The same effects are represented for the other variables, except board size. This variable has no effect in case of traditional sector, however is positively related to adding women to the board in technological sector.

Thus, we cannot accept Hypothesis 2, as the findings suggest the similar sign of effect, but with different values, that are slightly different.

Sectoral effect

The table consists of an unbalanced panel of firm-level data from 1,809 firms for the period 2010 - 2015, which were in the Bloomberg database. The dependent variable is the number of female directors added to the firm. Columns 1 and 2 report poisson regression, where each of the Column specify traditional or technological sector. Standard errors are adjusted for group correlation at the firm level in all specifications. Values of t-statistics or z-statistics are in brackets. All specifications include year dummy and firm fixed effects. Number of observations, and log likelihood are represented in the last three rows.

***, **, * shows significance at the 1%, 5%, 10% levels respectively.

· Firm risk and gender diversity

We measure risk-taking level as the volatility of a firm's return on assets (ROA) over one-year overlapping periods, applying the determination of risk by Khaw et Al. (2016). Also, we mentioned that the problem of reverse causality is typical for such studies. Instrumental variable (IV) regression allows for consistent estimation. Instrumental variable should explain gender representation of board and to be exogenously related to firm's outcomes. We used the interception of board size and existence of female directors on board as the instrumental variable. The interception represents a proxy for female connections of board size (Sila et Al., 2016, Lenard et Al., 2014).

Risk measure and gender diversity.

The table consists of an unbalanced panel of firm-level data from 1,809 firms for the period 2010 - 2015, which were in the Bloomberg database. Risk is lagged ROA over one year. Full description of variables is presented in Table. Column 1 reports OLS regression. Column 2 reports OLS regression with another specification. Column 3 reports GLS regression with firm fixed effects. Column 4 represents of IV (2SLS) regression, where % of Female Directors is instrumental variable and determines independence of board and interaction between board size and existence of female directors. Values of t-statistics or z-statistics are in brackets. All specifications include year dummy. Number of observations, and type of regression are represented in the last three rows.

***, **, * shows significance at the 1%, 5%, 10% levels respectively.

Columns 1 and 2 in Table represents OLS regressions. Column 1 reports negative association between proportion of women on board and firm risk, and the coefficient is close to zero. Board Size has no effect on firm risk. CEO duality, firm age, leverage, R&D and capital expenditures have positively influence firm risk.

We expect increase in firm risk if CEO is also chairman of the board as CEO represents insider and can actively push forward one's interests.

Firm age positively influence firm risk as over time the firm develops business connections and reputation, so it can take on more unjustified risks unlike young firms. On the other hand, we can expect that old firms would be more conservative and choose low-risky investments. However modern business conditions can destroy non-dynamic firms with conservative politics as there is high level of competition.

Most of studies suggest positive relation between R&D, capital expenditures and firm risk. R&D projects are risky due to long term and high uncertainty. Moreover, the outcomes of R&D projects might be effectively applied in business process. Our results consist with Sila et Al. (2016).

Negative relationship was investigated for firm size. It suggests that smaller firms are negatively reacted on risky projects. This result is consisted with Sila et Al. (2016) and Lenard et Al. (2014).

Column 2 represents another specification of model in Column 1. We used methodology by Lenard et Al. (2014), identifying gender diversity of board as interaction term of board size and existence of women on board. The sign has changed. Interaction of women with board shows positive relation with firm risk. There are few reasons: women can play role of «grey» directors or firms with initially high level of risk add women on boards. The last reason concerns problem of reverse causality and we check for it in Column 4.

We build GLS regression with firm fixed effect in Column 3. The results show insignificance of all variables, except capital expenditures. However, regression is relevant as F-statistics equals 2.79 with probability = 0.0004. We can conclude that on average firm's risk is driven by firm's financial factors, it does not mean that board structure has no influence on firm risk.

