**1. Introduction: Corporate Boards Vis-à-Vis Gender Diversity**

Topics in corporate finance and corporate governance research include the examination of such aspects of corporate board structure as the presence of independent directors, the formation of committees, and recently the presence of women. This paper discusses research attempts concerning the possible relationship between gender structure and the financial results of companies.

Research in empirical corporate finance is developing in many directions. Some studies have a sound theoretical setting, while some still need to be properly rooted in theory. Specific theories have proved to be unstable over time and space—as shown by empirics—and there is, perhaps, no need to strive for a unified theory of corporate finance. Instead, there is a growing demand for more "operational" results based on statistical data on companies (Gruszczy ´nski 2020). This paper contemplates an area that is in the developmental phase, apparently without solid theory, and, perhaps, that is an advantage.

Empirical studies on women and the corporation have emerged in recent decades in vast numbers, along with changes in societies' views on gender issues. The new subject of the corporate presence of women has naturally become a topic for research in corporate governance, corporate finance, corporate law, and other areas. Researchers have concentrated on various aspects of women's presence in corporations, including the relationship between women on boards of directors (BoDs) and financial results.

The presence of women on corporate boards is no longer questioned, with major efforts being constantly directed towards increasing the proportion of women on boards. This has become a political issue since the "natural" process of board evolution into bodies reflecting the gender structure of their respective societies seems to be rather lengthy. The result is that, in some countries, gender board quotas have been imposed, such as 40% in Norway, Spain, Iceland, and France, 33% in Belgium, and 30% in the Netherlands and Italy (Ahern and Dittmar 2012).

The European Commission in 2012 adopted a proposal for a directive "setting a minimum objective of having 40% of the under-represented sex in non-executive board-member positions in listed companies in Europe by 2020, or 2018 for listed public undertakings" (European Commission 2012). While the European Parliament voted in 2013 to back this law, until now, EU countries have not adopted the directive. In 2019, the Commission reported on "data confirming the positive impact of gender diversity in management on business performance, but also data indicating that the EU still scores low when it comes to equality in decision-making, and that the gap between Member States is widening" (European Commission 2019).

In Section 2, we propose an overview of this paper's subject, beginning with a brief account of theories regarding the female presence in organizational leadership, theories rooted in political science, sociology, psychology, economics, and finance. Furthermore, we comment on two meta-analyses summing up research devoted specifically to the association between women's presence on boards and company performance.

Section 3 presents a short survey of microeconometric methodologies applied in exploring gender vs. performance. The examples include studies that rely on techniques of multiple linear regression, panel data linear modelling, quantile regression, the diff-in-diff technique, and other methods. In Section 4, we show how econometric approaches may compete in discussing the direction of association between firm performance and women on BoDs for a sample of companies in Norway.

The study presented in Section 5 examines European firms' financial reports from the year 2015 and the association between women's presence on boards and their respective companies' performance. Applying binomial models, multiple regression, and quantile regression, we find that, for this sample, female presence on BoDs is not significantly related to firm performance.

Section 6 concludes.

#### **2. Women on Boards and Financial Results—Theoretical Underpinnings and Meta-Analyses**

There are multiple theories directed towards showing the necessity of female participation in all corporate structures, reflective of their presence in greater society. Aluchna and Krejner-Nowecka (2016) propose a list of such theories, including:


None of these theories tackle the question of the "impact" of female presence on corporate financial results. It seems that this issue is not theoretically solid and remains a "political" or "sociological" question rather than an economic or financial one. Eckbo et al. (2019) point out that "in principle, restricting shareholders' free choice of directors can reduce board effectiveness". There are studies pointing out that new female directors may lead to a reduction in firm value, that new and less experienced female directors may be "overly focused on monitoring and exhibit excessive risk aversion". On the other hand, "it is in principle possible for shareholders to benefit from the

diversity and broader skill set resulting from adding female directors". As can be seen from this paper, the evidence in each direction of reasoning is mixed.

