Do women want to work more or more regularly? Evidence from a … · markets, the 2017 Barcelona...

Do women want to work more or more regularly?Evidence from a natural experiment∗

Emma Duchini†, Clémentine Van Effenterre‡

This version: October 2018Click here for most recent version

Abstract

This paper provides causal evidence that children limit women’s chances of havinga regular Monday-Friday working schedule. We show that this constraint contributesto the persistence of the gender wage gap. Historically, French children in primaryschool have had no school on Wednesdays. In 2013, a reform reallocated some classes toWednesday mornings. Exploiting variations in the implementation of this reform overtime and across the age of the youngest child, we demonstrate that, once institutionalconstraints are relaxed, mothers are more likely to work on Wednesdays and to workfull-time. By working longer and more regular hours, mothers are able to close 6 per-cent of the gender wage gap. These effects on hours and wages are driven by high-skilledwomen. We show that a very simple theoretical framework can rationalize these findings.

JEL codes: H52, J13, J16, J22.Keywords: school schedule; temporal flexibility; female labor supply; child penalty.

∗We are grateful to Thomas Piketty and Gabrielle Fack for their advice and support. We also acknowledge Philippe Aghion,Samuel Berlinski, Richard Blundell, Antoine Bozio, Pierre-André Chiappori, Patricia Cortes, Monica Costa Dias, Lena Edlund,François Gerard, Claudia Goldin, Libertad Gonzalez, Julien Grenet, Xavier d’Hautfoeuille, Camille Hémet, Clément Malgouyres,Alan Manning, Alexandre Mas, Sandra McNally, Guy Michaels, Marion Monnet, Steven Pischke, Claudia Olivetti, Seyhun OrcanSakalli, Amanda Pallais, Alessandro Tarozzi, Miguel Urquiola, and participants at the UPF, PSE, LSE, Columbia and Harvardinternal seminars, the 2015 London EDP Jamboree, the 29th EEA conference, the Uppsala conference on gender and labormarkets, the 2017 Barcelona GSE Summer Forum, the 2018 ASSA Annual Meeting, and the 2018 SOLE conference, for theirconstructive comments and suggestions. We are especially grateful to the French Ministry of Education for giving us access tothe Enrysco database, to the Institut des Politiques Publiques (IPP) and to Dominique Meurs for their financial support onthis project. Van Effenterre further thanks the Alliance Program, the French National Research Agency through the programInvestissements d’Avenir (ANR-10-LABX 93-01), and the Institut du Genre for their additional financial support.

† University of Warwick, Department of Economics, Office S0.66, Coventry CV4 7AL, UK. Email: [email protected],Phone: +44 7491 530830

‡ Harvard Kennedy School, 79 JFK Street, Cambridge, MA 02138, USA. Email: [email protected],Phone: +1 857 210 2798

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https://www.dropbox.com/s/vmsedru8hwuad4t/JMP_vaneffenterre.pdf?dl=0

The diffusion of alternative work arrangements has gained greater attention in most ad-

vanced economies over the past decade. Advocates for these work arrangement in the policy

debate argue that workplace flexibility may facilitate work-life balance. This aspect can be

especially valuable for female workers who, despite large economic gains in the last century,

still contribute today to the majority of household activities (Bureau of Labor Statistics 2017).

An increasing number of studies suggest that women value temporal flexibility at work

more than men do (Filer 1985, Goldin and Katz 2011, Flabbi and Moro 2012, Wiswall and

Zafar 2017, Mas and Pallais 2017). However, workplace flexibility could contribute to the

persistence of the gender gap in earnings. Several papers document the existence of a part-

time pay penalty, and its relationship to occupational segregation (Manning and Petrongolo

2008, Fernández-Kranz and Rodríguez-Planas 2011). Besides, Goldin (2014), Goldin and Katz

(2016), and Cortes and Pan (2016) argue that women’s quest for flexibility can contribute

to explaining the persistence of the gender wage gap even within occupations, especially in

those professions where continuous presence at work and availability to work long hours are

particularly rewarded.

In this paper, we provide new causal evidence that children limit women’s chances of having

a regular Monday-Friday working schedule and that this contributes to the persistence of the

gender wage gap. We use a recent reorganization of the teaching time in France to study

how mothers’ demand for temporal flexibility at work evolves when institutional constraints

are relaxed. Next, we exploit the introduction of after-school extracurricular activities to

analyze women’s response to this implicit wage subsidy. Finally, we assess whether mothers

are rewarded when they increase their availability to work long and regular hours.

Since the introduction of compulsory primary education in 1882, French children have

always had a full day off in the middle of the week. This was first allocated to Thursday and

from 1972 onwards to Wednesday. While other aspects of the school calendar have changed

over the last decades, the break on Wednesday has always been maintained. Even though

women’s labor force participation in France has attained one of the highest levels across

OECD countries (OECD 2016b), French mothers work significantly less time on Wednesdays

than they do on the other working days of the week, as displayed in Figure 1. In contrast,

women with children in other developed countries such as the U.S, the UK, Germany, and

Spain distribute their working time uniformly over the week, and French fathers and women

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without children also have a regular working schedule. These work schedule patterns suggest

that children might be an impediment to French mothers’ participation in the labor market.

From 2008–2012, French children in kindergarten and primary school had 24 hours of

classes per week, spread over four days. In January 2013, the French government reduced

the length of the teaching time per day and added an extra half day of classes on Wednesday

morning, in order to lighten the daily workload of children without changing the total number

of weekly teaching hours. Moreover, to compensate for the shortening of each school day,

the government introduced three optional hours of extracurricular activities, at almost no

additional cost for families.

We use this reorganization of the teaching time and, in particular, the introduction of

classes on Wednesday morning, to study how the presence of children affects women’s chances

of having a regular Monday-Friday working schedule. To conduct this analysis, we focus on

mothers whose youngest child is of primary school age and compare them, with a difference-

in-differences strategy, to mothers whose youngest child is twelve to fourteen years old.1 The

data come from the quarterly version of the French Labor Force Survey and span the period

2009-2016. We exclude from the estimation sample all respondents working in schools, from

teachers to administrative staff, to ensure that our results do not capture the mechanical

impact of the reform on this group of workers.2

Our analysis provides the following findings. First, treated mothers take advantage of

the reform to adopt a regular working schedule, i.e a Monday-Friday weekly schedule. In

the pre-reform period, more than 40 percent of women with children of primary school age

stayed at home on Wednesday, compared to only 35 percent of those with older children.3

With the introduction of the reform, their probability of working on Wednesday rises by three

percentage points with respect to mothers in the control group. In other words, the reform

allows treated mothers to close 40 percent of the pre-reform Wednesday-gap with mothers of

older children, with their response getting larger over time.

This paper adds to evidence provided by event-studies such as Angelov, Johansson and

Lindahl (2016), Kleven, Landais and Sogaard (2018), Chung et al. (2017) and Kuziemko et al.1Middle school children go to class everyday and are aged between twelve and fourteen years old.2Nevertheless, our results are practically the same when we include the entire school personnel, or when

only excluding teachers.3The probability of working on any other day of the week does not differ between treated and control

mothers in the pre-reform period.

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(2018) on the presence of a "child penalty" for, respectively, Swedish, Danish, and Ameri-

can mothers.4 Moreover, the increased presence at work on Wednesday is in part explained

by a substitution of Wednesday work for Saturday work. This evidence is consistent with

the experimental evidence provided by Mas and Pallais (2017) on workers’ willingness to

pay to avoid working during the weekend, and more generally with the growing evidence on

the importance of leisure complementarities in explaining individuals’ labor supply choices

(Georges-Kot, Goux and Maurin 2017, Goux, Maurin and Petrongolo 2014).

Secondly, the reorganization of teaching time, coupled with the introduction of three hours

of extracurricular activities, allows treated mothers, and especially the highly educated, to

progressively shift from part-time to full-time contracts and to catch up with the control

group in terms of hours worked per week. This result stands in contrast to the evidence

suggesting that women’s own wage elasticity is lower in contexts of high female labor force

participation (Cascio 2009, Fitzpatrick 2010, Gelbach 2002, Goldin 2006, Havnes and Mogstad

2011).

More importantly, our results show that women get rewarded for a longer and more regular

presence at work. Thanks to the reform, treated mothers, compared to control ones, experience

a 1.5 percent increase in their hourly wages, relative to the pre-reform level, in less than three

years. Back-of-the-envelope calculations imply that this effect corresponds to a 6 percent

decrease in the pre-reform gender wage gap. This short-run wage effect does not seem to

arise from an increased likelihood of changing positions in the firm or finding better-paid job

opportunities, but rather from a re-definition of the existing contract.

High-skilled mothers seem especially responsive to the opportunity of working longer and

continuous hours. While mothers take advantage of the reform to work on Wednesday irre-

spective of their skills or occupation, the drop in part-time work and consequent increase in

hourly wages are driven by high-skilled mothers.5 These results do not exclude that in the

long-run low-skilled women could also become more likely to work full-time, thanks to the

reform. Yet, they suggest that switching from part-time to full-time work, while maintaining

the same job, may be easier in certain types of positions and firms. Moreover, in line with4In addition, this paper is also closely related to the recent study by Blundell, Pistaferri and Saporta-Eksten

(2017) highlighting the importance of children in shaping couples’ preferences over consumption and leisure.5Although the effect on hourly wages is not statistically different between high- and low-skilled mothers,

the point estimates are insignificant and practically zero for the latter.

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Goldin’s theory on the cost of flexibility in highly-paid professions, high-skilled mothers may

react more quickly to the reform precisely because they perceive that a longer and more reg-

ular presence at work may be particularly rewarding for their careers (Cortes and Pan 2016,

Goldin 2014).

We also study fathers’ labor supply decisions in this context. The LFS data confirm that

in the pre-reform period, fathers’ probability of working on Wednesdays did not differ from

that of the other days of the week. We find no evidence that the 2013 reform affects their labor

supply decisions, which suggests that, even in a country where female labor force participation

is high, a traditional division of gender roles in the household persists (Bertrand, Kamenica and

Pan 2015, Bursztyn, Fujiwara and Pallais 2017, Fernandez, Fogli and Olivetti 2004, Fernandez

2011, Folke, Rickne et al. 2016). These results speak to the literature on gender differences

in preferences for flexibility by showing that women’s greater taste for flexibility at work is

tightly linked to the presence of children.

Finally, we show that our empirical results are consistent with a simple theoretical frame-

work. We illustrate the effect of the reform in a canonical consumption/leisure two-period

model with promotion. We make the assumption that workers’ future wage rate after promo-

tion is a positive function of their present labor supply and we show how mothers’ optimal

time allocation responds to the provision of free childcare. The model also rationalizes why

we observe a greater labor supply response to the reform for high-skilled mothers.

We believe that our findings make important contributions to several strands of the litera-

ture on gender and family economics. In particular, by linking women’s demand for flexibility

to the presence of children, we complement the recent studies reporting gender differences in

preferences for flexibility (Filer 1985, Goldin and Katz 2011, Flabbi and Moro 2012, Wiswall

and Zafar 2017, Mas and Pallais 2017) and those providing event-study type of evidence on the

existence of a child penalty (Angelov, Johansson and Lindahl 2016, Chung et al. 2017, Kleven,

Landais and Sogaard 2018, Kuziemko et al. 2018). Secondly, by showing that mothers tend to

substitute weekend shifts for Wednesday work when institutional constraints are relaxed, we

contribute to the scarce but growing evidence on the importance of leisure complementarities

in explaining individuals’ labor supply choices (Georges-Kot, Goux and Maurin 2017, Goux,

Maurin and Petrongolo 2014, Mas and Pallais 2017). Finally, our finding that high-skilled

women are especially responsive to the opportunity of working regularly offers new insights to

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the literature documenting the existence of a part-time penalty and its relationship to occu-

pational segregation (Manning and Petrongolo 2008, Fernández-Kranz and Rodríguez-Planas

2011). Besides, it is also consistent with the growing evidence that women’s quest for flexi-

bility may be especially costly in occupations where workers have no close substitutes and a

regular interaction with clients and colleagues is particularly valuable to the firm (Cortes and

Pan 2016, Goldin 2014).

The paper proceeds as follows. Section 1 describes the institutional context and the data.

Section 2 presents the identification strategy. Section 3 presents the main results. We discuss

robustness checks in Section 4. In Section 5 we present a simple theoretical framework to help

interpret the empirical results. Section 6 concludes.

1 Institutional context and data description

1.1 The French primary school system

The French educational system is divided into three stages: elementary education, for children

aged six to eleven; secondary education – which, in turn, is divided into middle school (collège)

and high school (lycée) – and tertiary education. Education is compulsory from the age of six

to sixteen. However, parents can already send their children to free public pre-kindergarten

(école pre-maternelle) when they are two, or to kindergarten (école maternelle) at the age of

three. Today, 23 percent of two-year-old children and 95 percent of children aged three to five

attend this pre-school stage (Goux and Maurin 2010).

Public primary schools are financed by municipalities. The private sector comprises mainly

religious schools and receives fourteen percent of all primary school pupils.

With respect to the structure of the school calendar in primary school, France has always

been one of the countries with the longest holidays, highest number of hours per year, and

longest school day.

Since the introduction of compulsory primary education in 1882 (Loi Ferry), French chil-

dren have always had a full day off in the middle of the week. Until the end of the 1960s,

children spent five full days at school, with a break on Thursdays and Sundays, for a total of

30 hours per week. In 1969, Saturday afternoon school was abolished, and three years later,

in 1972, the break in the middle of the week was advanced from Thursday to Wednesday, and

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two hours of physical activities were added to the school week. Finally, in 2008, all classes on

Saturday were abolished and a 4-day school schedule, with six hours per day - plus a 2-hour

lunch break in the middle - was adopted.6

In the meantime, since the development of chronobiology in the 1980s, an intense debate

on the optimal structure of the school schedule has developed. Experts of this discipline point

out that primary school children need more frequent holidays and a shorter day at school.

