Gender Wage Gap and Firm Heterogeneity: Evidence from French Linked Employer-Employee Data

Transcription

1 Gender Wage Gap and Firm Heterogeneity: Evidence from French Linked Employer-Employee Data Preliminary Version, please do not quote Elise Coudin Sophie Maillard Maxime Tô February 17, 2017 Abstract In spite of their increase in education and professional experience over the past decades, women are still on average paid less than men on the French labor market. Beyond differentials in characteristics compared to men, do women tend to be employed in low-wage firms or does the gender wage gap grow within a given firm? We apply the approach of Card, Cardoso, and Kline (2016) on French data to disentangle the role of between-firm heterogeneity (sorting) and within-firm heterogeneity (bargaining) on the gender wage gap in France. More precisely, we use a two-way fixed effect specification model for wages, in which firm fixed effects differ between male and female wage-earners in order to account for within-firm gender differences of bargaining power or remuneration policy. We estimate this model with linked employer-employee data on all wage-earners of the French private sector between 1995 and 2014 and then restricting on managers. Our results on the whole wage-earner group suggest that the between-firm/sorting effect -the gender gap due to different sorting of male and female workers between firms- accounts for almost 11 % of the gender wage gap, whereas the within-firm/bargaining effect is very small. This may be explained by the protective role of the high French minimum wage level, which benefits more women than men, as the former are more likely to be paid at the minimum wage. For the group of managers, the sorting effect vanishes whereas the intra-firm/bargaining effect explains half of the gender wage gap. JEL Codes: J31, J71, J16 Keywords: gender wage gap, gender inequalities, linked employer-employee data, two-way fixed effect models, discrimination Insee and CREST IFS and UCL 1

2 1 Introduction In spite of the increase in women education and professional experience over the last decades, women still experience lower wages compared to men. In France, in 2014, women s hourly wages were on average 14.4 % lower than men s. Part of this gender gap can be attributed to differences in observed characteristics (qualification, experience, seniority, productivity, etc.) between the two populations of men and women. However, large gender wage discrepancies remain once productivity differentials are accounted for. The literature has tested several hypotheses in order to explain this residual gap (Bertrand, 2011; Blau and Kahn, 2016). Given the existence of occupational and industry segregation, gender specific sorting between firms has become a popular explanation (Manning and Swaffield, 2008). However, it remains difficult to identify this effect from unobserved individual productivity, and from other within firm differences in men and women wages. Card, Cardoso, and Kline (2016) propose to use matched employer-employee panel data in order to solve this problem. Using a simple wage posting model, they show that the gender wage gap can be decomposed into a sorting/between f irm and a bargaining/within f irm components in a Oaxaca-Blinder style decomposition, where the underlying wage structure is obtained from the estimation of Abowd, Kramarz, and Margolis (1999) like wage equations. This setting allows to control for individual unobserved heterogeneity, and to decompose the residual gap into two components: one due to the fact that men and women work in firms that pay different wages (sorting/ between-firm channel), and a second one that accounts for the fact that a given firm may pay men and women differently (bargaining/ within-firm channel). Our work contributes to the literature by applying the decomposition proposed by Card, Cardoso, and Kline (2016) to the French data. To our knowledge, this method has only been applied by Card, Cardoso, and Kline (2016) to Portuguese data, so our application brings new evidence on that topic. And the comparison between our results to results from Card, Cardoso, and Kline (2016) is also of interest, given the existing differences between the French and the Portuguese context. In 2

3 particular, France has had one of the highest minimum wage in developed countries. Compared to Portugal, the minimum monthly wage in France was more than twice higher in Such differences are likely to have a strong impact on the results of Card, Cardoso, and Kline (2016) decompositions since a high minimum wage prevent unskilled workers from bargaining their wage. Indeed, using the French matched employer-employee data from 1995 to 2014, our results show that the sorting effect accounts for almost 11 % of the gender wage gap, whereas the bargaining effect is very small. These results differ from Card, Cardoso, and Kline (2016) who find a larger bargaining effect. The existence of a high minimum wage thus benefits more women than men, as the former are more likely to be paid at the minimum wage. Focusing on the population of managers only, the sorting effect vanishes whereas the bargaining one explains half of the gender wage gap. The remainder of the paper is as follows. Section 2 summarizes the recent literature on the gender wage gap. Section 3 describes the French context covered by our data. The latter are documented in more details in Section 4. Section 5 presents the estimated model and discussed conditions for identification, Section 6 presents the results, Section 7 relates them to firm characteristics and the last section concludes. 2 Literature review Two trends of research have tried to document the persistence of the gender wage gap. The first one insists on the fact that women tend to be offered or to negotiate lower wages than their male coworkers. The broad range of economic, social and psychological determinants at stake in these inequalities is reviewed extensively by Bertrand (2011). The second one emphasizes that gender earning gaps have more to do with between-employer or between-occupation differences than with a clear-cut discrimination against women within given occupation and firm. In this approach, composition effects are a first-order question to analyze the gender gap. Since Groshen (1991), different papers have investigated this idea of a segregation of workers among employers and occupations (Barth, Bryson, Davis, and al., 2014; Ba- 3

