Clotilde Coron
email: coron.iae@univ-paris1.fr

Keywords: perceived gender equality, perceived managerial behaviors, case study francesa

How perceived managerial behaviors influence employees' perception of gender equality: the case of a French organization

Clotilde Coron

L'influence des comportements managériaux perçus sur la perception de l'égalité professionnelle par les salariés : le cas d'une organisation française

Résumé : Peu de recherches ont étudié l'influence des comportements managériaux perçus sur l'égalité professionnelle femmes-hommes perçue. Cette étude cherche à combler ce manque en mobilisant le cadre théorique de la justice organisationnelle pour étudier le cas d'une grande entreprise française. 52 entretiens ont été conduits pour formuler les hypothèses et un questionnaire a été conçu afin de les tester.

Les résultats indiquent que les comportements managériaux perçus influencent l'égalité professionnelle perçue. Les salariées femmes estiment que le respect par leur manager de la politique de l'entreprise et les efforts menés pour réduire l'autocensure des femmes sont importants, alors que les salariés hommes accordent plus d'importance aux efforts managériaux visant à assurer de la mixité dans les recrutements et promotions.

Mots-clés : égalité professionnelle perçue, comportements managériaux perçus, étude de cas La influencia de la percepción del comportamiento de los directivos en la percepción de la igualdad profesional de los empleados: el caso de una organización francesa Resumen: Pocos estudios investigan la influencia de la percepción del comportamiento de los directivos sobre la percepción de la igualdad entre mujeres y hombres. El presente estudio moviliza el marco teórico de la justicia organizativa para estudiar el caso de una gran empresa

Introduction

Gender equality in the workplace1 remains an issue in most developed countries [START_REF] Smyth | Field of Study and Gender Segregation in European Labour Markets[END_REF][START_REF] Cech | Mechanism or Myth? Family Plans and the Reproduction of Occupational Gender Segregation[END_REF], even when these countries define binding policies for companies on this matter, as is the case in the European Union [START_REF] Tomlinson | Gender equality and the state: a review of objectives, policies and progress in the European Union[END_REF][START_REF] Ackrill | Black Boxes' and 'fracture points': the regulation of gender equality in the UK and French construction industries[END_REF]. France is a good example of this phenomenon. France has defined an important number of legal obligations for companies concerning gender equality [START_REF] Ackrill | Black Boxes' and 'fracture points': the regulation of gender equality in the UK and French construction industries[END_REF], for example, regarding the presence of women serving on company boards (see Appendix, table A1), but gender inequalities remain significant [START_REF] Tomlinson | Gender equality and the state: a review of objectives, policies and progress in the European Union[END_REF], especially in terms of the pay gap [START_REF] Bozio | Réduire les inégalités de salaire entre les femmes et les hommes[END_REF], job segregation [START_REF] Minni | Femmes et hommes sur le marché du travail. Les disparités se réduisent mais les emplois occupés restent très différents[END_REF], and women's access to positions of responsibility [START_REF] Ferrary | Bipolarisation sexuelle des entreprises. Une étude des 50 plus grandes firmes françaises[END_REF][START_REF] Allemand | Le capital humain des femmes récemment nommées dans les conseils d'administration des sociétés françaises cotées à Paris[END_REF]Toé, 2014;[START_REF] Dardour | CEO compensation and board diversity: evidence from French listed companies[END_REF].

Even in companies that respect their obligations and that have defined a gender equality policy, inequalities remain, as shown by [START_REF] Charbeau | Évaluer une politique d'égalité professionnelle en entreprise : l'apport d'une analyse en termes de parcours[END_REF]. This can be partly explained by the fact that most gender equality policy measures require significant implementation by several actors, which could affect the effectiveness of the policy [START_REF] Guillaume | Quand les politiques volontaristes de mixité ne suffisent pas : les leçons du syndicalisme anglais[END_REF]. Among these actors, line managers/supervisors play an important role as HR partners [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF][START_REF] Allard | Family-Supportive Organizational Culture and Fathers' Experiences of Work-family Conflict in Sweden[END_REF] and decision makers [START_REF] Daverth | The subjectivity of fairness: managerial discretion and work-life balance[END_REF][START_REF] Parmentier | Female Creativity in Organizations: What is the Impact of Team Composition in Terms of Gender during Ideation Processes?[END_REF]. This raises a question about the role of managers in boosting gender equality in the workplace. This role requires managers not only to implement a gender equality policy but also to adopt behaviors that can be perceived as supporting gender equality [START_REF] Stainback | Women in Power: Undoing or Redoing the Gendered Organization?[END_REF].

The notion of perceived managerial behavior has been widely studied in the literature on organizational justice [START_REF] Jepsen | Female perceptions of organizational justice[END_REF][START_REF] Karam | Illuminating the 'Face' of Justice: A Meta-Analytic Examination of Leadership and Organizational Justice[END_REF]. Organizational justice theory suggests that paying attention to perceived managerial behavior is important, perhaps even more so than dealing with objectively observed managerial behavior [START_REF] Cropanzano | The Management of Organizational Justice[END_REF]. However, few studies consider perceived managerial behavior in relation to gender equality, though it seems that this link merits further study [START_REF] Stainback | Women in Power: Undoing or Redoing the Gendered Organization?[END_REF].

The present research focuses on studying this link. More precisely, it aims to estimate the influence of perceived managerial behaviors on perceived gender equality.

