Closing the Gap: Board Gender Quotas and Hiring Practices

We study the impact of board gender quotas on firms’ hiring and retention practices. We find that female director tenure significantly increases following the introduction of a quota in France in 2011, with stronger effects among less gender-diverse firms and firms that use networks for hiring. These findings suggest that (some) firms find it costly to comply with the quota law. We also find that female directors hired after the quo-ta are more independent, more experienced, more internationally diverse, and no less academically qualified than those hired before the quota. The gender gaps in most director characteristics also narrow. The evidence suggests that, despite their perceived costs, board gender quotas force firms to change their hiring practices, which allow firms to tap into a deeper talent pool.


Introduction
The introduction of mandatory gender quotas is one of the most radical regulations constraining the rights of shareholders to choose their representatives on corporate boards. Beginning with Norway, many European countries have recently passed similar gender quota laws, including Italy, Belgium, France, The Netherlands, Spain, and Germany. This trend has spread beyond Europe, with India, Israel, and, more recently, the state of California also enacting board gender balancing laws.
The introduction of gender quotas disrupts the equilibrium outcomes of directorial labor markets. This shock could lead firms to change the composition of their boards, resulting in boards that are not only more gender diverse, but also different in other dimensions. 1 Some argue that gender quotas force firms to select directors purely on gender, which could then lead to the selection of women without the required experience, qualifications, and independence (see, e.g., Wiersema and Mors, 2016). On the other side of the debate, some question whether the market for corporate directors is meritocratic (Doldor, Vinnicombe, Gaughan, and Sealy, 2012). Quotas could force companies to review their practices, expand the pool of male and female candidates, and may even ameliorate self-selection problems (Niederle, Segal, and Vesterlund, 2013).
In this paper, we study how board quotas affect firms' hiring and retention practices. The market for corporate directors may exhibit search and matching frictions. Such frictions could partly explain the underrepresentation of women in top jobs. The introduction of a quota may force firms to abandon selection and hiring practices -search technologies, in the terminology of Diamond and Maskin (1979) -that under-recruit qualified women. However, changing search technologies could be costly, which may explain firms' reluctance to do so.
We consider the introduction of a mandatory gender balance law in France in 2011. The labor market for directors in France is particularly interesting because of its reliance on one particular network -Grandes Ecoles graduates -whose (mainly male) members are 1 Although it is difficult to measure the value implications of individual board characteristics, some recent works find significant value effects of changes in board composition (Giannetti, Liao, and Yu, 2015;Hauser, 2018;Jenter, Schmid, and Urban, 2018). disproportionally represented on corporate boards. 2 This feature allows us to use the quota to study policy interventions in a thin labor market, i.e., a labor market in which most participants come from a relatively small pool.
We find that the departure rate of female directors falls after the introduction of the quota. After the quota, the median female director has 78% longer tenure than the median male director; before the quota, this difference was 14%. This finding suggests that firms use retention of female directors as a tool for adjusting to the quota. We also document an increase in the arrival rate of female directors and a decrease in the arrival rate of male directors. Our evidence reveals that, before the quota, the gender gap in departure rates was narrowing, and the gender gap in arrival rates was stable. These gaps have changed direction only after the introduction of the quota, which reinforces a causal interpretation of the evidence. These findings suggest that firms find it costly to comply with the quota law.
Our research design uses only male-female differences that are not explained by firmlevel variables (such as size or performance). We can perfectly control for any fixed or timevarying firm characteristic by using firm-year fixed effects. 3 Thus, time-varying trends in the demand for particular director attributes or aggregate changes in labor supply cannot explain the observed changes in gender differences.
If there were no frictions in the directorial labor market, how should firms adjust to board quotas? In that case, firms could replace male directors with newly hired female directors without changing any other relevant board characteristic. In particular, if the directorial labor market has an excess supply of female candidates, the introduction of quotas should not affect the departure rate of female directors. The fact that, after the quota, firms retain female directors for longer suggests that firms face (perceived or real) difficulties in hiring new female directors.
Firms whose hiring practices rely more on networks in which women are underrepresented may find it more challenging to hire female directors after the quota. Consistent with this interpretation, we find that the quota effect on the gender departure gap is more substantial for firms whose boards face more constraints when hiring female directors. We use two measures of constraints: (i) how distant a board is from the quota threshold and (ii) the proportion of elite Grandes Ecoles graduates on the board. The latter is in line with Nguyen (2012) and Kramarz and Thesmar (2013), who argue that a Grande Ecole degree is a good proxy for membership in elite business networks in France.
Having established that firms' search technologies change after the quota, we then turn to the question of how director characteristics change after the quota. We begin by documenting the existence of significant gender gaps in director characteristics in France. Before the introduction of the quota, female directors were significantly younger, less independent, less experienced, and less likely to have studied at an elite school than male directors. A natural concern is that quotas could widen such gaps by forcing firms to hire even less qualified female directors. Our evidence reveals that the opposite has happened: After the quota, most director characteristic gaps have either narrowed or remained unchanged. We find that, after the introduction of the quota, boards become not only more gender-diverse, but also more independent. Post-quota female directors are more independent, more experienced, and more internationally diverse than those hired before the quota. Most other gender gaps -qualification, expertise, age, and board assignments -have been narrowed or remained unchanged. Overall, we observe a push towards "closing the gender gaps" in board director characteristics. 4 All in all, our evidence presents an apparent paradox: Firms find it challenging to hire female directors after the quota, even though post-quota female directors display smaller gaps in observable characteristics relative to male directors. One possible explanation for this 4 The counter-intuitive effects of gender quotas on the quality of newly hired female directors echo the findings in the literature that studies gender quotas in politics. Contrary to the expectations of quota critics, Besley, Folke, Persson, and Rickne (2017) show evidence that gender quotas in political elections in Sweden did not affect the competence of elected women. Baltrunaite, Bello, Casarico, and Profeta (2014) similarly show that gender quotas in Italy improved the average educational attainment of elected politicians.
puzzle is that the introduction of a quota forces firms to abandon search technologies that under-recruit qualified women. An alternative search technology could allow firms to tap into a deeper talent pool, thus explaining the selection of more qualified female directors after the quota. 5 However, changing search technologies could be costly, explaining why some firms may instead prefer to retain female directors for longer.
A particular example of search technology is the practice of recruiting directors mostly through boards' social networks. Because there are few women in networks of Grandes Ecoles graduates, reliance on such a network naturally leads to the underrepresentation of women on boards. In principle, the use of such networks may be both rational and efficient: Employers may find it easier to evaluate candidates who are similar to themselves (see Cornell and Welch, 1996). However, the use of networks may also be a consequence of search frictions (see Mailath, Samuelson, and Shaked, 2000). 6 We find that both male and female directors appointed after the quota are less likely to be Grandes Ecoles graduates. This fact suggests that the quota may have created incentives for firms to change their search technologies, from networks to executive search firms, regardless of director gender. We briefly discuss some additional anecdotal evidence in line with this interpretation at the end of the article.
By considering the consequences of the introduction of the quota on director characteristics and turnover, we hope to learn how the market for corporate directors functioned before the quota. As the quota disrupts the existing equilibrium, observing how firms and directors react to this shock helps us learn something about the old equilibrium. A different question is 5 This argument has been used in the literature on affirmative action policies: "Whereas the policy is costly when it distorts the selection of the best-qualified individual, this need not be the case when the initial selection is suboptimal. If the bestqualified candidates fail to be selected or fail to apply, then the introduction of affirmative action may reduce if not eliminate these costs" (Niederle, Segal, and Vesterlund, 2013, p. 1). 6 A related but different explanation for the importance of networks is the hypothesis that elitist firms may have a higher propensity to stereotype women as being less competent at board work. Bordalo, Coffman, Gennaioli, and Shleifer (2019) provide evidence that people tend to overestimate the performance of men in male-type domains (see also Bordalo, Coffman, Gennaioli, and Shleifer (2016) and Jouini, Karenhke, and Napp (2018) for theories of stereotypes). See also Reuben, Sapienza, and Zingales (2015) on stereotypes and the under-representation of women in science.
6 what the characteristics of the new equilibrium will be. Because the transition period is very long, we cannot answer this question with confidence; director characteristics and turnover rates may still change over the years as they adjust to the new equilibrium, making it difficult to estimate long-run causal effects credibly.
Our work relates to that of Bertrand, Black, Jensen, and Lleras-Muney (2019), who show that the introduction of a gender quota on the boards of Norwegian companies improved the observable characteristics of female appointees. In addition to showing related results for France, our main contribution is to estimate the effect of the quota on female director retention rates and to investigate the importance of director networks on recruitment and retention decisions. Our work also differs in methodology and focus: We use within firm-year variation to estimate the effect of the quota on variables studied in the corporate board literature, such as independence, CEO experience, and industry expertise, among others.
In recent work, Hwang, Shivdasani, and Simintzi (2019) and Greene, Intintoli, and Kahle (2020) both study the effect of the California quota on stock returns and argue that observed negative effects are explained by firms not having access to a sufficiently large pool of qualified female candidates. Von Meyerinck, Niessen-Ruenzi, Schmid, and Solomon (2019) find similar performance effects of the quota, but attribute most of that effect to investors learning about Californian legislators' regulatory preferences. Although such results are not exactly comparable to ours or those of Bertrand, Black, Jensen, and Lleras-Muney (2019), they highlight the extent to which more evidence is needed before concluding whether board quotas have negative or positive effects on the qualifications of female directors.
Our results relate to the literature on the effect of affirmative action policies on gender differences. For example, Niederle, Segal, and Vesterlund (2013) show experimental evidence that the introduction of female "quotas" for winners in a competitive tournament increases the supply of qualified female participants. Another study that shows evidence of possible frictions in the selection of men versus women is Kaplan and Sorensen (2016). They find no significant differences between men and women with respect to observable characteristics.
Nonetheless, after controlling for these characteristics, women are still less likely to be hired as CEO than men. This paper contributes to a recent literature on the labor market for corporate directors, with a focus on director appointments and match formation (see e.g., Akyol and Cohen, 2013;Denis, Denis, and Walker, 2015;Matveyev 2016;Fahlenbrach, Kim, and Low, 2017;Adams, Akyol, and Verwijmeren, 2018;Becher, Walkling, and Wilson, 2017;Cai, Nguyen, and Walkling, 2017). Our main contribution to this literature is to show how the market for corporate directors functioned before the introduction of the quota, which disrupted the existing equilibrium.