And this was precisely the rationale for the 2013 reform. This reform shortened the school

day by an average of 45 minutes and, to maintain the total number of weekly hours, it added

half a day, usually on Wednesday mornings, and exceptionally on Saturdays. Moreover, to

compensate for the reduction in daily teaching time, the government urged municipalities to

provide free extra-curricular activities for children, for a total of three weekly hours. Precisely

because of this organizational burden, the government also gave municipalities the possibility

to implement the new schedule in either 2013–14 or 2014–15. Twenty percent of them chose

to do it in 2013; the rest only adopted the new system in 2014.7

The 2013 reform affected only kindergarten and primary school children. In middle and

secondary school, pupils have at least 24 hours of classes per week, spread over five days, and

this schedule has not been modified for a long time.8

6It would clearly be interesting to evaluate the impact of the 2008 reform on parents’ labor supply decisions,as well. However, there are at least two reasons why we choose not to do so. First, according to the 1998-99wave of the Multinomial Time Use Survey, all respondents, irrespective of their gender or presence of children,work an average of less than 2 hours on Saturday. This suggests that the abolition of Saturday classes forchildren of primary school age is unlikely to affect their parents’ working schedule. Secondly, as stressed below,the question on which days of the week a respondent works was only introduced into the Labor Force Surveyin 2013. Thus, the absence of this information would strongly limit our ability to understand how the 2008reform affects parents’ labor supply decisions.

7Each municipality can also choose how to allocate the extracurricular activities, whether to concentratethem on two days a week or spread them over the week. Unfortunately, disaggregated data by municipalityon the allocation of extracurricular activities are not available.

8Private schools had the freedom to implement the 2013 reform. By the end of the academic year 2014-2015, only fifteen percent of them, comprising 13.5 percent of French pupils attending a private school, hadadopted the new schedule. Although in our data we cannot tell whether families send their children to publicor private schools, we check that the aggregate proportions of students enrolled in public and private schoolsremains stable over the years of implementation of the reform. Parents are not moving their children fromone type of school to the other because of the reform. If anything, this implies that our estimates can be seenas ITT instead of ATE, as around twelve percent of the families in our sample are not affected by the reform(corresponding to 87 percent of the 14 percent of children attending private schools.)

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1.2 Data description

To study this setting and the consequences of the 2013 reform, we make use of two main

databases. First, we use the 2009-2016 waves of the French Labor Force Survey (Enquête Em-

ploi en Continu). This data set provides information on work-related statistics with quarterly

interviews of a representative sample of the French population. From the Labor Force Survey

we extract data on respondents’ age, level of education, marital status, labor market status,

income, and the structure of the household in which they reside. Crucially, we exploit the

information on the municipality of residence, the number of children respondents have, and

the age of their children.

Second, to identify the timing of the implementation of the 2013 reform across municipal-

ities, we exploit the Enrysco database. This is an administrative data set that was created by

the French Ministry of Education and provides a precise description of the weekly teaching

schedule for each school, in each municipality.

In the main analysis, we focus on the sample of mothers aged 18 to 55 whose youngest

child is between 6 and 14, for a total of 175,528 observations.9 In a series of robustness checks,

we also include mothers whose youngest child is 2 years old up to those whose youngest child

is 17. Analogously, to study fathers’ labor supply decisions, we consider men aged 18 to 55

whose youngest child is between 6 and 14, for a total of 149,794 observations. We exclude

from the main estimation sample all respondents working in schools, such as teachers, school

heads, school psychologists, and also the administrative staff, which corresponds to 10 percent

of all employed workers. This restriction ensures that any result we find is not simply driven

by the mechanical effect of the reform on this group of workers.10

As for the main outcomes of interest, we construct them as follows. To measure labor force

participation, we use a dummy equal to one if the woman belongs to the active population; we

measure part-time work using a dummy equal to one if the woman declares to work part-time

in her main job; next, we use a continuous variable indicating the number of hours worked

on average per week; and we construct a series of dummies that take the value one if the

woman works on each specific day of the week. In the French Labor Force Survey, the decision

to work on each day of the week is only measured from 2013 onward. For this reason, we9We do not consider younger mothers as less than 1 percent of women aged 15 to 17 have children in France.

10Our main findings remain practically unchanged when including the school personnel, see Table A.3 andTable A.4.

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complement the analysis on these outcomes by also considering another variable, available for

the entire sample period, and measuring the number of days worked per week. Finally, to

measure earnings, we consider log real net hourly wages. To construct this last variable, we

take the log of the ratio between real net monthly wages, which is directly available in the

Labor Force Survey, and hours worked per month, computed as four times the hours worked

per week. Respondents report their monthly wages only once out of the five times they are

interviewed. Thus, the sample size consistently falls when analyzing the impact of the reform

on wages. Final remark, all outcomes that concern employed women, such as hours or day

worked, daily labor supply, or part-time work, are set to missing for non-employed women.

Accordingly, when analyzing the impact of the reform at the intensive margin, we restrict the

sample to employed women.

1.3 Pre-reform period

Table 1 describes the characteristics of French mothers aged between 18 and 55 and interviewed

in the Labor Force Survey before the introduction of the 2013 reform. We regroup them

according to the age of their youngest child living in the household.

A few preliminary considerations are worth mentioning. First, mothers of younger children

tend to be not only younger but also more likely to hold a college degree, which is consistent

with the well-documented increasing trend in female education attainment common to many

OECD countries (OECD 2016a). This suggests that looking at incentives, constraints, and

choices of highly educated women is particularly relevant for predicting the behavior of future

generations. Second, mothers’ labor force participation is strongly correlated with their chil-

dren’s age and, in particular, it increases discontinuously as soon as their youngest child starts

attending primary school. Thirdly, conditional on participation, the probability of working

part-time decreases as the youngest child grows older and the average number of hours and

days increases accordingly.

However, what appears especially striking in this table is the large gap in the proportion

of mothers who work on Wednesdays as their youngest child moves from primary to middle

school. More than 40 percent of working mothers whose youngest child is in kindergarten

or primary school do not work on Wednesdays, and this proportion decreases by almost ten

percentage points as soon as the youngest child enrolls in middle school. Besides, such a

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pattern does not emerge at all when looking at the probability of working on any another

day of the week, such as Thursdays. These figures are consistent with the evidence obtained

from the Multinomial Time Use Survey that mothers are the main providers of childcare on

Wednesdays. As shown in Figure A.1 in the appendix, they are also in line with the results

of a survey on childcare arrangements for Wednesdays aimed at families with children aged

0-6. There, up to 70 percent of respondents declare that parents themselves take care of their

children when they do not have school on Wednesday.11

These figures show that the institutional constraint imposed by children’s school schedule

appears to bind for a large fraction of women. As a result, they adopted a flexible working

schedule in the pre-reform period.

To get more insight on who actually makes such a choice, from now on we mainly focus on

mothers whose youngest child is in primary school, as it appears uncontroversial to compare

their behavior to that of mothers with slightly older children. Table 1 shows that, except

for the allocation of their working time over the week, their behavior in terms of education,

marriage, and employment decisions closely resembles that of mothers whose youngest child

is in middle school.12

When we break down the previous figures by mothers’ characteristics, we notice that

women seem to cope in different ways with the institutional constraint imposed by children’s

school schedule, depending on their level of education, their occupation, sector, employer’s

characteristics and position in the household. Figure 2 shows that, before the reform, highly-

educated mothers tended to work significantly more hours per week than low-educated ones,

although in both groups more than 40 percent of mothers did not work on Wednesdays.13 In11A large fraction of mothers choose to stay at home on Wednesdays, despite the fact that other forms of

childcare, both public and private, are available for that day. This is consistent with the growing evidencethat parents, and particularly highly educated ones, are increasingly spending more time with their children(Bertrand, Goldin and Katz 2010, Ramey and Ramey 2010).

12Concerning mothers with children of kindergarten age instead, Table 1 clearly shows that their partici-pation rate in the labor market, as well as several observable characteristics, differ substantially from thoseof mothers with older children. This suggests that the incentives driving their decisions might differ as well.For instance, mothers with children between two and three in France are entitled to receive specific childcaresubsidies that are withdrawn as children enter primary school. In addition, kindergarten is not compulsoryand only 30 percent of families whose youngest child is two years old actually make use of this service (Gouxand Maurin 2010). For all these reasons, we prefer to exclude mothers with children aged two to five from ouranalysis. For these same reasons, we decide to exclude them as well from the regression analysis studying theimpact of the 2013 reform. However, our findings do not change substantially when we include them in thetreatment group. These results are available in Table A.5.

13Figure A.2 in the appendix shows that, among the highly-educated, mothers of primary-school age childrenwho have the same or a lower level of education than their partner are significantly more likely to stay at home

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other words, highly-educated mothers seem to compensate for their absence in the middle of

the week by working more hours on other days. This suggests that bargaining power plays

a role in the ability of workers to negotiate a flexible working schedule with their employer –

which is consistent with the evidence provided by Katz and Krueger (2016) that the recent

growth in freelance and contract work largely excludes the low-wage sector. Alternatively, dif-

ferential sorting into family-friendly firms by level of education, or the structure of occupations

might explain these pre-reform differences in participation on Wednesday.14 In this respect,

mothers working in managerial positions whose youngest children are in primary school are

even significantly less likely to work on Wednesdays than those working in other occupations

(Figure 3). However, these figures also suggest that highly-educated mothers – and especially

those having no substitute at work – perceive to bear a higher cost, in terms of productivity

losses and wage penalizations, than low-educated ones for their quest for flexibility.15

Overall, this descriptive analysis of the pre-reform period suggests that children limit

women’s chances of working regularly. However, it highlights that the possibility of adopting

a flexible schedule relates to the interplay of different factors, among which women’s bargaining

power at work, the structure of jobs, and the career cost of flexibility may play an important

role.16

on Wednesdays than other highly-educated mothers. The probability that a highly educated mother works onWednesdays is higher when she is more likely to be the breadwinner in the household, as her level of educationis higher than that of her husband. This pattern is consistent with the evidence provided by Bertrand, Goldinand Katz (2010), who show that, among female MBA graduates, those with richer husbands are the oneswho tend to have the longest job interruptions when they have a child. As they point out for their context,also in France it seems that richer husbands purchase more costly child-care time of their highly educatedwives, rather than more nannies. Interestingly, in couples where the woman has at most a high school degree,mothers’ probability of working on Wednesdays does not seem to vary with her role in the household.

14In some service occupations, such as shops, or restaurants, productive work can only be done whencustomers are present (Manning and Petrongolo 2008), implying that workers in these occupations might notbe able to work outside of peak time even if they want to.

15Consistent with this, Figure A.3 and Figure A.4 – reported in the appendix – using pre-reform data ex-tracted from the French match-employer-employee data set, add two elements to this picture. First, Figure A.3shows that, in France as in the United States (Goldin 2014, Wasserman 2015), women tend to be less repre-sented in occupations where men work more hours. Secondly, as depicted in Figure A.4, the gender wage gapwidens along both the male wage and the hours distribution. Overall, these pieces of descriptive analysis seemto suggest that women’s quest for flexibility may be particularly hurtful in highly-paid occupations. We donot use this data set to analyze the impact of the reform, as it is only available until 2013.

16All the figures presented in this paragraph, together with those broken down by occupation, sector, andemployer’s characteristics are also reported in Table A.1 and Table A.2 in the appendix.

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2 Empirical strategy

To study how the 2013 reform affects mothers’ employment decisions, we adopt a difference-

in-differences strategy. We define a woman as being treated if her youngest child is affected

by this reform, i.e women whose youngest child was 6 to 11 years old. We compare mothers

whose youngest child is between six and eleven with those whose youngest child is between

twelve and fourteen – corresponding to the age-interval of middle-school pupils. The graphical

analysis of pre-treatment trends in the labor supply measures we have chosen, displayed in

Figure 4,17 supports this choice, as the employment decisions of the treatment and control

group exhibit a comparable evolution.18

Next, in the main regressions, we consider both mothers living in municipalities that imple-

mented the reform in 2013 and those living in municipalities that postponed its introduction

to 2014.19

Finally, we exclude from the estimation sample all mothers working in schools, as teachers,

school heads, school psychologists or administrative staff.

We estimate the following specification on mothers aged 18 to 55, interviewed between

2009 and 2016, and whose youngest child is between six and fourteen years old:17This figure shows trends in selected outcomes, notably the probability of working on Wednesdays, the

number of days worked per week, the number of hours worked per week and log real net hourly wages. Fig-ure A.5 in the appendix reports the evolution of the other outcomes we study, that is, labor force participationand the decision to work part-time.

18Although the evolution of several labor supply measures is similar among mothers with children in kinder-garten and those with older children, we choose to exclude the former from the treatment group for the samereasons explained in the previous paragraph. Their baseline characteristics are indeed too different from thoseof our control group to assume that, absent the reform, they would respond to the same type of incentives.

19In principle, to identify the effect of the reform, we could exploit the variation over time and acrossmunicipalities in the implementation of the reform. In this way, we would compare mothers whose youngestchild is in the affected age-range and live in municipalities that introduced the reform in 2013, with thesame group of mothers who live in municipalities that postponed the implementation of the reform to 2014.However, we prefer not to adopt this strategy for two reasons. First and most importantly, a comparisonof the pre-trends in labor supply measures for these two groups of mothers – the graphs are available uponrequest – reveals that their dynamics seem to diverge before the implementation of the reform. Therefore, itis hard to claim that, absent the reform, the evolution of labor supply would have been the same across thesegroups. This concern is also confirmed by a formal test on the parallel trend assumption. In a regressionmodel that compares the evolution of labor supply for these two groups of mothers, we include a battery ofdummies taking the value one for mothers "treated in 2013", in the three waves before September 2013. A teston their joint significance leads us to reject the null for all the outcomes considered. Secondly, by adoptingthis strategy we would only be able to study the impact of the reform in its first year of implementation, giventhat, from 2014 onward, all municipalities adopted the new schedule. As it might take some time for its effectto manifest itself, we think that considering only its short-run impact would considerably limit the objectivesof our analysis.