This aim is rather original, as most studies measure gender equality using numerical indicators such as the general feminization rate [START_REF] Milewski | Pourquoi les politiques publiques sont-elles si peu suivies d'effets? Quelques interrogations[END_REF], the gender pay gap [START_REF] Smith | Gender, pay and work satisfaction at a UK university[END_REF], and the feminization rate of positions of responsibility [START_REF] Sheridan | Complex and contradictory: the doing of gender on regional development boards[END_REF]. Few academic works deal with employees' perceptions of gender equality. However, organizational justice theory indicates that perceived gender equality can influence general perceptions of fairness [START_REF] Bourguignon | The role of criticism in the dynamics of performance evaluation systems[END_REF] and, by extension, employees' behavior [START_REF] Colquitt | Justice at the Millenium: A Meta-Analytics Review of 25 Years of Organizational Justice Research[END_REF][START_REF] Beauregard | Fairness perceptions of work-life balance initiatives: effects on counterproductive work behaviour[END_REF] and loyalty toward their employers [START_REF] Cohen-Charash | The Role of Justice in Organizations: A Meta-Analysis[END_REF][START_REF] Hulin | Les attentes différenciées des talents selon le sexe : une approche par la justice procédurale et la justice distributive[END_REF]. Moreover, this aim constitutes a theoretical challenge in that it examines which types of perceived managerial behaviors are best able to increase perceived gender equality, given that both the literature on gender equality and the literature on organizational justice do not precisely define which types of managerial behaviors can influence perceptions of gender equality. From a managerial perspective, answering this question would help us more precisely define the role and duties of managers in promoting gender equality, with a view to improving the effectiveness of gender equality policies.

This paper presents a case study carried out in a French technology company in 2015. Such a company provides an interesting research field, because the technology sector suffers from an underrepresentation of women (36 % of women in this particular company). In addition, this company has defined a committed policy on gender equality. Organizational justice theory helped define the first set of general research propositions, starting with a qualitative study based on 52 semi-structured interviews conducted in two entities of the company.

Operationalized hypotheses were derived from this study and tested using three multiple generalized linear regression models on a database built with data from a survey conducted in this company (1,413 respondents).

In the first section of this paper, perceived gender equality and the theoretical framework of organizational justice are used to formulate research propositions regarding the influence of perceived managerial behaviors. In the second section, the case study is presented, along with the qualitative approach, the operationalized hypotheses, and the quantitative design. The third section outlines the main results, which are then discussed. The research shows that different types of perceived managerial behaviors play an important role in the perception of gender equality. Moreover, the most effective perceived managerial behaviors differ based on employees' gender. The managers' perceived compliance with policy and efforts to avoid female self-censorship and to achieve a work-life balance have a positive influence and significantly increase women's perceptions of gender equality, whereas managers' perceived efforts to promote gender diversity when recruiting and promoting and to maintain work-life balance significantly influence men's perceptions of gender equality.

Literature review

Gender equality in the workplace: the role of managers in implementing policies Gender equality has been the subject of a significant increase in legislation in France since the second half of the twentieth century, introducing obligations that specifically affect large companies [START_REF] Ackrill | Black Boxes' and 'fracture points': the regulation of gender equality in the UK and French construction industries[END_REF] (see Appendix, table A1). That explains why positions responsible for promoting gender equality have been created in French companies [START_REF] Laufer | L'Égalité professionnelle entre les femmes et les hommes[END_REF], as is the case, for example, in the US [START_REF] Dobbin | Inventing Equal Opportunity[END_REF]. Among other duties, "gender equality directors" define the gender equality policy and negotiate it with the unions. An intercompany association, AFMD ("Association française des managers de la diversité") was created to allow these managers to share about their practices and policies. Those managers often report to the Human Resources Departement, but their means and rooms for maneuver depend on the companies. However, policy implementation cannot be ensured by either this department or the unions [START_REF] Olgiati | Promoting gender equality in the workplace[END_REF]. Many everyday measures depend on the involvement of managers [START_REF] Woodhams | Gender-based equal opportunities policy and practice in small firms: the impact of HR professionals[END_REF]. For example, avoiding gender stereotypes when redacting a job offer [START_REF] Laufer | L'égalité des femmes et des hommes en entreprise. De nouvelles avancées dans la négociation ?[END_REF], giving priority to women when recruiting [START_REF] Laufer | Égalité professionnelle et GRH[END_REF], putting in place managerial coaching [START_REF] Ye | Gender and managerial coaching across cultures: female managers are coaching more[END_REF], avoiding gender stereotypes in performance management reviews [START_REF] Parmentier | Female Creativity in Organizations: What is the Impact of Team Composition in Terms of Gender during Ideation Processes?[END_REF], or paying attention to work-life balance [START_REF] Guillaume | La fabrication organisationnelle des dirigeants. Un regard sur le plafond de verre[END_REF] all imply managerial action. However, as [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF] point out, managers face competing demands (financial targets, production goals, etc.). Therefore, they may not perceive gender equality as an important part of their job, except when they are personally sensitized to the subject [START_REF] Woodhams | Gender-based equal opportunities policy and practice in small firms: the impact of HR professionals[END_REF]. This explains why numerous French companies, like their US counterparts, have instituted gender equality training programs for their managers [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF][START_REF] Dobbin | Inventing Equal Opportunity[END_REF][START_REF] Lanquetin | Égalité, diversité et… discriminations multiples[END_REF]. [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF] stress the need to train managers to reduce managerial bias, e.g., when recruiting or promoting employees.

Organizational justice and the importance of perceived managerial behaviors and perceived gender equality

However, academic literature on organizational justice has demonstrated that, more so than objectively observed managerial behaviors, perceived managerial behaviors/support/control are important to study, because they can influence job satisfaction and, ultimately, employees' behaviors. The theory of organizational justice deals with perceived fairness within organizations [START_REF] Schminke | Ethics, Values, and Organizational Justice: Individuals, Organizations, and Beyond[END_REF]Charbonnier-Voirin and El Akremi, 2016). More precisely, organizational justice theory often considers four types of perceived forms of fairness: distributive, procedural, interactional and informational [START_REF] Byrne | The History of Organizational Justice: The Founders Speak[END_REF][START_REF] Ambrose | The Role of Overall Justice Judgments in Organizational Justice Research: A Test of Mediation[END_REF]. Distributive justice corresponds to "the fairness of the outcomes received in a given transaction" (Byrne and Cropanzano, 2001, p. 4). Procedural justice corresponds to "the fairness of the process that leads to those outcomes" (Byrne and Cropanzano, 2001, p. 4). Interactional justice corresponds to "the effect of the interpersonal communication between the parties, highlighting the role of the person who made the allocations" (Jepsen and Rodwell, 2012, p. 725). Informational justice focuses on the explanations given about procedures and decisions (Jepsen and Rowell, ibid.). Perceived managerial behaviors are embedded in the frameworks of interactional and informational justice.