4 yard, Hellerstein, Neumark, and Troske, 2003; Nekby, 2003; Trond Petersen, 1995). However, many of these works suffer from ill-suited aggregation level or from a lack of representative data. Progresses made regarding linked employer-employee data availability and worker and firm heterogeneity estimation (Abowd, Kramarz, and Margolis, AKM hereafter; Lentz and Mortensen, 2010) push for a further analysis of the employee-employer sorting process to understand wage inequalities. How to reconcile these two prospects? A fruitful approach of composition effects on the labor market is the one of Pendakur and Woodcock (2009). They assessed the relative part of the glass ceiling (the part of the inequalities due to the clustering of minorities in low-earning jobs) and of the glass door component (due to a segregation of minority workers into low-wage firms). Further, Card, Heining, and Kline (2013) showed that the rise of West German wage inequality was the result of a combination of growing heterogeneity among workers, among firms premia and an increasing assortativeness in worker assignment to employers. Cardoso, Guimaraes, and Portugal (2012) and Card, Cardoso, and Kline (2016) (hereafter CCK, 2016) provided evidence on the gender wage gap contribution of firms in Portugal. To do so, the latter built a model to decompose the role of firms in gender earning gap into a bargaining/ within-firm effect - the gender wage difference of a given employer after controlling for individual heterogeneity - and a sorting/between-firm effect - the wage impact of different distributions of women and men in firms. Applying their model to Portugal data, they found that firms account for 21 % of the mean gender log-wage gap, with a 15 to 20 % sorting channel, and a 1 to 6 % bargaining channel. 3 French context and gender wage gap trends In France such as in other countries, Work arrangement (Goldin, 2014) play an important role to explain the gender earning gap. According to Meurs and Ponthieux (2006), 75 % of the gender annual earning gap is due to differences in labor structure, with the amount of hours worked being the first explanatory factor. Muller (2012) calculated that in companies with ten employees or more (where 41 % of workers 4

5 are women) the gender annual earnings gap is 24 %, whereas the hourly wage one is 14 %. Part-time jobs are much more common among women (31 % of female employees vs 7 % of male employees work part-time) and account for a big part of the annual gender wage gap. However, previous works have also shown that job prospect and bargaining opportunity discrepancies play key roles in widening the gender wage gap. Female workers have a significantly lower access to high-paid jobs than to low-paid jobs. Using conditional quantile regressions, Lucifora and Meurs (2006) show the existence of a glass ceiling effect, especially in the private sector in France, as well as in Italy. Focusing on full-time executives aged in French private and public sectors and depicting gender discrepancies in accessing a job at a given wage rank, Gobillon, Meurs, and Roux (2015) find that the probability for women to get a job at the bottom of the wage distribution (5 th percentile) is 9 % lower than for males but that this gap increases to 50 % lower at the top of the wage distribution (95 th percentile). In the rest of this paper, we let apart the question of gender working time discrepancies and focus on hourly wage gap between men and women. Figure 1 describes the evolution of the average hourly log wage for males and females from 1995 to 2014 in the private sector and the evolution of the gender wage gap relative to male wage over the period. Male and female wages have increased regularly - in particular around year 2000 when workers have benefited from the working time reduction ( Loi des 35 heures ) while monthly wages were held constant. The gender wage gap in euros has remained stable over the period, but the relative gender wage gap has decreased (16.8 % in 1995 vs 14.4 % in 2014) because of hourly wage gains. 4 Data 4.1 DADS panel and firm information Our main data is the DADS Panel. Every year, firms have to deliver information on their employees - wages but also job and firm characteristics to the French fiscal services. Since 1976, the INSEE (the French National Institute of Statistics) has 5