Editors of the book "Womenin corporate boards. Aninternational perspective" (Aluchna and Aras 2018) state that "Female presence and involvement on boards improves firm performance, transforms corporate governance and leads to the transition towards more responsible business". This general observation should be limited, at least in regard to the aspect that can be statistically/econometrically examined—i.e., relating women's presence on boards and firm performance. As in many instances of research in corporate finance and corporate governance, this relationship may differ across countries, regions, time spans, samples, etc. Explaining those differences without a unified theory is a task outside the scope of economics and finance.

To this end, we reference the comprehensive meta-analysis provided by Halliday et al. (2020) that addresses gender diversity questions in the framework of psychology. They "integrate psychological theory related to implicit biases and agency theory, with institutional theory, to propose that the national context for gender equality moderates the extent to which characteristics of organizational leadership relate to female board representation". This comprehensive analysis begins with 1604 studies published in or before 2018. The final set examined in the authors' paper consists of 158 studies, mostly journal articles, from the period 2004–2018. The "sample" contains 60,648 organizations from 36 countries. Their final conclusion stresses the "importance of the national context for gender equality as a boundary condition for understanding the relationship between organizational leadership characteristics and female board representation". The national context is important, but this observation is, in fact, the only solid result from so comprehensive a meta-analysis.

There are attempts, however, to place the question of gender into the theoretical framework of economics/finance. For example, Taghizadeh-Hesary et al. (2019) show the disparity in the lending behavior of banks to small and medium-sized enterprises (SMEs) based on their owners' gender. They use the production function approach, distinguishing the capital of male- and female-owned companies. The major assumption is that "the loan default risk of female-owned companies is greater than the default risk of male-owned companies", placed in the context of Asia, where customarily female entrepreneurs face greater credit constraints than their male counterparts. Along with this assumption, it is shown that, indeed, there is gender-based inequity in bank lending. To mitigate this issue, the authors propose a governmental credit guarantee for female-owned enterprises and, subsequently, demonstrate that this would increase GDP growth. The elegant mathematical structure is then followed by a statistical–econometric analysis on a sample of 1492 Iranian SMEs in which it is shown that, actually, "female-owned SMEs perform lower relative to male counterparts as they have a higher default ratio and lower profitability, liquidity, and coverage". To sum up, what we really have here is a theoretical dispute, but it has no relevance to the empirical exercise that is the substance of this paper.

What remains as a major research possibility in examining gender edge vis-à-vis corporate categories is the application of a statistical–econometric methodology. Such research attempts typically use microdata on large numbers of companies and may be placed under the label of "financial microeconometrics" (Gruszczy ´nski 2020).

There are at least two meta-analyses in this direction. Post and Byron (2015) use results from 140 studies (92 published, 48 unpublished) and examine "whether results vary by firms' legal/regulatory and socio-cultural contexts". The conclusion is mixed. On one side "female board representation is positively related to accounting returns" (*r* = 0.047; significantly higher than zero), and on the other "the relationship between female board representation and market performance is near-zero" (*r* = 0.014; not significantly different from zero). The authors indicate that much depends on the countries in

question: the relationships are stronger in countries with greater gender parity. In a sense, this appears to be a similar conclusion to the analysis by Halliday et al. (2020) 1.

Pletzer et al. (2015) present a meta-analysis of 20 studies from peer-reviewed journals that examine the possible relationship of female presence on corporate boards and firm financial performance. The primary conclusion is that the "mere representation of females on corporate boards is not related to firm performance". The authors explain that their analysis, unlike that of Post and Byron (2015), follows "a more rigorous and controlled methodological approach by investigating the relationship between percentage of females on corporate boards and firm financial performance, operationalized as return on assets, return on equity, and Tobin's *Q*". The primary hypothesis here is "that female representation on corporate boards is either positively or negatively related to firm financial performance, but that the magnitude of such a relationship is likely to be small".

Thus, the empirical research, as evidenced in three meta-analyses, does not convey the message of a significant relationship between women's presence on boards and firm performance. The primary outcome is that the mere representation of females in the governing bodies substantially relates to the "national context". A similar conclusion may also be attributed to research by Carrasco et al. (2015). The authors use Hofstede cultural dimensions methodology and apply it to a comprehensive data set from 32 countries from 2010. It turns out that two of the four Hofstede dimensions are related to the level of female representation on BoDs. These are power distance and masculinity. Companies in the countries where unequal distribution of power in institutions is accepted have relatively fewer women on BoDs. It is also the case in countries where values associated with the masculine role dominate. Thus, the national context seems to be an important determinant of female presence on boards.