Institutional Background
In this section, we describe some of the institutional details that are relevant for our analysis: Board gender quotas in France (Subsection 2.1), board regulations in France (Subsection 2.2), and French business elites (Subsection 2.3).

Board gender quotas
In France, the Zimmermann-Copé law, adopted on January 27, 2011, requires a minimum of 20% of women on company boards from January 2014 on, rising to 40% on January 1, 2017.
When a firm has a dual board (a supervisory board and a management board), the law applies only to the supervisory board. Within boards, the quota applies to all members-insiders and outsiders-with one exception: Directors representing employees, who are usually union representatives.
The law applies to all listed companies and to non-listed companies employing at least 500 employees 8 or with revenues of at least EUR 50 million. The legal forms that are subject to this law are limited liability corporations (Sociétés Anonymes), limited partnerships that include at least one general partner plus some limited partners who buy shares in the entity (known as "commandite par actions" corporations), and Societas Europaea (the European company statutes). All listed companies have to adopt one of these three legal forms. Non-listed companies can opt for other legal forms, which are not subject to quotas (SARL, sociétés à responsabilité limitée, which have no boards, or SAS, sociétés anonymes simplifiées, in which boards are optional). Because we consider only large listed firms in France, the quota applies to all of them. Notice that delisting is not sufficient to avoid the quota; we find no evidence of delisting to adopt a different legal form. (Belgium). Even Germany, initially reluctant to consider quotas, adopted in December 2014 a law establishing a gender quota of 30%, which became effective in 2016 for the largest listed companies.