6 Figure 1: Average hourly log wage for women and men since 1995 Source: DADS, Panel Tous Salariés. Scope: Metropolitan France. The statistical unit is the individual*year*firm triplet. Workers aged less than 16 or more than 65 are excluded. Self-employed farmers, craftsmen, shopkeepers, trainees, apprentices and private household workers are excluded. gathered these comprehensive files and has built a panel of workers containing both individual and firm information (more details on the available variables can be found in the appendices). Agriculture sector and self-employment are excluded from the panel, and the public sector has been phased in during the 1980s (public hospital employees in 1984; local and central civil servants in 1988). The panel statistical unit is the workerxfirmxyear level: for each worker, we know for which firm she has been worked for at any time. Until 2001, the panel included roughly 1/24th of all salaried workers. The inclusion criterion was then extended to double the panel size. The sample is selected by a simple random process, based on individuals date of birth. Significant changes in the panel construction occurred in 2002 and 2009, accounting for potential shocks in series. Other collection irregularities were pointed 6

7 out in 2003, 2004 and In our analysis, we focus on private sector employees during the period. This choice is mainly guided by the fact that hourly wages were not available before For companies in the sample we are also able to gather additional administrative information using the unique firm identifier available in DADS files. We use FARE ( Fichier approché des résultats d ESANE ) which includes the firm s name, address, industry, founding date, total employment, as well as income statement and balance sheet items. Especially, we can track back firm value-added for years 2014 to Table 3 gives an overview of some of the variables available in FARE. 4.2 EDP panel We are also able to supplement the matched employers-employees data with individual information on workers. The Permanent Demographic Sample (EDP) is a large-scale socio-demographic panel gathering information taken from the official publications of the registry office for births, marriages and deaths since 1968, along with census information from 1968, 1975, 1982, 1990 and Information derived from the annual census surveys (which replaced exhaustive census in 2000) is also integrated. The sample corresponds broadly to a 4 % survey of the population living in France. Like DADS, selection to EDP is based on date of birth. As EDP and DADS dates of birth partly coincide (around 13 % of the DADS panel is also in EDP before 2012 and approximately 43 % in 2012), we are able to merge the two data sets. This additional information (household characteristics, date of marriages, divorces, number of children, children s date of birth, and education level) allows for a much more detailed analysis of the gender wage gap, and to link job and firm mobility to personal events over the life cycle (as in Wilner, 2016). Descriptive statistics are provided in Tables 1 and 2. Separate description is given for all individuals from the survey ( Before estimation sample ) and individuals actually included in the estimation sample ( After estimation sample ). Finally, the DADS-EDP database allows to identify bargaining and sorting effects for 910,724 observations, that is 102,744 employees, working in the dual largest set of connected firms (see below). 7

8 Table 1: Descriptive statistics on before and after-estimation worker samples 8 Before estimation sample After estimation sample Male Female Male Female Variable N Mean N Mean N Mean N Mean Net wage (in 2014 e) 956,925 23, ,976 16, ,090 23, ,885 16,867 (26,830) (13,549) (26,467) (14,158) Net hourly log-wage 952, , , , (0.48) (0.40) (0.49) (0.40) Age 956, (10.9) 691, (10.9) 527, (11.0) 411, (11.0) Professional experience 956, (11.0) 691, (10.1) 527, (11.0) 411, (10.1) Seniority 956, (7.7) 691, (7.4) 527, (7.9) 411, (7.4) Education #1 (no degree) 956, % 691, % 527, % 411, % Education #2 956, % 691, % 527, % 411, % Education #3 956, % 691, % 527, % 411, % Education #4 956, % 691, % 527, % 411, % Education #5 956, % 691, % 527, % 411, % Education #6 956, % 691, % 527, % 411, % Education #7 956, % 691, % 527, % 411, % Educ. #8 (master/phd) 956, % 691, % 527, % 411, % No child 956, % 691, % 527, % 411, % 1 or 2 children 956, % 691, % 527, % 411, % 3 or more children 956, % 691, % 527, % 411, % Is or has been married 956, % 691, % 527, % 411, %

9 Table 2: Descriptive statistics on before and after-estimation worker samples (end) 9 Before estimation sample After estimation sample Male Female Male Female Variable N Mean N Mean N Mean N Mean Professionals 956, % 691, % 527, % 411, % Managers 956, % 691, % 527, % 411, % Technicians 956, % 691, % 527, % 411, % Clerks 956, % 691, % 527, % 411, % Operatives 956, % 691, % 527, % 411, % Paid hours 956,925 1,582 (574) 691,976 1,393 (602) 527,090 1,537 (595) 411,885 1,380 (606) Part-time job 956, % 691, % 527, % 411, % Open-ended contracts 443, % 335, % 239, % 196, % Fixed-term contracts 443, % 335, % 239, % 196, % Temporary agency work 443, % 335, % 239, % 196, % Other short term jobs 443, % 335, % 239, % 196, % Agriculture 956, % 691, % 527,090 1% 411, % Manufacturing 956, % 691, % 527, % 411, % Construction 956, % 691, % 527, % 411, % Trade 956, % 691, % 527, % 411, % Services 956, % 691, % 527, % 411, % 10 or less worker firms 956, % 691, % 526, % 411, %