Perceived managerial behaviors are included in each facet of organizational justice [START_REF] Rupp | The utility of a multifoci approach to the study of organizational justice: A meta-analytics investigation into the consideration of normative rules, moral accountability, bandwidth-fidelity, and social exchange[END_REF]. For example, [START_REF] Allard | Family-Supportive Organizational Culture and Fathers' Experiences of Work-family Conflict in Sweden[END_REF] deal with perceived work-family support from top managers and supervisors. [START_REF] Cropanzano | The Management of Organizational Justice[END_REF] turn their interest to perceived managerial fairness in recruiting, appraising, rewarding, managing conflicts and downsizing. [START_REF] Colquitt | Justice at the Millennium, a Decade Later: A Meta-Analytic Test of Social Exchange and Affect-Based Perspectives[END_REF] deal with "supervisor-focused justice" and its influence on trust and organizational citizenship behavior. Hence, organizational justice theory emphasizes that perceived managerial behaviors can influence perceived fairness [START_REF] Cropanzano | The Management of Organizational Justice[END_REF][START_REF] Rupp | The utility of a multifoci approach to the study of organizational justice: A meta-analytics investigation into the consideration of normative rules, moral accountability, bandwidth-fidelity, and social exchange[END_REF] but without answering the question of which managerial behaviors influence justice perception [START_REF] Karam | Illuminating the 'Face' of Justice: A Meta-Analytic Examination of Leadership and Organizational Justice[END_REF]. Links between gender and organizational justice are polymorphic, and academic research has led to contradictory results [START_REF] Hulin | Les attentes différenciées des talents selon le sexe : une approche par la justice procédurale et la justice distributive[END_REF][START_REF] Nurse | Grievance management and its links to workplace justice[END_REF]. For example, some works show that women are found to place a greater value on interactional justice and a lower value on distributive justice than men (Jepsen and Rodwall, 2012), whereas some studies show that this is true only when gender is put into interaction with race [START_REF] Simpson | Gender, organizational justice perceptions, and union organizing[END_REF]. Most researches that combine gender and organizational justice use gender as a variable structuring perceived fairness, but they do not use organizational justice as a conceptual framework to better understand gender equality.

However, a parallel can be established between perceived fairness and perceived gender equality. Indeed, gender equality and organizational justice share the fundamental assumption of ethical and normative treatment (as Rupp et al., 2006, recall for CSR). Organizational justice theory shows that people form perceptions as to whether the way they are being treated is fair or unfair and that this perceived fairness influences their behaviors [START_REF] Cropanzano | Procedural and Distributive Justice Are More Similar Than You Think: A Monistic Perspective and a Research Agenda[END_REF][START_REF] Rupp | The utility of a multifoci approach to the study of organizational justice: A meta-analytics investigation into the consideration of normative rules, moral accountability, bandwidth-fidelity, and social exchange[END_REF]. In the same way, individual employees have their own perceptions of gender equality within their work environment. Hence, this suggests the need to study perceived gender equality, that is, the perception that employees have of their company's situation regarding gender equality. However, few works consider and measure perceived gender equality. Works dealing with gender equality in the workplace generally measure three dimensions: 1) gender equality as measured by key indicators, for example, the gender pay gap [START_REF] Lyons | Gender pay equity, wage fixation and industrial relations reform in Australia: One step forward and two steps backwards?[END_REF][START_REF] Moore | The changing face of employment relations: equality and diversity[END_REF], or women's access to positions of responsibility [START_REF] Ferrary | Bipolarisation sexuelle des entreprises. Une étude des 50 plus grandes firmes françaises[END_REF][START_REF] Sheridan | Complex and contradictory: the doing of gender on regional development boards[END_REF]; 2) the link between gender equality and other variables, for example, work satisfaction [START_REF] Smith | Gender, pay and work satisfaction at a UK university[END_REF]; and 3) the influence of gender on several variables, for example, work participation [START_REF] Markey | Gender, part-time employment and employee participation in Australian workplaces[END_REF], perceived fairness [START_REF] Jepsen | Female perceptions of organizational justice[END_REF], or job satisfaction [START_REF] Huang | Social expectations, gender and job satisfaction: Front-line employees in China's retail sector[END_REF].

In summary, the following points can be emphasized:

-The literature on organizational justice emphasizes perceived managerial behaviors and perceived fairness (and a parallel can be made with perceived gender equality) but without paying much attention to which types of managerial behaviors influence justice perceptions, and this literature gives contradictory results regarding the link between gender and perceived fairness.

-The literature on gender equality does not pay much attention to perceived managerial behaviors or perceived gender equality. This paper is aiming at narrowing these research gaps by studying the influence of perceived managerial behaviors on perceived gender equality. [START_REF] Yin | Applications of Case Study Research[END_REF] underlines that a case study should start with some theoretical propositions, which suggest sets of relationships between acts or events. This helps select the case study and specify what needs to be explored. [START_REF] Yin | Applications of Case Study Research[END_REF] suggests to define those theoretical propositions according to the literature. In this paper, linking literature about gender equality, specifically the gendered organizations field, and organizational justice, helps define two research propositions, one focusing on perceived managerial behavior and the role of manager in promoting gender equality, the second exploring gendered perception of the manager role.

Research propositions

Perceived managerial behavior

The literature on gendered organizations shows that managers are key to the implementation of the gender equality policy [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF] and can act on it in several ways: by implementing company agreements [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF][START_REF] Laufer | Égalité professionnelle et GRH[END_REF][START_REF] Dobbin | Inventing Equal Opportunity[END_REF], by paying attention to gender diversity when recruiting and promoting [START_REF] Macneil | The role of organizational learning in soft regulation of workplace gender equality[END_REF], by preventing female self-censorship [START_REF] Pigeyre | Femmes dirigeantes : les chemins du pouvoir[END_REF][START_REF] De | Mentoring for gender equality and organizational change[END_REF], and by contributing to work-life balance [START_REF] Muzio | Editorial: researching gender, inclusion and diversity in contemporary professions and professional organizations[END_REF][START_REF] Daverth | The subjectivity of fairness: managerial discretion and work-life balance[END_REF][START_REF] Macneil | The role of organizational learning in soft regulation of workplace gender equality[END_REF].