Boards in France
Under French law, the size of the board may range from three to 18 members. French firms can adopt either a unitary board or a dual board, with a supervisory board and a management board. The maximum term for a director is six years, but directors can serve on multiple consecutive terms. Thus there is no biding constraint on a director's tenure.
According to the AFEP-MEDEF code, independent directors should account for at least half the members of the board in widely-held companies. In closely-held companies, independent directors should account for at least a third of the board. After twelve years on the board, independent directors lose their independent status. The governance code recommends that the outside directors meet periodically without the executive directors. An outside director should not hold more than five directorships in listed corporations, including foreign corporations. An executive director should not hold more than three directorships in listed corporations, including foreign corporations. This limit does not apply to directorships held in subsidiaries and holdings.
French law does not cover the number or composition of board committees, which are determined by each board. However, French firms typically have at least three committees: audit, nomination, and compensation.

French Business Elites
The higher education system in France has two separate blocks: universities and elite establishments called Grandes Ecoles. In contrast with universities, where entrance after high school is guaranteed by law, Grandes Ecoles are highly selective and their students represent only 5% of the total of those who enroll in higher education each year. In addition to excellent high school records, the selection entrance at Grandes Ecoles is based upon an examination that requires two years of intensive preparation (Classes Préparatoires aux Grandes Ecoles).
In France, the majority of business and governmental elites (administrative, scientific, and executive) are former students of the Grandes Ecoles. For instance, around two-thirds of the chief executives in France's largest firms graduated from the Grandes Ecoles (for more details, see Dudouet and Joly, 2010). Due to historical reasons, these business elites not only benefit from a highly selective education but also pervasive political and social connections. After World War II, numerous former civil servants (from the Ministry of Finance or the Ministry of Industry) who graduated from the Grandes Ecoles began to be hired at top-level management positions by big companies (especially state-owned and privatized companies) (for more details, see Bertrand, Kramarz, Schoar, and Thesmar, 2018).
A second distinctive feature of Grandes Ecoles is the under-representation of women among the student body. According to Albouy and Wanecq (2003), among graduates from Grandes Ecoles who were born during the 1949-1958 period, 2,432 are male and 546 are female (respectively 1,829 and 732 among graduates who were born during the 1959-1968 period).
Ecole Polytechnique (the top engineering Grande Ecole) did not accept female candidates until 1972 and had in 2015 less than 20% female students. Moreover, between 1989 and 2009, the proportion of female graduates from the Ecole Nationale d' Administration was only around 25-30% (Larat, 2015).

Data
We analyze an unbalanced panel of corporate directors over the period 2003 to 2017 using data from Management Diagnostic's BoardEx database. The sample consists of 5,189 firm-year observations for 706 unique French firms. For comparison, we also use 94,013 firm-year observations for 14,162 individual U.S. firms. 9 Most firms are publicly listed, but BoardEx also has data on some large private companies. Table 1 presents selected summary statistics of firm characteristics for two subsamples: Before and after 2010 (see Appendix A1 for the definition of all variables used in this section). The average firm size (book assets) in France is similar before and after 2010. French firms display significantly lower returns on assets after 2010. Such differences underscore the importance of controlling for time-varying firm effects. Table 1  We use data at the directorship level. The unrestricted sample includes 52,010 directorfirm-year observations for France and 713,162 director-firm-year U.S. observations. In our analysis, we use only outside (i.e., non-executive) directors; thus, we exclude 11,535 directorfirm-year observations for France and 158,373 director-firm-year observations for the U.S. in which the director is an executive of the firm. We also exclude observations with missing values for age and tenure, which leaves us with a sample of 36,817 director-firm-year 9 Other European countries are less useful as "quota-free" comparators. In addition to the fact that several other European countries have introduced quotas, the European Commission published in 2012 a proposal for a directive on improving the gender balance among directors, which is still on the council agenda. Some European countries, such as the UK, have also adopted soft laws in their corporate governance codes.
observations for France and 525,799 observations in the U.S. sample. Because of missing data, the sample is smaller when we use some selected outcome variables. Table 2 compares outside director characteristics between France and the U.S. by gender. 10 The average number of board seats held by male directors is virtually identical in both countries (2.13 board seats), which suggests that the markets for corporate directors in these countries share some similarities. However, among French boards, female directors hold fewer board seats (1.87 seats) than do male directors, while among U.S. boards, the reverse is true; female directors hold an average of 2.78 seats.
Relative to male directors, female directors are younger and more likely to be formally independent. There is a gender gap in top executive experience, which is slightly more pronounced in France than in the U.S. sample. The gender gap in industry expertise is larger in France (6 percentage points) than in the U.S. (2 percentage points).
In France, female directors are also less likely than their male counterparts to be a graduate from a set of nine elite Grandes Ecoles. 11 The difference is substantial: While 38% of all male directors come from this small set of schools, only 22% of female directors hold similar degrees. This fact is not surprising, given that Grandes Ecoles (especially Ecole Nationale d'Administration and most engineering schools) have a relatively small proportion of female students. In our sample, the school with the lowest representation of female directors is Ecole Polytechnique, with slightly less than 7% of female directors among its graduate-directors. 12 By contrast, in the U.S., 28% of all directors hold an Ivy League degree, with no difference between male and female directors. The difference between France and the U.S. reflects the highly selective and unique nature of the French higher education system, in that more prestigious schools tend to have more significant gender imbalances. 10

Gender Gaps in Turnover
How do firms adjust to board gender quotas? To comply with the law, firms need to change their recruitment and retention policies. In this section, we investigate the effect of the quota on director arrival and departure rates. In 3.1, we define these rates and explain how they relate to board gender quota targets. In 3.2, we offer some predictions under different assumptions about the functioning of the market for directors. In 3.3, we show our empirical results.