10 Table 3: Descriptive statistics on before and after-estimation firm samples 10 Before estimation sample After estimation sample Variable N Mean N Mean Number of employees in the firm 205, ,179 (993) (1,444) Share of female employees 205, ,239 (0.352) (0.077) Value added before tax (2014) 107,022 5,855 8,704 45,775 (96,514) (146,001) Value added before tax (2013) 110,466 5,728 8,512 47,500 (96,132) (145,210) Value added before tax (2012) 113,443 5,525 8,159 48,880 (90,697) (136,767) Gross operating surplus 107,022 1,233 1,921 45,775 (38,241) (57,256) Operating income before tax 107,022 1,060 1,520 45,775 (36,808) (49,963) Net overall sales 107,022 21,509 30,598 45,775 (288,915) (416,844)

11 5 Disentangling Bargaining from Sorting effects 5.1 A rent-sharing model Following Card, Cardoso, and Kline (2016), at each period t, wages result from a simple Nash-bargaining between individual i with outside option a it and firm J(i, t), with a surplus S i,j(i,t) associated with i s job. Thus the wage maximizing the surplus is the weighted sum of a it and S i,j(i,t), where the weight γ is supposed to be gender specific (G(i) {F, M}): w it = a it + γ G(i) S i,j(i,t) (1) Specifying the individual outside option, Card, Cardoso, and Kline (2016) obtain a reduced form wage equation from that rent-sharing model: w it = α i + X it β G(i) + ψ G(i) J(i,t) + r it, (2) where α i is an individual fixed component, β G(i) are sex-specific returns to productive characteristics X it, and ψ G(i) J(i,t) are gender-specific firm effects. The gender-specific firm effects account for firm-specific pay premia, and are directly linked to the gender specific bargaining power γ G(i). 5.2 Computing sorting and bargaining effects To recover the bargaining effect, γ G(i), from the reduced-form equation (2), Card, Cardoso, and Kline (2016) apply a Oaxaca-Blinder decomposition to the firm specific parameters: E [ ψj(i,t) M g = M ] E [ ψj(i,t) F g = F ] = E [ ψj(i,t) M ψj(i,t) F g = M ] (3) }{{} (i) Bargaining effect + E [ ψj(i,t) F g = M ] E [ ψj(i,t) F g = F ] }{{} (ii) Sorting effect The average gap due to firm-specific wage components can be decomposed as (i) the average of the difference of firm s component for men and women (bargain- 11

12 ing effect), and (ii) differences between the average firm effect for women (sorting effect). Note that, as in the case of any Oaxaca-Blinder type of decomposition, the decomposition is not unique, and the choice of the reference group may not be innocuous. 5.3 Estimation The empirical counterpart of equation (2) is an AKM model estimated separately for men and women. In our application we include the following time-varying regressors: age and its square, experience on the labor market and its square, seniority in the company and its square and year dummies. In an alternative specification we also include family characteristics. The models are estimated separately for men and women and only for workers employed in companies hiring both male and female employees. As is usual for this kind of model, we gather firms with ten workers or less so as to compute the regression on a maximum number of workers. Finally, we present results for the dual largest connected set of workers and firms, that is to say on men (resp. women) among the largest connected set of the male (resp. female) estimation and whose company also employs women (resp. men) in the female estimation largest connected set. The OLS estimate of equation (2) is unbiased provided that: [ ( E (r it r i ) 1 J(i,t)=j 1 T )] T 1 J(i,t)=j = 0, j {1... J}. (4) t=1 This condition is active for firm movers from the first to the last period (otherwise, 1 J(i,t)=j 1 T T t=1 1 J(i,t)=j is always equal to zero). In each firm, conditional on mobility, the expected effect of wage unobserved factors (r it ) should not deviate from its time-average value ( r i ). Given that r it encompasses shocks on worker, firm or match between worker and firm productivity, the exogeneity condition holds if mobility between firms is not correlated with shocks on firm profits, on match surplus and on individual productivity. The exogenous mobility assumption is not directly testable from the data. However, we can gather elements in line with some of its main predictions. 12