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Yicmt = γm + δt +π ∗Xicmt +α ∗Y st_Child_btw_6_11c (1)

+ β ∗Y st_Child_btw_6_11 ∗Post_Sep_2013ct +uicmt

where i stands for each interviewed woman, c for the age of the youngest child, m for

the municipality of residence and t for the wave in which the woman is interviewed. Yicmt

represents the outcome considered. This is either labor force participation, the decision to work

part-time or full-time, hours worked per week, days worked per week, the decision to work on

each specific day of the week, or the logarithm of real net hourly wages. The vector Xicmt

includes all the individual variables that can affect women’s labor supply decisions. These

comprise age, age squared, level of education, number of children, marital status, and presence

of other members in the household; Yst_Child_btw_6_11c is a dummy equal to one if the

youngest child is between 6 and 11, therefore α measures the impact of having a youngest child

of primary school age. Post_Sep_2013ct is a dummy equal to one starting from September

2013 for those mothers living in municipalities that introduced the reform in 2013, and from

September 2014 for mothers living in municipalities that postponed the implementation to

2014. The main coefficient of interest is β, which captures any deviation from a parallel

evolution in the outcome of interest between the treatment and the control group due to the

implementation of the new schedule in primary schools. In all regressions we also include

municipality of residence and wave of interview fixed effects, γm and δt, respectively. Finally,

in all specifications, standard errors are clustered at the municipality level to account for any

correlation of the outcomes for women residing in the same municipality.20

3 The impact of the 2013 reform

The main results of our analysis are reported in Table 2, Table 3, and Table 4. First, the

reform does not trigger any response at the extensive margin – Table 2, column 1 – which

should not be surprising given that 86 percent of treated mothers are already active.21 How-20We also estimated specifications with standard errors clustered at the level of age-youngest-child-×-quarter-

of-interview. All our results are robust to this alternative choice.21This result does not vary by level of education, and there is no evidence of heterogeneous effects on this

margin.

13

ever, the reorganization of the teaching time, coupled with the introduction of three hours of

extracurricular activities, leads treated mothers to adopt a longer and more regular working

schedule. In particular, column 2 of Table 2 shows that, following the implementation of the

reform, the probability of working part-time significantly decreases by 2 percentage points for

treated mothers compared to the control group, or by 5 percent with respect to the pre-reform

mean. Accordingly, the point estimate on hours worked per week in column 3 is also positive,

though the coefficient fails to be significant. Next, columns 4 to 6 of Table 2 tell us how

mothers re-organize their overall weekly working schedule, following the 2013 reform. Besides

increasing the amount of hours worked per week, treated mothers also significantly increase

the number of days they work, by halving the pre-reform gap with the control group on this

margin. Crucially, in column 5, we can see that this increase in the number of days worked

per week corresponds to a three-percentage-point rise in the probability that treated mothers

work on Wednesdays, significant at the one percent significance-level. Interestingly, as shown

in column 6, this effect is in part accompanied by a reduction of weekend work. In other words,

some mothers who, prior to the reform, worked on Saturdays – probably to compensate for

their absence on Wednesdays – take advantage of the reorganization of the school schedule to

allocate their Saturday hours to Wednesday. This result points towards a distaste for weekend

work, which is line with the recent evidence proposed by Mas and Pallais (2017) on workers’

positive willingness to pay to avoid working on the weekend.

Importantly, the last column of Table 2 tells us that, thanks to the reform, treated mothers

also experience an increase of more than 1 percent in their (log) hourly wages.22 To dig into

the mechanisms behind these main results we proceed as follows.

First, in Table 3, we show how the reform affects the decision of treated mothers to work

on the other days of the week. With the exception of Saturday, their likelihood of working

on any other day of the week does not change with respect to the pre-reform period, in22The sample size changes from the first to the other columns in Table 2. In the first column, we consider all

mothers aged 18-55 whose youngest child is between 6 and 14, with the exception of those working in schools.In the other columns, we restrict the sample to employed mothers. Besides, the sample further falls in columns5 and 6, as in the French Labor Force Survey the decision to work on each day of the week is only measuredfrom 2013 onward. However, the fact that the reform also has a significant impact on the number of daysworked per week shows that the effect on the probability of working on Wednesdays does not merely dependon the span of time over which this outcome is observed. Finally, as respondents report their monthly wagesonly once out of the five times they are interviewed, the sample size further falls in the last column, where weanalyze the impact of the reform on log real net hourly wages. For completeness, we checked that the otherresults do not change when estimated on this restricted sample, and this table is available upon request.

14

comparison with control mothers. This clearly suggests that the main constraint mothers face

when deciding how to allocate their weekly labor supply comes from their children’s schedule.

Next, in Table 4 we break down our results by level of education. The rationale for perform-

ing this exercise is to understand whether the observed increase in hourly wages represents

a reward for a longer and more regular presence at work. If this was the case, we would

expect high-skilled mothers to be more responsive to the opportunity of working regularly,

as they are probably less substitutable and more likely to play a key role for their firm. In

other words, highly educated mothers should be those facing the highest cost of flexibility.

The results reported in Table 4 strongly support this hypothesis.23 First, following the 2013

reform, highly-skilled mothers significantly increase the number of hours worked per week by

an average of almost 1 hour – with their coefficient being significant at 5 percent and sta-

tistically different from the one on low-skilled mothers. Secondly, highly-educated mothers

see their (log) hourly wages increasing by more than 3 percent, with this coefficient being

significant at 10 percent. This effect corresponds to a 10 percent decrease in the pre-reform

gender wage gap.24 On the contrary, the point estimate for low-skilled women is practically

zero and not significant - though not statistically different from that on high-skilled mothers.

In other words, the positive effects on full-time work and hourly wages for the entire sample

seem to be completely driven by the impact on highly-educated mothers.

In addition, this same result holds for mothers who work in managerial and professional oc-

cupations, although in this case the point estimates for the log hourly wages are not significant

- nor statistically different from the estimates on mothers working in other occupations.25

Overall, these results provide causal evidence that the availability to work long and regular23We choose to estimate a regression on the entire sample, and interact all regressors with the subgroups

considered, except for municipality fixed effects. We also report the p-value of the test on the equality of theimpact of the reform across the two subgroups. To ease the reading of this table, we also report a graphicalrepresentation of its results in Figure 5.

24To obtain this estimate we proceeded as follows. The reform triggers a 3 percent increase in the hourlywages of high-skilled mothers, relative to their pre-reform level, or 0.44 euros per hour. We also calculate thatthe pre-reform gender gap in real net hourly wages between high-skilled men and women whose youngest childis of primary school age amounts to slightly less than 5 euros. Therefore, the impact of the reform correspondsto β ∗wageW /(wageM −wageW ) = 0.03 ∗ 14.87/(19.48− 14.87) = 0.0968.

25As shown in Table A.6, we find that, at least in the short run, this wage effect does not seem to arisefrom an increased likelihood of finding better-paid job opportunities, but rather from a re-definition of thesame contract. In particular, we test whether, following the introduction of the reform, treated mothers aremore likely to work in high-skilled occupations or in managerial positions (Table A.8), and find no evidencefor these changes. Interestingly, we do see that high-skilled women are significantly more likely to participatein on-the-job training (Table A.7), and this may help explain the increase in hourly wages.

15

hours appears to be rewarding and significantly contributes to reduce the gender wage gap.26

In Section 5, we show that a very simple theoretical framework can rationalize these findings,

using few assumptions from the empirical literature in personnel economics.

In principle, the institutional constraints imposed by children’s school schedule in France

might affect the employment decisions of both parents. Yet, as suggested already by the

Multinational Time Use Survey data, the Labor Force Survey confirms that, before the reform,

fathers worked on Wednesdays as much as on the other days of the week. In particular, 76

percent of fathers worked on Wednesdays, exactly as on the other days of the week, whereas

only 56 percent of mothers did so. As a consequence, we expect to see that the reform does

not have any impact on fathers’ employment decisions, as shown in Table 5 and Table 6.

Overall, our findings show that even in a country in which a high proportion of women

participate in the labor market, a strict division of roles persists within households with

children, and that institutional constraints bind only for women. Therefore, removing barriers

to work for women might play the double role of enhancing the attachment to the labor market

and of helping to change gender norms.

4 Robustness checks

To validate our results we run the following robustness checks. First, we verify that the

parallel-trend assumption holds in our context. In other words, we check that, without the

reform, the evolution of mothers’ labor supply would have been the same for the treated and

control groups. Secondly, we show that our findings are robust to variations in the definition

of the control group.

To support the validity of the parallel-trend assumption, besides visually inspecting the

pre-treatment trends in labor supply measures, we first analyze the dynamic impact of the26We analyzed other dimensions of heterogeneity as well, but no striking difference emerged along them. In

particular, we studied whether the response to the reform differs between mothers working in the private sectorand those employed in the public sector, by firm size, number of children, role of mothers in the householdor by ranking occupations on the basis on men’s average hours worked, or men’s returns to working longhours. All these results are available upon request. We also considered the possibility that the response differsdepending on the distance to the employer’s premises, and found that this is not the case. However, we haveto acknowledge that our measure of distance is not too accurate, as we can only calculate it for respondentsresiding and working in two different municipalities. For instance, we cannot compute it for mothers residingand working in big cities like Paris, where commuting time might be an important factor affecting the planningof the working schedule. Hence, these results should be considered with caution.

16

reform, and then we estimate the impact of a battery of placebo reforms on the main outcomes

of interest. Figure 6 provides a graphical analysis of the treatment dynamics. In particular,

it shows the coefficients of the leads and lags in the treatment, estimated with this regression:

Yicmt = γm + δt + π ∗Xicmt +α ∗Y st_Child_btw_6_11c (2)

+∑t

βt ∗Y st_Child_btw_6_11 ∗ quarterct +uicmt

where t corresponds to the first quarter of 2013 when the outcome is the decision to work on

Wednesdays, and to the last quarter of 2012 for all the other outcomes. The first thing to

note is that the coefficients on the quarters pre-reform are always insignificant. This strongly

suggests that we are identifying a causal impact of the reform, rather than picking the effect of

other elements that were already affecting the treatment and control groups differently before

the introduction of this intervention. In addition, this lack of effect before the implementation

of the reform rules out significant anticipation effects. Moreover, these regressions allow us

to implicitly perform a placebo test. In the first year of implementation of the reform, we

should see any impact on mothers living in municipalities that postponed its introduction to

2014. As these represent 80 percent of our sample, when we look at the impact of the reform

on both groups of municipalities at the same time, this is exactly what we observe. None of

the coefficients capturing the impact from September 2013 to August 2014 is significant in the

two regressions

In Figure 7, we graphically report the estimates of the impact of several placebo reforms,

obtained by pretending that the government intervention took place before its actual intro-

duction, and excluding the actual treatment period from the estimation sample. Reassuringly,

with the exception of a fake March 2011 reform on the number of days worked per week,

none of these placebo reforms appears to have a significant effect on the outcomes of interest,

suggesting that in our main regression we are not simply capturing the impact of factors that

systematically affect treated and control mothers differently.27

In Figure 8, we document the evolution of the estimates of the impact of the reform on each27Unfortunately, we cannot run these robustness checks on the outcome measuring the decision to work on

Wednesdays, given that the question concerning labor supply at daily frequency is not available in the LaborForce Survey before 2013.

17

outcome of interest, when changing the size of the control group. As we can see, restricting

or expanding the control group does not affect either the magnitude or the significance of the

reform coefficients. These graphs show that our results are not sensitive to the definition of

the control group we adopt in the main specification.

Finally, we take several steps to account for the risk of Type I error when looking at the

impact of the reform on multiple outcomes and for several subgroups (see Appendix A.4).

In Table A.9 and Table A.10, we show that our results are robust to correcting standard

errors for multiple hypothesis testing. The method we use is the False Discovery Rate (FDR)

control, or the expected proportion of all rejections that are type-I errors, which involves a

p-value adjustment less severe than some other methods such as the Familywise Error Rate

control or the Bonferroni correction, as long as one is willing to tolerate some type-I error

in exchange for a less stringent adjustment. Specifically, we use the sharpened two-stage

q-values introduced in Benjamini, Krieger and Yekutieli (2006) and described in Anderson

(2008). In Appendix A.4.2, we also use modern machine learning tools and provide a non-

standard approach to treatment heterogeneity building on recent applications in the context

of randomized controlled experiments (Athey and Imbens 2016, Wager and Athey 2018, Davis

and Heller 2017, Bertrand et al. 2017). This method confirms the existence of heterogeneous

effects of the reform by level of education.

Overall, this battery of robustness checks strongly supports the validity of our identification

strategy.

5 Theoretical framework

In this section, we show that we can rationalize our empirical findings in a very simple con-

ceptual framework that explores the link between inter-temporal labor supply decisions, free

childcare provision and wage penalty associated to working few hours. We illustrate the effect

of the reform in a canonical consumption/leisure two-period model where the probability of

promotion between the two periods is increasing with hours worked during the first period.

18

5.1 Setting

Consider an individual28 (mother) who derives utility from consumption c and leisure l in

period 1 and 2 by supplying hours of work.29

max{c1,c2,l1,l2}

u(c1, l1) + βE[u(c2, l2)]

and c1 ≤ h1w1

c2 ≤ h2w2

with u(.) increasing and strictly concave, and where h1, h2 represent the hours spent working

in period 1 and 2. For simplicity, we exclude the possibility of savings from the model.

In this partial equilibrium framework, the wage rate at period 1, w1, is determined ex-

ogenously, while the wage in period 2 depends on a probability of promotion p.30 In terms

of incentives compensation, this wage structure corresponds to a worker who receives input-

based pay with continuous incentives: the worker can decide over the amount of input supplied,

rather than choosing ex-ante between different bundles of hours and other workplace ameni-

ties. The time-based pay assumption is relevant in settings where output and/or quality are

not very observable (Lazear 2018), which is consistent with characteristics of the sample of

working mothers with high level of education, or working in managerial occupations.

w2 =

wH with probability p

wL with probability (1− p)

with wH > wL

28We think that it is justified to focus on individual labor supply model rather than using joint labor supplymodels a la Chiappori, Iyigun and Weiss (2009) or Hurder (2013) in order to be consistent with our empiricalresults. Indeed, we do observe a reaction to the reform also for single mothers, second we show that fathers’labor supply is not responsive to the reform. Moreover, women’s reaction to the reform is not statisticallydifferent across types of households. Therefore it is relevant and simpler to focus on the labor supply of womenalone.

