Turning back the clock: Beliefs about gender roles during lockdown

We study the impact of lockdown measures on beliefs about gender roles. We collect data from a representative sample of 1,000 individuals in France during the first COVID-19 lockdown in 2020. To measure beliefs about gender roles, we use questions from the 2018 wave of the European Values Study, and match respondents from the two surveys to compare beliefs before and during lockdown. We find evidence that the lockdown period was associated with a shift towards more traditional beliefs about gender roles. The effects are concentrated among men from the most time-constrained households and from households where bargaining with a partner over sharing responsibility for household production was likely to be an issue. Finally, we find evidence that beliefs about gender equality may be a luxury good: beliefs in equal gender roles increase with household income. Overall, our results suggest that men are more likely to hold egalitarian beliefs about gender roles when these beliefs are not costly for them


Introduction
Families' ability to outsource household production has been one of the driving factors behind women's increased participation in the labor market (Goldin, 2006).It is also associated with beliefs in more equal gender roles.1 Throughout Europe, the share of individuals who agree with statements such as "When a mother works for pay, the children suffer" and "A job is alright but what most women really want is a home and children" has decreased since the European Values Study (EVS) first measured beliefs about gender roles in 1990 (Figure 1).In countries where enrolment rates in early childhood education and care services are higher (Figure 2) and the employment rates of mothers are higher (Figure 3), more individuals tend to believe in equal gender roles.
The COVID-19 crisis reversed families' ability to outsource household production, especially in the first months of the crisis.In early 2020, many governments implemented lockdown measures, which generally involved the closing of child care facilities and schools.For many households, these lockdown measures meant an increase in household production constraints.Research conducted in France (Champeaux and Marchetta, 2021;Ducoudré and Périvier, 2020), Italy (Biroli et al., 2021;Del Boca et al., 2020;Mangiavacchi et al., 2021), Spain (Farré et al., 2020), the United Kingdom (Sevilla and Smith, 2020;Hupkau and Petrongolo, 2020;Golin, 2021), and the United States (Biroli et al., 2021;Carlson et al., 2021) finds that lockdown measures significantly increased the constraints on households with young children, and that women took responsibility for the largest share of parental care, often by taking time off work (Albanesi and Kim, 2021;Alon et al., 2020aAlon et al., ,b, 2021)).
Did the reversal in families' ability to outsource household production also lead to a reversal in beliefs about gender roles?Previous research has found that men and women tend to support more equal gender roles when household production constraints are removed (Pedulla and Thébaud, 2015).But what happens to men's and women's beliefs about gender roles when household production constraints are reinstated?In this paper, we study whether beliefs in gender equality are entrenched once acquired or whether they can be reversed.We study two channels through which the lockdown measures could have impacted beliefs about gender roles.The first channel relates to the increased time constraints that some households faced during lockdown.The lockdown measures were an exogenous shock on households' ability to outsource household production, as well as on individuals' ability to work.Depending on the industry and occupation of partners, households differed in their availability for parental care: parents could be working from home, temporarily unemployed or still working outside the home if their employment was in a critical sector.If there is a relationship between the ability to outsource household production and individuals' beliefs about gender roles, then individuals from the most time-constrained households-households with young children and households where the partners were still working during lockdown-would be more likely to revert to traditional beliefs about gender roles during lockdown.
The second channel we explore relates to bargaining within couples over who should take care of the extra household production constraints during lockdown.Previous research has suggested that the work-related constraints of each partner are a determinant of who takes care of household production (Presser, 1994).According to the available time theory of household division of labor (Presser, 1994), the partner who is the least constrained by work is generally the one who spends the most time on household production.However, in households where both partners continued to work during lockdown, there was not always one partner who could "naturally" take care of the extra household production constraints.If there is a relationship between bargaining over who takes care of household production and individuals' beliefs about gender roles, then individuals from households where partners had to bargain-that is, households where both partners either worked from home or worked outside the home during lockdown-would be more likely to revert to traditional beliefs about gender roles.Indeed, beliefs in traditional gender roles can serve as a focal-point equilibrium in a noncooperative bargaining game between partners (Lundberg andPollak, 1993, 1996).
We study changes in beliefs about gender roles using data from a survey we designed during the first lockdown period in France, and that a survey institute conducted on a representative sample of 1,000 individuals from the French working population.We measure beliefs about gender roles by asking respondents about their opinions on six statements from the EVS. 2 We examine changes in beliefs about gender roles by combining responses to our survey with the responses of individuals from the latest wave of the EVS for France. 3We perform a Nearest-Neighbor Match on respondents' observable characteristics from both surveys to estimate how the respondents to our survey would have likely responded before lockdown to the EVS questions about gender roles.
We then use the predicted values to estimate changes in beliefs during lockdown.
We find empirical evidence of a shift in beliefs towards traditional gender roles during the first lockdown period.This shift is concentrated among fathers of young children (12 years old or under).
For instance, we find a significant increase in the percentage of men with young children who agree with the statement "A man's job is to earn money; a woman's job is to look after the home and family" (15.1 percentage point increase) and "All in all, family life suffers when the woman has a fulltime job" (14.2 p.p. increase).This result is consistent with a time-constraint channel, although only for men.
We then focus our analysis on opposite-sex couples with young children living in the household.
Consistent with the available time theory (Presser, 1994), when men were relatively more available at home than their female partner, they took responsibility for the largest share of the increase in household production. 4When women were relatively more available at home than their male partner, they took responsibility for the largest share of the increase in household production.
When both partners were equally available, they shared responsibility for the increase in household production.We find evidence that the shift in beliefs towards more traditional gender roles is concentrated among men from this third group.That is, we find that men were more likely to declare believing in traditional gender roles during lockdown when both partners were either working from home or still working outside the home.This result suggests that some men believe in less equal gender roles when a conflict may occur over who should take responsibility for household production.This result points to a role of gender norms in marital bargaining, as described in the seminal model by Lundberg andPollak (1993, 1996).
Why might men be more likely than women to shift their beliefs towards traditional gender roles when household production constraints increase?Beliefs about equal gender roles may be guided by motivated reasoning (Epley and Gilovich, 2016).When public policies remove household production constraints, holding gender equal beliefs is not costly for men.But when public policies reinstate household production constraints, holding gender equal beliefs can become costly for men.Some men may then shift beliefs towards more traditional gender roles to avoid taking more responsibility for household production.This interpretation is consistent with research that shows that women have stronger preferences for equally sharing household production responsibilities when the couple has a young child (Auspurg et al., 2017).In previous research, Pedulla and Thébaud (2015) also found that women's support for equal gender roles tends to be more elastic than men's to the removal of household production constraints.Our results suggest that men's beliefs in traditional gender roles are more elastic than women's when household production constraints increase.This interpretation of our results suggests that beliefs in gender equality may be a luxury good.
As household income increases, households can outsource household production more easily, which could lead to increased beliefs in equal gender roles.We examine this luxury good hypothesis by using cross-country European data from the latest wave of the EVS (pre-pandemic) to estimate the relationship between household income and beliefs about gender roles.Our results are consistent with egalitarian beliefs about gender roles being a luxury good: throughout Europe, both men and women are more likely to believe in equal gender roles as they move up the income distribution.
We also find that women tend to believe in more equal gender roles than men across the entire income distribution.
The paper is structured as follows.Section 2 describes the data, including information on how we match respondents of the Lockdown and the EVS datasets.Section 3 provides descriptive evidence on beliefs about gender roles and household production constraints.Section 4 presents the results of our estimates of changes in beliefs about gender roles during lockdown, which can be related to household production constraints.Section 5 discusses our results by studying the relationship between beliefs about gender roles and income.Section 6 presents results of robustness checks.Section 7 concludes.