Arrival and Departure Rates
To clarify the mechanics of how firms adjust to board quota policies, here we derive an expression for the change in the policy variable (the proportion of women on the board) as a function of the gender gaps (i.e., differences) in director arrival and departure rates.
where $ and % are the numbers of newly appointed women and men, respectively, and $ and % are the number of women and men, respectively, who exited the board. Define the net arrival rates for men and women, respectively, as We can then write 1 in terms of net arrival rates and the initial proportion of women: The change in the proportion of women is then Finally, define the (gender) arrival rate gap and the (gender) departure rate gap as: Thus, we have In sum, for an initial level of the policy variable, 0 , this variable increases only if the departure rate gap is larger than the arrival rate gap (i.e., if > ). Equation (8) also shows that firms can increase the speed of adjustment to a quota in three non-mutually exclusive ways: (i) a smaller arrival rate gap, (ii) a larger departure rate gap, and (iii) a lower net arrival rate for men.
In Subsection 3.3, we obtain estimates of the effect of the quota on and (and also on % in some specifications). We use these estimates to make inferences about how firms choose to adjust to the quota shock.

Predictions
Consider first, as a benchmark, a frictionless labor market for directors, with sufficiently large numbers of both men and women who are qualified for board work. In particular, suppose there is a slack labor market for female directors. For an initial value of the policy variable 0 , it is thus possible to adjust to any desired target 3 > 0 by replacing the required number of men with newly hired women. Alternatively, firms can fire men without replacement, reduce the departure rate of women, or both. However, if a firm does not want to change the size of its board nor the average tenure for incumbent directors, replacing men with newly hired women is the most efficient method of complying with the quota. We assume that this is the case in our frictionless benchmark. After the quota, we should then see a decrease in the arrival rate gap, driven both by lower arrival rates for men and by higher arrival rates for women. If there is sufficient time for adjustment, firms should also not change the male departure rate, so the departure gap should be unchanged. In sum, in the frictionless benchmark, after the quota, we expect (i) a decrease in the arrival rate gap and (ii) no change in the departure rate gap.
In contrast with this frictionless benchmark, some firms may face -real or perceivedincreasingly higher costs of hiring female directors. That is, the labor market for female directors may be tight. In this case, firms that either cannot or do not wish to hire more female directors can still adjust to the quota by decreasing the departure rate of female directors. In this case, we predict (i) a decrease in the arrival rate gap and (ii) an increase in the departure rate gap.
Comparing the empirical predictions of these two extreme cases, note first that, in both cases, the arrival gap decreases. In a slack labor market for female directors, all adjustments work through arrival rates, and thus the departure gap should not change. In a tight labor market for female directors, firms may instead choose to decrease the female departure rate and increase the male departure rate (board size would decrease so that the quota could be met without having to hire new women), implying an increase in the departure gap. But the arrival rate of women should not change; the lower arrival of men should fully explain any change in the arrival gap.
We expect reality to lie somewhere between these two extremes. Less-constrained firms should adjust more through the arrival gap and less through the departure gap. Our null hypothesis is that of a slack market, so that the change in the departure gap ( ) due to the quota is zero. The alternative hypothesis is that the quota has a positive effect on the departure gap.
We would expect to see more constrained firms to experience both larger increases in the departure gap and lower decreases in the arrival gap.