29We choose not to explicitly model the time spent with the child as a separate argument of the utilityfunction. While the utility derived from spending time with the child is likely to affect women’s decision, itis unclear how this channel would a play a key role in a dynamic setting, so we prefer to abstract from it forsimplicity.

30In a general equilibrium framework, it is of course plausible that wages would adjust as a response tochanges in labor supply, or that in the presence of displacement effects, the labor supply of other workersmight be affected. Our empirical analysis does not allow us to investigate these channels therefore we chooseto let them aside here.

19

A key assumption here is that p is a function of hours worked in period 1, i.e promotion is

more likely to occur with high level of labor supply in period 1. This assumption relies on a

line of research on compensation and incentives in the workplace (Lazear 2018), in particular

regarding relative scheme of performance and tournament theory. In this setting, h1 is akin to

an imperfect signal of each player’s performance. A greater h1 signals a greater performance

and increases the probability of promotion. Other channels could also justify this functional

form such as learning-by-doing or the existence of set-up costs making the first hours of worked

less productive than the others.

Consistent with empirical evidence showing that the jump in pay for promotions at high

levels is greater than that at low levels (Eriksson 1999, Belzil and Bognanno 2008), ∆w, the

gap between wH and wL, is higher for high levels of education. Let’s write ei the level of

education of a mother i.

∆w = ∆w(ei) with ∆′w(ei)> 0 and ei ∼ U(0,1)

Without loss of generality, let’s assume that wL2 = w1, i.e if the mother is not promoted, she

stays with the same wage rate. The wage differential before/after promotion – rather than

the initial wage rate per se – will be a key channel in the model. We can write:

∆w = wH2 −wL2 = wH2 −w1 > 0

To summarize, assumptions on the wage dynamics write as follows:

p= f(h1) with ∂f

∂h1> 0

∆′w(ei)> 0

For simplicity, we set:

f(h1) = h1

Once promotion is granted (or not), the state of the world is realized, and the mother can

optimally allocate her time knowing her budget constraint (i.e the value of w2).

20

5.2 Optimal labor supply

We solve the program by backward induction: we first find optimal labor supply in period 2

(h∗2), and then incorporate indirect utility functions of period 2 within the objective function

of period 1.

5.2.1 Optimal labor supply in period 2

max{c2,l2}

u(c2, l2) s.t

w2(1− l2)− c2 ≥ 0

h2 + l2 ≤ 1

with u(c, l) = α log(c) + (1−α) log(l)

Maximizing with respect to c2, l2 and using the budget constraint the time constraint, we

find:31 c∗2 = αw2

l∗2 = 1−α

h∗2 = α

(3)

As the utility function is a standard Cobb-Douglas function, the optimal labor supply in period

2 does not depend on the wage rate w2. The condition for an interior solution is 0< α < 1. We

can then derive the indirect utility functions in states of the world where promotion occurred

(H) or did not (L).

V2(wH2 ,α) = α log(wH2 ) +α log(α) + (1−α) log(1−α)

V2(wL2 ,α) = α log(wL2 ) +α log(α) + (1−α) log(1−α)

31Given that u(.) is a standard Cobb-Douglas utility function continuously differentiable, the solutions areknown to be interior and are characterized by the first-order conditions.

21

5.2.2 Schooling constraint

Let’s assume now that the mother can only choose to work as long as the child is in school.32

If s is the time that the child can spend at school, the time constraint is such that h∗2 ≤ s.33

Therefore, the condition under which the schooling constraint is not binding writes as follows:

h∗2 < s ⇐⇒ α < s (4)

5.2.3 Optimal labor supply in period 1

The problem in period 1 will differ from period 2’s as the representative mother incorporates

here future earnings in present labor supply decision. We substitute indirect utility functions

for both states H and L in period 1.

max{c1,l1}

u(c1, l1) + β[pV2(wH2 ,α) + (1− p)V2(wL2 ,α)]

s.t

c1 ≤ (1− l1)w1

h1 + l1 ≤ 1

Substituting the constraints into the expression:

α log(h1w1) + (1−α) log(1−h1) + β[f(h1)V H2 + (1− f(h1))V L

2 ]

with f(h1) = h1. The solution writes:

h∗1 = 12 −

12βαK +

√β2α2K2 + 1 + (4α− 2)βαK

2βαK

with K = log(wH

wL

)(and ∆w the exponential transformation of K), where h∗1 is the unique

interior solution. Proof is given in Appendix A.6.1.

In contrast to period 2, h∗1 here depends on the wage rate in period 2. If w1 = wL, i.e no32Implicitly, we make the assumption here that mothers cannot buy private childcare. This is consistent

with anecdotal evidence of low utilization pre-reform of childcare facilities on Wednesday, and could be explainboth by the limited provision of high-quality childcare or by the prevalence of social norms according to whichmothers should be taking care of their children when they are not at school.

33For simplicity, we assume here that s is constant across periods.

22

wage growth between period 1 and 2, the optimal labor supply in period 1 would be greater

or equal to the one in period 2. This captures one key component of the model which is that

the optimal labor supply in period 1 incorporates future gains in earnings due to promotion.

The condition under which the schooling constraint is not binding is:

h∗1 = 12 −

12βαK +

√β2α2K2 + 1 + (4α− 2)βαK

2βαK < s

Therefore, certain mothers will not attain their optimal labor supply in period 1 but will

have to choose s. The following comparative statics help us characterize who are these mothers

whose labor supply in period 1 is suboptimal.

5.3 Comparative statics

We can derive the following comparative statics for h∗1.

Proposition: the optimal labor supply in period 1, h∗1, is an increasing function of α, β

and ∆w, when the schooling constraint is not binding.

dh∗1dα > 0 (i)

dh∗1dβ > 0 (ii)

dh∗1d∆w

> 0 (iii)

Proof is given in Appendix A.6.2. Propositions (i) and (ii) are intuitive: mothers who

value the future more (high β) are likely to work more in period 1 to increase the probability

of promotion in period 2. Mothers with high α value consumption more than leisure and

are likely to work more at both periods. Proposition (iii) states the following: the higher

the jump in pay for promotions, the higher the hours worked in period 1. Mothers with a

high level of education ei have therefore greater incentives to increase their labor supply in

period 1 given that the expected gain associated to the promotion is larger for them. This

23

comparative statics is going to be the key mechanism rationalizing our empirical results. We

now investigate what are the implications of this proposition in the context of the reform.

5.4 Interpretation of the reform

Our reform corresponds to an increase in s, i.e a relaxation of the schooling constraint. Given

the positive relation between h∗1 and ∆w, the diagram presented in Appendix A.5 illustrates

the impact of the reform. The shift from s to s′ reduces the share of mothers whose labor

supply is at the level of the schooling contraint rather than at their optimal.

• The welfare of women whose optimal labor supply in period 1 was lower than s, i.e for

whom the schooling constraint was not binding, is unchanged.

• The welfare of women who were bunching at s in period 1 increases: a significant share of

these mothers (represented by the blue line on the diagram) is able to reach her optimal

labor supply h∗1. On the other hand, those who do not achieve their optimal labor supply

and who bunch at s′ also see their utility increase.34

Given the positive relation between ei and ∆w, the level of education of the least educated

mother working s′ rather than her optimal h∗1 in the first period has increased with the reform.

Consistent with our empirical results, highly educated mothers are more likely to increase their

labor supply as a response to an increase in s, because their expected gains from promotion

are higher.

6 Discussion and conclusion

This paper studies women’s employment decisions in a context where institutions limit their

chances of having a regular working schedule. From 1972, French children in kindergarten and

primary school have had no school on Wednesday. In 2013, a reform reallocated some classes to

Wednesday morning. This setting allows us to study which factors influence women’s demand

for temporal flexibility, and whether this quest for flexibility can help explain the persistence

of the gender wage gap.34A formula of the total welfare gains for these highly-educated mothers is indicated in Appendix A.5

24

To conduct this analysis we use a difference-in-differences strategy and compare mothers

whose youngest child is of primary school age to mothers whose youngest child is of middle

school age, where children have school all week days.

We find that the presence of children, combined with institutional constraints, strongly

limit mothers’ chances of working regularly. Once institutional constraints are removed, moth-

ers tend to adopt a long and regular working schedule. In particular, they are less likely to

work part-time and more likely to work on Wednesdays.

Moreover, we show that high-skilled mothers are particularly responsive to the opportu-

nity of adopting a longer and more regular working schedule. On the one hand, this might be

because low-skilled women are trapped into occupations where full-time work is scarce (Man-

ning and Petrongolo 2008). On the other hand, this may suggest that high-skilled mothers

perceive that a regular presence at work is particularly rewarding for them (Cortes and Pan

2016, Goldin 2014).

Overall, our findings have a clear policy implication. While both traditional gender norms

and the structure of jobs and pay evolve slowly,35 governments should continue to reduce

institutional constraints on women’s regular work, even in countries with high rates of female

labor force participation. This consideration is particularly important in light of the growing

debate about the possibility of having a four-day school week that has recently spread in

many countries such as the United States and the United Kingdom (Brookings Institute 2017,

The Guardian 2015). Our findings clearly show that these policies might hurt mothers’ labor

market prospects, and this could be especially so for the high-skilled.

35See, in this respect, the work by Wasserman (2015), showing that imposing a cap on workweek for certainmedical specialities makes women more likely to choose such specialities.

25

Tables and figures

0

1

2

3

4

5

6

7

Hour

s wo

rked

per

day

France U.S Germany Spain United Kingdom

Wednesday Other working daysObs: France=2099, U.S=9966, Germany=4140, Spain=10533, UK=3778Source: MTUS-ATUS

Womenwith children younger than 12

0

1

2

3

4

5

6

7

Hour

s wo

rked

per

day



Womenwithout children

0123456789

Hour

s wo

rked

per

day



Menwith children younger than 12

Figure 1. Working time across European countries

Notes: The figures report bar graphs representing the average number of hours spent at work by, respectively,mothers with children younger than 12 years old, women without children, and fathers of children youngerthan 12, in France, the U.S, Germany, Spain, and the United Kingdom. Working time includes paid work, paidwork at home, second job, and travel to/from work. To highlight the peculiarity of the French case, we showthe working time declared for Wednesday separately from that reported for the other days of the week. Thegraph is constructed using the 1991-2010 averages of the Multinational Time Use Survey, and the 2003-2016averages of the American Time Use Survey for the U.S.Source: Multinomial Time Use Study, 1991–2010 averages, American Time Use Survey, 2003-2016 averages.

26

T-test 1 % (***) T-test 1 % (***)

24

28

32

36

40

Avg.

num

ber o

f hou

rs w

orke

d pe

r wee

k

No college degree College degree or more No college degree College degree or more

Youngest child aged 6-11 Youngest child aged 12-14Sample: Working women whose youngest child is between 6-14 years old, excluding schoolpersonnel.Obs: Youngest child aged 6-11=65116, Youngest child aged 12-14=30858

by level of education

Hours worked per week

T-test n.s T-test n.s

45

50

55

60

65

70

% o

f mot

hers

No college degree College degree or more No college degree College degree or more


by level of education

Share of mothers working on Wednesday

Figure 2. Mothers’ labor supply by level of education - Pre-reform period

Notes: These figures report bar graphs representing labor supply measures for mothers whose youngest childis between six and eleven, in green, and mothers whose youngest child is between twelve and fourteen, in blue.In the top graph, we report average hours worked per week, while at the bottom, we represent the proportionof mothers working on Wednesday. In each graph, we compare mothers who have at most a high-school degreewith those who have at least college education. All figures refer to the pre-reform period, and we exclude theschool personnel when computing them. On each bar, we also report 95 percent-confidence intervals. Finally,for each age interval of the youngest child, we indicate the results of T-tests for the difference in means betweenthe two subgroups.Source: French Labor force Survey 2009-2013.

27

T-test 1 % (***) T-test 1 % (***)

24

28

32

36

40

Avg.

num

ber o

f hou

rs w

orke

d pe

r wee

k

Non-managerial occ. Managerial occ. Non-managerial occ. Managerial occ.


by type of occupation


T-test 10 % (*) T-test n.s

45

50

55

60

65

70

% o

f mot

hers

Non-managerial occ. Managerial occ. Non-managerial occ. Managerial occ.


by type of occupation

Share of mothers working on Wednesday

Figure 3. Mothers’ labor supply by type of occupation - Pre-reform period -

Notes: These figures report bar graphs representing labor supply measures for mothers whose youngest childis between six and eleven, in green, and mothers whose youngest child is between twelve and fourteen, in blue.In the top graph, we report average hours worked per week, while at the bottom, we represent the proportionof mothers working on Wednesday. In each graph, we compare mothers working in managerial occupationswith those employed in other professions. All figures refer to the pre-reform period, and we exclude the schoolpersonnel when computing them. On each bar, we also report 95 percent-confidence intervals. Finally, foreach age interval of the youngest child, we indicate the results of T-tests for the difference in means betweenthe two subgroups.Source: French Labor force Survey 2009-2013.

28

40

50

60

70

80

90

Prop

ortio

n of

mot

hers

2013 A I1 2014 I2 2015 2016

Quarter

Youngest child between 6-11Youngest child between 12-14

Working on Wednesday

4.4

4.6

4.8

5

Aver

age

num

ber o

f day

s w

orke

d pe

r wee

k

2009 2010 2011 2012 2013 A I1 2014 I2 2015 2016

Quarter


Days worked per week

32

34

36

38

Aver

age

num

ber o

f hou

rs w

orke

d pe

r wee

k

2009 2010 2011 2012 2013 A I1 2014 I2 2015 2016

Quarter



2.3

2.35

2.4

2.45

2.5

2.55

Log

net h

ourly

wag

e (in

€)

2009 2010 2011 2012 2013 A I1 2014 I2 2015 2016

Quarter


Log net hourly wage

Figure 4. Trends in mothers’ labor supply measures by age of the youngest child

Notes: The graphs show the evolution of different labor supply measures over the period 2009-2016. Thesample includes all mothers aged 18-55 whose youngest child is between the age of six and fourteen, with theexception of those working in schools. We represent in red treated mothers, that is, those whose youngest childis between six and eleven years old. Mothers whose youngest child is of middle-school age, or control mothers,are represented in blue. The vertical bar named "A" corresponds to April 2013, when municipalities announcein which year they will introduce the reform. The bar called "I1" corresponds to September 2013, when 20percent of municipalities implement the reform. The bar labelled "I2" corresponds to September 2014, whenthe rest of municipalities implement the reform. Finally, 95-percent confidence intervals are also reported.Source: French Labor Force Survey 2009-2016.