Fitted values
Source: The data for beliefs about gender roles are from the fifth wave (2017) of the EVS (EVS, 2020).The data for enrolment rates are from the OECD Family Database, and are for 2017 or the latest year available.The OECD defines these enrolment rates as the "percent of children enrolled in early childhood education and care services (ISCED 0 and other registered ECEC services), 0-to 2-year-old".The EVS data are available at https: //europeanvaluesstudy.eu/methodology-data-documentation/survey-2017/.The OECD data are available at https://www.oecd.org/els/family/database.htm, Table PF3.2.
Notes: This figure presents the correlation between the percentage of individuals who agree or strongly agree with the statement "a man's job is to earn money; a woman's job is to look after home and family" and the enrolment rates in early childhood education and care services in European countries.The value of the Pearson correlation is 0.86 and is significant at the 1% level.Source: The data for beliefs about gender roles are from the fifth wave of the EVS (EVS, 2020).The data for maternal employment rates are from the OECD Family Database, and are for 2019 or the latest year available.The OECD defines maternal employment rates as employment rates for women (15-64 year olds) with at least one child aged 0-14, who are working full-time or part-time.The EVS data are available at https://europeanvaluesstudy.eu/ methodology-data-documentation/survey-2017/.The OECD data are available at https://www.oecd.org/els/family/database.htm,Table LMF1.2.Notes: This figure presents the correlation between the percentage of individuals who agree or strongly agree with the statement "a man's job is to earn money; a woman's job is to look after home and family" and maternal employment rates in European countries.The value of the Pearson correlation is 0.51 and is significant at the 5% level.