Empirical Results
We consider two outcome variables: a departure indicator and an arrival indicator. The departure indicator takes the value of one at year if the director is no longer listed as a director of the same firm in year + 1. The arrival indicator takes the value of one at year if the director is not listed as a director of the same firm in year − 1. In the year in which a firm leaves the sample (typically 2017), director departure information is missing. Similarly, in the year in which a firm first appears in the sample, director arrival information is missing. Thus, the sample is mechanically reduced when we use departure and arrival data. In Table 3, we show average departure and arrival rates for directors, before and after (including) 2010, for both France and the U.S. samples. Both departure and arrival rates are higher in France than in the U.S.
sample. Average departure and arrival rates do not differ meaningfully before and after 2010.
Let &'( be a director-level outcome variable (e.g., the departure indicator or the arrival indicator) for director in firm at fiscal year and let & take the value of 1 if director is female and zero otherwise. We use and to denote the random variables associated with these variables. We define the gender gap in variable as In words, the gender gap is the difference between the mean value of for male and female directors. We can estimate ) by a simple regression of &'( on & and a constant, or equivalently, by the difference in means between the two groups. First, male departure rates are higher than female departure rates, both before and after the quota. That is, the departure gender gap is positive. Second, before the quota, male and female departure rates seem to co-move; such co-movement is no longer visible after the quota.    Figure 2 shows the evolution of arrival rates. Female arrival rates are higher than male arrival rates; the arrival rate gap is negative. Before 2010, the arrival gap is mostly stable. The gap widens significantly in 2010 and then gradually narrows. Throughout the quota period, female arrival rates remain at levels mostly above those from the pre-quota period. Note that, by definition, arrival rates are higher in periods of high board turnover. Unless board turnover rates permanently increase, we should expect female arrival rates to return to their pre-quota level once firms reach their targets. Arrival rates for men decrease after the quota, but the difference is economically small. In sum, the descriptive analysis shows that the quota period is associated with larger departure rate gaps and (more negative) arrival rate gaps. The increase in the departure rate gap indicates the existence of a tight labor market for female directors, where firms have difficulties in recruiting female directors. On the other hand, the female arrival rate also increases, suggesting that, despite the challenges in hiring women, the increased demand for new female directors is accompanied by an increase in the pool of female director candidates.
This descriptive analysis is informative but has some limitations. One such limitation is the possibility that the observed gender gaps are a consequence of endogenous matching of firms and directors. For example, suppose that firms with typically low turnover ratios are also more likely to hire female directors. Then, the lower departure rates for female directors would not be a consequence of a desire to retain female directors; it is simply that some firms have low board turnover. One could use firm fixed effects to address this issue partially, but it is likely that characteristics that are relevant for matching, such as firm performance, change over time (see, e.g., Table 1). We thus use firm-year fixed effects '( to eliminate all sources of variation at the firm-year level. Such an approach means that our estimates of the residual gender gaps (i.e., after accounting for firm-year effects) are free from any time-varying endogenous matching considerations at the firm level, including matching on firm performance, size, age, and other characteristics.
Because we only use within firm-year variation, our estimated gender gaps measure differences between male and female directors in the same firm and at the same time. These gender gaps are meaningful because they reflect true differences between male and female directors, which are free from firm-level selection issues. Of course, this does not mean that gender "causes" these gaps. Our goal is not to attribute the gaps to an underlying cause, but instead to estimate the potential impact of the quota on the magnitude of such gaps.
We first consider the effect of the quota on departure rates. The dependent variable, We thus have the following specification: where &( is a vector of director-level covariates. Note that ( is absorbed by the fixed effects and, therefore, 3 is not directly recoverable. The effect of the quota on the (residual) gender gap in departure rates is given by: which can be directly estimated from (10). An estimator for *+ is a before-after estimator of the average effect of the quota on the departure rate gap. 13 A before-after estimator is all we need if we assume that gender gaps have no time trends. Figure 1 suggests that this is a conservative assumption. If anything, the departure rate gap was declining before 2010; a counterfactual continuation of this trend would imply that (11) underestimates the effect of the quota on the departure rate gap.
13 Because we are comparing male and female directors, !" can also be interpreted as a difference-in-differences estimator of the effect of the quota on female director departures, under the assumption that trends for male and female directors would have been similar in the absence of the quota.
Because we cannot rule out the possibility that some of the gender gaps change over time independently of the introduction of the quota, we also run regressions in which we use U.S. firms as a control group. The advantage of using U.S. firms is that, until very recently, with the unique case of California, there has been no realistic threat of legal action against those U.S. firms that do not promote gender balance on boards. In contrast, in most leading European countries, such legal actions were taken or seriously discussed during our sample period.
The obvious drawback is that U.S. firms may operate in a very different environment. Differences in gender gap trends between France and the U.S. may exist because of differences in competition, regulation, governance practices, and business cultures, among other reasons.
With such caveats in mind, we also run the following regression with data from both France and the U.S.: where ' is an indicator variable that takes the value of one if the firm is in France (i.e., the firm is "treated") and zero otherwise. Notice that 3 , 6 and 7 are absorbed by the fixed effects. 14 The difference-in-differences effect of the quota on the gender gap is thus given by: If the gender gap has no trends that are unrelated to the quota, then *+ = ,, . Otherwise, ,, is preferred. 15 Table 4 shows estimates of the effect of the quota on the departure rate gap. In Columns 1 to 4, we run more saturated versions of the model in (10), from no controls to a full set of 14 According to our notation, any variable that does not have a d subscript is absorbed by the firm-year fixed effects.
15 ## can also be interpreted as a triple-difference estimator of the effect of the quota on female director departures.
controls increasingly. In Column 3, we add a measure of director tenure (number of years on the board) and a fourth-order polynomial of age. 16 In Column 4, we add five additional director-level covariates: the number of other directorships, and indicators for family independence, formal independence, membership in core committees, and industry expertise. The number of observations now falls because of some missing data. Columns 1 to 4 show estimates of the effect of the quota on the departure rate gap that range from 3.7 to 5.2 percentage points. Such differences in departure rates imply economically significant differences in expected tenure. Using the estimates from Column 1, we find that, before the quota, the (median) male and female director tenures were very similar: 4.2 and 4.8 years, respectively (a tenure gap of -0.6 years). The quota reduces the tenure gap by 2.2 years: After the quota, the median male director tenure falls to 3.6 years, while the median female director tenure increases to 6.4 years. That is, after the quota, the median female director has 78% longer tenure than the median male director; before the quota, this difference was 14%.
Columns 5 to 8 show the difference-in-differences estimates as in model (12), using the U.S. as a control. We find estimates of the effect of the quota on the departure rate gap that range from 3.2 to 4.9 percentage points. Note also that, from the coefficient on the Post 2010 variable in Column 1, we see that the increase in male departures was about 1.9 percentage points, implying that the decrease in female departures that can be attributed to the quota was at least 2.7 percentage points. That is, the gender departure gap widens after the quota both because male directors are less likely to be retained and (mostly) because female directors are more likely to be kept after the quota. As can be seen from Figure 1, the increase in male departure rates after the quota is mostly explained by the last year of the period. 16 Fourth-order polynomials -or quartics -of age are typically used in labor economics when studying gender effects (see, e.g., Goldin, 2014). Alternative specifications for tenure and age yield very similar results.
We conclude that the quota appears to (i) increase the departure gap (i.e., relatively more female retention than male retention) and (ii) decrease the arrival gap (i.e., relatively more female arrivals than male arrivals). The evidence thus rejects the frictionless benchmark, which predicts that all adjustments should occur gradually through arrivals, with no change in departure rates.
The evidence fits with the hypothesis that firms faced (real or perceived) constraints when hiring female directors and thus needed to use improved retention rates in addition to hiring new female directors. To test this hypothesis more directly, we use the number of women on the board before the quota as a proxy for how constrained firms are. The idea is that firms with more women on boards before the quota are less constrained and thus have less of a need to adjust through departure rates. In Table 6, columns 1 to 4, we re-run our departure and arrival regressions after splitting the sample into two: firms with above-median distance to the quota (more constrained) and firms with below-median distance to the quota (less constrained). These regressions retain only firms that are present both before and after the quota, which reduces the size of the sample. For brevity, we report only two specifications for each regression type. 17 From Columns 1 and 2, we see that the quota has virtually no effect on gender departure gaps for the less constrained firms, as hypothesized: the point estimates are less than one percentage point and statistically indistinguishable from zero. In contrast, for the set of more constrained firms, the effect of the quota is quite large, with estimates varying from 8.4 to 12.5 percentage points. The difference between the effects in each group is statistically significant. These results strongly suggest that (some) firms used retention rates as a tool for complying with the quota.
Columns 3 and 4 replicate the same regressions for arrival rates. As expected, firms with more women on boards did not have to increase their arrival rates of women as much. The results for arrivals highlight one difficulty of using distance-to-threshold as a measure of constraints: By definition, firms that are far from the threshold (40% women on the board) need to hire more women and thus will have high arrival rates. In contrast, those firms that are closer to the threshold do not need to do much more. That is, the distance-to-the-threshold variable conflates labor market constraints and the size of the required adjustment.
As an alternative measure of constraints that is not contaminated by the size of the required adjustment, we consider a measure of board elitism. There is evidence that networks based on shared educational backgrounds affect the selection of executives and directors in France (Nguyen (2012); Kramarz and Thesmar (2013)). Thus, here we measure board elitism by the proportion of Grandes Ecoles graduates on the board. Columns 5 and 6 show the estimates of the effect of the quota on the departure gap for high-elitism (more constrained) and low-elitism (less constrained) firms. We defined the set of high-elitism firms as those whose proportion of Grande Ecoles graduates on their boards is above the sample median. We find that more elitist firms (more constrained) use retention as a tool for adjusting to the quota.
Less elitist firms (less constrained) display lower or insignificant changes in the departure rate gap. Interestingly, Columns 7 and 8 show that less constrained firms adjust more through arrivals (i.e., they hire more women) than their more constrained counterparts. The differences between the two groups are not statistically significant, but the economic differences are meaningful. This result is in line with the hypothesis that some firms find it more challenging to hire female directors and thus adjust more through departures than through arrivals.

