Children’s well-being and intra-household family relationships during the first COVID-19 lockdown in France

Objective: This article explores the consequences of the first COVID-19 lockdown in the spring of 2020 in France on intra-family relationships and 9-year-old children’s socio - emotional well-being. Background: On 17th March 2020, France began a strict lockdown to contain the COVID-19 pandemic, with school closures and limited outings permitted until early June. All family routines and work-life arrangements were impacted. A major concern relates to how these measures impacted family and child well-being. Method: We use data from the Elfe Sapris survey, administered during the first lockdown to about 5,000 families part icipating to the Etude longitudinale française depuis l’enfance (Elfe), a nationally representative birth cohort of children born in 2011. We analysed correlations between parents’ socioeconomic and living conditions on four relational indicators: the experience of lockdown, the quality of relationships between parents and children, and between siblings, and an indicator of children’s socio -emotional well-being, the Strengths and Difficulties Questionnaire (SDQ). Results: The impact of the lockdown on family well-being was conditional on socio-economic factors and their changes over the period. Deterioration of households’ financial situation and having to work outside the home during lockdown was negatively correlated with family relationships and children’ s socio-emotional well-being. Conclusion: Overall, our results suggest that while France’s first lockdown was a relatively positive period for many households with a primary-school-aged child, we highlight that restrictions exacerbated existing difficulties for disadvantaged families.


Introduction
On 17th March 2020, France began a strict lockdown of its entire population in order to contain the COVID-19 epidemic, with school closures and restrictions on outings until early June. Workers could continue their professional activities if they could be adapted to teleworking or if their activities were considered essential. While most pupils were offered some form of distance learning, parents often had to supervise and facilitate lessons and homework. All family routines and work-life arrangements were impacted, with families living almost in a vacuum.
A growing number of studies highlight how COVID-19 restrictions affect adults' wellbeing and mental health (Adams-Prassl et al. 2020a;Daly, Sutin & Robinson 2020;Hazo & Costemalles 2021;Pierce et al. 2020). They show an increase in the proportion of adults, especially young adults, reporting high levels of psychological distress with the intensification of restriction measures. However, less is known about how these measures impact children's well-being, including the direct effects of stay-at-home measures, school closures, and social distancing, as well as the indirect effect of changes in their parents' socio-economic status and living conditions. In this article, we explore the consequences of France's strict lockdown on family relationships and children's socio-emotional wellbeing.
Because the lockdown restricted people to their own homes, family resources (including cultural, financial, and living conditions) might have become more important. During the lockdown, out-of-home resources, such as schools, leisure activities, and social support from extended families and peers, which usually moderate the role of family resources on family well-being, were either completely unavailable or diminished. Therefore, household-based resources may have become more important in predicting family and child well-being. While some family resources were unlikely to change during the period, such as parental education or housing conditions, others might have been affected by the lockdown and COVID itself, such as parent physical and mental health, or by the economic crisis; some families experienced a drop in income and a deterioration in their employment situation. We assess the role of family resources and their variation in predicting change in family well-being during the lockdown.
We make use of data from the Elfe Sapris survey, a web survey administered during the first French lockdown in April and May 2020 to about 5,000 families participating to the Etude longitudinale française depuis l'enfance (Elfe), France's generalist nationally representative birth cohort study. These data provide indicators of well-being measured both before and during the COVID-19 pandemic. We focus on four relational indicators: the experience of lockdown, the quality of relationships between parents and children and between siblings, and an indicator of children's socio-emotional well-being, the Strengths and Difficulties Questionnaire (SDQ).

Review of the literature
Families and the family environment are intrinsically linked to the wellbeing of its members (Bronfenbrenner, 1986). Family systems theory posits that family members are part of an interdependent system in which each individual impacts and is impacted by every other individual in the family (Minuchin, 1974). As such, a growing body of literature has explored the role of family functioning on family well-being (Moore, Chalk, Scarpa, & Vandivere, 2002). Describing the impact of shocks, such as the lockdowns, on family functioning is crucial to our understanding of the determinants of family and child well-being.
Family functioning refers to the social and structural properties of the family environment and has been found to be a strong predictor of family and child well-being. Family functioning relates to the interactions and relationships within the family (including between the parents, between the parents and the child(ren), and between siblings), the levels of family conflict and cohesion, adaptability and organisational skills, etc. Positive family functioning describes an environment with warm, low conflict relationships, well-defined roles, high levels of group cohesion, etc. Family functioning has been connected with a number of outcomes in adults and children, including physical, social and mental health outcomes.
In our paper, we focus on describing changes in family functioning and child wellbeing and how they correlate with indicators of the household's experience of the pandemic. We therefore review the existing literature on the impact of the lockdowns on family functioning and child well-being. While we do not have available data on adult wellbeing, family functioning is likely to also have an impact on parents' wellbeing; we therefore also review literature on the impact of the pandemic on adult well-being. Given that this literature is more abundant than that on family functioning or on child wellbeing, we begin with this topic.