Data
In this section, we describe the datasets that we combine to perform our analysis.The first dataset is the "Lockdown survey", which includes information from the survey that we designed and that IPSOS, a survey agency, conducted on a representative sample of 1,000 working individuals in France during the first lockdown period, between May 4th and May 8th, 2020. 5The second dataset is the "EVS survey", which includes data from the fifth wave of the EVS for France, from 2018.We then describe how we match respondents of both surveys to build the dataset for our examination of changes in beliefs about gender roles during lockdown.
When the first lockdown in France occurred on March 17th, 2020, all Lockdown survey respondents were at least 18 years old and were either employed or independent workers.The survey agency applied a quota sampling method to ensure that the respondents were representative of the French population, based on gender, age, professional activity, as well as the region and the type of environment (rural or urban) where the respondent lived at the time of the survey.6Since time constraints were an issue during lockdown, we opted for a short, ten-minute, online survey.
The Lockdown survey includes questions from the EVS (2020) to measure respondents' beliefs about gender roles.The EVS dataset for France includes information collected between March 3rd and August 16th, 2018, two years before the first COVID-19 lockdown.We kept the same format as the EVS questions, asking respondents whether they strongly agree, agree, disagree, or strongly disagree with six statements about gender roles, which we describe in Section 3.1.For each statement measuring beliefs about gender roles, we construct a binary variable equal to one if the respondent answered either agree or strongly agree, and zero if the respondent answered either disagree or strongly disagree.These six measures of beliefs are the main dependent variables of our analysis.
After collecting the responses for each statement during lockdown, we match respondents from our survey with respondents from the EVS.Because we do not have panel data to measure within respondent variations in beliefs regarding gender roles before and during lockdown, we conduct a Nearest-Neighbor Match to estimate the Lockdown survey respondents' beliefs before lockdown.
To have a matching set of respondents, we selected the 871 individuals in France from the EVS who were at least 18 years old and employed when they answered the survey in 2018.
Table 1 provides descriptive statistics for the variables that we use from both surveys to conduct the matching exercise.The two datasets include information on respondents: gender, age, education, marital status, number and age of children, and geographic location. 7For respondents with partners (67% in the Lockdown dataset and 57% in the EVS dataset), we also have information on their partner's employment. 8In the Lockdown dataset, we use the information about the employment status of the respondent's partner before lockdown for our matching exercise.This is an important variable, because it likely reflects prior beliefs about gender roles.For instance, the wife of a male respondent who believes in traditional gender roles is more likely to be a housewife.
The employment status of partners is roughly the same in the EVS dataset as in the Lockdown dataset.
The characteristics of respondents in the EVS survey are generally similar to the ones of the Lockdown survey.The main difference between the two datasets relates to education: respondents from the Lockdown survey have higher education on average than respondents from the EVS survey.The matching exercise takes into account such differences.We predict the Lockdown survey respondents' beliefs before lockdown by conducting a Nearest-Neighbor Match with Mahalanobis distances on the following characteristics: age, education category, marital status, the region the respondent lives in, the number of children living in the household, and the employment status of the partner before lockdown.We conduct an exact match on whether the respondent is female and whether the respondent has a child who is 12 years old or under living in the household.
We use the predicted values from the matching exercise to construct the outcome variable on beliefs before lockdown for the Lockdown respondents. 9We describe the results of our predictions in Section 3.1.The precision of the predictions relies crucially on the quality of the match.In Section 6, we present the results of alternative matching strategies; they suggest that our predicted values are within bounds.In particular, we calculate average treatment effects (ATE) using different matching characteristics, and also using Euclidean distances.We find that the ATE remain stable in terms of both significance and magnitude across different matching alternatives.Notes: In the EVS, we selected the 871 individuals who had a professional activity when they were surveyed, to match the sample from the Lockdown survey.The "Other" category in marital status includes individuals who are either separated, divorced or widowed.The "Other" category in the partner's employment status includes individuals who are retired, housewives or househusbands, students, unemployed and searching or not searching for a job.
The "Number of children" variable only takes into account respondents who have at least one child living in the household (18 or younger).The "Higher education" variable includes individuals who have at least a Bachelor's degree (in France, a degree validating three years of higher education).

Descriptive evidence
We describe the main outcome variables of our analysis in Section 3.1.In Section 3.2, we describe the variables we use to measure the impact of lockdown on household production constraints.

Measures of beliefs about gender roles
We interpret agreement with any of the six statements reported in Table 2 as representing beliefs in more traditional gender roles.
Statements ( 1) and ( 2) can be associated with a belief in traditional gender roles for women: "When a mother works for pay, the children suffer" and "All in all, family life suffers when the woman has a fulltime job".About one out of four men and women agree with these statements during lockdown (Table 2).Compared to our estimates of beliefs before lockdown (from the Nearest-Neighbor Match), we observe an increase in the percentage of both men and women who agree with the first statement (8 p.p. for men, and 3 p.p. for women).We also observe a small increase for the second statement for men (4 p.p.), and a decrease for women (3 p.p.).10