Gender Gaps in Director Characteristics
In the previous section, we show that some firms increased female director retention after the quota. Increased retention is an indication of difficulties in hiring new female directors. If firms find it challenging to recruit qualified female directors, then we would expect the gender gaps in director qualifications to increase after the quota. In this section, we investigate this hypothesis.
We group director characteristics into three sets: Measures of director independence (formal independence, family independence, foreign nationality), measures of experience and qualifications (top executive experience, industry experience, age, MBA degree, and Grande Ecole degrees), and variables measuring board assignments (number of directorships and membership of core committees). 18 Gender gaps are defined as in (9). Table 7 presents comparisons of characteristics (means, before and after) for female directors (Panel A) and male directors (Panel B). Table 8 shows before and after comparisons of gender gaps in characteristics (defined as the difference between male and female characteristics).
We first consider the differences in measures of director independence. Before 2010, 33% of all female directors were classified as formally independent. After 2010, this number jumps to 57%. As an alternative measure of independence, we find that before the quota, 80% of all female directors were not directly related to the families that control their firms. After the quota, this number increases to 92%. Finally, we use nationality as a proxy for independence, with non-French nationals being less likely to be closely associated with the firm's management. We find that, before the quota, 9% of all female directors are foreign nationals; this number increases substantially to 21% after the quota.
Based on these three (admittedly imperfect) measures, it is clear that female directors have become significantly more independent after the quota. But perhaps a general trend towards more independent boards, and not the quota, could explain these results. To address this possibility, we consider what happened to the independence of male directors in the same period. From Panel B, we see that male formal independence remains essentially unchanged (the point estimate decreases by two percentage points after the quota). After the quota, male directors are two percentage points more likely to be related to the family that controls the 18 A related question is the effect of the quota on director compensation. French boards are similar to U.S. boards: They typically offer the same compensation package to all outside board members. Committee appointments (including chair assignments) and attendance thus fully explain observed within-board variation in outside director compensation (see Adams and Ferreira, 2008). After one controls for such factors, director compensation has no additional information about the value of directors, making an analysis of compensation uninformative (we do consider though the effect of the quota on committee appointments). For an analysis of director fees in France, see Reberioux and Roudaut (2019). For an analysis of director compensation by gender in the UK, where compensation packages are not standardized, see Gregory-Smith, Main, and O'Reilly (2014).
firm. Moreover, after the quota, men are as likely to be foreign nationals as before. In sum, there is no clear trend in increasing independence among men.
What about the differences between men and women? We define the gap in independence measures by the difference in the value of such measures between male and female directors. From Table 8, we see that, before 2010, male directors were more independent than female directors: The formal independence gap was 13 percentage points, the family inde- Next, we consider differences in professional experience and qualifications. Table 7 shows that post-quota female directors are seven percentage points more likely to have top executive experience (either as CEO or an executive suite position) than pre-quota female directors. Table 8 shows that the gender gap in senior executive experience was 25 percentage points before the quota; after the quota, this gap shrinks to 14 percentage points.
In terms of same industry experience, post-quota female directors are six percentage points more likely to have this type of experience than pre-quota female directors. The gender gap in industry experience shrinks from ten percentage points to six percentage points (alt- hough not statistically precise). The gender gap in age was just over five years before the quota, and there is no economically or statistically significant change in this gap after the quota. The average age of female directors increases by half a year, but this change is not statistically significant.
Concerning educational qualifications, there was virtually no gender gap in MBA degrees to begin with, and this gap does not change significantly after the quota. In contrast, female directors are less likely to be a graduate from a set of nine elite Grandes Ecoles. The difference is substantial: 14 percentage points before and 15 percentage points after the quota.
This fact is not surprising, given that Grandes Ecoles (especially Ecole Nationale d'Administration and most engineering schools) include (even until recently) only a small proportion of female graduate students. Interestingly, the proportion of both female and male directors with Grandes Ecoles degrees falls in the period after the quota, suggesting the firms have become less likely to rely on Grandes Ecoles networks for recruiting directors.
We conclude that some experience gaps have narrowed after the quota, while education gaps did not change. Such results are surprising in light of the oft-used argument that quotas force firms to lower their standards when selecting female directors.
We now consider differences in board assignments. Before the quota, there were significant gender gaps in both the number of board seats and the likelihood of sitting on core board committees: Men held 0.59 more board positions and were 13 percentage points more likely to be members of core committees than women. Interestingly, the gender gap in board seats vanishes after the quota, mainly because male directors now hold fewer seats on average.
More surprising is the fact that the gender gap in appointments to core board committees decreases by six percentage points. This fact suggests that boards have not relegated their female directors to unimportant tasks after the quota.
Tables 9 to 12 show our regression estimates for the effect of the quota on the gender gaps in director characteristics. In the absence of an ideal control group for director gender gaps in France, we use U.S. boards. As our goal is to investigate the hypothesis that quotas may increase gender gaps in independence, qualifications, and experience, our approach, however imperfect, can produce evidence to cast doubt on this hypothesis. For each characteristic, we present results for three different specifications: (i) a regression of the characteristic on the female indicator, a post-quota indicator, and the interaction between the two, (ii) firm-year fixed effects with French data only, and (iii) firm-year fixed effects with the U.S. as a control group. When interpreting the results, we maintain the assumption that trends in differences between male and female director characteristics are either absent or absorbed by the control group. Table 9 reports the estimates of the effect of the quota on proxies for director independence. Column 1 shows that, without any controls, the gender gap in formal independence was 12.6% before the quota, and that, after the quota, this gap narrows by 25.4 percentage points. Column 2 shows that these conclusions remain unchanged if we use within firm-year variation only: The quota reduces the gender gap in independence by 23.3 percentage points.
Column 3 shows difference-in-differences estimates using the U.S. as a control group. The estimate of the effect of the quota is 23.8 percentage points. In all cases, the formal independence gap is reversed after the quota, with female directors being more likely than male directors to be classified as independent. We also conclude that, for formal independence, neither the inclusion of firm-year fixed effects nor the use of the U.S. as a control group has much of an impact on the estimates.
We find similar results for family independence. The quota reduces the family independence gap by 13.9 percentage points in Column 5 and 10.2 percentage points in Column 6.
In both cases, the gender gap vanishes after the quota. After the quota, the foreign nationality gap is reduced by roughly 13 percentage points, according to both the before-after estimator (Column 8) and the difference-in-differences estimator (Column 9). We note, however, that, in the case of foreign nationality, the U.S. is probably a less convincing control group. Overall, using within firm-year variation makes little difference to our conclusions: female independence levels significantly increase after the quota. Table 10 shows that the gender gap in top executive experience is reduced by 6.9 to 10.7 percentage points after the quota. We find the smallest effects when using the U.S. as a control; Column (3) reveals a modest trend towards increasing female top executive experience in the U.S. sample. In contrast, we find no statistically significant effect of the quota on the gender gap in industry expertise. The results for age are a bit more mixed. Although there is no economically or statistically significant change in the gender gap in age after the quota in France, the U.S. gender gap in age decreases by about 1.2 years after 2010, indicating perhaps a modest trend towards closing the gender gap in age. Thus, when the U.S. is used as a control, the point estimate for the effect of the quota is an increase of the gap by 1.23 years. However, this estimate is still not statistically different from zero (despite the considerable size of the sample). We conclude that there is no statistically reliable evidence of an increase in the gender gap in age after the quota.
Concerning educational qualifications (Table 11), we again find no evidence of a gender gap in MBA degrees. For Grande Ecole degrees, we find no change in the gender gap, which is about 14%. Yet, importantly, firms have become less likely to hire both male and female directors with Grande Ecole degrees after 2010. 19 This result suggests that quotas might have forced companies to review their hiring practices and expand their networks.
Overall, we conclude that the quota is associated with a substantial decrease in the gender gap in top executive experience. No other gender gaps in experience and education changed significantly after 2010.
Results from Table 12 confirm that the gender gap in board seats in France is fully closed after the quota. The effect of the quota on the gender gap appears smaller when compared to the U.S. because, in the U.S., female directors experienced a more substantial increase in their number of board seats than male directors did. The effect of the quota is large and significant, even after correcting for this possible trend. After controlling for firm-year fixed effects, there is no evidence of a change in the gender gap in core committee assignments.