13 Figure 2: Mean wage evolution for male movers conditional on origin and destination firm average wage Note: a male worker moving from a firm paying average wages below the bottom quartile (quartile 1) of the wage distribution to a firm above top quartile (quartile 4) gets a average 11.2 % increase in wage. Symmetrically a male going from an above top quartile firm to a below bottom quartile firm can expect a 11.1 % drop in wage. Figure 3: Mean wage evolution for female movers conditional on origin and destination firm average wage Note: A female worker moving from a firm paying average wages below the bottom quartile (quartile 1) of the wage distribution to a firm above top quartile (quartile 4) gets a average 11.7 % increase in wage. Symmetrically a female going from an above top quartile firm to a below bottom quartile firm can expect a 7.4 % drop in wage. 13

14 First, on the whole, wage gains and wage losses associated with entering or leaving high/low paying firms look symmetric. This is the main message in Figures 2 and 3. For instance, Figure 2 shows the average wage evolution for male movers according to the average wage of their coworkers before and after mobility. Thus, a male worker moving from a low paying firm (origin quartile = 1) to a high paying firm (destination quartile = 4) gets a average 11.2 % increase in wage. Symmetrically a male going from a high paying firm (origin quartile = 4) to a low paying firm (destination quartile = 1) can expect a 11.1 % drop in wage. Besides symmetry, the exogenous mobility condition implies there is on average no transitory wage shock driving firm-to-firm mobility of workers. Figures 4 and 5 plot two-year before and two-year after mobility average wages according to the average wage of their coworkers before and after mobility. The no-transitory wage shock assumption requires that the after-mobility coworkers wage cannot be predicted by before-mobility wage evolution, and reversely the before-mobility coworkers wage should not be correlated with the after-mobility wage trend. Figure 4: Mean wage trend for males two years before and two years after a mobility conditional on origin and destination firm average wage Note: A male worker moving from a firm paying average wages below the bottom quartile (quartile 1) of the wage distribution to a firm above top quartile (quartile 4) is paid on average 2.25 two years before moving, 2.39 the year before his mobility, 2.52 the year he moves and 2.65 the following year. Symmetrically a male going from an above top quartile firm to a below bottom quartile firm can expect to be paid 2.70 two years before moving, 2.67 the year before his mobility, 2.35 the year he moves and 2.42 the following year. 14

15 Figure 5: Mean wage trend for females two years before and two years after a mobility conditional on origin and destination firm average wage Note: A female worker moving from a firm paying average wages below the bottom quartile (quartile 1) of the wage distribution to a firm above top quartile (quartile 4) is paid on average 2.15 two years before moving, 2.26 the year before his mobility, 2.40 the year he moves and 2.53 the following year. Symmetrically a female going from an above top quartile firm to a below bottom quartile firm can expect to be paid 2.47 two years before moving, 2.52 the year before his mobility, 2.30 the year he moves and 2.32 the following year. Overall, this hypothesis looks checked for either male or female workers that were working in high paying firms before mobility. Observation is perhaps not as clear for workers going from lowest to highest paying firms but there is no evidence of transitory wage shocks correlated with mobility. Based on these elements and as CCK, we cannot reject that the exogenous mobility is reasonable enough to model wage in our data. 5.4 Firm-effect normalization AKM-type of models require a normalization of the firm-fixed effects (Abowd, Creecy, and Kramarz, 2002) because they are in fact only identified up to a constant. Here, we have to make consistent normalization to enable comparison of firm-fixed effects between gender. We follow Card, Cardoso, and Kline (2016) and fix to zero on average both male and female firm-fixed effects in firms in which there is structurally little rent to share between workers and so, little risk of sharing differentials between female and male workers. So, first we choose as reference accommodation and food services firms, as this industry is the one for which the value-added per 15

16 worker is the lowest. As alternative choice we also consider to fix on average to zero both female and male firm-fixed effects in firms with the lowest log-va per worker. Figure 6 motivates this normalization: there is a positive relation between the productivity of the firm and the premia its female and male workers get. Figure 6: Firm effects according to log per capita value-added Note: Firms are among the dual connected set: for these firms we are able to estimate a female and a male fixed effect. Firms are gathered into 100 bins according to their log per capita value-added. For each VA per capita bin we plot the corresponding average female and male firm effect before any normalization. 6 Results for the private sector The CCK models are estimated on the dual largest connected set of wage-earners and firms related to each other by worker mobilities between firms. In order to estimate both female-related and male-related firm-fixed effects, workers and firms have to be related by both female and male mobilities. This dual largest connected set counts 117,909 workers (amongst them 52,636 women). Results for the whole group of workers and then focusing on managers are reported successively. 16

