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It’s a good time to be a female business executive in America. The percentage of firms with female CEOs is rising, and a recent report by the Women Business Collaborative predicts that the number of S&P 500 firms led by women will roughly double by 2025. The share of women in board of directors seats at Russell 3000 firms has increased from 15.1 percent to 25.2 percent in just the last five years. The number of female MBA students has also increased, rising toward parity in one of the few areas of higher education where women don’t already outnumber men.

But just at the moment when women are seizing more career success than ever before through their talent and tenacity, we’re seeing an increasing demand for diversity mandates, such as requiring more female directors on corporate boards. While rules like these might seem like a welcome move toward feminist equality, the empirical and legal argument is shaky.

Earlier this year, Nasdaq introduced a rule requiring that listed companies have at least one woman on their board. As a self-regulatory organization, Nasdaq required the assent of the Securities and Exchange Commission (SEC) to implement this rule, which the agency gave in August. California’s legislature also passed a law in 2018 requiring firms headquartered in the state to have at least one woman on their board and another law in 2020 broadening that mandate to include board members from additional underrepresented communities. By the end of 2021, California will require corporations with six or more directors to have a minimum of three female directors.

When Nasdaq leadership submitted its board diversity proposal to the SEC, it cited multiple studies and reports to support its contention that gender and ethnic diversity of corporate boards was not just socially desirable but good for business. A detailed analysis by the Heritage Foundation’s David Burton, however, found that Nasdaq’s argument was exaggerated and misleading. “A thorough examination of the literature and of the materials cited in Nasdaq’s submission shows that its empirical assertions have virtually no basis in the literature,” Burton concluded.

Which raises a compelling question—what does the academic evidence actually show? First, it’s important to define firm performance. Many “business case” claims about the advantages of women on corporate boards use market capitalization as a measure of firm performance; but market cap is typically a measure of firm size, and bigger firms always have bigger boards and thus more female directors. Firm performance is best measured by accounting-based (operating income divided by assets) and market-based (market-to-book ratio) measures. Renée Adams of Oxford University‘s Saïd Business School argued that most studies to date were limited by this and similar problems (data, selection and causal inference).

One particularly problematic research issue is the failure to account for endogeneity in the data—for example, that firms with better financial performance might tend to appoint more female directors rather than female directors being responsible for better outcomes. A recent study that fully accounts for endogeneity published in The Leadership Quarterly found that Norway’s mandatory 40 percent increase in female directors corresponded with a significant adverse effect on firm performance relative to similar firms in Sweden, Denmark and Finland that did not face a mandatory quota over a seven year period. By contrast, Spain has a “soft” board gender quota of 40 percent, but the only penalty for non-compliance is the potential loss of public contracts. A recent study of Spain’s quota found that firms dependent on public contracts were significantly more likely to increase the share of female directors, but even these more quota-compliant firms did not actually receive more public contracts.

study examining France’s mandate for 40 percent female representation on public firms’ corporate boards found that 25 percent of newly appointed female directors had close family ties to the company, such as the daughter, granddaughter, sister, niece, or spouse of the founder or CEO. By contrast, about 28 percent had degrees from prestigious academic institutions. Research also identified the possibility that some firms that fall under the quota will shift their organizational form; in Norway, some publicly listed firms simply de-listed to avoid the quota.

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One of the few studies of the recent California mandate found that among all 602 public firms headquartered in California, there was a large and negative stock market reaction to this announcement, resulting in a 1.2 percent decline in firm value, with even greater effects for firms that must add more female directors. The authors’ robust analyses suggest that for every female director a California-based public firm was required to add by 2021, there was a 0.5 percent loss in shareholder wealth.

While the case that mandated gender diversity will improve corporate financial performance is weak, the negative social effects on women themselves could prove significant. In a comment letter to the SEC, the nonprofit Independent Women’s Forum (IWF) opposed the adoption of the Nasdaq rule, warning that it would “threaten the progress made by millions of women and minorities by giving them special treatment, thus insinuating that they cannot succeed without it.” Tokenism and concerns about hiring-by-quota have plagued members of underrepresented groups for decades, at times significantly undermining their professional status and reputation. A recent report by the Diligent Institute also questioned whether female board members are being welcomed to exercise leadership, rather than just membership, in their new roles. This suggests female directors brought on merely to satisfy a diversity quota might not gain positions, such as committee and board chair, consistent with full-fledged board membership.

The IWF submission also echoed concerns in the comment letter submitted by the Competitive Enterprise Institute, which emphasized that men and women often have different educational and career priorities. While there is now a pipeline of qualified female board candidates rising through the ranks in many industries, there are still significant differences between the number of men and women specializing in, for example, petroleum engineering versus consumer retail. A recent law review article also noted that directors increasingly face significant legal liabilities—the status of board membership carries risks that not every executive candidate will welcome.

All of this omits the basic question of whether diversity requirements like those adopted by Nasdaq and California are consistent with the U.S. Constitution and existing laws like the Civil Rights Act of 1964. Many critics are skeptical that these rules will survive legal challenge. There are currently at least two lawsuits challenging the Nasdaq rule, by the Alliance for Fair Board Recruitment and the National Center for Public Policy Research. Regarding California’s law, the state legislature may also have overreached. In comments at a recent public forum on corporate governance and diversity, UCLA’s Stephen Bainbridge suggested the Golden State’s law would likely not survive a federal challenge, since many of the firms it seeks to regulate are incorporated in other states.

This is an exciting time for women and men to lead companies as executives and as board directors, but the best real-world data we have supports a system based on merit, not mandatory quotas.

Richard Morrison is a research fellow at the Competitive Enterprise Institute.

Siri Terjesen is the Phil Smith professor of entrepreneurship and associate dean, research and external relations at Florida Atlantic University’s College of Business and visiting professor at the Norwegian School of Economics.

The views expressed in this article are the writers’ own.