Before embarking on specific issues of methodology, we point to the paper by Ferreira (2015) who clearly subscribes to the view of this paper. He states that research does not show a clear "business case for gender quotas", nor does it support the contrary: that female participation on BoDs reduces firm profitability.

However, there is always the question of the methodological quality of the research. This is discussed in the next section.

#### **3. Financial Microeconometrics: Selected Empirical Studies on Gender vs. Performance**

## *3.1. Methodological Considerations*

In this section, we concentrate on specific studies, as well as on financial microeconometrics methodologies. Indications remain that the inconclusive outcomes might be embedded in the research question itself, as shown in Section 2, and may also be the result of an improper methodological setup.

Our argument, in some way, coincides with the line taken by Adams (2016) in her important paper published in the special issue of *The Leadership Quarterly* on strategic questions of female participation on boards vis-a-vis challenges faced by the research2. She argues that "more research needs to be done to understand the benefits of board diversity". The principal problems are data limitations, selection, and causal inference. This is in line with the reasoning presented by the same author in the paper Adams (2017) on possible flaws in corporate governance research. Gruszczy ´nski (2018) indicates similar questions in the paper on good practices in corporate governance and accounting research.

For example, a significant correlation between the measure of female presence on boards and the measure of firm performance should not be interpreted as a causal relationship if the endogeneity problem is not taken into account. This is a situation in which the gender variable, being exogenous in the linear regression model explaining the performance variable, is also correlated with an error term. It

<sup>1</sup> These authors present another meta-analysis on how the female presence on boards relates to corporate social performance (Byron and Post 2016). Based on 87 studies from more than 20 countries, the authors find that this relationship is positive and is stronger in countries with higher stakeholder protection and gender parity.

<sup>2</sup> I thank an anonymous reviewer for referring this paper to me.

means the gender variable is correlated with another explanatory variable that has not been included in the model. Such a variable may be, for example, firm size: it is more likely that women are appointed to the boards of larger companies. Company size may also be a determinant of its performance. There are various types of remedies for endogeneity. One group includes techniques that aim at the source of the variability of the exogenous variable: the instrumental variables approach, or such methods as diff-in-diff or regression discontinuity design. An example of diff-in-diff is given later in this section. The second group comprises techniques that use panel data or matching estimation (Roberts and Whited 2013).

The techniques mentioned above belong to what are referred to as new microeconometrics or 'metrics' and are presented in the seminal books of Angrist and Pischke (2009, 2015), among other sources. The primary issue is how to "prove" causality between the variables. Thi appears to offer a way of solving the primary question here: what is the impact of female directors on firm performance? However, most techniques advocate the use of experiments or natural experiments. Adams (2016) points out that an experiment is impossible: "To experimentally identify the causal effect of gender diversity on firm performance, one would have to randomly assign female directors to firms and then measure subsequent firm performance". The same view is held by Ferreira (2015): "Causal effects will always be too hard to estimate, unless governments unintentionally help us with badly designed policies that randomly assign quotas to some firms and not to others".

The question is whether regression analyses may suffice without searching for causality. Obviously, regression tools are valuable, as evidenced in corporate finance and corporate governance research. Regression outcomes may even be close to ascertaining causality, especially when we use panel techniques (Gruszczy ´nski 2018). On the other hand, to properly design and execute research with endogeneity in mind is sometimes hard, as pointed out in the survey paper of Atanasov and Black (2016).

Another concern should be raised here: the question of the statistical significance of the explanatory variables in the regression-type model. It is often the case in empirical corporate finance that some insignificant variables are not removed from the model due to their merit in research. Such practice is admissible and correct. Putting too much weight on statistical significance may not be correct (for more, see Gruszczy ´nski 2020, section 2.8). Today, this is the subject of worldwide discussion among researchers who, in their hundreds, recently endorsed the call to "retire statistical significance" (Amrhein et al. 2019).