Discussion and Conclusions
Some view the introduction of mandatory gender quotas on corporate boards as a significant intrusion on a company's right to select its leadership. It is thus essential to study the impact of such a policy on the way that firms recruit and retain their directors. From a theoretical perspective, the effect of board quotas on hiring and retention policies is ambiguous. On the one hand, companies may be forced to recruit and retain less qualified candidates in order to comply with the law. On the other hand, companies may be forced to switch to a different search technology, which may lead to an improved ability to identify suitable candidates. The evidence in this paper is more consistent with the latter hypothesis.
The effect of board quotas on firm policies is likely to vary across different contexts. In more competitive labor markets, with few institutional and cultural barriers to women in business, one would expect quotas to have virtually no effect on how firms select their directors.
By contrast, in thin markets, especially where director selection is made through networks, firms may have to change their practices substantially to comply with the law.
One story that can rationalize the evidence in this paper is as follows. It might be that some firms used search technologies that excluded several potentially qualified individuals from the pool of candidates. This practice does not mean that firms discriminated against women per se; discrimination may happen indirectly and incidentally as a consequence of existing hiring norms. Slow-changing hiring practices may thus represent a real search friction.
Large, mature, and profitable firms, such as those in our sample, may survive or even thrive despite such practices. It may also be that hiring through social connections is ultimately beneficial to firms because of the connections themselves, even if firms pass up opportunities to hire better-qualified candidates. The introduction of the quota then forces firms to abandon such practices and replace them with more inclusive -and perhaps more efficient -practices.
This explanation is consistent with some existing anecdotal evidence. The business media has reported many instances of changes in hiring practices as a consequence of the quota. Here are a couple of examples: The quota may also have affected the supply side of the director labor market. Before the quota, most women knew that opportunities to be on boards were rare. After the quota, many more women chose to train to become a director. For example, since 2010, the Institut Français des Administrateurs, a non-profit organization of directors, offers a degree "Le Certificat Administrateur de Sociétés" (executive education over six months) aimed at people who would like to become a director. Over the period 2010-2016, 54% of the participants have been women.
The debate on the effect of quotas on firm performance is still unsettled (see e.g., Eckbo, Nygaard, and Thorburn, 2019). The impact of quotas on firms' recruitment policies has received much less attention, but it is of significant importance, regardless of their performance implications. Coordinated changes in hiring practices may have trickle-down effects that percolate through the whole economy, with significant implications for the labor market for business professionals. Although it is difficult to measure such externalities with confidence, identifying the effects of the policy on the labor demand side is a necessary first step.