Statement (3) measures respondents' beliefs regarding gender norms: "A job is alright but
what most women really want is a home and children".This statement measures whether the respondent believes that women in general have a preference for traditional gender roles.It is therefore a measure of second-order beliefs: it measures what the respondent believes that other people believe, that is, gender norms.Research suggests that beliefs in gender norms have an impact on individuals' behaviors regarding gender equality in the household and women's participation in the labor market (Bursztyn et al., 2020).Our descriptive statistics suggest that the lockdown period is not significantly associated with a change in individuals' second-order beliefs: 28% of women agree with the statement before lockdown compared to 25% during lockdown, whereas 26% of men agree with the statement before lockdown compared to 28% during lockdown.
Statement (4) measures the extent to which individuals associate both men and women with traditional gender roles: "A man's job is to earn money; a woman's job is to look after the home and family".We observe an increase in the percentage of men who agree with this statement: from 8% before lockdown to 16% during lockdown.We observe a smaller increase for women, from 7% to 11%.The difference between men and women during lockdown is statistically significant.Notes: This table shows descriptive statistics for the main outcome variables, which are binary variables equal to one if response is "Agree" or "Strongly Agree" for each statement.
Statements are (1) Kids: "When a mother works for pay, the children suffer".(2) Family: "All in all, family life suffers when the woman has a fulltime job".(3) Home: "A job is alright but what most women really want is a home and children".(4) Money: "A man's job is to earn money; a woman's job is to look after the home and family".(5) Politics: "On the whole, men make better political leaders than women do".(6) Business: "On the whole, men make better business executives than women do".Finally, statements ( 5) and ( 6) suggest that men have a comparative advantage for activities related to economic and political leadership: "On the whole, men make better political leaders than women do" and "On the whole, men make better business executives than women do".Our descriptive statistics suggest a strong increase in the percentage of men (but not women) who agree with these two statements.Before lockdown, our estimates suggest that 7% of male respondents agree with both statements.During lockdown, 17% of men agree with both statements.
Overall, we do not observe a polarization of beliefs.Instead, we observe a shift in the distribution of answers, with fewer individuals strongly disagreeing and more individuals agreeing with the statements during lockdown (see Figure A1 in the Appendix).
Among the six statements, two have been asked by the EVS over several waves: "When a mother works for pay, the children suffer" (statement (1)) and "A job is alright, but what women really want is a home and children" (statement (3)).Descriptive evidence, which we present in Figure 4, shows that the share of individuals in France who agree or strongly agree with these two statements decreased steadily between 1990 and 2018.In 2020, we observe a clear trend reversal for both statements.Notes: This figure shows the change over time of respondents' opinions about two statements regarding gender roles that the EVS has included in its survey since 1990.In France, the EVS collected data for its 2nd wave in 1990, its 3rd wave in 1999, its fourth wave in 2008, and its fifth wave in 2018.We included these two statements in our Lockdown survey; the data were collected in May 2020.For each wave, we selected EVS respondents who were either employed (full-time or part-time) or self-employed, before calculating the percentage of respondents who either agree or strongly agree with each statement.

Time constraints during lockdown
Time constraints increased substantially during lockdown in households with young children.
In the Lockdown survey, we asked respondents to report the number of hours per day that they and their partner spent on parental care and housework, before and during lockdown.During lockdown, about two extra hours a day on average were spent on parental care in households with at least one young child.We find that mothers took responsibility for a larger share of the additional parental care during lockdown.In households with young children, female respondents spent an average of 5.8 hours a day on parental care during lockdown (3.3 hours before lockdown), compared to 4.5 hours for male respondents (3.1 hours before lockdown).These increases and gender differences are consistent with findings from other countries (e.g Adams-Prassl et al., 2020;Biroli et al., 2021;Carlson et al., 2021;Farré et al., 2020;Sevilla and Smith, 2020;Golin, 2021).
Figure 5 shows the change in hours spent per day by mothers relative to fathers on parental care and housework, for each of the nine categories of employment situations, during lockdown (Table 3 shows the share of couples, with and without young children, in each category).Although the large standard errors of the estimates reflect the imprecise measurement11 of the time-use variables, the figure provides suggestive evidence that men increased the time spent on parental care compared to their female partner in the three situations where they were relatively more available at home to take care of household production: when they were not working and their female partner was working either from home or outside the home, and when they were working from home and their female partner was working outside the home. 12The figure also shows that women took responsibility for a larger share of the increase in parental care that took place during lockdown when they were relatively more available at home.These two pieces of evidence are consistent with the available time theory (Presser, 1994): the partner who is the most available at home will "naturally" take responsibility for a larger share of household production.Time availability is a coordination device for couples bargaining over who will take care of household production.However, in households where both partners were equally likely to be at home (both were not working, both were working from home or both were working outside the home), Figure 5 suggests that male and female partners shared responsibility for the increase in parental care and housework during lockdown.While couples who were not working during lockdown had time for parental care and housework during lockdown, couples where both partners were either working from home or working outside were likely to be highly time-constrained.In these situations, the available time theory (Presser, 1994) suggests that couples need to bargain over who takes care of household production.Notes: This figure presents the nine situations that opposite-sex couples were in during the first lockdown period.Each partner, male (M) or female (F) was either not working, working from home (WfH) or working outside the home (outside).We included respondents who declared working partly from home, partly outside from home, in the WfH category.The vertical axis shows the change in the number of hours spent by the female partner relative to her male partner on parental care (dark green) and housework (light green), during lockdown (compared to before lockdown).A positive value means that the female partner increased the time she spent on childcare or housework compared to her male partner during lockdown.A negative value suggests that the male partner spent relatively more time on the activity than his female partner during lockdown, compared to before lockdown.The estimated model controls for the following characteristics: age, level of education, number of children, marital status, number of hours worked, and region fixed effects.Bars represent 95% confidence intervals.