Organizational justice theory highlights the way managerial behaviors inform justice perceptions [START_REF] Karam | Illuminating the 'Face' of Justice: A Meta-Analytic Examination of Leadership and Organizational Justice[END_REF]. Works in this field also suggest dealing with perceived managerial behavior rather than objectively observed managerial behavior [START_REF] Rupp | The utility of a multifoci approach to the study of organizational justice: A meta-analytics investigation into the consideration of normative rules, moral accountability, bandwidth-fidelity, and social exchange[END_REF].

However, these works often do not specify which types of managerial behaviors are expected to inform perceived fairness [START_REF] Karam | Illuminating the 'Face' of Justice: A Meta-Analytic Examination of Leadership and Organizational Justice[END_REF], except for the work of [START_REF] Cropanzano | The Management of Organizational Justice[END_REF]. Thus, at this stage, research proposition P1 remains rather general.

P1: Perceived managerial behaviors influence perceived gender equality.

Gendered perception of the manager role

Perceptions of gender equality might themselves be gendered, of course [START_REF] Acker | Inequality Regimes: Gender, Class, and Race in Organizations[END_REF]. For example, in some studies, women are found to have a "higher threshold for reaction to unjust reward allocation" (Moore, 1990, p. 51) and report similar levels of perceived fairness at work as men [START_REF] Jepsen | Female perceptions of organizational justice[END_REF], perhaps because they are unaware of discrimination [START_REF] Moore | Discrimination and deprivation: the effects of social comparisons[END_REF]. They also report higher job satisfaction than men in Western countries, perhaps because they have lower expectations [START_REF] Huang | Social expectations, gender and job satisfaction: Front-line employees in China's retail sector[END_REF]. Conversely, [START_REF] Singer | The application of relative deprivation theory to justice perception of preferential selection[END_REF] asserts that other studies find that women working in non-gender-segregated occupations experience deprivation due to a gender pay gap, a result confirmed by [START_REF] Smith | Gender, pay and work satisfaction at a UK university[END_REF]. Other work on gender equality emphasizes that women give more importance to gender equality than men [START_REF] Johansson | The business case of gender equality in swedish forestry and miningrestricting enabling organizational change[END_REF][START_REF] Scala | Bureaucratic role perceptions and gender mainstreaming in Canada[END_REF]. This may create a difference between women and men concerning the role that supervisors play in gender equality. However, these studies often fail to specify this difference or measure it precisely. Thus, at this stage, research proposition P2 remains rather vague.

P2: The link between perceived managerial behaviors and perceived gender equality varies

based on the employees' gender.

Case study and qualitative approach

To operationalize these propositions, a qualitative approach is used. Then, a quantitative approach is mobilized to test the hypotheses.

Case study

Technologix2 is an international company whose headquarters are based in France, with 90,000 employees in France itself. In France, the majority of the workers have civil service contracts because Technologix was initially a French administrative organization.

Technologix faces several persistent issues of gender equality: the feminization rate has not evolved for more than 10 years (36% of the workforce is female), and the feminization rate of the 800 most important jobs in the company stood at a mere 23% in 2014. Specifically, this low feminization rate can also be explained by the fact that Technologix is in the technology sector, which is generally a very male-dominated field.

However, Technologix has put in place a committed policy on workplace gender equality.

In 2011, the company's third gender equality agreement laid out voluntary measures: parity of preselection lists of candidates in recruitment and the provision of an additional promotion budget specifically for women. In 2014, the fourth agreement reaffirmed most of the measures of the third agreement. The gender equality team of 5 people is part of a Diversity Department, reporting to the Head of Human Resources. Hence, Technologix constitutes a good paradigm of the obstacles encountered on the path toward gender equality: a committed policy, but one that does not give the expected results [START_REF] Woodhams | Gender-based equal opportunities policy and practice in small firms: the impact of HR professionals[END_REF].

The paper uses a qualitative study to transform the general research propositions presented at the end of the literature review into hypotheses and a quantitative study to test them [START_REF] Yin | The Case Study Crises: Some Answers[END_REF][START_REF] Yin | Mixed Methods Research: Are The Methods Genuinely Integrated of Merely Parallel?[END_REF]. [START_REF] Kaplan | Combining Qualitaive and Quantitative Methods in Information Systems Research: A Case Study[END_REF] offer an interesting insight into the mix of qualitative and quantitative methods in case studies, as they use both interviews and survey questionnaires.

They emphasize the added value of this combination, which allows the researcher to specify and qualify the results. In this paper, the qualitative part is used only to inform and operationalize the hypotheses. This constitutes a specific example of mixed-methods research [START_REF] Burke | Toward a Definition of Mixed Methods Research[END_REF] with a case study.

Design of the qualitative study

The qualitative study is an embedded case study [START_REF] Yin | Case Study Research -Design and Methods[END_REF], as semi-structured interviews were conducted in 2 entities of Technologix, which were selected for the variety of their population. Twenty-eight semi-structured interviews were conducted in a technical entity employing approximately 800 employees (22 % women), the majority of whom were civil servants. Twenty-four semi-structured interviews were conducted in a commercial entity employing approximately 900 employees (39 % women), the majority of whom were executives and contract staff. In both entities, interviews were conducted with HR people (12 for both entities), managers (21) and employees (19). The average duration of the interviews was 1 h 30 min. The interviews were not recorded, as their purpose was not to conduct in-depth research about managerial behaviors concerning gender equality but rather to operationalize the research propositions by identifying some managerial behaviors that could influence perceived gender equality. However, extensive notes were taken during the interviews, leading to files containing approximately 4,000 words for each transcription. Following both research propositions, the generic purpose of the interviews was to identify and understand the perceptions of gender equality and to identify some managerial behaviors that could inform these perceptions. However, the interview guide was different for each actor. The HR people and managers were asked about the following: the gender equality policy (e.g., "What do you think about the policy defined by Technologix concerning gender equality?"); the role of the managers (e.g., "How are your relationships with the managers in the entity?" for the HR and "In your mind, as a manager, what can you do to promote gender equality?" for managers); and their perception of the company's situation regarding gender equality (e.g., "What do you think about the situation of Technologix concerning gender equality?"). Employees were asked about possible feelings of gendered discrimination, the importance of the manager and what managers could do to promote gender equality (e.g., "Do you have the feeling that your manager promotes gender equality?").