The impact of lockdowns on adult well-being
There is a wide literature on the impact of contextual shocks on adult well-being, such as the literature on adult mental health during economic recessions (Chang et al. 2013;Dagher, Chen & Thomas 2015;Reibling et al. 2017). A more specific emerging literature examines the impact of the COVID-19 pandemic on adult well-being. For instance, Fetzer et al. (2020) document an increase in Google searches related to economic anxiety during and after the initial global spreading of the novel coronavirus. Adams-Prassl et al. (2020a) show how state-wide stay-at-home orders implemented across the US in March and April 2020 had negative mental health consequences, particularly for women, while there was less evidence of an effect on men's mental health. The increase in the prevalence of mental health problems during the COVID-19 pandemic was confirmed by nationally representative longitudinal data (McGinty et al. 2020;Pierce et al. 2020;Daly, Sutin & Robinson 2020). Regardless of country context, psychological distress was highest among young adults (Giuntella et al. 2021;Pierce et al. 2020;Hazo & Costemalles 2021;Peretti-Watel, Alleaume & Léger 2020).
Most of this literature has looked at the general population of adults, irrespective of parenthood status. Yet parents might have had a different experience of the pandemic and its lockdowns, and characteristics linked to parenthood (single parenthood, the presence of school aged children in the home, etc.) appear to be important determinants of wellbeing during the pandemic. Using UK data, Banks and Xu (2020) and Pierce et al. (2020) observed that the most negative impacts were for mothers with children under the age of five, as well as lone parents. Adams-Prassl et al. (2020a) found that the negative effect on women's mental health remains significant even when controlling for increased financial worries and increased childcare responsibilities. This increase in women's mental health problems could be due to the increased burdens of childcare and housework brought on by lockdown restrictions that disproportionately impacted women (Hupkau & Petrongolo 2020;Del Bocca et al. 2020), or who may have reversed the division of labor in egalitarian couples (Hank & Steinbach 2020). Women have also suffered disproportionately in the labour market, as they are more likely to work in sectors impacted by lockdown measures (Alon et al. 2020).
Parents' well-being during the pandemic may have been influenced by several factors. On one hand, the time spent by parents with their children increased dramatically (Hupkau & Petrongolo 2020;Kreyenfeld & Zinn 2021;Craig & Churchill 2021;Petts, Carlson, & Pepin 2021). Parents usually report enjoying spending time with their children, which is in turn associated with higher levels of well-being . Indeed, many employed parents report wanting to spend more time with their children (Milkie et al., 2004). Given research on the benefits of 'family time', we might expect a positive influence on parents' well-being and, consequently, on parent-child relationships.
On the other hand, these benefits are not equally distributed across socioeconomic groups or according to parental gender. Mothers benefit less than fathers from time with children and experience parenting time as more stressful than fathers, possibly because they carry out more mundane childcare tasks . Indeed, Coyne et al. (2020) described the stressful 'collision of roles, responsibilities, and expectations' (i.e., as a parent, spouse, employee, caregiver, and teacher) experienced by parents during a lockdown. These findings might suggest that increased parenting time during lockdown might have had a negative impact on parents, particularly mothers and those who already had more constraints on their time.
Furthermore, the living conditions and economic situations of parents are also important for family life. The COVID-19 pandemic has triggered a major job crisis (OECD 2020). In France, the decline of the number of people in employment (by -0.9% between the end of 2019 and the end of 2020) was relatively contained, thanks to governmentsponsored furlough schemes and the widespread use of working from home arrangements. While employment figures have remained relatively stable, the average wage fell over the same period, by up to 4.9% in the private sector, as furlough schemes did not always fully replace wages. Furthermore, these overall figures hide important inequalities: in 2020, it was the least qualified workers and those in unstable employment that were more at risk to lose their employment or see their overall revenues decrease (Insee 2021). Hence, financial uncertainty might be an additional source of stress for more disadvantaged households, with negative consequences on intra-family relationships. Workers with precarious employment conditions and those who cannot work from home (mainly less skilled workers) have been particularly exposed to job uncertainty. Because of lockdown restrictions limiting movement, living conditions also became more important. For example, the mental health of people living in small spaces was more affected than those living in larger homes (Amerio et al. 2020).
Early results suggest that a negative impact on parental well-being is likely. Qualitative work from the US suggests that, because of pandemic-related disruptions to paid work and childcare routines, mothers increased their time with their children, resulting in increased stress, anxiety, and frustration with their children. This was especially true for mothers whose disrupted childcare arrangements were coupled with intensive work pressures and/or pressure to follow intensive parenting practices (Calarco et al. 2020). Similarly, during the pandemic, telecommuting mothers experienced increased levels of anxiety, loneliness, and depression (Lyttelton, Zang & Musick, 2020).