Results
In this section, we examine whether individuals believed in more traditional gender roles during lockdown.First, we study the impact of lockdown measures on all individuals (Section 4.1).Second, we focus on the beliefs of individuals who were the most time-constrained during lockdown: parents with young children (Section 4.2).Finally, we examine the changes in beliefs of individuals from households where both partners were either working from home or working outside during lockdown, compared to other households where time constraints were lower (because partners were not working) or where partners had a "natural" way of distributing responsibility for household production (because one partner was relatively more at home) (Section 4.3).

Benchmark results
We analyze the changes in beliefs about gender roles during lockdown by estimating the following regression: where the outcome variable Y it is a binary variable equal to one if respondent i answered agree or strongly agree to a gender role statement at time t.The outcome before lockdown is defined as the estimate from the matching exercise for the beliefs of respondent i.The main variable of interest, Lockdown, is a binary variable equal to zero for the period before lockdown and one for during lockdown.In France, the share of individuals who agree with unequal gender roles has steadily decreased since 1990 (Figure 4).If the lockdown period were not associated with a shift in beliefs, we would expect β 1 to be negative, as the trend observed between 1990 and 2018 would continue in 2020.Female is a binary variable equal to one if the respondent is a woman.The coefficient on the interaction term (β 3 ) measures whether the impact of the lockdown period is different between male and female respondents.The vector of characteristics X includes both time variant and time invariant characteristics: age of the respondent, number of children, marital status, level of education, number of hours worked by the respondent at time t, and fixed effects for the region where the respondent lives.Finally, ϵ it is the idiosyncratic error term.Our benchmark model estimates equation (1) using ordinary least squares (OLS).Notes: The dependent variable is a binary variable equal to one if response is "Agree" or "Strongly Agree" for each of the following statements.(1) Kids: "When a mother works for pay, the children suffer".(2) Family: "All in all, family life suffers when the woman has a fulltime job".(3) Home: "A job is alright but what most women really want is a home and children".(4) Money: "A man's job is to earn money; a woman's job is to look after the home and family".(5) Politics: "On the whole, men make better political leaders than women do".(6) Business: "On the whole, men make better business executives than women do".All columns control for the following characteristics: age, level of education, number of children, marital status, number of hours worked, and region fixed effects.Significance levels: *** p<0.01, ** p<0.05, * p<0.1.Robust standard errors in parenthesis.
Table 4 presents the benchmark results, including all respondents.We find a statistically significant effect of lockdown on four out of six measures of beliefs about gender roles.The first lockdown period is associated with a statistically significant increase in the probability of agreeing with the following statements: • "When a mother works for pay, the children suffer" (9.9 p.p. increase, Column (1)), • "A man's job is to earn money; a woman's job is to look after the home and family" (6.7 p.p. increase, Column (4)), • "On the whole, men make better political leaders than women do" (9.4 p.p. increase, Column (5)), • and "On the whole, men make better business executives than women do" (7.5 p.p. increase, Column ( 6)).
We also find a weakly significant increase for "All in all, family life suffers when the woman has a fulltime job" (5 p.p. increase, Column (2)).The only outcome variable that does not change during lockdown is statement (3) on gender norms ("A job is alright but what most women really want is a home and children").
The interaction term between Lockdown and Female is always negative: individuals who changed their beliefs during lockdown were mainly men, especially regarding statements (1), (2), and (5).
Our results suggest that the lockdown period is associated with an increase in more traditional beliefs in gender roles, especially among men.

The relationship between time constraints and beliefs
Since time constraints significantly increased for parents of young children during lockdown, we add in equation (1) a binary variable equal to one if there is at least one child who is twelve years old or under living in the household, and we allow lockdown to differentially impact men and women with and without young children living in the household.We use the variable on children living in the household as a proxy for increased time constraints for the whole sample of respondents.
We find that men with young children increased their beliefs towards unequal gender roles during lockdown.In Figure 6 (see also Table A2 in the Appendix), we show the estimated change in beliefs during lockdown for four categories of respondents separately: men and women, and whether or not they were living with young children during lockdown.We find a significant increase in the percentage of men with young children who agree with all six statements during lockdown.The increases range from a 13 p.p. increase for "When a mother works for pay, the children suffer", to a 15.1 p.p. increase for "A man's job is to earn money; a woman's job is to look after the home and family".
While we find strong and consistent evidence of an increase in beliefs in unequal gender roles for fathers with young children, the results for other men are more mixed.We find a significant but Source: Lockdown Survey (2020).
Notes: This figure shows the marginal effect of lockdown on the probability of agreeing with each statement for four groups of individuals: men with and without children twelve years old or under, and women with and without children twelve years old or under.To calculate these coefficients, we use the regressions for which we present the results in Table A2.All respondents (single individuals, same-sex couples, and opposite-sex couples) are included in the results we present.Bars represent 95% confidence intervals.
The full model estimated in Table A2 is: 20 much smaller increase in beliefs in traditional gender roles for statements (1) and ( 5).However, we also find that men without young children are less likely to agree with the statement "A job is alright, but what most women really want is a home and children" during lockdown.
Finally, we generally do not find that women's beliefs changed significantly during lockdown, whether they had young children living in the household or not.The only significant result we find is that women with young children agreed more often with the statement "When a mother works for pay, the children suffer". 13verall, these results suggest that the increased time constraints that households with young children faced during lockdown are associated with a shift in beliefs towards more traditional gender roles.This shift is concentrated among fathers.