29

No college degree

College degree or more

Non managerial occupations

Managerial occupations

P=0.387

P=0.912

-.01 0 .01 .02 .03 .04 .05 .06 .07 .08

Estimate

Obs: by occupation = 141654, by level of education = 123632

Work on Wednesday

No college degree




P=0.056

P=0.049

-.1 -.09 -.08 -.07 -.06 -.05 -.04 -.03 -.02 -.01 0 .01 .02 .03 .04 .05

Estimate


Part-time

No college degree




P=0.07

P=0.069

-1 -.5 0 .5 1 1.5 2 2.5 3

Estimate



No college degree




P=0.112

P=0.114

-.05 -.025 0 .025 .05 .075 .1 .125 .15

Estimate



No college degree


P=0.212

P=0.414 Non managerial occupations


-.02 -.01 0 .01 .02 .03 .04 .05 .06

Estimate


Log net hourly wages

Figure 5. Labor supply response - Subgroup analysis

Notes: The graphs show the estimated impact of the reform on labor supply decisions of different subgroups.We report these estimates for the following outcomes: the decision to work on Wednesday, the decision to workpart-time, hours worked per week, days worked per week and the log of real net hourly wages. To conduct thissubgroup analysis, we estimate a regression on the entire sample, and interact all regressors with the subgroupsconsidered, except for municipality fixed effects. Otherwise, all regressions include the standard covariates,namely age and age square, marital status, number of children, a dummy for immigration status, municipalityand wave fixed effects, dummies for the level of education, and a dummy for the presence of other membersin the household. For each subgroup, we present the coefficient of the treatment interacted with the subgroupconsidered. We also report 90-percent confidence intervals, as well as the p-value of the test on the equality ofthe impact of the reform across the two subgroups. The estimation sample includes all mothers, aged 18 to55, whose youngest child is between six and fourteen, with the exception of those working in schools.Source: French Labor Force Survey 2009-2016.

30

-.1

-.05

0

.05

.1

Estim

ate

2013 I1 2014 I2 2015 2016

Work on Wednesday

-.1

-.05

0

.05

.1

Estim

ate

2013 I1 2014 I2 2015 2016

Part-time work

-.2

-.1

0

.1

.2

Estim

ate

2013 I1 2014 I2 2015 2016


-3

-2

-1

0

1

2

3

Estim

ate

2013 I1 2014 I2 2015 2016


-.2

-.1

0

.1

.2

Estim

ate

2013 I1 2014 I2 2015 2016


-.1

-.05

0

.05

.1

Estim

ate

2013 I1 2014 I2 2015 2016

Work on Saturday

Figure 6. Dynamic response to the reform

Notes: These graphs report the dynamic response to the reform concerning the decision to work on Wednesday,the decision to work part-time, days worked per week, hours worked per week, log real net hourly wages, andthe decision to work on Saturday. The coefficients are obtained from the estimation of regression 2 on the years2012-2016. We also report 95-percent confidence intervals. The estimation sample includes all mothers, aged18 to 55, whose youngest child is between six and fourteen, with the exception of those working in schools. Theimplementation dates "I1" and "I2" correspond to, respectively, the last quarter of 2013 and the last quarterof 2014.Source: French Labor Force Survey 2009-2016.

31

TREATMENT SEPT 2013

Placebo reform Jan 2013


Placebo reform March 2011


-.06 -.04 -.02 0 .02 .04

Estimate

Work part-time

TREATMENT SEPT 2013





-1 -.5 0 .5 1

Estimate


TREATMENT SEPT 2013





-.08 -.06 -.04 -.02 0 .02 .04 .06 .08

Estimate


TREATMENT SEPT 2013





-.04 -.03 -.02 -.01 0 .01 .02 .03 .04

Estimate


TREATMENT SEPT 2013





-.1 -.05 0 .05 .1

Estimate

No college degree College degree or more


Figure 7. Placebo reforms

Notes: The figure shows the impact of a series of placebo reforms on the decision to work part-time, hoursworked per week, days worked per week, and the log of real net hourly wages. In each graph, the first coefficientrefers to the impact of the 2013 reform, while the other estimates refer to the impact of, respectively, a placeboreform implemented at the beginning of 2013, one taking place in January 2012, one happening in March2011, and one in March 2010. In all but the last graph, the coefficients are obtained from the estimation ofregression 1. As for the last graph concerning the impact of the placebo reforms on hourly wages by educationallevel, the coefficients are obtained from the estimation of regression 1 on the entire sample, and interactingall regressors with the subgroups considered, except for municipality fixed effects. For each subgroup, wepresent the coefficient of the treatment interacted with the subgroup considered. In all graphs, we also report90-percent confidence intervals. The estimation sample includes all mothers, aged 18 to 55, whose youngestchild is between six and fourteen, with the exception of those working in schools. When estimating the impactof the placebo reforms, we exclude the actual treatment period from the estimation sample.Source: French Labor Force Survey 2009-2016.

32

6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-.06 -.04 -.02 0 .02 .04 .06

Estimate

Working on Wednesday

6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-.05 -.04 -.03 -.02 -.01 0 .01 .02

Estimate

Work part-time

6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-1 -.5 0 .5 1

Estimate


6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-.06 -.04 -.02 0 .02 .04 .06 .08

Estimate


6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-.04 -.03 -.02 -.01 0 .01 .02 .03 .04

Estimate


6-11 vs. 12-13

6-11 vs. 12-14

6-11 vs. 12-15

6-11 vs. 12-16

6-11 vs. 12-17

-.02 0 .02 .04 .06 .08

Estimate

No college degree College degree or more


Figure 8. Changing the definition of the control group

Notes: The figure reports the coefficients capturing the effect of the reform on the main outcomes of interest.In all but the last graph, the coefficients are obtained from the estimation of regression 1, where controlsinclude age and age square, marital status, number of children, a dummy for immigration status, municipalityand wave fixed effects, dummies for the level of education, and a dummy for the presence of other membersin the household. In each graph, the first coefficient is estimated on a sample that comprises only motherswhose youngest child is between six and thirteen years old. Then, we progressively enlarge the control group.Mothers working in schools are always excluded from the estimation sample. As for the last graph reportingthe impact of the reform on hourly wages by educational level, the coefficients are obtained from the estimationof regression 1 on the entire sample, and interacting all regressors with the subgroups considered, except formunicipality fixed effects. For each subgroup, we present the coefficient of the treatment interacted with thesubgroup considered. The sample restrictions are the same as in the other graphs. Finally, in all graphs, wereport 90-percent confidence intervals.Source: French Labor Force Survey 2009-2016.

33

Table 1 – Descriptive statistics of mothers’ characteristics by age of the youngest child

Youngest child aged between

0-1 2-5 6-11 12-14 15-18

Age 31.60 34.96 40.46 44.54 46.69(4.77) (5.17) (5.04) (4.40) (4.04)

Married 0.95 0.89 0.83 0.80 0.79(0.21) (0.31) (0.38) (0.40) (0.41)

Immigrant 0.08 0.09 0.09 0.09 0.09(0.27) (0.29) (0.29) (0.28) (0.28)

College degree or more 0.56 0.48 0.38 0.30 0.27(0.50) (0.50) (0.48) (0.46) (0.44)

No college degree 0.44 0.52 0.62 0.70 0.73(0.50) (0.50) (0.48) (0.46) (0.44)

Number of children 1.69 1.88 1.89 1.51 1.10(0.80) (0.81) (0.73) (0.58) (0.31)

Labor Force participation 0.63 0.79 0.86 0.87 0.85(0.48) (0.41) (0.35) (0.34) (0.35)

Hours worked per week 34.31 33.96 34.38 34.85 35.05(9.36) (10.19) (10.89) (11.28) (11.50)

Part-time work 0.35 0.37 0.36 0.34 0.32(0.48) (0.48) (0.48) (0.47) (0.47)

Days worked per week 4.61 4.63 4.70 4.78 4.79(0.88) (0.89) (0.90) (0.87) (0.90)

Work on Wednesday 0.51 0.57 0.59 0.67 0.69(0.50) (0.49) (0.49) (0.47) (0.46)

Work on Thursday 0.61 0.72 0.74 0.76 0.74(0.49) (0.45) (0.44) (0.43) (0.44)

Saturday 0.21 0.23 0.23 0.24 0.23(0.41) (0.42) (0.42) (0.42) (0.42)

Monthly wages (in Euros) 1,609 1,566 1,579 1,617 1,612(882) (927) (1,044) (1,107) (963)

N 27,132 51,981 65,630 31,043 24,771

Notes: The table presents summary statistics for mothers’ characteristics,computed for each age-interval of their youngest child living in the house-hold. The studied sample comprises all French mothers aged between 18and 55, and interviewed in the French Labor Force Survey before the im-plementation of the reform. Mothers working in schools are not includedwhen computing these figures.Source: French Labor Force Survey 2009-2013.

34

Tab

le2–

Labo

rsu

pply

resp

onse

toth

ere

form

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Labo

rforce

Part-tim

eHou

rsworked

Daysworked

Workon

Workon

Lognet

participation

perweek

perweek

Wednesday

Saturday

hourly

wages

Treatm

ent

0.00842

-0.0215∗∗

0.328

0.0404∗∗

0.0335∗∗∗

-0.0201∗∗

0.0151∗

(0.00621)

(0.00979)

(0.219)

(0.0191)

(0.00951)

(0.00890)

(0.00863)

Youn

gest

child

betw

een6-11

-0.015∗∗∗

0.0336∗∗∗

-0.676∗∗∗

-0.0904∗∗∗

-0.0687∗∗∗

-0.00340

0.0148∗∗

(0.0041)

(0.00688)

(0.159)

(0.0121)

(0.00921)

(0.00832)

(0.00583)

Observatio

ns175,528

133,979

133,979

133,979

61,816

61,816

43,012

R2

0.169

0.155

0.169

0.140

0.097

0.136

0.342

F38.81

19.77

24.38

7.840

22.35

19.85

112.0

Pre-treatm

entmean

0.85

0.36

34.4

4.7

0.59

0.23

11.5

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,ob

tained

from

theestim

ationof

regressio

n1.

The

diffe

rent

columns

referto

theou

tcom

econsidered.Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,nu

mbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesforthelevelo

fedu

catio

n,an

dadu

mmyforthe

presence

ofothermem

bers

intheho

usehold.

The

estim

ationsamplecomprise

sallm

others

who

seyoun

gest

child

isbe

tweensix

andfourteen

yearsold,

with

theexceptionof

thoseworking

inscho

ols.

Incolumns

2to

7,weon

lyconsider

mothers

who

are

employed

atthetim

eof

theinterview.The

samplesiz

efalls

incolumns

5an

d6,

asin

theFrench

Labo

rFo

rceSu

rvey

thedecisio

nto

workon

each

dayof

theweekis

measuredon

lyfrom

2013

onward.

The

samplesiz

efurthershrin

ksin

thelast

column,

asrespon

dentsrepo

rttheirmon

thly

wages

only

once

outof

thefiv

etim

estheirareinterviewed.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

35

Tab

le3–

Dai

lyla

bor

supp

lyre

spon

seto

the

refo

rm

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Mon

day

Tuesda

yWednesday

Thu

rsda

yFriday

Saturday

Sund

ay

Treatm

ent

-0.00188

0.00125

0.0335∗∗∗

0.00158

0.00073

-0.0201∗∗

-0.00533

(0.00875)

(0.00755)

(0.00951)

(0.00782)

(0.007

82)

(0.00890)

(0.00569)

Ygst

child

btw

6-11

0.0008

-0.0091

-0.0687∗∗∗

-0.0111∗

-0.00953

-0.00340

-0.00268

(0.00778)

(0.00661)

(0.00921)

(0.00675)

(0.006

96)

(0.00832)

(0.00548)

Observatio

ns61,816

61,816

61,816

61,816

61,816

61,816

61,816

R2

0.085

0.087

0.097

0.088

0.083

0.136

0.112

F20.38

35.92

22.35

30.82

28.27

19.85

5.536

Pre-treatm

entmean

0.70

0.77

0.59

0.75

0.75

0.23

0.09

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,obtainedfrom

theestim

ation

ofregressio

n1.

The

diffe

rent

columns

referto

theou

tcom

econsidered,c

orrespon

ding

tothedecisio

nto

workeach

specificda

yof

theweek.

Allregressio

nsinclud

eagean

dag

esqua

re,m

arita

lstatus,

numbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesforthelevel

ofeducation,

andadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

The

estim

ationsample

comprise

sallem

ployed

mothers

who

seyo

ungest

child

isbe

tween

sixan

dfourteen

yearsold,

with

the

exceptionof

thoseworking

inscho

ols.