17 6.1 All employees Results for the all employee group are reported in Table 5, for more details see also Table 4. First, we comment results that do not depend on the normalization choice. On the largest connected set, the gender wage gap amounts roughly to 17 %. The sorting effect accounts for around 11 % of this wage gap 1. Women are more likely than men to be employed in low-paying firms, even once worker productivities are accounted for. Table 4: Summary of two-way fixed effects models and model estimates Model (1) Model (2) Male Female Male Female Age Age 2 / Experience Experience 2 / Seniority Seniority 2 / Number of children Age of the last born child Number of observations 518, , , ,488 Adjusted R-squared Wage variance Firm effects variance Worker effects variance Worker-firm effects covariance Year dummies, individual fixed effects and firm fixed effects are included in the regressions but are not reported here. In addition to the number of children and the difference between 18 and the age of the last born child we include interaction between these two variables and being born on October 2 or 3- demographic data collection was not complete for people born those days. Estimates of the bargaining effect and of the total contribution of firms on gender wage gap can vary with the normalization choice but results are quite similar for the two options detailed above. The total role of firms on gender wage gap is positive, around 9 % of the gender wage gap (see Figure 10 for industry by industry firm effect 1 We comment sorting effect calculated using female premia and the corresponding bargaining effect, computed with male assignment in firms as reference but we report results for the opposite reference in Table 5. 17

18 gap) and is mainly due to the sorting effect, whereas the bargaining effect is very small, and if anything negative, around -2 % of the gender wage gap. This means that, once productivity differentials are accounted for, on average on the overall sample of workers women tend to receive the same and if anything higher firm pay premia than men. This apparently counterintuitive result may be explained by the role of the minimum wage in France. Indeed, the high level of minimum wage in France may act like a protection for low-paid workers, among which women are overrepresented, in contrast with workers with higher wages. This may also explain why Card, Cardoso, and Kline (2016) on Portuguese data, find a greater contribution of firms to the gender wage gap with both higher sorting and bargaining effects. More generally, the bargaining effect may also capture rent-sharing differential between types of job positions, let say managers versus non managers, which we attribute here to gender differentials because women are less represented than men in managerial positions. This is the reason we repeat the same estimation strategy focusing on the group of managers only. 18

19 Table 5: Sorting and bargaining contributions to the gender wage gap (all employees) 19 Normalization based on... Accommodation and food services firms Lowest log VA per worker firms Total gender log wage gap Gender log wage gap due to firms: including sorting effect including bargaining effect (a) (b) (c) (d) Nb of observations 938,975 Nb of firms (10+ w.) 10,987 Number of workers 117,907 Calculation of sorting and bargaining are based on model (1) estimates. Column (a) reports sorting effect calculated using female premia: E[ψJ(i,t) F g = M] E[ψF g = F ]. The J(i,t) corresponding bargaining effect is in column (c) and computed with male assignment in firms as reference: E[ψJ(i,t) M ψf g = M]. Oppositely (b) gives the estimates for the J(i,t) sorting effect measured with male premia: E[ψJ(i,t) M g = M] E[ψM J(i,t) g = F ] and (d) for the bargaining effect based on female assignment in firms: E[ψM J(i,t) ψf g = F ]. In J(i,t) both cases sorting and bargaining effects add up to the gender log wage due to firms: (a)+(c)=(b)+(d)= column 3.

20 6.2 Managers Results for the manager group are reported in Tables 6 and 7. The gender wage gap in the dual connected set of managers is also around 17 % as in the all employee group but other results differ greatly. First, the sorting effect is very small around 4 % of the gender wage gap: female and male managers are roughly distributed similarly in low and high-paying firms. Second, the bargaining effect is much higher than for the all employee group: male managers obtain higher firm-premia than female managers in the same firm, even once productivity (through worker fixedeffect) is accounted form. This bargaining effect accounts for half of the gender wage gap. This results is consistent with a glass-ceiling effect affecting female managers and lowering their access to higher paying job positions, see Gobillon, Meurs, and Roux (2015). Table 6: Summary of two-way fixed effects models and model estimates for the manager sample Model (1) Model (2) Male Female Male Female Age Age 2 / Experience Experience 2 / Seniority Seniority 2 / Number of children Age of the last born child Number of observations 55,527 28,624 55,527 28,624 Adjusted R-squared Wage variance Firm effects variance Worker effects variance Worker-firm effects covariance Year dummies, individual fixed effects and firm fixed effects are included in the regressions but are not reported here. In addition to the number of children and the difference between 18 and the age of the last born child we include interaction between these two variables and being born on October 2 or 3- demographic data collection was not complete for people born those days. 20