Each interview was coded with descriptive codes. This was carried out across broad "analysis units" (most of them were paragraphs). Then, investigations were limited to the parts of the interviews dealing with managerial behaviors and perceived gender equality. Indeed, the purpose was to identify managerial behaviors mentioned by HR, managers and all employees (female and male) as supporting and promoting gender equality. That is why the analysis of the interviews with the managers focused on the parts in which they talked about their role as managers; for the interviews with employees and HR, the research focused on the parts in which they talked about the managers and specifically the managerial behaviors that could help or, on the contrary, hamper gender equality. Then, these different behaviors were categorized into 6 types of managerial behaviors that promote gender equality 3 .

3 See Table 1 for an illustration.

The role of managers concerning gender equality: operationalized hypotheses

The interviews with the managers show that they are aware of the importance of their role concerning gender equality.

"I think gender equality is a subject that's fairly well-established, and now what we're trying to work on is the percentage of women in some professional fields. For example, the proportion of women is not very high in technical professions, but it's the opposite in communications and HR. […] So, the message we are sending out internally is that our jobs are of interest to both men and women." -Manager, technical entity, male Employees (specifically women) also express the view that their managers could play a role and promote gender equality through their actions, with some of the interviewees concluding that managers play the most important role in gender equality, specifically because they make recruitment and promotion decisions.

"I have changed managers many times, and given these circumstances, it is very difficult to move up the professional ladder because it depends a lot on the manager." -Employee, commercial entity, female These interviews also reveal differences between women and men. Women tend to be more aware of gender inequalities, as expected, but are also more likely to highlight different types of managerial behaviors than men.

Interviews with HR show that they rely heavily on managers for the implementation of the gender equality policy. They are also relatively critical of some managers who are supposedly reluctant to support the "cause" of gender equality.

"I am not convinced that managers are as aware of gender equality issues as HR recruiters." -HR, recruitment, commercial entity, female "Now I am in a very technical entity, with very few women, and the vision that managers have of women's contribution is really weak. A manager does not think that a woman who does not come from the technical field can enter the technical field." -HRBP, technical entity, male Thanks to this qualitative material, 6 types of managerial behaviors have been identified from interviews with the HR, managers and employees. Table 1 indicates these behaviors and illustrates them with interview extracts.

Table 1: Types of managerial behaviors identified in the interviews

Table 1 allows proposition P1 to be specified and transformed into operationalized hypotheses. The generic proposition was the following: "Perceived managerial behaviors influence perceived gender equality". This proposition can be subdivided into six hypotheses related to each managerial behavior.

H1a: The perceived managerial behavior "following the rules and company agreements concerning gender equality" positively influences perceived gender equality.

H1b: The perceived managerial behavior "trying to constitute gender-diverse teams" positively influences perceived gender equality.

H1c: The perceived managerial behavior "being vigilant about gender diversity when awarding internal promotions" positively influences perceived gender equality.

H1d: The perceived managerial behavior "reassuring one's teams to avoid the phenomenon of female self-censorship in the context of career advancement" positively influences perceived gender equality.

H1e: The perceived managerial behavior "contributing to a work environment that is good for work-life balance" positively influences perceived gender equality.

H1f: The perceived managerial behavior "showing exemplary conduct regarding gender equality" positively influences perceived gender equality.

Additionally, the interviews show that the importance accorded to each managerial behavior promoting gender equality is gendered. Hence, proposition P2 can be specified and transformed into hypothesis H2: H2: The link between each perceived managerial behavior (H1a-H1f) and perceived gender equality varies based on employees' gender.

However, it is difficult to precisely measure the link between these discernable managerial behaviors and perceived gender equality with the interviews and thus to test these hypotheses.

That is why a questionnaire survey as well as multiple linear regressions were used, which allowed the links between the variables to be quantified.

Design of the quantitative study

The subsequent questionnaire has been designed from the interviews and administered online in June-July 2015.

Every item (except in the identification section) used a 10-point Likert scale: (1 = completely disagree, 10 = completely agree). The choice of 10 points was consistent with internal use in the company. A 10-point scale also has the advantage that people are familiar with rating things on a scale of 10 [START_REF] Dawes | Do data characteristics change according the number of scale points used? An experiment using 5-point, 7-point and 10-point scales[END_REF]. [START_REF] Wittink | The measurement imperative[END_REF] show that a 10point scale is more precise, allowing changes to be detected more easily and needing a smaller sample to be reliable. Table 2 presents the questions and items used in the analysis.

The variables indicated in Table 2 are used as measures of perceived managerial behaviors and perceived gender equality. The semi-structured interviews were used to define the items.

As explained above, the interviewees mentioned some (perceived) managerial behaviors as promoting gender equality, which allowed items 5-10 to be formulated to test hypotheses H1a-H1f: implementing company agreements (H1a), paying attention to gender diversity when recruiting (H1b) and promoting (H1c), avoiding female self-censorship (H1d), contributing to work-life balance (H1e), and showing exemplary conduct (H1f).

Concerning perceived gender equality (items 11-14), the respondents were asked about three main dimensions: access to responsibilities, gender diversity recruitment, and work-life balance. Interestingly, the gender pay gap was not mentioned by the interviewees as being important in gender equality ("To my knowledge, the salary catch-up exercise has ended in our entity, because the HR experts saw that there was no gender pay gap." -Manager, technical entity). This could be due to the company's history as a former public administration, where wages were heavily dependent on collective grids. As a result, this dimension is not included in the questionnaire; instead, a general question about gender equality (question 14) was added that covered equal pay.

Thus, the questionnaire is empirically based on the interviews. Cronbach's alphas give sufficient internal consistency for each axis. Hence, this study mixes criteria of reliability stemming from quantitative research (Cronbach's alphas) and criteria provided by qualitative research (questionnaire defined thanks to the interviews, which allow the researcher to "capture authentically the lived experiences of people", ibid., 49) [START_REF] Onwuegbuzie | The Validity Issue in Mixed Research[END_REF].