Ast

heFrench

Labo

rForce

Survey

starts

includ

ingqu

estio

nson

the

allocatio

nof

working

timealon

gtheweekon

lyin

2013,the

sampleconsidered

here

only

comprise

swom

eninterviewed

betw

een2013

and2016.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

36

Tab

le4–

Labo

rsu

pply

resp

onse

toth

ere

form

bysu

bgro

up

Working

onWed

nesday

Hou

rswo

rked

perwe

ekLo

gne

tho

urly

wages

Estim

ate

Pre-treatmentmean

Estim

ate

Pre-treatmentmean

Estim

ate

Pre-treatmentmean(ine)

Pane

lA.E

ducatio

nallevel

Nocollege

degree

0.0252∗∗

0.59

-0.0277

33.26

0.0081

10(0.0123)

(0.289)

(0.0119)

College

degree

ormore

0.0427∗∗∗

0.58

0.840∗∗

36.28

0.0322∗

15(0.0156)

(0.361)

(0.0142)

P-value

diffe

rence

0.386

0.069

0.211

N61,816

133,979

43,012

Pane

lB.T

ypeof

occu

patio

nsNon

-man

agerialo

ccup

ations

0.0285∗∗∗

0.59

0.054

33.79

0.008

10.45

(0.009)

(0.238)

(0.008)

Man

agerialo

ccup

ations

0.0329

0.57

1.273∗∗

38.29

0.0266

19(0.0241)

(0.602)

(0.0210)

P-value

diffe

rence

0.999

0.070

0.41

N75,511

142,990

46,197

Not

es:The

tablerepo

rtstheim

pact

ofthereform

onlabo

rsupp

lydecisio

nsof

diffe

rent

subg

roup

s.To

cond

uctthis

analysis,

wec

hooset

oestim

atea

regressio

non

thee

ntire

sample,an

dinteract

allregressorsw

iththes

ubgrou

psconsidered,

except

form

unicipality

fixed

effects.O

therwise

,allregressio

nsinclud

ethe

stan

dard

covaria

tes,na

melyagea

ndages

quare,

marita

lstatus,

numbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesfor

thelevelo

fedu

catio

n,an

dadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

Foreach

subg

roup

,wepresent

thecoeffi

cientof

thetreatm

entinteracted

with

thesubg

roup

considered.Wealso

repo

rtthep-valueof

thetest

onthe

equa

lityof

theim

pact

ofthereform

across

thetw

osubg

roup

s.The

estim

ationsampleinclud

esallm

others,a

ged18

to55,w

hose

youn

gest

child

isbe

tweensix

andfourteen,w

iththeexceptionof

thoseworking

inscho

ols.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

37

Tab

le5–

Fath

ers’

labo

rsu

pply

resp

onse

toth

ere

form

(1)

(2)

(3)

(4)

(5)

(6)

Labo

rforce

Part-tim

eHou

rsworked

Daysworked

Workon

Workon

participation

perweek

perweek

Wednesday

Saturday

Treatm

ent

-0.00633

-0.00239

0.0247

0.00824

0.00861

-0.00175

(0.00395)

(0.00378)

(0.224)

(0.0135)

(0.00655)

(0.00866)

Youn

gest

child

betw

een6-11

-0.00427

0.00647∗∗∗

-0.498∗∗∗

-0.0142

-0.0225∗∗∗

0.0145∗

(0.00264)

(0.00242)

(0.160)

(0.00952)

(0.00610)

(0.00815)

Observatio

ns149,794

135,127

135,127

135,127

66,499

66,499

R2

0.101

0.111

0.175

0.140

0.085

0.112

F11.3

4.106

16.98

2.086

34.21

6.035

Pre-treatm

entmean

0.96

0.03

42.81

5.09

0.82

0.22

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

onfathers,ob

tained

from

theestim

ation

ofregressio

n1.

The

diffe

rent

columns

refert

otheou

tcom

econsidered,b

eing

,respe

ctively,labo

rforce

participation,

column1,

thedecisio

nto

workpa

rt-tim

e,column2,

numbe

rof

hoursworkedpe

rweek,

column3,

numbe

rof

days

workedpe

rweek,

column4,

anddecisio

nto

workon

Wednesday

andSa

turday,c

olum

ns5an

d6.

Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,nu

mbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

and

wavefix

edeff

ects,du

mmiesforthelevelof

education,

andadu

mmyforthepresence

ofothermem

bers

inthe

household.

The

estim

ationsamplecomprise

sallfathers

who

seyo

ungest

child

isbe

tweensix

andfourteen

years

old,

with

theexceptionof

thoseworking

inscho

ols.

Incolumn2to

6,werestric

tthesampleto

fatherswho

are

employed

atthetim

eof

theinterview.The

samplesiz

efurthershrin

ksin

columns

5an

d6,

asin

theFrench

Labo

rFo

rceSu

rvey

thedecisio

nto

workon

each

dayof

theweekis

measuredon

lyfrom

2013

onward.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

38

Tab

le6–

Dai

lyla

bor

supp

lyre

spon

seto

the

refo

rm-

Fath

ers

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Mon

day

Tuesda

yWednesday

Thu

rsda

yFriday

Saturday

Sund

ay

Treatm

ent

0.00346

0.000656

0.00861

0.00764

0.00564

-0.00175

0.00183

(0.00728)

(0.00637)

(0.00655)

(0.00677)

(0.00691)

(0.00866)

(0.00569)

Youn

gest

child

betw

een6-11

-0.0170∗∗∗

-0.0124∗∗

-0.0225∗∗∗

-0.0195∗∗∗

-0.0101∗

0.0145∗

0.00776

(0.00652)

(0.00548)

(0.00610)

(0.00580)

(0.00593)

(0.00815)

(0.00556)

Observatio

ns66,499

66,499

66,499

66,499

66,499

66,499

66,499

R2

0.082

0.089

0.085

0.088

0.088

0.112

0.120

F19.18

43.34

34.21

30.14

31.26

6.035

2.770

Pre-treatm

entmean

0.76

0.82

0.79

0.79

0.79

0.22

0.09

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

onfathers,

obtained

from

theestim

ation

ofregressio

n1.

The

diffe

rent

columns

referto

thedecisio

nto

workeach

specificda

yof

theweek.

Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,

numbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

and

wavefix

edeff

ects,du

mmiesforthelevelof

education,

andadu

mmyforthepresence

ofothermem

bers

inthe

household.

The

estim

ationsamplecomprise

sallfathers

who

seyoun

gest

child

isbe

tweensix

andfourteen

yearsold

who

areem

ployed

atthetim

eof

theinterview,w

iththeexceptionof

thoseworking

inscho

ols.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

39

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Cortes, Patricia, and Jessica Pan. 2016. “When Time Binds: Returns to Working Long Hoursand the Gender Wage Gap among the Highly Skilled.” Institute for the Study of Labor (IZA),IZA Discussion Papers 9846.

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42

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43

A AppendixA.1 Additional tables and figures – Institutional context

Parents

Grand-parents

Other childcare arrangements

0 10 20 30 40 50 60 70 80Percent

Childcare arrangementsWednesday 8am-7pm

Figure A.1. Childcare arrangements for children between 0 and 6 - 2002/2013

Notes: The figure shows the childcare arrangements families adopt prior to the introduction of the reform, totake care of their children when these are not in school on Wednesday. The sample comprises 8461 parentswith children aged 0 to 6 interviewed in 2002, 2007, and 2013 - prior to the introduction of the reform.Source: CNAF survey on childcare arrangements.

A1

T-test 1 % (***) T-test n.s

45

50

55

60

65

70

% o

f wom

en w

orkin

g on

Wed

nesd

ay

[W edu > M edu] [W edu ≤ M edu] [W edu > M edu] [W edu ≤ M edu]

W college degree or more W no college degreeSample: Working women whose youngest child is between 6-11 years old, excluding schoolpersonnel.Obs: College degree=5833, No college degree=7119

by type of householdMothers whose youngest child is 6-11

T-test n.s T-test 1 % (***)

45

50

55

60

65

70

% o

f wom

en w

orkin

g on

Wed

nesd

ay

[W edu > M edu] [W edu ≤ M edu] [W edu > M edu] [W edu ≤ M edu]

W college degree or more W no college degreeSample: Working women whose youngest child is between 12-14 years old, excluding schoolpersonnel.Obs: College degree=2296, No college degree=3866

by type of householdMothers whose youngest child is 12-14

Figure A.2. Proportion of women working on Wednesday by type of household -Pre-reform period

Notes: The figures report bar graphs representing the percentage of women working on Wednesday amongmothers whose youngest child is between six and eleven, at the top, and mothers whose youngest child isbetween twelve and fourteen, at the bottom. In each graph, we consider women with at least a collegedegree separately from those without college degree. Within each of these two groups, we compare womenwhose educational level is strictly higher than their partner’s, labelled "W edu > M edu", with women whoseeducational level is at most equal to their partner’s, called "W edu ≤ M edu". All figures refer to the pre-reform period, and we exclude mothers working in schools when computing them. On each bar, we also report95 percent-confidence intervals. Finally, for each educational level, we indicate the results of T-tests for thedifference in means between the two types of household.Source: French Labor force Survey 2009-2013.

A2

0

.2

.4

.6

.8

1

Shar

e of

fem

ale

wor

kers

400 650 900 1150 1400 1650 1900

Men's mean hours worked

Fitted line Craftsmen and small business

Managerial and professional occupations Intermediary occupationsEmployees Elementary occupations

Pre-reform period

Figure A.3. Women representation along the male hours distribution

Notes: The figure reports the relationship between the share of female workers and the average number ofhours worked by occupation (3-digit classification). The graph is constructed using a representative sample ofthe French matched-employer-employee data set for the period 2009-2012.Source: French matched-employer-employee database 2009-2012 (DADS).

A3

-.4

-.3

-.2

-.1

0

Res

idua

l gen

der g

ap

450 700 950 1200 1450 1700

Men's mean hours worked



Pre-reform period

Gender wage gap along the male hours distribution

-.4

-.3

-.2

-.1

0

Res

idua

l gen

der g

ap

8 9 10 11 12

Men's log mean wage



Pre-reform period

Gender wage gap along the male wage distribution

Figure A.4. Gender wage gap by occupation

Notes: The graph depicts the gender wage gap by occupation (3-digit classification). The top graph reportsthe relationship between the residual gender wage gap and the average number of hours worked by occupation.The bottom graph reports the relationship between the residual gender wage gap and (log) male average annualearnings by occupation. The residual gender wage gap corresponds to the female coefficient in a regression of(log) annual earnings on (log) annual hours worked, age, age squared, level of education and a female dummy,estimated separately for each 3-digit occupation. The graph is constructed using a representative sample ofthe French matched-employer-employee data set for the period 2009-2012.Source: French matched-employer-employee database 2009-2012 (DADS).

A4

25

30

35

40

45

Prop

ortio

n of

mot

hers

wor

king

par

t-tim

e

2009 2010 2011 2012 2013 A I1 2014 I2 2015 2016

Quarter


Working part-time

40

50

60

70

80

90

Prop

ortio

n of

mot

hers

2013 A I1 2014 I2 2015 2016

Quarter


Working on Thursday

0

10

20

30

Prop

ortio

n of

mot

hers

2013 A I1 2014 I2 2015 2016

Quarter


Working on Saturday

82

84

86

88

90

Prop

ortio

n of

act

ive

mot

hers

2009 2010 2011 2012 2013 A I1 2014 I2 2015 2016

Quarter


Labor force participation

Figure A.5. Trends in mothers’ labor supply measures by age of the youngest child

Notes: The graphs show the evolution of different labor supply measures over the period 2009-2016. Thesample includes all mothers aged 18-55 whose youngest child is between the age of six and fourteen, with theexception of those working in schools. We represent in red treated mothers, that is, those whose youngest childis between six and eleven years old. Mothers whose youngest child is of middle-school age, or control mothers,are represented in blue. The vertical bar named "A" corresponds to April 2013, when municipalities announcein which year they will introduce the reform. The bar called "I1" corresponds to September 2013, when 20percent of municipalities implement the reform. The bar labelled "I2" corresponds to September 2014, whenthe rest of municipalities implement the reform. Finally, we report 95-percent confidence intervals.Source: French Labor Force Survey 2009-2016.

A5

Table A.1 – Descriptive statistics - Youngest child between 6-11

No college N College degree N P-valuedegree or more T-test

Hours worked per week 33.26 40,491 36.28 24,625 0.00Part-time 38.52 42,936 32,07 24,625 0.00Days worked per week 4.74 40,491 4.63 24,625 0.00Work on Wednesday 59.33 9,043 58.23 6,927 0.16Work on Saturday 29.05 9,043 15.99 6,927 0.00Monthly wages 1,277 13,181 2,110 7,674 0.00

Non-managerial N Managerial N P-valueoccupations occupations T-test

Hours worked per week 33.70 55,179 38.3 9,894 0.00Days worked per week 4.7 55,179 4.66 9,894 0.24Part-time 37.72 55,179 26.94 9,894 0.00Work on Wednesday 59.23 13,211 57.27 2,716 0.06Work on Saturday 26.12 13,211 10.16 2,716 0.00Monthly wages 1,369 17,746 2,811 3,098 0.00

Low W High M N High W Low M N P-valueT-test

Hours worked per week 33.98 31,779 35.16 23,235 0.00Part-time 40.06 31,779 33.23 23,235 0.00Days worked per week 4.66 31,779 4.7 23,235 0.00Work on Wednesday 56.26 7,571 60.09 5,383 0.00Work on Saturday 24.25 7,571 22.16 5,383 0.00Monthly wages 1,553 10021 1,666 6560 0.00

Firm size ≤ 20 N Firm size >20 N P-value T-testT-test

Hours worked per week 34.86 12,824 34.29 52,292 0.00Part-time 35.17 12,824 36.3 52,292 0.02Days worked per week 4.78 12,824 4.68 52,292 0.00Work on Wednesday 60.34 3,577 58.42 12,393 0.00Work on Saturday 27.84 3,577 22.1 12,393 0.00Monthly wages 1,502 3,868 1,602 16,987 0.00

Public sector N Private sector N P-value


Notes: The table reports pre-reform summary statistics for mothers whose youngestchild is between six and eleven. The figures are reported separately for the sub-groups indicated on top of each table section. In the last column of the table,we report the p-value of the T-tests for the difference in means between the twosubgroups.

Source: French Labor Force Survey 2009-2013.

A6

Table A.2 – Descriptive statistics - Youngest child between 12-14

No college N College degree N P-valuedegree or more T-test

Hours worked per week 33.69 21,435 37.55 9,423 0.00Part-time 37.43 21,435 27.29 9,423 0.00Days worked per week 4.81 21,435 4.73 9,423 0.00Work on Wednesday 66.94 5,026 66.83 2,815 0.92Work on Saturday 28 5,026 15.59 2,815 0.00Monthly wages 1,322 6,938 2,344 2,864 0.00

Non-managerial N Managerial N P-valueoccupations occupations T-test

Hours worked per week 34.06 26,357 39.65 4,475 0.00Part-time 36.44 26,357 22 4,475 0.00Days worked per week 4.79 26,357 4.78 4,475 0.67Work on Wednesday 66.88 6,563 66.88 1,252 0.99Work on Saturday 25.93 6,563 11.01 1,252 0.00Monthly wages 1,396 8,412 2,979 1,384 0.00

Low W High M N High W Low M N P-valueT-test

Hours worked per week 34.49 15,167 35.60 8,931 0.00Part-time 38.66 15,167 32.32 8,931 0.00Days worked per week 4,77 15,167 4,78 8,931 0.25Work on Wednesday 65.84 3,793 68.63 2,371 0.02Work on Saturday 24.51 3,793 22.51 2,371 0.07Monthly wages 1,564 4,747 1,741 2,829 0.00

Firm size ≤ 20 N Firm size >20 N P-value T-testT-test


Public sector N Private sector N P-value


Notes: The table reports pre-reform summary statistics for mothers whose youngestchild is between twelve and fourteen. The figures are reported separately for thesubgroups indicated on top of each table section. In the last column of the table,we report the p-value of the T-tests for the difference in means between the twosubgroups.