Impacts on child outcomes
A substantial body of literature suggests that various family functioning processes, such as parent-child relationships, affect child well-being (Pinquart 2017). The COVID pandemic and associated lockdowns produced an extraordinary situation for families, with stay-athome measures requiring them to remain indoors, in close proximity, for an unprecedented amount of time. This unusual situation caused upheaval for family routines and added burdens on parents as school and childcare settings were closed, forcing them into new roles (as substitute teachers, for example), while they also adapted to new working conditions or the loss of employment. As mentioned previously, time spent with children increased. Financial concerns and uncertainty about the future would have added to family stress, impacting the ability to parent and implement family routines. As the pandemic and its lockdowns therefore impacted key determinants of family functioning (parental stress, financial uncertainty etc.), we can hypothesise that the Covid lockdowns could have had an impact on family functioning processes, notably the quality of family interactions and relationships, family conflict, and family adaptability.
In spite of a challenging context, there is evidence that family relationships did not suffer across the board during the first lockdowns. For example, the Understanding Society May COVID survey found that parents' assessments of their relationships with their children stayed the same (70%) or improved (26%) during the first UK lockdown. Only 4% reported that their relationships had worsened. These figures varied little across households' demographic and socio-economic characteristics, except for a slight advantage among parents who worked from home and parents who could spend more time helping with schoolwork (Perelli-Harris & Walzenbach, 2020).
However, family functioning might have been particularly impacted by the lockdown in more complicated or volatile family contexts. For example, an increased risk of family violence and child abuse during a period when families face stressful situations and are cut off from their external social support might not be surprising (Brown et al. 2020). Yet, although such complex family situations might increase during lockdown restrictions, they remain relatively rare and may not be picked up by standard surveys, which may therefore hide extremes, i.e., the negative impact of lockdowns on family functioning for more vulnerable groups. Indeed, child protective services across countries have reported an increase in cases of child abuse during the pandemic (Thomas et al. 2020).

Impacts on family functioning
Covid lockdowns might have had an impact on child outcomes directly, through disruptions to key services for children such as school, as well as indirectly, through negative impacts on parental well-being and family functioning. Indeed, disruptions in education, physical activity, and opportunities for socialising have been associated with children's uncertainty and anxiety during lockdowns (Jiao et al., 2020;Lee, 2020;Liu et al., 2020). A variety of international studies suggest that school closures during the 2020 lockdowns had large, negative effects on student learning. For example, Maldonado and De Witte (2020) found that Belgian primary school students exposed to school closures experienced large decreases in mathematics and language scores.
The lockdowns also affected families' abilities to engage their social networks and decreased the opportunity to socialise, which could have an impact on a variety of outcomes, including mental health, family functioning, and well-being, as well as child learning and cognition. For example, Agostinelli et al. (2020) used US data to show that the forced separation from friends imposed by lockdowns and school closures negatively affected children's academic performance, an effect which was greater among children who were already behind at school.
Inequalities in family resources might be particularly salient during lockdowns as institutions, services, and networks that might mitigate the impact of family resources on child well-being closed or became less accessible. The literature shows that school closures have a larger and more negative impact on more disadvantaged children. Engzell, Frey, and Verhagen (2020) found that in the Netherlands, a country with a relatively short 8week lockdown and a high degree of technological preparedness, large learning losses were evident for students of less advantaged families. There are many channels through which lockdown measures, such as school closures, may have affected child outcomes differently according to family background. Some outcomes, such as children's learning, may have been directly impacted by reduced contact time with teachers, with more affluent children suffering less as they are more likely to have access to remote learning. A number of indirect channels have also been proposed. For example, Andrew et al. (2020) using English data and Grewenig et al. (2020) using German data found that less advantaged children are more likely to substitute school time with less productive activities such as TV and video games.
Another, more indirect, channel through which the pandemic could affect child outcomes is changes in family functioning and parenting behaviours. Distance learning requires a large degree of parental input (from technological support to supervision, tutoring, and disciplining their children throughout their learning). Not all parents are equally able to provide these inputs, and their ability to do so varies depending on the family's cultural, financial, and material resources. Time constraints are also likely to matter, particularly if parents continue to work. Because time constraints are likely to be more important for parents who work outside the home and for parents with more limited time resources (e.g., single parents), time constraints are also likely to vary according to family resources. For example, Adams-Prassl et al. (2020b) showed that workers with less income were more likely to be unable to work from home during the US spring lockdowns.
In addition to differences in the quantity of parenting children may receive during the pandemic, the quality of these inputs might also differ. For example, Agostinelli et al. (2020) showed that parents (particularly those from more disadvantaged backgrounds) were more likely to adopt an authoritarian parenting style during the US spring lockdowns. Similarly, using data from Singapore, Chung, Lanier, and Wong (2020) found that parents who reported a greater impact of the pandemic (because of an impact on finances or job loss) also reported higher levels of parental stress, which was in turn associated with an increased use of harsh parenting and less parent-child relationship closeness.