Table 2: Measures and questions / items

Responses were received from 1,413 employees out of the 10,000 who had been sent an email with a URL link to the questionnaire (corresponding to a return rate of 14.4%, typical for online surveys in this company). Forty-five percent of respondents were women, compared to the 36% feminization rate at Technologix. This imbalance is certainly due to selection bias; answering this survey was not mandatory, and women are generally more interested in gender equality than men [START_REF] Johansson | The business case of gender equality in swedish forestry and miningrestricting enabling organizational change[END_REF][START_REF] Scala | Bureaucratic role perceptions and gender mainstreaming in Canada[END_REF]. However, this bias exists for all respondents (men who answered are surely more interested in the topic than most men) and that this paper focuses on the differences between respondents, so the bias does not preclude an interesting analysis of the data. Table 3 gives more details about the sample.

Table 3: Respondents' sample and the Technologix population

As shown in Table 3, managers and employees working in support functions and computing were more interested in completing the survey. The sample was not adjusted to respect the overrepresentation of people most interested in the topic.

Main quantitative results: perceived managerial behaviors are important, but their importance differs based on employees' gender

Descriptive statistics

Table 4 presents the descriptive statistics. For each item, the mean for the sample is given and then the separate means for females and males. A t-test (Student's test) revealed whether the differences between females and males were significant.

Table 4: Descriptive statistics

Table 4 shows that Technologix respondents express more positive points of view about the role of their manager in maintaining work-life balance (mean 7.20) and complying with company agreements (7.07) than in avoiding female self-censorship (6.22) or taking into account gender diversity when recruiting (6.36). Concerning perceived gender equality, worklife balance (6.45) is considered as being less achieved than women's access to responsibilities (6.94) or the feminization rate of recruitment (6.63).

This also indicates that the differences between the perceptions of women and men are important. Concerning the role of the manager, perceptions differ about compliance with the rules and company agreements and about the vigilance concerning gender diversity when promoting. Women have a more negative perception than men on both dimensions. Perceptions of gender equality are even more polarized based on gender: women have a more negative perception of the situation in their work environment. They are more likely to consider that there are problems with gender diversity, equal access to promotions, work-life balance, and gender equality in general. Women also tend to consider that there are more problems regarding women's access to positions of responsibility (table 4: 5.99, against 6.41 for the feminization rate of recruitment, for example), whereas men tend to consider that there are more problems regarding work-life balance (6.67, against 6.82 for the feminization rate of recruitment, for example).

Table 5 gives the correlation matrix. All the items are positively and significantly correlated.

The table shows that the influence of the manager on perceived gender equality is significant: the more that the respondents are positive about their managers' behavior concerning gender equality, the more positive are their perceptions of gender equality.

Table 5: Correlation matrix

Tests of the hypotheses

To test the hypotheses, three generalized multiple linear regression models were used. They all explain perceived gender equality (question 14) by perceived managerial behaviors. Model 1 concerns the whole population, while Model 2 concerns only women and Model 3 only men.

The aim of this separation is to test hypothesis H2.

The choice to consider only item 14 (and not items 11-13) for perceived gender equality is explained by the fact that this question comprises all the dimensions of gender equality and not only gender diversity, equal access to positions of responsibility, or work-life balance.

Cronbach's alpha between those four items is sufficient to ensure reliable consistency, even when considering only question 14.

The results of Model 1 are shown in Table 6.

Table 6: Model 1 -"In my work environment, in general, there is no problem regarding gender equality"

Model 1 indicates that gender is a significant explanatory variable in perceived gender equality: all things being equal, women tend to have a more negative perception than men. Age also influences perceived gender equality: older employees (46+) express a more positive perception. The respondents from the innovation and multimedia fields tend to express a more negative perception than the respondents from the commercial professional field. Managerial status does not influence perceived gender equality.

Concerning the role of the manager, the model shows that almost every perceived managerial behavior positively influences perceived gender equality. Perceived compliance with policy, actions on gender diversity when recruiting and promoting, and efforts to avoid female self-censorship or to create a work environment that is good for work-life balance positively and significantly influence perceived gender equality. However, the exemplarity of the manager does not seem to have a significant impact. This could be explained by the fact that the other dimensions capture all the dimensions of managerial exemplarity.

Hence, almost all hypotheses H1 (H1a-H1e) are validated. H1f is not.

The results of Model 2 and Model 3 are given in Table 7.

Table 7: Models 2 and 3 -"In my work environment, in general, there is no problem regarding gender equality" by gender

Both models give significant results, and it is interesting to compare them. For women, age plays a role (older employees are more positive), as does the professional field (the employees from the innovation and multimedia fields are more negative). For men, only employees in the 46-55 age range express a more positive perception than the younger employees.

The influence of perceived managerial behaviors on perceived gender equality varies based on employees' gender. For women, perceived compliance with policy and efforts to avoid female self-censorship and to maintain a work-life balance influence the perceived gender equality positively and significantly. Conversely, for men, perceived compliance with policy and efforts to avoid female self-censorship are not significant for perceived gender equality.

However, perceived efforts to promote gender diversity when recruiting and promoting and to maintain work-life balance influence perceived gender equality positively and significantly, as does managerial exemplarity.

Hence, hypothesis H2 is validated. Indeed, it is not the same type of managerial behavior that influences perceived gender equality for women and men.

Discussion

This research deals with the role that perceived managerial behaviors play in perceived gender equality. The results demonstrate the behaviors' importance. The managers' perceived compliance with gender equality rules and their efforts to promote gender diversity and women's access to responsibilities, to reduce female self-censorship, and to maintain work-life balance have a positive and significant impact on perceived gender equality. However, these impacts differ based on employees' gender. Male employees seem to place more importance on gender diversity (when recruiting and promoting) and on managerial exemplarity in general, whereas female employees tend to place more importance on compliance with policy and efforts to reduce female self-censorship. Efforts to maintain work-life balance are important for both female and male employees.

The results initiate a discussion with the literature on organizational justice and gender equality in the workplace.