A7

A.2 Alternative samples

Table A.3 – Labor supply response to the reform - Including school personnel

(1) (2) (3) (4)Labor force Part-time Hours worked Days workedparticipation per week per week

Treatment 0.00628 -0.0194∗∗ 0.344∗ 0.0401∗∗(0.00552) (0.00916) (0.208) (0.0178)

Youngest child between 6-11 -0.0144∗∗∗ 0.0351∗∗∗ -0.775∗∗∗ -0.0940∗∗∗(0.00380) (0.00642) (0.152) (0.0115)

Observations 193614 152052 152052 152052R2 0.162 0.143 0.149 0.131F 38.92 20.77 23.81 10.04Pre-treatment means 0.858 0.356 34.39 4.666

Notes: This table shows the coefficients capturing the effect of the reform, obtained fromthe estimation of regression 1. The different columns refer to the outcome considered,being respectively labor force participation, column 1, the decision to work part-time,column 2, number of hours worked per week, column 3, and number of days worked perweek, column 4. All regressions include age and age square, marital status, number ofchildren, a dummy for immigration status, municipality and wave fixed effects, dummiesfor the level of education, and a dummy for the presence of other members in thehousehold. The estimation sample comprises all mothers whose youngest child is betweensix and fourteen years old, including school personnel. In column 2, 3, and 4, we onlyconsider mothers who are employed at the time of the interview.*** Significant at the 1 percent level.** Significant at the 5 percent level.* Significant at the 10 percent level.


A8

Tab

leA

.4–

Dai

lyla

bor

supp

lyre

spon

seto

the

refo

rm-

Incl

udin

gsc

hool

pers

onne

l

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Mon

day

Tuesda

yWednesday

Thu

rsda

yFriday

Saturday

Sund

ay

Treatm

ent

-0.00196

0.000698

0.0328∗∗∗

0.000935

0.00229

-0.0147∗

-0.00273

(0.00792)

(0.00692)

(0.00882)

(0.00716)

(0.00719)

(0.00768)

(0.00491)

Ygst

child

btw

6-11

-0.000755

-0.00865

-0.0677∗∗∗

-0.00965

-0.00837

-0.00214

-0.00243

(0.00695)

(0.00603)

(0.00829)

(0.00607)

(0.00630)

(0.00716)

(0.00465)

Observatio

ns75684

75684

75684

75684

75684

75684

75684

R2

0.079

0.086

0.090

0.085

0.082

0.115

0.098

F23.49

45.93

32.02

37.31

36.67

19.42

5.030

Pre-treatm

entmeans

0.700

0.769

0.573

0.741

0.742

0.207

0.0761

Not

es:Thistableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,obtainedfrom

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ation

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n1.

The

diffe

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columns

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theou

tcom

econsidered,correspo

ndingto

thedecisio

nof

working

each

dayof

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eek.

Allregressio

nsinclud

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quare,marita

lstatus,nu

mbe

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adu

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unicipality

andwavefix

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The

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mothers

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seyoun

gest

child

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tweensix

andfourteen

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eof

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interview,including

scho

olpe

rson

nel.AstheFrench

Labo

rFo

rceSu

rvey

starts

includ

ingqu

estio

nson

the

allocatio

nof

working

timealon

gtheweekon

lyin

2013,the

sampleconsidered

here

only

comprise

swom

eninterviewed

betw

een2013

and2016.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

A9

Tab

leA

.5–

Labo

rsu

pply

resp

onse

toth

ere

form

-Y

oung

est

chil

dbe

twee

n2

and

11

(1)

(2)

(3)

(4)

(5)

Part-tim

eHou

rsworkedpe

rweek

Daysworkedpe

rweek

Workon

Wednesday

Workon

Saturday

Youn

gest

child

btw

2-11*P

ostSept13

-0.00916

0.138

0.0354∗∗∗

0.0288∗∗∗

-0.00605

(0.00686)

(0.148)

(0.0128)

(0.00656)

(0.00589)

Youn

gest

child

btw

2-11

0.0324∗∗∗

-0.644∗∗∗

-0.0710∗∗∗

-0.0512∗∗∗

-0.00276

(0.00475)

(0.112)

(0.00887)

(0.00648)

(0.00582)

Observatio

ns278352

278352

278352

130082

130082

R2

0.105

0.118

0.087

0.068

0.094

F41.27

44.89

21.01

62.25

47.51

Pre-treatm

entmeans

0.375

34.12

4.648

0.565

0.227

Source:French

Labo

rFo

rceSu

rvey

2009-2016.

Note:

this

Tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,obtainedfrom

theestim

ationof

regressio

n1.

The

diffe

rent

columns

refert

otheou

tcom

econsidered,b

eing

,respe

ctivelythedecisio

nto

workpa

rt-tim

e,nu

mbe

rofh

ours

perw

eek,

numbe

rofd

aysworkedpe

rweek,

anddecisio

nto

workon

Wednesday

andSa

turday.Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,nu

mbe

rof

child

ren,

adu

mmyfor

immigratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesforthelevelo

fedu

catio

n,an

dadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

The

estim

ationsamplecomprise

sallm

others

who

seyoun

gest

child

isbe

tweentw

oan

dfourteen

yearsold,

who

areem

ployed

atthetim

eof

theinterview,e

xcluding

scho

olpe

rson

nel

***p<

0.01,*

*p<

0.05,*

p<0.1.

A10

A.3 Alternative mechanisms

Table A.6 – Labor supply response to the reform - Tenure and training

(1) (2) (3)Tenure in the company Contract duration On the job training

Treatment 0.318∗ 0.120 0.0106(0.174) (0.134) (0.0069)

Youngest child between 6-11 -0.403∗∗∗ -0.161 -0.0022(0.129) (0.142) (0.0037)

Observation 132,824 10,433 133,979

R2 0.247 0.573 0.167

F 126.9 20.75 80.47

Pre-treatment mean 9.949 1.178 0.163

Notes: The table shows the coefficients capturing the effect of the reform, obtained from theestimation of regression 1 on tenure and training. The first column refer to the tenure in thecompany, the second to contract tenure, both measured in years, the last outcome measures on-the-job training. We present the results for the sample of all mothers, aged 18 to 55, employedat the time of the interview whose youngest child is between six and fourteen years old, withthe exception of those working in schools. Regressions include age and age square, maritalstatus, number of children, a dummy for immigration status, municipality and wave fixed effects,dummies for the level of education, and a dummy for the presence of other members in thehousehold.*** Significant at the 1 percent level.** Significant at the 5 percent level.* Significant at the 10 percent level.


A11

Tab

leA

.7–

Labo

rsu

pply

resp

onse

toth

ere

form

byed

ucat

iona

lle

vel

-T

enur

ean

dtr

aini

ng

Tenu

rein

thecompa

nyCon

tractdu

ratio

nOnthejobtraining

Estim

ate

Pre-treatmentmean

Estim

ate

Pre-treatmentmean

Estim

ate

Pre-treatmentmean

Nocollege

degree

0.462∗

9.421

0.033

1.153

-0.013

0.116

(0.245)

(0.119)

(0.0114)

College

degree

ormore

0.343

10.81

1.007

1.25

0.0405∗

0.239

(0.170)

(0.151)

(0.0015)

P-value

diffe

rence

0.373

0.251

0.0601

N132,822

10,433

133,979

Not

es:The

tablerepo

rtst

heim

pact

ofthereform

onlabo

rsup

plydecisio

nsof

diffe

rent

subg

roup

s.To

cond

uct

this

analysis,

wechoo

seto

estim

atearegressio

non

theentir

esample,

andinteract

allregressors

with

the

subg

roup

sconsidered,except

formun

icipality

fixed

effects.Otherwise

,allr

egressions

includ

ethestan

dard

covaria

tes,

namelyagean

dagesqua

re,m

arita

lstatus,

numbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,

mun

icipality

andwavefix

edeff

ects,d

ummiesfor

thelevelo

fedu

catio

n,an

dadu

mmyfort

hepresence

ofother

mem

bers

intheho

usehold.

Foreach

subg

roup

,wepresentthecoeffi

cientof

thetreatm

entinteracted

with

thesubg

roup

considered.Wealso

repo

rtthep-valueof

thetest

ontheequa

lityof

theim

pact

ofthereform

across

thetw

osubg

roup

s.The

estim

ationsampleinclud

esallm

others,a

ged18

to55,w

hose

youn

gest

child

isbe

tweensix

andfourteen,w

iththeexceptionof

thoseworking

inscho

ols.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

A12

Tab

leA

.8–

Labo

rsu

pply

resp

onse

toth

ere

form

-C

hang

ein

occu

pati

on

(1)

(2)

(3)

(4)

(5)

(6)

Farm

ers

Craftsm

enan

dMan

ageriala

ndInterm

ediary

Employees

Elem

entary

smallb

usiness

professio

nalo

ccup

ations

occupa

tions

occupa

tions

Treatm

ent

0.002

-0.007∗

-0.0006

0.006

0.00388

-0.005

(0.002)

(0.003)

(0.006)

(0.008)

(0.008)

(0.005)

Youn

gest

child

betw

een6-11

-0.0048∗∗∗

0.006∗∗∗

0.007∗

-0.002

-0.0014

-0.0052

(0.0014)

(0.0027)

(0.004)

(0.005)

(0.006)

(0.0037)

Observatio

n166,178

166,178

166,178

166,178

166,178

166,178

Pre-treatm

entmean

0.008

0.044

0.129

0.254

0.470

0.0913

Not

es:The

tablerepo

rtstheim

pact

ofthereform

onchan

gesin

occupa

tions.Ea

chou

tcom

ecorrespo

ndsto

adu

mmyvaria

ble

equa

ltoon

eifthemotherw

orks

intheoccupa

tion.

Wepresentt

heresults

fort

hesampleof

allm

others,a

ged18

to55,e

mployed

atthetim

eof

theinterview

who

seyoun

gest

child

isbe

tweensix

andfourteen

yearsold.

Regressions

includ

eagean

dagesqua

re,

marita

lstatus,

numbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesforthelevel

ofeducation,

andadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

***Sign

ificant

atthe1pe

rcentlevel.

**Sign

ificant

atthe5pe

rcentlevel.

*Sign

ificant

atthe10

percentlevel.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

A13

A.4 Multiple outcomes and subgroup analysis

Measuring the impact of the reform on multiple outcomes, as well as heterogeneous treatment

effects by subgroup can raise the probability of a Type I error. We take a number of steps to

ensure that our results are not just the result of data mining. We first present estimates of the

different outcomes with adjusted p-values to account for multiple hypothesis testing. We also

use modern machine learning tools and provide a non-standard approach to treatment hetero-

geneity building on recent applications in the context of randomized controlled experiments

(Davis and Heller 2017, Bertrand et al. 2017).

A.4.1 Multiple hypothesis testing

Table A.9 and Table A.10 present estimates of the effect of the reform on labor supply outcomes

obtained from the estimation of regression 1 for which we further provide adjusted p-values

to account for multiple hypothesis testing.

The method we use is the False Discovery Rate (FDR) control, or the expected proportion

of all rejections that are type-I errors, which involves a p-value adjustment less severe than

some other methods such as the Familywise Error Rate control or the Bonferroni correction, as

long as one is willing to tolerate some type-I error in exchange for a less stringent adjustment.

Specifically, we use the sharpened two-stage q-values introduced in Benjamini, Krieger and

Yekutieli (2006) and described in Anderson (2008).

A14

Tab

leA

.9–

Rob

ustn

ess

chec

ks-

P-v

alue

adju

sted

for

mul

tipl

ehy

poth

esis

test

ing

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Labo

rforce

Part-tim

eHou

rsworked

Daysworked

Workon

Workon

Lognet

participation

perweek

perweek

Wednesday

Saturday

hourly

wages

Treatm

ent

0.00842

-0.0215

0.328

0.0404

0.0335

-0.0201

0.0151

AdjustedP-

value

0.176

0.06

0.156

0.061

0.004

0.061

0.114

Observatio

ns175,528

133,979

133,979

133,979

61,816

61,816

43,012

R2

0.169

0.155

0.169

0.140

0.097

0.136

0.342

F38.81

19.77

24.38

7.840

22.35

19.85

112.0

Pre-treatm

entmean

0.85

0.36

34.4

4.7

0.59

0.23

11.5

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,ob

tained

from

theestim

ationof

regressio

n1.

The

diffe

rent

columns

referto

theou

tcom

econsidered

with

adjusted

p-values

toaccoun

tformultip

lehy

pothesis

testing.

Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,nu

mbe

rof

child

ren,

adu

mmyforim

migratio

nstatus,

mun

icipality

andwavefix

edeff

ects,d

ummiesforthelevelo

fedu

catio

n,an

dadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

The

estim

ationsamplecomprise

sallm

others

who

seyoun

gest

child

isbe

tweensix

andfourteen

years

old,

with

theexceptionof

thoseworking

inscho

ols.

Incolumns

2to

7,weon

lyconsider

mothers

who

areem

ployed

atthetim

eof

theinterview.The

samplesiz

efalls

incolumns

5an

d6,

asin

theFrench

Labo

rFo

rceSu

rvey

thedecisio

nto

workon

each

dayof

theweekismeasuredon

lyfrom

2013

onward.

