

The collapse of major financial institutions during the financial crisis caused a dramatic fall in global credit markets. This fall led to a severe reduction in the availability of external finance and impeded firms' ability to invest (Duchin et al., 2010). This raises the question of whether the negative relationship between gender diversity and foreign acquisition premium may have been driven only by the effect of the global financial crisis. Further, Samarakoon (2011) reports that, during the financial crisis, the US stock market plummeted by 43%. Thus, it is essential to test whether the short- and long-term outcomes of foreign acquisitions by female directors may be affected by the financial crisis. We control for the financial crisis effects using three variables, representing the periods prior to, during and after the crisis. The financial crisis variable takes the value one for the years of the financial crisis, 2008 and 2009, and zero otherwise (Frankel & Saravelos, 2012; Lins et al., 2017).¹⁵ The dummy variable prior (post) to the financial crisis takes the value one for the years before (after) the financial crisis period, and zero otherwise. For these periods, we employ dummy indicators for the periods during and after the crisis, relative to the period before the crisis.

Table 9 indicates that our earlier findings individually and collectively remain strongly consistent after excluding the effects of the financial crisis and the period after it. Overall, our results are consistent with Chen et al. (2019) that the financial crisis effect will be minimal since female directors are cautious rather than overconfident in valuing investment perspective during non-crisis years. Thus, firms with female directors may experience less shock during a financial crisis compared to male director counterparts.

5.6 Critical mass of board gender diversity

The critical mass theory suggests that a certain threshold of female directors in the boardroom is essential for exerting a significant influence (e.g., García-Meca et al., 2022). Specifically, a strand of prior research on the critical mass of female directors argues that the presence of a single female on a board is often perceived as token representation, the inclusion of two females is regarded as a noticeable presence, while the participation of three or more females engenders a commanding and influential voice (Liu et al., 2014). Accordingly, we test the critical mass of female directors by replacing our main independent variable (the percentage of female directors) with three dummy variables that capture boards with one, two, or three or more female directors.

Our findings provide in Table 10 empirical support for the critical mass theory in the context of foreign M&A deals in China. In particular, we observe that the presence of three or more female directors in the boardroom is associated with significant reductions in the acquisition premiums paid for foreign targets. Furthermore, the market reacts positively in the short term to the announcement of foreign acquisitions by acquirers with three or more female directors. In the long term, acquirers with three or more female directors on their boards experience improved operating performance following foreign M&A deals.¹⁶

5.7 Board gender diversity and the market reaction to the announcement of foreign M&A using the market model

In Appendix B, we estimate acquirers' CAR over a 3- and a 5-day event window around the announcement of foreign acquisitions deals using a market-adjusted model. We get similar results to Section 4.3, that the market responds positively to foreign acquisitions made by acquirers with more female directors on the board.

5.8 Relaxed sample selection criteria

In Appendix C, we relaxed our sample selection criteria by including multiple foreign M&A deals during the same year and overweighting-contested deals. Our results are all qualitatively consistent with our main findings.