The importance of perceived managerial behaviors for perceived gender equality complements the literature dealing with gender equality in the workplace, which states that a gender equality policy cannot succeed without the involvement of managers, because gender equality policy includes measures and actions carried on by managers [START_REF] Woodhams | Gender-based equal opportunities policy and practice in small firms: the impact of HR professionals[END_REF]. Indeed, few authors focus on perceived managerial behaviors and on perceived gender equality. This paper demonstrates that managers also play a role in the perception of gender equality in the workplace. This adds a new dimension to take into account when designing managerial training programs on gender equality [START_REF] Kalev | Best practices or best guesses? Assessing the efficacy of corporate affirmative action and diversity policies[END_REF][START_REF] Lanquetin | Égalité, diversité et… discriminations multiples[END_REF].

Moreover, this work complements this literature by giving precise examples of managerial behaviors that influence perceived gender equality. This gives valuable insight for managerial training programs: these programs need to make managers aware of the importance of showing visible support to gender equality. This study also engages in a discussion with the organizational justice theory. The study gives precise examples of managerial behaviors, which previous academic work has scarcely explored so far [START_REF] Karam | Illuminating the 'Face' of Justice: A Meta-Analytic Examination of Leadership and Organizational Justice[END_REF]. For example, "following the rules and company agreements concerning gender equality" can act as an example of managerial behaviors for procedural justice. However, if the parallel between organizational justice and gender equality is extended, these results indicate that new dimensions could be added to organizational justice. Indeed, the behaviors "being vigilant about gender diversity when awarding internal promotions" or "contributing to a work environment that is good for work-life balance", or even "reassuring one's teams to avoid the phenomenon of female self-censorship in the context of career advancement", cannot be directly linked to procedural, distributive, interactional or informational justice. [START_REF] Fraser | Justice sociale, redistribution et reconnaissance[END_REF] helps identify these new dimensions, as she links gender, feminism and social justice. She emphasizes three paradigms for social justice in relation to feminism and its different movements: reducing gender inequalities (redistribution), valuing differences (recognition), and promoting women's participation (participation). Some of the identified managerial behaviors correspond to these paradigms. For example, "reassuring one's teams to avoid the phenomenon of female self-censorship in the context of career advancement" can be linked to the redistribution paradigm, since this behavior aims to reduce the gender inequalities concerning female self-censorship; "contributing to a work environment that is good for work-life balance" corresponds to the recognition paradigm, since the behavior implies the questioning of the dominant cultural norms of careers, e.g. availability and presenteeism [START_REF] Fraser | Social justice in the age of identity politics: Redistribution, recognition, participation[END_REF]; and "trying to constitute gender-diverse teams" corresponds to the representation paradigm, as the behavior is based on the idea that women have to participate in the labor force and the economic and political life [START_REF] Halpern | Les dilemmes de la justice sociale[END_REF]. However, these three paradigms are not covered by the four dimensions of organizational justice. This emphasizes the necessity to add these paradigms to the dimensions of organizational justice in relation to gender equality. This necessity can be explained by the fact, emphasized by [START_REF] Fraser | Social justice in the age of identity politics: Redistribution, recognition, participation[END_REF], that gender equality implies going against established androcentric standards and that this dimension of struggle is not taken into account by organizational justice.

The variations in expectations regarding managerial behaviors based on gender are partly explained by the literature but nevertheless generate a discussion, specifically with the works from the organizational justice field. This literature is uncertain about the influence of gender on the expectations of both the company and the managers. For example, some authors suggest that women tend to place more importance on processes, while men place more importance on results [START_REF] Simpson | Gender, organizational justice perceptions, and union organizing[END_REF]; other authors demonstrate that this is not true [START_REF] Hulin | Les attentes différenciées des talents selon le sexe : une approche par la justice procédurale et la justice distributive[END_REF]. However, little research has examined the influence of different types of perceived managerial behaviors on perceived gender equality based on employees' gender. This research shows that women and men value different aspects of managerial behavior. For women, following the rules and avoiding female self-censorship is important, while paying attention to gender diversity when recruiting and promoting is important for men. This is consistent with the studies showing that women tend to place more importance on processes ("following the rules"), while men place more importance on results ("trying to constitute gender-diverse teams"). However, the identification of precise managerial behaviors and the measurement of variations in perception based on gender introduces new results to the contradictory literature dealing with gendered expectations. This raises a question about the reasons for this gendered difference, which has been only partly addressed [START_REF] Jepsen | Female perceptions of organizational justice[END_REF][START_REF] Hulin | Les attentes différenciées des talents selon le sexe : une approche par la justice procédurale et la justice distributive[END_REF].

Finally, this research emphasizes the importance of considering perceived, and not simply measured, gender equality. In this respect, in this study, while women and men may work in the same organization, they do not have the same perceptions of gender equality. Women express more negative perceptions than men on the four dimensions studied (access to positions of responsibility, the feminization rate of recruitment, work-life balance, and gender equality in general). This can be explained by the concept of relative deprivation [START_REF] Moore | Discrimination and deprivation: the effects of social comparisons[END_REF][START_REF] Singer | The application of relative deprivation theory to justice perception of preferential selection[END_REF]. This concept is not new but has been poorly used in recent research. The literature also shows contradictory results on relative deprivation: some studies suggest that men as well as women experience relative deprivation insofar as it concerns gender inequalities, whereas other studies consider that only women experience relative deprivation [START_REF] Singer | The application of relative deprivation theory to justice perception of preferential selection[END_REF]. However, the results presented here emphasize that in France in 2015, women are more aware of gender inequalities than men, which sustains and updates relative deprivation theory. More precisely, regarding the dimensions, the most negative perceptions of women are related to access to positions of responsibility, while for men, the most negative perceptions are related to worklife balance. This suggests that women are more sensitive to career inequalities. Work-life balance constitutes the only dimension that unambiguously concerns both women and men. This could explain why men are more sensitive to this dimension than the others.

Conclusion

The findings presented here have several managerial implications. They give precise examples of behaviors that can be expected from managers, which can help design a managerial training program for gender equality in the workplace. Managers should show more explicitly that they support gender equality. This could involve not only paying attention to female selfcensorship and gender diversity but also contributing to creating a work environment suitable for work-life balance. Actually, the results show that perceived managerial efforts to promote gender equality can influence perceived gender equality, even if they do not influence concrete gender equality. For example, perceived efforts to promote gender diversity when recruiting can have effects on perceived gender diversity, even if these efforts do not result in a higher feminization rate. This research also shows how perceptions of gender equality differ between women and men, indicating that increasing men's awareness regarding gender inequalities might be useful to ensure that a gender equality policy is understood and implemented in the workplace.

