*3.2. Selected Empirical Studies*

From the plethora of studies on the topic, we choose a few, one of which specifically represents the "new microeconometrics" methodology. All belong methodologically to financial microeconometrics (Gruszczy ´nski 2020).

Ionascu et al. (2018) examine Romanian companies listed on the Bucharest Stock Exchange 2012–2016 (343 firm-year observations). Their results indicate that, on average, the diversity of BoDs has no significant impact on firm performance. In the authors' words: "although firm performance seems to be positively correlated with gender diversity of the boards, the association is not robust and ceases to be significant after endogeneity is controlled for". The method employed is panel data linear regression with a dependent variable representing performance. There are three such variables attempted: return on assets (ROA), Market-To-Book ratio, and Tobin's *Q*. Such a setup is typical for most studies. The gender diversity variable is one of the explanatory variables in the regression. The authors consider three such variables: the proportion of female members on a board, a dummy variable indicating a woman as president of the board, and an interaction variable being the product of the first two variables. A major problem is always the selection of other predictors (explanatory variables, controls). The authors also try to perform the same analysis for profitable companies with a

marginally better result: for profitable companies, the relationship between female presence and firm performance is then marginally positive3.

Gordini and Rancati (2017) use panel data analysis to establish the relationship between female presence (gender diversity) on boards and firm performance for 918 listed companies in Italy between 2011 and 2014. The authors use Tobin's *Q* as the measure of firm performance. The "female" variables are four (sequentially): a dummy representing at least one woman on the BoD, the percentage of female directors, the Blau index, and the Shannon index. The last two indices measure the gender diversity of the BoD with limits of zero (no diversity) and 0.5 or 0.69—perfect diversity or 50:50, respectively. According to Italian law from 2011, it is mandatory that there be at least one woman on a BoD. Nevertheless, only 73% of boards in the sample fulfilled this law. This variable specifically turns out to be insignificant in the models explaining Tobin's *Q* with other typical control variables. Other "female" variables are significantly positively related to Tobin's *Q*. Strangely enough, the authors placed ROA as one of the performance measures among the controls. The authors maintain that their study shows a "positive and significant effect" on Tobin's *Q* of the three variables measuring the presence of women on BoDs in Italy.

Examples of studies using the simple methodologies are as follows:


Another study referenced here uses the more sophisticated approach of quantile regression. Conyon and He (2017) investigate 3000 US companies for the period 2007–2014 (over 18,000 firm-year observations). With two dependent variables, ROA and Tobin's *Q*, and a number of typical controls, the authors examine the association between the percentage of women on BoDs and firm performance. Firstly, they report OLS and fixed-effects OLS estimation results. The OLS gives a mixed message: a significant and positive association between women on boards and Tobin's Q, and a significant and negative association between women on boards and ROA. After controlling for firm-level fixed effects, the board gender diversity variable becomes insignificant in both cases. Now, the authors claim that the assumption (in OLS regressions) that "the board gender effect is constant across the performance distribution is not valid". Alongside such reasoning, a quantile regression is employed, which provides very promising results supporting the authors' main hypothesis: "Board gender diversity has a significantly larger positive impact on firm performance in high-performing firms than in low-performing firms". The paper shows that searching for a relationship between female presence on BoDs and performance requires sometimes more than simple techniques of multiple regression.

The new microeconometrics (as coined in Section 3.1) are represented in this survey by Sila et al. (2016), who investigate 1960 US firms with 13,581 firm-year observations for the period 1996–2010. The authors examine the gender diversity of corporate boards and its possible effect on company risk. The methodology employed applies linear regression, binomial probit, and diff-in-diff with matching. In stage (1), the authors use the binomial probit to explain the probability that at least one female director is appointed in a company in a given year. The major predictor is the risk variable defined (in one variant) as the variability of daily stock returns in the preceding year. The number of firm years with the appointment of at least one director is 7101. It is shown that risk may well predict a female appointment.

<sup>3</sup> Interestingly, an earlier study examining companies listed on the Bucharest Stock Exchange (2007–2011) by Vintilă et al. (2014) showed a mostly significant relationship between female representation on BoDs and firm value.

In stage (2), the authors estimate linear regression, with risk being explained by the proportion of women on the board and other control variables. The method used for estimation is GMM for a dynamic panel system. In effect, the authors find no evidence of a relationship between equity risk and a female appointment. In stage (3), an alternative strategy for identifying this relationship is applied with the use of diff-in-diff and matching. This amounts, here, to estimating the following model:

$$\begin{array}{c} \text{Risk}\_{it} = \ \ \_0 + \alpha\_1 \text{Female} \stackrel{\leftarrow}{APP} \stackrel{\leftarrow}{APP} \stackrel{\leftarrow}{int} \text{Post} \stackrel{\leftarrow}{Period}\_{it} + \alpha\_2 \text{Female} \stackrel{\leftarrow}{APP} \stackrel{\leftarrow}{APP} \stackrel{\leftarrow}{impact} \stackrel{\leftarrow}{M} \stackrel{\leftarrow}{i} \\ \text{+} \alpha\_3 \text{Post} \stackrel{\leftarrow}{Period}\_{it} + \text{ CONTR} \!\!/ \ \_ \text{it} \ \! \!/ \ + \ \varepsilon\_{it} \end{array}$$

The variable *Female Appointmentit* = 1 for firms in treatment group, =0 otherwise. Firms comprising the treatment group appoint exactly one female director in year *t* to replace a departing male director (must be older than 60). The variable *Post Periodit* = 1 in the post-treatment period, =0 in the before-treatment period.

The firms from the treatment group are matched to similar control firms that represent a group with a male director appointed to replace another male director (there are 153 matches possible). Matching is made with the propensity score and nearest-neighbor techniques. The model is estimated for both sets of data: for propensity score and for nearest-neighbor. The authors find that the *Female Appointmentit* ∗ *Post Periodit* variable is not significant in either version of the model. In other words, this is the causal evidence that appointments of female directors and male directors do not result in different risks. The final conclusion is that a board with a higher proportion of female directors is no more or less risk-taking than a more male-dominated board.

The research by Sila et al. (2016) is an example of how to use techniques of identifying the causal relationship between the gender structure of the board and the firm performance (in this case: equity risk).

Examples presented in this subsection are intended to show the diversity of possible methodological approaches that are available in the microeconometric toolbox and that may be used in regard to corporate governance questions like the one considered in this paper. The major hypothesis here remains as before: there is no solid evidence for a significant association between female presence on BoDs and firm performance across countries, regions, time spans, and samples.