The

samplesiz

efurthershrin

ksin

thelast

column,

asrespon

dentsrepo

rttheirmon

thly

wages

only

once

outof

thefiv

etim

estheirareinterviewed.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

A15

Tab

leA

.10–

Rob

ustn

ess

chec

ks-

P-v

alue

adju

sted

for

mul

tipl

ehy

poth

esis

test

ing

-D

aily

labo

rsu

pply

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Mon

day

Tuesda

yWednesday

Thu

rsda

yFriday

Saturday

Sund

ay

Treatm

ent

-0.00188

0.00125

0.0335

0.00158

0.00073

-0.0201

-0.00533

AdjustedP-

value

0.926

0.926

0.004

0.926

0.926

0.084

0.815

Observatio

ns61,816

61,816

61,816

61,816

61,816

61,816

61,816

R2

0.085

0.087

0.097

0.088

0.083

0.136

0.112

F20.38

35.92

22.35

30.82

28.27

19.85

5.536

Pre-treatm

entmean

0.70

0.77

0.59

0.75

0.75

0.23

0.09

Not

es:The

tableshow

sthecoeffi

cients

capturingtheeff

ectof

thereform

,ob

tained

from

theesti-

mationof

regressio

n1.

The

diffe

rent

columns

referto

theou

tcom

econsidered,c

orrespon

ding

tothe

decisio

nto

workeach

specificda

yof

theweek,

with

adjusted

p-values

toaccoun

tfor

multip

lehy

poth-

esistesting.

Allregressio

nsinclud

eagean

dagesqua

re,m

arita

lstatus,nu

mbe

rofc

hildren,

adu

mmy

forim

migratio

nstatus,m

unicipality

andwavefix

edeff

ects,d

ummiesforthelevelo

fedu

catio

n,an

dadu

mmyforthepresence

ofothermem

bers

intheho

usehold.

The

estim

ationsamplecomprise

sall

employed

mothers

who

seyoun

gest

child

isbe

tweensix

andfourteen

yearsold,

with

theexception

ofthoseworking

inscho

ols.

AstheFrench

Labo

rFo

rceSu

rvey

starts

includ

ingqu

estio

nson

the

allocatio

nof

working

timealon

gtheweekon

lyin

2013,t

hesampleconsidered

here

only

comprise

swom

eninterviewed

betw

een2013

and2016.

Sour

ce:French

Labo

rFo

rceSu

rvey

2009-2016.

A16

A.4.2 Subgroup analysis using machine learning

The goal of this analysis is to confirm differences in predicted impacts of the reform across

occupations and educational levels. We build upon recent applications of machine learning

techniques in the context of randomized control trial studies (Davis and Heller 2017, Bertrand

et al. 2017) to go one step further in analyzing heterogeneity in the treatment effect of the

reform. We follow the causal forest algorithm of Athey and Imbens (2016) and Wager and

Athey (2018) in order to identify expected impact of the reform conditional on a set of co-

variates.36 Causal forest can be particularly useful, relative to some other machine learning

algorithms, such as a lasso, because it allows for non-linearities and automatic detection of

interactions.

We follow Bertrand et al. (2017) and set the parameters as displayed in Table A.13. We

apply our model on the sample of mothers whose youngest child is between 6 and 14, who are

employed at the time of the interview, and for whom wages are reported, with non-missing

values for baseline covariates and outcomes of interest (N=21,561). Given our sample size,

we choose α = 50% for the share of the sample used to construct the model (the training

sample) and the one used for inference (the test sample). We adapt the algorithm so that the

determination of the training sample is stratified by our treatment variable and by municipality

(treatment*municipality). Features included in the model are presented in Table A.14.

The general idea is that we first use the model in order to predict a women’s expected

treatment effect for each outcome based on her covariates. Following the methodology applied

by Davis and Heller (2017) and Bertrand et al. (2017), we then investigate whether predictions

of the model do capture treatment heterogeneity in our data. We create a dummy variable

equal to one if the mother has a predicted treatment effect on labor market outcome in the top

50% or the bottom 50% of predictions. We then compare the sociodemographic characteristics

of treated mothers in the top and the bottom 50% of the distribution of predicted effect, and

we see which dimension stands out. Therefore the descriptive statistics are computed on the36We use the R function causal_forest from the packages causalTree, randomForestCI, hte and

ElasticSynth (Athey and Imbens 2016, Wager and Athey 2018).

A17

restricted sample of mothers whose youngest child is between 6 and 11.

Results of this balancing test for the conditional average treatment effect on part-time rate

and the log real net hourly wage are presented in Table A.11 and Table A.12 respectively. We

provide P-value adjusted for multiple hypothesis testing. Note that for Table A.11, given that

the impact of the reform on the probability of working part-time is negative, belonging to the

bottom 50% of the effects means experiencing the highest decrease. Overall, these results are

consistent with the heterogenous effects described in Section 3. The share of mothers with at

least a college degree is significantly higher in the bottom 50% of the distribution of predicted

conditional effects on part-time (higher effects) than in the top 50%. We observe the reversed

pattern for high school graduates: they are less likely to be part of the group most affected by

the reform. Single women are less likely to experience a high decrease in part-time rate as well,

although they work on average more hours than married mothers in the baseline. Finally, we

do not observe sharp geographic differences across these groups: the share of mothers living in

cities located in urban areas, or where the reform was implemented in 2013 rather than 2014n

does not differ significantly between the two groups.

Turning to the impact on hourly wage in Table A.12, we observe again that mothers with

at least a college degree are significantly more represented in the top 50% of the distribution

of predicted conditional effects on hourly wage (higher effects) than in the bottom 50%. We

observe another pattern of differences across occupations: women working in managerial occu-

pations and intermediary occupations are more likely to be in the top 50% of the distribution

of predicted conditional effects on hourly wage, while employees and elementary occupations

are overrepresented at the bottom 50% of the conditional average treatment effects.

Overall, this approach confirms qualitatively the patterns of heterogeneity we observed by

educational levels and across occupations.

A18

Table A.11 – Conditional Average Treatment Effect - Part-time

Bottom 50% Top 50% Difference P-valueof predicted effects of predicted effects

Age 41.21 40.54 -0.668 0.001College degree or more 0.665 0.283 -0.382 0.001High school graduates 0.261 0.564 0.303 0.001Single 0.040 0.171 0.131 0.001Immigrant 0.123 0.073 -0.050 0.001Farmers 0.002 0.000 -0.002 0.137Craftsmen, small business 0.000 0.000 0.000 0.397Managerial occupations 0.003 0.003 -0.000 0.869Intermediary occupations 0.369 0.031 -0.338 0.001Employees 0.247 0.246 -0.001 0.973Elementary occupations 0.285 0.615 0.330 0.001Reform in 2013 0.289 0.290 0.000 0.973Urban area 0.683 0.739 0.056 0.001

N 2,091 2,091 Total for estimation = 21,561

Notes: The table shows the descriptive statistics of treated mothers’ characteristics according to thepredicted effect the reform has on the probability of working part-time. The conditional averagetreatment effect is computed using the R function causal_forest (Athey and Imbens 2016, Wagerand Athey 2018). The estimation sample comprises mothers whose youngest child is between 6 and14, who are employed at the time of the interview, and for whom wages are reported, with non-missingvalues for baseline covariates and outcomes of interest. Parameters and features of the model arepresented in Table A.13 and Table A.14 respectively. The descriptive statistics are then computed onthe restricted sample of mothers whose youngest child is between 6 and 11. We report the P-value ofthe T-test adjusted for multiple hypothesis testing. Note that given that the effect on the probabilityof working part-time is negative, belonging to the bottom 50% of the effects means experiencing thehighest decrease.


A19

Table A.12 – Conditional Average Treatment Effect - Log real hourly wage

Bottom 50% Top 50% Difference P-valueof predicted effects of predicted effects

Age 41.04 40.72 -0.317 0.063College degree or more 0.311 0.637 0.327 0.001High school graduates 0.542 0.283 -0.259 0.001Single 0.090 0.120 0.030 0.004Immigrant 0.112 0.084 -0.028 0.005Farmers 0.000 0.002 0.002 0.128Craftsmen, small business 0.000 0.000 0.000 0.353Managerial occupations 0.001 0.005 0.004 0.021Intermediary occupations 0.028 0.372 0.343 0.001Employees 0.298 0.196 -0.102 0.001Elementary occupations 0.604 0.296 -0.308 0.001Reform in 2013 0.302 0.277 -0.025 0.095Urban area 0.721 0.701 -0.020 0.191

N 2,091 2,091 Total for estimation = 21,561

Notes: The table shows the descriptive statistics of treated mothers’ characteristics according tothe predicted effect the reform has on their hourly wage. The conditional average treatment effectis computed using the R function causal_forest (Athey and Imbens 2016, Wager and Athey2018). The estimation sample comprises mothers whose youngest child is between 6 and 14, who areemployed at the time of the interview, and for whom wages are reported, with non-missing values forbaseline covariates and outcomes of interest. Parameters and features of the model are presented inTable A.13 and Table A.14 respectively. The descriptive statistics are then computed on the restrictedsample of mothers whose youngest child is between 6 and 11. We report the P-value of the T-testadjusted for multiple hypothesis testing.


Table A.13 – Parameters for Causal Forest

Parameter ValueNumber of treesin the forest 10,000B

Minimum numberof treatment and control 10units per leafFraction of the sample used tobuild each tree 0.5β

Fraction of the subsampleused for training 0.5δ

A20

Table A.14 – Features for Causal Forest

Variable Type

Age ContinuousAge square ContinuousMarital status BinaryNumber of children (2, 3 or more) BinaryImmigration status BinaryMunicipality fixed effects BinaryWave on interview fixed effects BinaryLevel of education (3 categories) BinaryType of occupations (6 categories) BinaryPresence of other young members in the household BinaryPresence of other older members in the household BinaryUrban area Binary

A21

A.5 Visualisation of the impact of the reformh∗1

∆w(ei)

1

0

s′

s

B B′

Share bunching under s

Share bunching under s′

This diagram plots the relationship between a change in the time the child spends at school

s and period 1’s optimal labor supply according to the mother’s level of education. ∆w is a

mapping of ei (continuous and increasing) therefore ∆w is rank-preserving of ei. B represents

the mother with the lowest level of education ei who is working s rather than her optimal h∗1 in

the first period. With the reform, the constraint moves from s to s′. This shift translate into

B→B′: the level of education of the least educated mother working s′ rather than her optimal

h∗1 in the first period has increased. The line in blue represents the share of mothers who were

bunching under s and who can work their optimal h∗1 under s′. We can then characterize the

welfare gains associated to the reform according to mothers’ level of education.

Welfare gains The gain in welfare can be characterized by:37

WG= (B′−B) dh∗1

d∆w[V1(h∗1)−V1(s)]︸︷︷︸

Mothers bunching under s

+ (1−B′) dh∗1

d∆w[V1(s′)−V1(s)]︸︷︷︸

Remaining bunchers under s′

where V1(.) is the indirect utility function in period 1.37Again here we do not make any assumption on the value the mother attributes to the time spent with her

child.

A22

A.6 Proofs of the theoretical model

A.6.1 Optimal labor supply

The maximization problem in period 2 is straightforward. Given optimal labor supply in

period 2 (h∗2 = α), we can substitute period 2’s indirect utility functions into the maximization

problem of period 1. Recall that the two indirect utility functions in period 2 for state H and

state L write:

V2(wH2 ,α) = α log(wH2 ) +α log(α) + (1−α) log(1−α)

V2(wL2 ,α) = α log(wL2 ) +α log(α) + (1−α) log(1−α)

Substituting the constraints into the expression, the problem writes:

α log(h1w1) + (1−α) log(1−h1) + β[f(h1)V H2 + (1− f(h1))V L

2 ]

We differentiate with respect to h1

∂

∂h1= 0⇐⇒ α

h1− 1−α

1−h1+ βV H

2 − βV L2 = 0

Rearranging this expression, we find:

α+h1(−1 + βV H2 − βV L

2 ) +h21(−βV H

2 + βV L2 ) = 0 (5)

For simplicity, let’s write:

V H2 −V L

2 = α log(wH2 )−α log(wL2 ) = α log(wH2wL2

)= αK

By construction, K is strictly positive. We can compare the optimal labor supply across the

two periods, as shown in (3). The optimal labor supply in period 1, h∗1, solves

h1 = α+ βαKh1− βαKh21︸︷︷︸

A23

which incorporates future gains in earning due to promotion. We can rewrite (5) as a polyno-

mial of h1 and solve it:

α+ (βαK − 1)h1− βαKh21 = 0 (6)

∆ = β2α2K2 + 1 + (4α− 2)βαK

For 1> α > 0 and 1> β > 0 , ∆> 0 and the system (6) has two solutions:

h′∗1 = 1−βαK+

√β2α2K2+1+(4α−2)βαK−2βαK

h′′∗1 = 1−βαK−

√β2α2K2+1+(4α−2)βαK−2βαK

(7)

h′′∗1 is the only positive root. Moreover, limK→+∞h

′′∗1 = 1, therefore h′′∗1 is the interior solution

to the maximization problem in period 1.

A.6.2 Comparative statics

Assuming β > 0 and α > 0, we can rewrite h∗1 to derive some comparative statics.

h∗1 = 12 −

12βαK +

√β2α2K2 + 1 + (4α− 2)βαK

2βαK︸︷︷︸A

A24

dh∗1dK = 1

2βαK2 +A′

A′ =2βαK2√∆

[2β2α2K+(4α−2)βα]−2βα√∆

(2βαK)2

= 2βαK+(4α−2)4K√∆

−√∆

2βαK2

= K2β2α2+(2α−1)βαK−∆2β2α2K

√∆

= −1−βαK(2α−1)2β2α2K

√∆

dh∗1dK = 1

2βαK2 − 1+βαK(2α−1)2β2α2K

√∆

=√∆−1−βαK(2α−1)

2β2α2K√∆

Given that

2β2α2K√∆> 0

for β > 0 and α > 0, then

dh∗1dK

> 0⇔ g(K) =√∆− 1− βαK(2α− 1)> 0

which is true for K > 0, β > 0 and α > 0.

As ∆w is the exponential transformation of K, we can write:

dh∗1d∆w

> 0

The problem is symmetric for dh∗1dβ .

A25

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