The relationship between parental occupations and beliefs
To further corroborate the evidence that the change in beliefs among men is driven by an increase in household production constraints, we exploit the variation in individual occupations generated by the lockdown measures, whereby some respondents and their partners stopped working, worked from home, or worked outside of the home.For this analysis, we only keep respondents who were parents of at least one young child living in the household during lockdown, because we want to examine the beliefs of individuals in a potential bargaining situation with their partner over taking responsibility for household production, in particular parental care.In the benchmark model in equation ( 1), we add a binary variable equal to one if the respondent and the respondent's partner both worked outside or both worked from home during lockdown, and we include an interaction term with the gender variable.Comparing parents in the different ways that the lockdown measures impacted their work arrangements is a way for us to proxy potential bargaining issues over which partner should take care of household production during lockdown.
The overall pattern of results in Figure 7 shows that the change in beliefs towards traditional gender roles is concentrated among men from the households where both partners were either working from home or working outside during lockdown (see also not per se the increased time they spent on parental care or housework.Indeed, men who were relatively more available for parental care and housework were not the ones whose beliefs shifted.
The men who were more likely to shift to traditional beliefs were the ones from households where both partners were equally unavailable to take responsibility for household production.
We interpret this result as evidence that men may adopt more traditional beliefs when they are in a bargaining situation with their female partner over the division of tasks in the household.
Adopting more traditional beliefs is less costly for men than for women, as the burden of household production would fall more heavily on women according to traditional divisions of labor.Women, however, are less likely to revert to traditional beliefs about gender roles.They may be more likely to maintain egalitarian beliefs because these beliefs enable them to share the work on parental care and household chores.

Discussion
Our results suggest that families' ability to outsource household production shape beliefs about gender roles.Before governments implemented lockdown measures, parents could find substitutes for household production, through publicly provided services (such as public schools and subsidized day care services) or by hiring help, for instance from low-skilled workers (Cortés and Pan, 2019).
Previous research has found that access to substitutes for household production enables high-skilled women to work longer hours and to earn higher wages, leading to higher household income for those who can afford to outsource household production (Cortés and Pan, 2019).
If the ability to outsource household production is positively associated with beliefs in equal gender roles and with household income, then we expect egalitarian beliefs and household income to be positively associated.More specifically, if beliefs in equal gender roles increase with income, then these egalitarian beliefs are a luxury good.
We examine the relationship between beliefs about gender roles and income by using crosscountry data from the fifth wave of the EVS.We conduct a regression analysis where an individual's agreement with each statement is the dependent variable and household income decile is the main independent variable, controlling for gender, age, marital status, number of children, and country fixed effects.On the whole men make better business executives than women do
Notes: We use data from 30 different countries to examine the relationship between beliefs in equal gender roles and income.The figure presents the estimates of an OLS regression, controlling for gender, age, number of children, marital status, and country fixed effects.We include all working individuals from the full dataset of the fifth wave of the EVS.
Figure 8 depicts the predicted percentages of men and women who agree with each statement by household income decile.The results show that beliefs in gender equality are a luxury good: as income levels increase, both men and women are more likely to believe in equal gender roles.This relationship is strongest for the statements ascribing a role to women.We also find that women are more likely than men to agree with equal gender roles.

Estimation and matching alternatives
Our estimations rely on the predictions from the Nearest-Neighbor Match.In this section, we present the results of several analyses we conducted to test the robustness of our estimates to different empirical strategies and alternatives to our baseline matching exercise.
First, instead of matching respondents from the EVS survey and our Lockdown survey, we estimate our benchmark model using an OLS cross section analysis.Respondents from both surveys are representative of the French population, and descriptive statistics comparing respondents from both surveys (Table 1) suggest that both samples are comparable (the main difference between the two datasets concerns the education variable).Using this unmatched dataset, we find similar results to the analysis on the matched dataset.Results in Table A4 in the Appendix suggest that the lockdown period is associated with a statistically significant increase in beliefs in unequal gender roles across the same four out of six statements.Statement (2) is also significant in the unmatched dataset.Furthermore, the results from the unmatched dataset confirm that the main effects are different for men and women, and that men's beliefs are associated with a change during lockdown.
Second, we run our baseline model directly on the matched data.Compared to the main analysis (Table 4), we use the control variables from the Nearest-Neighbor Match in this exercise.Table A5 in the Appendix presents the results, which are similar in size and significance compared to the ones we present in Table 4.
Finally, Table A6 in the Appendix compares average treatment effects estimated using different respondent characteristics to conduct the match, and using either Mahalanobis distances (columns (1) to ( 6)) or Euclidean distances (columns (7) to ( 12)).The ATE for our baseline model is Model 1 with Mahalanobis distances.We find that our ATE are comparable to the other models and to Euclidean distances.