21 Table 7: Sorting and bargaining contributions to the gender wage gap (managers) 21 Normalization based on... Miscellaneous manufacturing firms Art and show business firms Total gender log wage gap Gender log wage gap due to firms: including sorting effect including bargaining effect (a) (b) (c) (d) Nb of observations 88,031 Nb of firms (10+ w.) 975 Number of workers 15,006 Calculation of sorting and bargaining are based on model (1) estimates. Column (a) reports sorting effect calculated using female premia: E[ψJ(i,t) F g = M] E[ψF g = F ]. The J(i,t) corresponding bargaining effect is in column (c) and computed with male assignment in firms as reference: E[ψJ(i,t) M ψf g = M]. Oppositely (b) gives the estimates for the J(i,t) sorting effect measured with male premia: E[ψJ(i,t) M g = M] E[ψM J(i,t) g = F ] and (d) for the bargaining effect based on female assignment in firms: E[ψM J(i,t) ψf g = F ]. In J(i,t) both cases sorting and bargaining effects add up to the gender log wage due to firms: (a)+(c)=(b)+(d)= column 3.

22 7 Firm-fixed effects and firm characteristics In this section, we investigate whether male and female firm effects can be related to observable firm characteristics. This exercise does not aim at assessing causal relationships: for instance, there is no reason to believe that firm wage policy derives from firm financial reports rather than the other way around or, more likely, that they are simultaneous outputs of the firm activity. Even if no causal conclusions should be expected from this section we think characterizing firms that distribute high or low firm premia to either sex or tend to differentiate male and female in rent-sharing can be useful to analyze gender inequality issues. The k-means algorithm is a simple iterative method to partition a given dataset into k clusters. It consists in successive assignments to closest centroids and relocations of centroids until convergence (for more details see for instance Steinley, 2006). We use it to distinguish common patterns among firms with close firm effects (be it female or male effects). We implement the clustering method on the ( ) ψj M, ψj F j=1...j vector and we analyze the average characteristics within each cluster. First, we choose k = 5 the number of clusters as for this k the explanatory gain starts to be really small. We also conducted the analysis for k = 7 and the general message is not affected. Figure 7 presents the average female firm effect and the average male firm effect within each cluster. Firms in cluster 1 (442 firms) are characterized by high male firm effects and female firm effects close to their overall average. In those firms, on average, there is some bargaining effect contributing to the gender wage gap. Firms in cluster 2 (1 801 firms) pay very close to zero firm premia to both their male and female workers: their are very similar in their wage-policy to what would be the representative firm of the economy (orange point, labeled overall in Figure 7). Cluster 3 (612 firms) also pay almost null firm effects to their male workers but give negative firm premia to their female workers (positive bargaining effect). Oppositely, cluster 4 (720 firms) is characterized by zero female firm effects and negative male firm effects (negative bargaining effect). Finally, cluster 5 (500 firms) pay high premia to female workers, and positive but lower premia to their male employees. 22

23 Figure 7: Female and male firm effects by cluster These clusters are defined based on the firm effect vector. What do they look like when focusing on their financial characteristics? Figure 8 presents how clusters stand out in terms of a set of firm variables. For each variable, say firm equity, it indicates the standardized average cluster deviation from the overall average equity. Firms in cluster 1 are on average the biggest and most productive companies, whatever the chosen indicator, in spite on a relatively low level of fixed assets/equity/investments. Firms in cluster 2 can be characterized by a high level of capitalization and with a high share of operative workers- we can think that manufacturing firms are typically well represented in cluster 2. Clusters 3 and 4 both gather small firms with high shares of clerk workers, cluster 4 exhibiting somewhat better productivity indicators. Cluster 5 is constituted on average of relatively productive companies, also characterized by a little share of low-skilled jobs and a high degree of international openness. Hence, the two groups of firms that pay the highest premia to their workers, either male or female, are also those that are the most productive and that concentrate high-skilled and experienced workers. 23

24 24 Figure 8: Cluster characteristics

25 These elements should also be related to those in Figure 9 which gives the share of men in each cluster relative to the overall male worker share. It indicates that if clusters 1-3 are very close to the average male/female ratio, women are over represented in cluster 4 and under represented in cluster 5. Strikingly, if the over representation of women in cluster 4 is in line with favorable female premia relative to male ones, it is not the case in cluster 5: women are fewer in cluster 5 whereas this cluster pay the highest female premia. Figure 9: Deviation in male worker share in each cluster On the whole, firms in cluster 5 tend to reduce the bargaining effect -because they pay higher premia to their female than to their male workers- but may contribute to the sorting effect because they also count fewer women than the overall economy. Oppositely, cluster 1 and 3 tend to increase the bargaining effect rather than the sorting effect (female premia are lower than male premia and neither sex is particularly prominent among those firms). Firms in cluster 4 diminish the overall firm contribution in the gender wage gap, since they combine higher female premia and a high share of female workers. 25