However, some limitations, specifically methodological, raise new questions and open up new research perspectives. There is, undeniably, a selection bias framing these results, as only those people most interested in the topic answered the questionnaire: a bias that will account for some of the differences between the findings of this paper and other similar case studies. In addition, this study was conducted in a French company with certain specificities (established commitment toward gender equality, for example), which prevents us from being able to generalize the results to France in general and further afield. Furthermore, only one question was asked regarding each type of managerial behavior. This seemed sufficient, as the precise managerial behaviors were identified thanks to the interviews, but certain researchers argue that perceptions should be gathered on the basis of more than a single item. In addition, respondents

were not asked about their manager's gender, which could have given some valuable information, since there are many interactions between gender, manager's gender, and gender equality. Last but not least, only a part of the substantial amount of qualitative material was used to identify the managerial behaviors and thus to define the hypotheses and build the questionnaire. This might be slightly reductive and prevents a thorough understanding of the mechanisms by which managerial behaviors affect perceived gender equality.

The results of this exploratory study call for broader studies on the role that managers play in the implementation of gender equality policy and in perceived gender equality. For example, taking into account the gender of the manager could constitute another avenue for research.

Another point of interest would be to conduct a larger study with an international dimension to compare results between countries. This work also calls for deeper analyses that would increase an understanding of the different values that women and men put on various managerial behaviors. The relevant academic literature has produced contradictory results on the value that women and men place on gender equality and on gendered expectations of companies and managers, and it would be useful for gender studies to stabilize the scientific knowledge on the topic. Another research path would be to pay attention to the evolution of perceived gender equality in relation to the evolution of the feminization rate and the gender equality policy of the company. Table 1: Types of managerial behaviors identified in the interviews

Tables

Table 8

 8 summarizes which hypothesis is validated or not validated.

Table 8 :

 8 Validation of hypotheses

Type of perceived managerial behavior sustaining gender equality Interview extract

  diversity and that if there are two candidates with equal skills, I may prefer to nominate a woman. They accept it fully." -Manager, commercial entity, female "I think there is a real movement, we are far from having achieved anything, but there is a real movement, there are women managers, and I feel a desire to promote women." -Employee, commercial entity, female Reassuring one's teams to avoid the phenomenon of female self-censorship in the context of career advancement "My boss offered me the chance to join a group for 'high-potential' women who can become managers, so I was happy." -Employee, commercial entity, female Our managers are very well-informed about policy, major trends and agreements. They do not need an HR controller. I say to myself, 'hopefully it will last'. Obviously I will play my part if one day it changes, but at the moment managers are trying to promote women." -HR, technical entity, male

	Following the rules and company agreements	"Someone from my team is on maternity leave. So I
	concerning gender equality	went to find out about the company rules about
		maternity leave, I asked my HRBP and my colleagues."
		-Manager, commercial entity, female
	Trying to constitute gender-diverse teams	"I think my manager recruited me notably because I'm
		a woman." -Employee, technical entity, female
	Being vigilant about gender diversity when	"In my Steering Committee, they know that I pay
	awarding internal promotions attention to gender Contributing to a work environment that is "Our jobs do not pose any problems in terms of family
	good for work-life balance	constraints, because network maintenance is organized
		so as not to be based on sudden availability
		requirements." -Manager, technical entity, male
	Showing exemplary conduct regarding gender	"
	equality

Table 3 :

 3 Respondents' sample and Technologix population

	Survey
	(%

of the category in the respondents' population) (% of women in the category) Technologix (Dec. 2014) (% of the category in Technologix population) (% of women in the category)

	Age	<35	134 (9.5%) (%F: 47.0%)	Not available

Table 4 :

 4 Descriptive statisticsIn my work environment, there is no problem regarding access for women to responsibilities.In my work environment, there is no problem regarding the feminization rate of recruitment.

	Item

Table 7 :

 7 Models 2 and 3 -"In my work environment, in general, there is no problem regarding gender equality" by genderMy manager follows the rules and company agreements concerning gender equality. My manager tries to constitute gender-diverse teams. My manager is vigilant about gender diversity when awarding internal promotions. My manager reassures her/his team to avoid the phenomenon of female self-censorship in the context of career advancement. My manager contributes to a work environment that is good for work-life balance.

	Model 2: Female	Model 3: Male
	Beta coefficients (t-	Beta coefficients (t-
	stat)	stat)

* p<0.1; ** p<0.05; *** p<0.01

Workplace gender equality refers to a state of equal ease of access to rewards, resources and opportunities regardless of gender. It includes for example gender diversity (fair representation of people of both genders within the company), equal access to positions of responsibility, equal pay, …

"Technologix" is an alias used to guarantee the anonymity of the company.

Hypothesis

Validation H1a: The perceived managerial behavior "following the rules and company agreements concerning gender equality" positively influences perceived gender equality.

Validated

H1b: The perceived managerial behavior "trying to constitute gender-diverse teams" positively influences perceived gender equality.

Validated

H1c: The perceived managerial behavior "being vigilant about gender diversity when awarding internal promotions" positively influences perceived gender equality.

Validated

H1d: The perceived managerial behavior "reassuring one's teams to avoid the phenomenon of female self-censorship in the context of career advancement" positively influences perceived gender equality.

Validated

H1e: The perceived managerial behavior "contributing to a work environment that is good for work-life balance" positively influences perceived gender equality.

Validated

H1f: The perceived managerial behavior "showing exemplary conduct regarding gender equality" positively influences perceived gender equality.

Not validated H2: The link between each perceived managerial behavior (H1a-H1f) and perceived gender equality varies based on employees' gender. Ameline Law: sets a three-year timetable for companies to close the gender pay gap 2011

Validated

Appendix

Cope-Zimmermann Act: sets quotas (40%) for women on boards of directors 2014

Real Gender Equality Act: Equal pay becomes a mandatory part of negotiations -Sanctions for companies which do not respect their legal obligations are strengthened