Social-desirability bias
We check whether social-desirability or type-of-interview bias can explain our results.Indeed, respondents to our survey may have been more willing to express beliefs in unequal gender roles because our survey was conducted online, compared to the EVS survey which was conducted in person.We measure desirability bias by using data from the fifth wave of the EVS for six countries (Denmark, Finland, Germany, Iceland, the Netherlands, and Switzerland), where some respondents were interviewed in person and other respondents were surveyed online.In these countries, we compare respondents who answered each statement in the online version of the survey with the in-person interview version of the survey.
In Panel A of Table A7 in the Appendix, we show results of regressions where the coefficient on the variable Online survey measures the difference in the share of individuals who agree with each statement in the online version of the survey compared to the in-person interviews.We find that men are significantly more likely to agree with three statements (statements (3), ( 5), and ( 6)) in the online version, but men are not significantly more likely in the online version to agree with most of the statements that associate women with traditional gender roles.
While social-desirability bias may explain part of our results, it is unlikely to explain a large share of the effects that we find for three reasons.First, the economic significance of the coefficients in Table A7 is smaller compared to the changes that we measure through our lockdown survey.
Second, in our analysis, we make the conservative assumption that respondents would not have changed their beliefs between 2018 and before the lockdown.But had the decreasing trend of agreement on these statements continued, we would have expected a decrease in the share of respondents who agree with these statements in 2020 compared to 2018.Finally, Panel B of Table A7 shows that type-of-interview reporting bias generally does not depend on having young children in the household.This result further suggests that the effects we find during lockdown are not mainly driven by social-desirability bias.

Conclusion
In this research, we study whether beliefs about gender roles are entrenched or whether a shock that increases household production constraints can lead individuals to shift their beliefs towards more unequal gender roles.We find that more men believed in unequal gender roles during the first lockdown period in France.We find that men from households with young children and from households where both partners continued working either from home or outside the home during lockdown were more likely to shift beliefs.Women's beliefs, however, mainly did not change.These results suggest that time constraints and bargaining within the household were likely drivers of changes in beliefs about gender roles.Finally, we find evidence consistent with beliefs about gender equal roles being a luxury good for both men and women.
Our findings suggest that the increase in beliefs in equal gender roles that has occurred in many European countries, since at least the early 1990s, are likely related to families' ability to outsource household production.When governments implement policies that prevent the outsourcing of household production (such as during the lockdown period), then beliefs in traditional gender roles may increase.Our results suggest that individuals-men especially-may revert to traditional beliefs in gender roles when household production constraints increase.
Our findings also add to research conducted during the pandemic which has found that conflict within couples increased during the first lockdown period (e.g.Arenas-Arroyo et al., 2021).Our findings point to an important role of beliefs regarding gender roles: beliefs in traditional gender roles may be motivated beliefs that serve as a coordination mechanism when couples are in a potential conflict over who should take responsibility for household production.
The effects we measure may be only short run effects: when lockdown measures disappear, household production constraints also disappear, and men may revert to beliefs in more equal gender roles.However, the length of the COVID-19 crisis could lead to long run impacts on individuals' beliefs, as well as women's participation in the labor market. 14The literature has highlighted that long-lasting shocks in gender roles can shape gender identity norms, which can explain cross-country differences in labor force participation of women in the long run (Alesina et al., 2013).For example, during World War II, women entered the labor market due to men's military involvement in the war; this change in gender roles persisted across generations and led to an increase in female labor force participation in the long run (Fernández et al., 2004).We observe an opposite effect during lockdown measures.The effects that we find regarding beliefs about gender roles may have long run repercussions, even when lockdown measures are relaxed and households can outsource household production again.Notes: The dependent variable is a binary variable equal to one if response is "Agree" or "Strongly Agree" for each of the following statements.(1) Kids: "When a mother works for pay, the children suffer".(2) Family: "All in all, family life suffers when the woman has a fulltime job".(3) Home: "A job is alright but what most women really want is a home and children".(4) Money: "A man's job is to earn money; a woman's job is to look after the home and family".(5) Politics: "On the whole, men make better political leaders than women do".(6) Business: "On the whole, men make better business executives than women do".All columns control for the following characteristics: age, number of children, marital status, level of education, number of hours worked, and region fixed effects.Corresponding marginal effects can be found in Figure 6.Significance levels: *** p<0.01, ** p<0.05, * p<0.1.Robust standard errors are in parentheses.Notes: The dependent variable is a binary variable equal to one if response is "Agree" or "Strongly Agree" for each of the following statements.(1) Kids: "When a mother works for pay, the children suffer".(2) Family: "All in all, family life suffers when the woman has a fulltime job".(3) Home: "A job is alright but what most women really want is a home and children".(4) Money: "A man's job is to earn money; a woman's job is to look after the home and family".(5) Politics: "On the whole, men make better political leaders than women do".(6) Business: "On the whole, men make better business executives than women do".All columns control for the following characteristics: age, number of children, marital status, level of education, number of hours worked, and region fixed effects.Corresponding marginal effects can be found in Figure 7. Significance levels: *** p<0.01, ** p<0.05, * p<0.1.Robust standard errors are in parentheses.Notes: Data include respondents' beliefs about gender roles in six countries where a mixed-method (online survey or in-person interview) was applied for data collection: Denmark, Finland, Germany, Iceland, Netherlands, and Switzerland.See Table 3 for the description of the six statements.All regressions include regional fixed effects, as well as controls for age, level of education, marital status, and whether the respondent has children living in the household.Full results are available on request.Significance levels: *** p<0.01, ** p<0.05, * p<0.10.Notes: This figure shows the percentage of respondents who answered "Strongly disagree", "Disagree", "Agree" or Strongly Agree" to each of the six statements on beliefs about gender roles, for each survey.All 871 EVS and 1,000 Lockdown respondents are included.