Research question and hypotheses
In this article, we describe changes in a number of family outcomes during France's spring 2020 lockdown. This was an exceptional period for families. During this first lockdown, only critical activities, such as healthcare, food distribution and basic services, were permitted. Telework was mandatory when possible, and furlough schemes were in place for all other activities. Schools and childcare services were closed, teachers could set school work by email or through digital workspaces. Parents, especially those of younger children, were expected to manage schooling at home. Outings were limited to a onekilometre radius for up to an hour a day, with no access to parks and green spaces, and needed to be justified through a signed declaration.
We focus on families with at least one primary-school aged child. Unlike previous studies that focus on children of different ages, the use of a birth cohort ensures a sample of children of similar ages. This is particularly important because children's reactions to lockdown might differ by age, with younger children being more negatively affected than teenagers (Ravens-Sieberer et al. 2021).
We focus on the role of families' cultural, financial, and material resources in predicting these outcomes. Given the literature above, we hypothesise that disrupted living conditions during lockdown, which gave families more time together but also increased burdens on parents and distanced children from schools and peers, might have had both positive and negative impacts on family well-being.
On one hand, positive outcomes can be predicted if families have the right resources and conditions to take advantage of the lockdown as a period of fewer time pressures and more quality time together. On the other hand, we can hypothesise negative outcomes for households given the increased domestic and parental burdens, the lack of interaction with the wider family and social networks, and the lack of sports and leisure activities. These restrictions might have increased family stress, particularly in households with lower levels of resources to moderate these negative impacts.
Therefore, our hypotheses are based on the idea that family well-being during the lockdown might have varied with the cultural, financial, and material resources of the household: H1: We predict a more positive experience of lockdown, parent-child and siblings relationships and child well-being among families with higher levels of education, who are better equipped to support their children's learning and whose children might have had more academic success before the introduction of the lockdown, therefore requiring less input from their parents to support distance learning.
H2a: We predict a more negative experience of lockdown, parent-child and siblings relationships and child well-being among families whose financial and/or professional situations deteriorated during the lockdown, which might have increased parental stress and decreased their mental well-being, with a follow-on impact on family relationships and the ability to provide effective parenting.
H2b: We predict a worse experience of lockdown, parent-child and siblings relationships and child well-being among households with fewer material resources, notably resources linked to housing. During the pandemic, parents and their children spent significantly more time in their homes, which became their place of work, school, and leisure. We therefore expect that the experience of lockdown differs for those living in larger houses with outside spaces and those in crowded spaces with no outdoor space.