26 8 Conclusion In this paper, we investigated the gender wage gap in France. Using matched employer-employee data, we followed Card, Cardoso, and Kline (2016) decomposition of the residual wage gap remaining after controlling for individual unobserved heterogeneity. We first showed that our sample fulfills with the requirements for identification of the sorting and bargaining effects. Our estimates on the whole population of individuals show little evidence for bargaining effects, the main share of the gap being explained by gender specific sorting between firms. This decomposition is robust to the normalization choice made for estimation. This effect contrasts with the findings of Card, Cardoso, and Kline (2016), who find much larger bargaining effects. We can explain these differences by the particular institutional context we consider. Indeed, the existence of a large minimum wage in France does not allow for bargaining margin at the bottom of the distribution of wages. This result is compatible with the fact that we find a much larger bargaining effect when considering managers only. 26

27 References Abowd, J., R. H. Creecy, and F. Kramarz (2002): Computing person and firm effects using linked longitudinal employer-employee data., Center for Economic Studies, US Census Bureau, ( ). Abowd, J., F. Kramarz, and D. Margolis (1999): High wage workers and high wage firms, Econometrica, 67(2), Barth, E., A. Bryson, J. C. Davis, and al. (2014): It s where you work: Increases in earnings dispersion across establishments and individuals in the US., National Bureau of Economic Research. Bayard, K., J. Hellerstein, D. Neumark, and K. Troske (2003): New Evidence on Sex Segregation and Sex Differences in Wages from Matched Employee- Employer Data, Journal of Labor Economics, 21(4), Bertrand, M. (2011): New perspectives on gender, Handbook of labor economics, 4, Blau, F. D., and L. Kahn (2016): The Gender Wage Gap: Extent, Trends, and Explanations, Discussion paper. Card, D., A. Cardoso, and P. Kline (2016): Bargaining, sorting, and the gender wage gap: Quantifying the impact of firms on the relative pay of women., The Quarterly Journal of Economics, 131(2), Card, D., J. Heining, and P. Kline (2013): Workplace Heterogeneity and the Rise of West German Wage Inequality, The Quarterly Journal of Economics, 128(3), Cardoso, A. R., P. Guimaraes, and P. Portugal (2012): Everything You Always Wanted to Know about Sex Discrimination, IZA Discussion Paper, (7109). Gobillon, L., D. Meurs, and S. Roux (2015): Estimating gender differences in access to jobs., Journal of Labor Economics, 33(2). Goldin, C. (2014): A Grand Gender Convergence: Its Last Chapter, American Economic Review, 104(4), Groshen, E. L. (1991): The Structure of the Female/Male Wage Differential: Is It Who You Are, What You Do, or Where You Work?, Journal of Human Resources, 26(3),

28 Lentz, R., and D. T. Mortensen (2010): Labor market models of worker and firm heterogeneity, Annual Review of Economics, 2(1), Lucifora, C., and D. Meurs (2006): The public sector pay gap in France, Great Britain and Italy., Review of Income and Wealth, 52(1), Manning, A., and J. Swaffield (2008): The Gender Gap in Early-Career Wage Growth, The Economic Journal, 118(530), Meurs, D., and S. Ponthieux (2006): L écart des salaires entre les femmes et les hommes peut-il encore baisser?, Economie et Statistique, ( ), Muller, L. (2012): Les écarts de salaire entre les hommes et les femmes en 2009, Dares Analyses, (16). Nekby, L. (2003): Gender differences in rent sharing and its implications for the gender wage gap, evidence from Sweden, Economics Letters, 81(3). Pendakur, K., and S. Woodcock (2009): Glass Ceilings or Glass Doors? Wage disparity within and between firms, IZA Discussion Paper, (4626). Steinley, D. (2006): K-means clustering: A half-century synthesis, British Journal of Mathematical and Statistical Psychology, 59(1), Trond Petersen, L. A. M. (1995): Separate and Unequal: Occupation- Establishment Sex Segregation and the Gender Wage Gap, American Journal of Sociology, 101(2), Wilner, L. (2016): Worker-firm matching and the parenthood pay gap: Evidence from linked employer-employee data., Journal of Population Economics, pp

29 Figure 10: Average gender firm effect gap in each industry Firm effects are normalized setting the average firm effects in the accommodation and food service industry to zero, for either sex. 29

30 30 Figure 11: PCA variable set in dimension 1 and 2 space

31 31 Figure 12: PCA variable set in dimension 2 and 3 space

32 32 Figure 13: PCA variable set in dimension 1 and 3 space