**5. European Data: Microeconometric Exercise**

The final part of this paper presents another study within the search for a relationship between female presence on BoDs and firm performance, this time for European companies in 2015. The data used in this study were collected by Olesiejuk<sup>4</sup> (2017) from the Amadeus (Orbis) database. There are 1194 observations selected on an availability basis (non-random sample), representing the same number of European companies and their financial statements for the year 2015.

The companies represent 18 countries, primarily Italy (49% of observations) and Spain (23%), followed by the UK (7%), Sweden (7%), and Norway (4%). The average number of BoD members is 3.57 and all the BoD members are male in 57% of the cases. Due to the large proportion of Italian companies in the full sample, we also consider a "no Italy" (limited) sample with 614 observations (companies).

In line with the research results presented in this paper, our search starts with finding predictors/correlates of the dummy variable *WomaninBoD* (=1 when there is at least one woman on the board, =0 otherwise). For the full sample, the *WomaninBoD* variable has the mean 0.4263—i.e., in 509 cases out of 1194, *WomaninBoD* = 1. In the limited sample, the *WomaninBoD* variable has the mean 0.4495—i.e., in 276 cases out of 614, *WomaninBoD* = 1.

The list of potential predictors for the variable *WomaninBoD* in the dataset includes more than 50 variables5; however, *WomaninBoD* is significantly correlated with only a few.

Tables 1 and 2 present the linear correlation coefficients of *WomaninBoD* with other variables that are significantly different than zero. Most correlations are low. Our plan now is:


<sup>4</sup> The Olesiejuk (2017) study is not used here.

<sup>5</sup> Since not all companies in the sample are listed, no market-based variables are available for the sample.


**Table 1.** Correlation of *WomaninBoD* with selected explanatory variables. Full sample.



\* indicates *p* < 0.05; Explanation of terms: gearing ratio = (non-current liabilities + current loans)/(shareholder funds) × 100; solvency ratio = (shareholder funds)/(total assets); *ROCE* = return on capital employed = (P/L before tax + extr. items + interest paid)/(shareholder funds + non-current liabilities); ROA = return on total assets = P/L before tax + extr. items/total assets; net assets turnover = (operating revenue)/(shareholder funds + non-current liabilities); non-current liabilities = long term debt + other non-current liabilities.

Tables 3 and 4 present the results of the first stage: estimating the logistic regression of *WomaninBoD* against some variables, but not more than two at a time. This is because of the high multicollinearity among the prospective correlates of *WomaninBoD*.

**Table 3.** Estimation results of binomial logit (logistic regression) for *WomaninBoD* as the outcome variable. Full sample (*n* = 1194) with *WomaninBoD* = 1 for 509 observations.


**Table 4.** Estimation results of binomial logit (logistic regression) for *WomaninBoD* as the outcome variable. Limited sample (*n* = 614) with *WomaninBoD* = 1 for 276 observations.


The classification tables for logistic regressions are formed on the basis of Cramer's rule (Cramer 1999). This possibility is often neglected. When samples are unbalanced, Cramer (1999) advocates the use of a cut-off point α equal to the proportion of ones in the sample. In effect, the success rates for *yi* = 1 and *yi* = 0 are better spread than for the typical cut-off point of 0.5 (Gruszczy ´nski 2019).

The interpretation effect of logistic regressions lies in showing that—despite poor correlation with prospective covariates—the variable *WomaninBoD* may formally be "explained" with such models. Classification results are rather weak but sensible—the fit measure of around 0.7 is common in microeconometric applications in corporate finance.

Now we place *WomaninBoD* among the regressors in the typical model considered in previous sections of this paper where the outcome variable is firm performance. After the correlation check, one should expect that *WomaninBoD* is insignificant in any model attempted in the classical way—i.e., as multiple regression, and, in fact, that is the case here. As an example, Tables 5 and 6 present the estimation results of two regressions: one for the full sample and one for the limited sample.


**Table 5.** Estimation results of multiple regressions with *WomaninBoD* as the predictor variable and *ROCE* as the dependent variable. Full sample (*n* = 1194).

Standard errors in brackets; \* indicates *p* < 0.1; \*\* indicates *p* < 0.05.

**Table 6.** Estimation results of multiple regressions with *WomaninBoD* as the predictor variable and *ROA* as the dependent variable. Limited sample (*n* = 614).


Standard errors in brackets; \*\* indicates *p* < 0.05.

As shown in Tables 5 and 6 multiple regressions for performance against *WomaninBoD* reveal no significance of this variable, even in a typical setup for controlling the endogeneity—i.e., with the control variable being the size of the company, here represented by the *logassets* variable (see Adams 2016, Table 1).

The next step would be searching for relationships between *WomaninBoD* and firm performance along the distribution of the performance variable. In other words, we may try to employ quantile regressions as in the paper of Conyon and He (2017), mentioned in Section 3. Tables 7 and 8 present the results of the quantile regressions estimation for the full sample and for the limited sample. We used the setup from the multiple regression:



**Table 7.** Estimation results of quantile regressions with *WomaninBoD* as the predictor variable and *ROCE* as the dependent variables. Full sample (*n* = 1194).

Standard errors in brackets; \*\* indicates *p* < 0.05.

**Table 8.** Estimation results of quantile regressions with *WomaninBoD* as the predictor variable and *ROA* as the dependent variables. Limited sample (*n* = 614).


Standard errors in brackets; \* indicates *p* < 0.1; \*\* indicates *p* < 0.05.

Quantile regressions were performed for centiles 25, 50, and 75. Tables 7 and 8 show that, along the full distribution of the performance variables, we do not see any connection between female presence on the boards and firm performance. This evidence is, to some extent, stronger than that resulting from multiple regressions.

Again, for this particular dataset, the association of women on boards and performance of companies seems not to be present.

The study presented in this section may be the starting point for a more thorough investigation. Firstly, the dataset could be improved by taking into consideration the time dimension and applying panel econometric techniques. Secondly, the differences between countries could be better examined—e.g., by considering further controls. Those may be governance-specific variables like country shareholder protection strength (Byron and Post 2016) and Hofstede dimension variables (Carrasco et al. 2015).

## **6. Conclusions**

The results of research on the association of female presence on boards and firm performance worldwide are not consistent. This might be due to a lack of solid theories on this particular issue. The general reasoning points in all three possible directions: female presence and performance are (1) related negatively, (2) related positively, and (3) not related. Outcome (3) is advocated in this paper. We present examples of research showing all three types of associations. On the basis of selected works, we also show the variety of microeconometric methodologies that might be applied in the search for the relationship between female presence on boards and firm performance.

In the empirical part of the paper, we present a study of this association for a sample of European companies in 2015. With the use of binomial modelling, multiple regression, and quantile regression, we find that female presence on BoDs is not significantly related to firm performance for the sample of European companies.

This, together with the picture emerging from the paper's first part, leads to us stating that, perhaps, searching for an association between women on boards and performance is not fundamental. However, modern business societies worldwide may need to boost the female presence within managerial bodies. Current econometric research provides evidence that this is not harmful to corporate results.

**Funding:** This research received no external funding.

**Acknowledgments:** The author thanks Agnieszka Olesiejuk for the permission to use data collected by her.

**Conflicts of Interest:** The author declares no conflict of interest.

### **References**


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