To deal with problem of misspecification, we estimate IV regression with firm fixed effects in Column 4. Assuming weak level of board independence can negotiate women' contribution in decision making process, we determinate gender diversity on board as interaction of board size with existence of women on board and level of board independence. The results suggest negative association between proportion of women on board and firm risk on the 1% level, indicating that every lag increase in proportion of women on board will reduce the variability of ROA by 14.7%. It consists with result in Column 1. The results do not differ, the proportion of female directors is still negatively related to firm risk and board size has a positive relationship with firm risk. Thus, our results continue to hold when we use another measure of risk. We accept IV specification as the most relevant due to robustness check (see Table). Hence, our findings support the statement of Hypothesis 3.

Risk measure and gender diversity. Robustness. The table consists of an unbalanced panel of firm-level data from 1,809 firms for the period 2010 - 2015, which were in the Bloomberg database. WACC is weighted average cost of capital from the Bloomberg database. Full description of variables is presented in Table. Column 1 reports OLS regression. Column 2 reports OLS regression with another specification. Column 3 reports GLS regression with firm fixed effects. Column 4 represents of IV (2SLS) regression, where % of Female Directors is instrumental variable and determines independence of board and interaction between board size and existence of female directors. Values of t-statistics or z-statistics are in brackets. All specifications include year dummy. Number of observations, and type of regression are represented in the last three rows.

***, **, * shows significance at the 1%, 5%, 10% levels respectively.

· Independence of board and gender diversity

We use the methodology by Terjesen et Al. (2016), the study of which investigate similar effects of gender diversity.

Table represents the results. We estimate simultaneous effect of female and independent directors in Column 1. The results report opposite effect, gender diversity positively influence Tobin's Q at the 1% level, while independent directors have negative effect at the 1% level. Moreover, the effect by women on board is higher, a 1% increase in proportion of female directors reduces Tobin's Q by 1%, while a 1% increase in proportion of independent directors increases Tobin's Q by 0.5%.

Independence and gender diversity.

The table consists of an unbalanced panel of firm-level data from 1,809 firms for the period 2010 - 2015, which were in the Bloomberg database. Performance is represented by logarithm of Tobin's Q (ratio of the firm's market value to its book value of assets). Column 1 - 5 reports GMM regression. The lag percentages of independent and female directors on the board, the lag of board the board size are selected as the initial set of instruments. Column 1 reports simultaneous effect of female and independent directors on the firm's Tobin's Q. Columns 2 and 3 reports the effect of the share of female and independent directors separately. Column 4 reports the interaction. Column 5 reports the effect of a dummy variable with the value of 1 if the board has at least one woman on board while maintaining the variable share of independent directors.

Values of t-statistics are in brackets. All specifications include year and sectoral dummy. Number of observations, type of regression and endogeneity test are represented in the last three rows.

***, **, * shows significance at the 1%, 5%, 10% levels respectively.

Assuming linear model, the results suggest that female directors are more important to firm. Also, the results report negative effect by board size on Tobin's Q, providing the evidence, that larger boards are less-effective decision-makers (Adams and Ferreira, 2009; Terjesen et Al., 2016)

The same results are obtained in Column 2 and 3, where the effect by female and independent directors on Tobin's Q was tested separately. Both coefficients are positive and statistically significant. Moreover, the marginal effect by female director is higher and more significant than the effect by independent directors. This result confirms previous findings.

Column 4 and 5 includes intercept of the percentages of female and independent directors on board. We exclude proportion of women because of high level of correlation, we solve this problem through instrumental variable (see the description of Table). The results show an absence of effect by independent directors on boards. Intercept in Column 4 represents weak positive influence (0.0001) at the 1% level. However, dummy variable represents strong positive effect on Tobin's Q (65.4%). Though, we conclude that independence of board is stronger when the board is more gender diversified, it supports Hypothesis 4.

Concerning control variables, the results suggest permanent positive effect by logarithm of ROA and proportion of institutional ownership. Institutional investors are good monitors (Bushee, 1998; Bushee et Al. 2014) and often initiate increase of gender diversity on boards.

We have already tested firm performance through Tobin's Q and ROA and provided different effects by gender diversified board on these two variables. In Table we provide the same estimations, but on ROA. Simultaneous estimation of proportion of female and independent directors on boards shows an absence of effect by independent directors, however female directors represent positive association with ROA.