A1 Variable Definitions
Firm characteristics (Source: Compustat) Firm Size Total assets in billions of euro (France) or dollars (U.S.).

Return on Assets (ROA)
Operating income before depreciation scaled by total assets.

Board characteristics (Source: BoardEx)
Board Size The number of board members. Proportion of independent directors The ratio of independent directors on the board.

Proportion of women on board
The ratio of female directors on the board.

Age
Director age in years.
Time on board Director tenure in years.

Female
Indicator equal to one if the director is female, zero otherwise.

Family Independence
Indicator equal to one if the director does not share his/her last name with at least one other director, zero otherwise.

Formal Independence
Indicator equal to one if the director is reported as independent, zero otherwise.
Number of directorships Number of current board seats in listed firms held by the director.
Core Committee Member Indicator equal to one if the director is member of the audit, compensation, nomination, strategy, executive or governance committee, zero otherwise.

Industry Expertise
Indicator equal to one if the sector of the firm where the director is a board member is the same of at least one firm in his/her employment history.

Ivy League
Indicator equal to one if a director has a degree from an Ivy League University.

Top Executive Experience
Indicator equal to one if the director has or had at least one c-suite position and/or CEO position in his/her employment history.
Foreign Nationality Indicator equal to one if the director who holds a board seat in France (resp, in the U.S.) is not a French (resp, U.S.) citizen.

Table 1 -Firm and Board Characteristics
This    , and all observations with missing information for director age and tenure are excluded. "Additional director controls'' include dummy variables set equal to one if the director shares the same name of at least one director within the same board, if the director is an independent director, if the director is a member of at least one major committee (e.g., compensation, nomination, or audit committees), and the total number of directorships held by the director. "Tenure'' is the number of years since the director first joined the board. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better.
(1)  , and all observations with missing information for director age and tenure are excluded. "Additional director controls'' include dummy variables set equal to one if the director shares the same name of at least one director within the same board, if the director is an independent director, if the director is a member of at least one major committee (e.g., compensation, nomination, or audit committees), and the total number of directorships held by the director. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better.
(1)  This table reports OLS estimates of the treatment effects of the quota ("Post 2010'') on director departures and arrivals for two separate groups of boards: "more constrained" and "less constrained." We use two different definition of constraints. In the first one, boards are considered more constrained if they have above median distance to the quota threshold before 2010. In the second definition, boards are considered more constrained in the first group if the proportion of their directors who graduated from an elite Grande Ecole is above the median (highelitism boards). Only the treatment effects on the gender gaps in departure and arrival rates are shown. "Additional director controls'' include dummy variables set equal to one if the director is a graduate either from a Grande Ecole or from the Ivy League, if the director shares the same name of at least one director within the same board, if the director is an independent director, if the director is a member of at least one major committee (e.g., compensation, nomination, or audit committees), and the total number of directorships held by the director. "Tenure'' is the number of years since the director first joined the board. Observations are defined at the firm-year-director level. The sample includes only outsiders (non-executive directors) in France, and all observations with missing information for director age and tenure are excluded. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better. (1)

Table 9 -The Effect of the Quota on The Gender Gap in Independence
This table reports OLS estimates of the treatment effects of the quota ("Post 2010'') on the difference between male and female director characteristics (i.e., gender gaps). The relevant treatment effects are "Female X Post 2010'' for models without the U.S. as a control and "Female X Post 2010 X Treated'' for models where U.S. is used as a control; the effect on gender gaps (male -female) is the negative of these estimates. Observations are defined at the firm-year-director level. The sample includes only outsiders (non-executive directors), and all observations with missing information for director age and tenure are excluded. The dependent variable is a dummy set equal to one if the director has a particular characteristic (formal independence, family independence, or foreign nationality) at the end of the fiscal year. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better.
(1)  This table reports OLS estimates of the treatment effects of the quota ("Post 2010'') on the difference between male and female director characteristics (i.e., gender gaps). The relevant treatment effects are "Female X Post 2010'' for models without the U.S. as a control and "Female X Post 2010 X Treated'' for models where U.S. is used as a control; the effect on gender gaps (male -female) is the negative of these estimates. Observations are defined at the firm-year-director level. The sample includes only outsiders (non-executive directors), and all observations with missing information for director age and tenure are excluded. The dependent variable is either a dummy set equal to one if the director has a particular characteristic (top executive experience or industry experience) or the director's age in years at the end of the fiscal year. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better. (1)

Table 11 -The Effect of the Quota on The Gender Gap in Educational Qualifications
This table reports OLS estimates of the treatment effects of the quota ("Post 2010'') on the difference between male and female director characteristics (i.e., gender gaps). The relevant treatment effects are "Female X Post 2010'' for models without the U.S. as a control and "Female X Post 2010 X Treated'' for models where U.S. is used as a control; the effect on gender gaps (male -female) is the negative of these estimates. Observations are defined at the firm-year-director level. The sample includes only outsiders (non-executive directors), and all observations with missing information for director age and tenure are excluded. The dependent variable is a dummy set equal to one if the director has a particular characteristic (an MBA degree or an elite Grande Ecole degree) at the end of the fiscal year. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and tstatistics are reported in brackets. Boldface indicates statistical significance at 10% or better. (1)

Table 12 -The Effect of the Quota on The Gender Gap in Board and Committee Appointments
This table reports OLS estimates of the treatment effects of the quota ("Post 2010'') on the difference between male and female director characteristics (i.e., gender gaps). The relevant treatment effects are "Female X Post 2010'' for models without the U.S. as a control and "Female X Post 2010 X Treated'' for models where U.S. is used as a control; the effect on gender gaps (male -female) is the negative of these estimates. Observations are defined at the firm-year-director level. The sample includes only outsiders (non-executive directors), and all observations with missing information for director age and tenure are excluded. The dependent variable is the number of board seats held by a director or a dummy set equal to one if the director is a member of a core board committee at the firm at the end of the fiscal year. The sample period is from 2003 to 2017. Standard errors are clustered at the firm level and t-statistics are reported in brackets. Boldface indicates statistical significance at 10% or better. (1)

about ECGI
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