Figure 2 .
Figure 2. Correlation between beliefs about gender roles and enrolment rates in early childhood education and care services, OECD countries

Figure 3 .
Figure 3. Correlation between beliefs about gender roles and maternal employment rates, OECD countries

Figure 4 .
Figure 4. Changes in beliefs about gender roles in France, between 1990 and 2020 and the corresponding marginal effects that we show in this Figure are equal to:• γ1 for men without children who are 12 years old or under • γ1 + γ5 for men with children who are 12 years old or under • γ1 + γ3 for women without children who are 12 years old or under • γ1 + γ3 + γ5 + γ7 for women with children who are 12 years old or under.

Figure 8 .
Figure 8. Relationship between beliefs about gender roles and income categories, by gender

Figure A1 .
Figure A1.Distributions of respondents' answers to the six statements on beliefs about gender roles, EVS 2018 and Lockdown 2020 surveys

Table 2 .
Share of respondents who agree with each statement, before and during lockdown, by gender Source: Lockdown Survey (2020).

Table 3 .
Job combinations between partners during lockdown This table shows the different work combinations that opposite-sex couples were in during lockdown."F" refers to the female partner, and "M" refers to the male partner.Figure 5. Impact of lockdown on time spent on parental care and housework by individuals in opposite-sex couples, by job situation Source: Lockdown Survey (2020).

Table 4 .
Impact of lockdown on beliefs about gender roles, benchmark model Source: Lockdown Survey (2020).
Figure 6.Impact of lockdown on respondents' beliefs about gender roles, by having children twelve or under living in the household Table A3 in the Appendix).This pattern suggests that what drives the change in beliefs among fathers with young children isFigure 7. Impact of lockdown on respondents' beliefs about gender roles, by occupational categories This figure shows the marginal effect of lockdown on the probability of agreeing with each statement for four groups of individuals: men in household where both partners work (from home or outside) or other, and women in household where both partners work (from home or outside) or other."BothWfHorboth working outside"represents the situations where partners experience an increase in household time constraints.To calculate these coefficients, we use the regressions for which we present the results in TableA3in the Appendix.Only opposite-sex couples with children below age 12 are included in the results we present.Bars represent 95% confidence intervals. Notes:

Table A1 .
Percentage of respondents from each region of France, EVS and Lockdown surveys Source: EVS and Lockdown Survey (2020).

Table A2 .
Impact of lockdown on respondents' beliefs about gender roles, by having children twelve years old or under living in the household

Table A3 .
Impact of lockdown on respondents' beliefs about gender roles, by occupational categories during lockdown

Table A4 .
Impact of lockdown on respondents' beliefs about gender roles, Cross-sectional evidence This table describes the results of our baseline regression described in equation (1), using a dataset that includes directly the responses from the EVS and Lockdown surveys (unmatched dataset).See TableA2for the description of the six statements.All columns control for the following characteristics: age, level of education, number of children, marital status, and region fixed effects.We use the same control variables as the results presented in Table4, except for number of hours worked, because the EVS dataset does not include this information.Significance levels: *** p<0.01, ** p<0.05.Robust standard errors are in parentheses.

Table A5 .
Impact of lockdown on beliefs in gender roles, Direct match This table shows the corresponding results of Table4using the matched sample directly, and using the variables that we used to conduct the Nearest-Neighbor Match as controls: age, level of education, marital status, the number of children living in the household, the partner's employment status, and region fixed effects.See TableA2for the description of the six statements.Significance levels: *** p<0.01, ** p<0.05, * p<0.1.

Table A6 .
Impact of lockdown on beliefs in gender roles, ATE using different Nearest-Neighbor Matching modelsNotes: This table shows ATE of Nearest-Neighbor Matching models where the matching variables differ by model.Model 1 with Mahalanobis distance is the one we use for our main matching exercise.It matches on age, marital status, education, number of children, region, employment status of partner, and exact matches on female and having a child 12 or under.Model 2: matches on age, marital status, education, number of children, region, and exact matches on female and having a child 12 or under.Model 3: matches on age, marital status, education, number of children, region, and exact matches on female.Model 4: matches on age, marital status, education, region, and exact matches on female.Model 5: matches on age, marital status, education, and exact matches on female.Model 6: matches on age, education, number of children, region and exact matches on female and having a child 12 or under.Model 7: matches on age, marital status, education, number of children, region, employment status of partner, and exact matches on female.Model 8: matches on age, marital status, number of children, region, employment status of partner, and exact matches on female.Significance levels: *** p<0.01, ** p<0.05, * p<0.10.Robust standard errors are in parentheses.

Table A7 .
Analysis of response bias, in person interview versus self-administered, EVS 2018