Independence and gender diversity.

The table consists of an unbalanced panel of firm-level data from 1,809 firms for the period 2010 - 2015, which were in the Bloomberg database. Performance is represented by logarithm of gross ROA (ROA is the net income before extraordinary items and discounted operations divided by book value of assets). Column 1 - 5 reports GMM regression. The lag percentages of independent and female directors on the board, the lag of board the board size are selected as the initial set of instruments. Column 1 reports simultaneous effect of female and independent directors on the firm's Tobin's Q. Columns 2 and 3 reports the effect of the share of female and independent directors separately. Column 4 reports the interaction. Column 5 reports the effect of a dummy variable with the value of 1 if the board has at least one woman on board while maintaining the variable share of independent directors. Values of t-statistics are in brackets. All specifications include year and sectoral dummy. Number of observations, type of regression and endogeneity test are represented in the last three rows.

***, **, * shows significance at the 1%, 5%, 10% levels respectively.

Separate estimation reports the same results as for Tobin's Q. Columns 4 and 5 represents high significance of presence of women on board that is similar with Tobin's Q, however intercept of percentage of female and independent directors reports still positive, but weaker effect that is closer to zero. On average, the effects by gender diversity on ROA is twice weaker than the effect on Tobin's Q, it can be one of the possible explanation of the difference in results on performance in Tables.

4. Results interpretation and discussion

The results show that female directors on corporate boards can differently affect firm performance. Market performance (Tobin's Q) is positively associate to boards' gender diversity, whereas operational performance is not. The estimation of firm risk-taking with gender diversified board represented positive influence by interacted board size and female director, though we cannot affirm that female directors decrease risk level of firm. Moreover, estimation of models in frame of independence issue showed that in case with ROA female directors much weaker influence independence level of board. To get more detail understanding of such differences between operational and market performance it would be better to provide a research on board structure only. Overall, we assume that on average female directors has no significant effect on operational process of firms, however the existence of women on leadership positions meet social challenges and attract new investments, increasing market performance.

Estimation of sectoral effects shows insignificant difference between sectors and probability of adding female director on the board. We, thus, conclude that sectoral specific does not play a huge role and women are attracted despite social stereotypes.

We also supported the findings about the relationship between board size and firm performance. The relationship in our results is permanently negative for both Tobin's Q and ROA. Larger boards face a problem of finding consensus, so the decisions can be not effective. The same results were obtained in estimations of Hypothesis 4, where performance was tested through independence of board. Thus, higher diversity of board cannot solve the problem of size, conversely, higher diversification would contribute more confusion in decision-making process.

Our research highlights practical and theoretical issues. Practically, our findings support the significance of effects by gender diversified boards. The results on performance suggest that increasing in proportion of female directors on board is not just tokenism, as it significantly influence firm performance, risk-taking level and independence of board. Theoretically, we show that looking through double effects is more effective way for researches, i.e. studying simultaneous types of diversity. We find support for theories of gender behaviors and agency.

In frame of this study, we had several limitations up to unavailability of data:

· Time length. Greater period would give more accurate results, providing bigger value of data about firms.

· Board data. The analysis, containing more complex data about directors' characteristics (for instance, whether female director is also independent), would be more accurate.

Conclusion

The research highlights the role of female directors on corporate boards. After analysis of existing literature, we emphasize risk-taking of firm and independence of board as main instruments through which female directors could affect firm performance. Based on prior findings that female directors have no define effect on firm performance, we predict that proportion of women on corporate board has no effect on firm performance. Our results rejected prediction.

Supplementary analyses help to understand the nature of contribution by female directors. We estimate the relationship between gender diversified boards and risk-taking of firm and find that female directors negatively affect firm risk. Also, we predict that female directors on boards enhance independence of board. Our findings support this prediction and moreover, such interaction leads to higher effectiveness of firm.

Our study extends prior research by identifying several conditions under which gender diversified boards can contribute more to firm performance, though gender diversity is important issue for corporate governance.

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Appendix

Description of variables

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