A specific COVID survey from a national child birth cohort
The Elfe-SAPRIS 1 data was collected through a web survey conducted as part of the Elfe (French longitudinal study since childhood) study, a population-based cohort following children born in continental France from the time of their birth in 2011 onwards (Charles et al. 2020). 2 The Elfe-SAPRIS survey was administered to the 13,696 Elfe parents with a valid e-mail address between 16th April and 3 rd May 2020, during the first lockdown (see Figure A1 in the Appendix). A second questionnaire was administered between 2 nd May and June 21 st . The children in the sample were 9.5 years old on average at the time of the Sapris survey. The survey questions covered coronavirus-related health, household socioeconomic characteristics, children's activities, family relationships, and child wellbeing (as assessed by parents). A total of 4,877 questionnaires were completed. The response rate of 38% is relatively low, and was lower among younger parents, those living in urban areas -especially the Paris metropolitan area-and in apartments, those with a 1 This survey is part of a larger project, SAPRIS (Health, perception, practices, relations, and social inequalities during the COVID-19 crisis), a series of coordinated add-on surveys administered to the participants of existing cohorts of adults (e.g., E3N-E4N and Nutrinet) and children (Elfe and Epipage2, a cohort of children born prematurely) (Bajos et al. 2021). 2 Children were born at a random sample of 341 maternity units throughout continental France and were sampled at four intervals with initial data collection occurring in April, June/July, September/October, and November/December 2011. Interviews were carried out in the maternity unit shortly after a child's birth, by telephone roughly two months post-birth, and again when the child was approximately 1, 2, 3.5 and 5.5 years of age. Data were collected on diverse topics, including socioeconomic background, parenting, child development, and living conditions. lower levels of education, immigrants and non-working mothers. While the response rate is lower than comparable web surveys that have been performed previously on the Elfe cohort 3 , the population structure of respondents is very similar to a previous web survey conducted when the child was 7 and half.
In this article, we focus on the 4,485 households who completed the Elfe-SAPRIS survey either during the first round, and otherwise during the second round, provided responses for the four outcomes considered, and responded in the pre-lockdown waves. Notably, we make use of information on previous child well-being, collected when the children were 5.5 years old. Controlling for this variable is crucial in order not to attribute pre-existing socio-emotional problems to a lockdown effect. We thus exclude 144 respondents with missing values on pre-lockdown child well-being measurement. Table A1 in the Appendix provides a description of our sample. It is composed mainly of multi-child families (82%) with two parents (88%). Single-parent and blended families each accounted for 6% of the sample. As we wanted to keep single parents in the sample and control for both partners professional situation for couples, we added an additional category for the variable describing parental professional status when only one carer is present in the child's household. In two-thirds of cases, one parent had at least a bachelor's degree, while there was more variability in household incomes. The lockdown led to significant changes in the employment status of the parents, as 18% of mothers and 14% of fathers stopped working. A large share of employed parents switched to full teleworking during lockdown, and more so for mothers than fathers; 33% and 25%, respectively. 19% of mothers and 14% of fathers experienced different forms of employment during confinement, identified here as "mixed work situations" (e.g. some partial unemployment and some paid employment; some on-site employment and some teleworking). A quarter of families experienced a loss of income. The living conditions of the children were mostly favourable for the majority of our sample (82% live in a house and 11% in a flat with external space. Two-thirds of the children were able to isolate themselves easily to relax or study). But a significant proportion reported this was difficult (for 14% of children) or impossible (for 18% of them). Half of the children spent between two and three hours a day on school work; 28% spent more than three hours; and 17% spent between one and two hours. A very small proportion (2%) worked less than one hour per day. For school work, 45% of the children were helped by both parents, 28% by their mother only, and 6% by their father only. One-fifth of the children received no help.

Family experience of the lockdown
The main respondent (usually the mother) was asked the following question about the family's experience of the lockdown: 'For your family life, how were the effects of the lockdown'? The five response options were: very negative, negative, no effect, positive, and very positive. We built two dummy variables, one for the two negative items (equal to 1 for a negative response and 0 otherwise), and one for the two positive items (equal to 1 for a positive response and 0 otherwise). Extreme answers were not very frequent (8% for very positive and almost 0% for very negative).

Family relationships
We used two questions about family relationships during the lockdown. The first question concerned parent(s)-child relationships: 'Would you say that your relationship with your child(ren) today is: better than usual, the same as usual, or more strained than usual?'. The second question concerned sibling relationships (for the 3,076 families with more than one child): 'Would you say that the relationship between your children today is: better than usual, the same as usual, or more strained than usual?' We construct two dummy binary variables, one indicating degrading relationships and one for improving relationships.

Child socio-emotional difficulties
Children's socio-emotional difficulties were measured during the lockdown survey, as well as in a previous survey, using the reduced form of the Strengths and Difficulties Questionnaire (SDQ) total difficulties score, a standard measure used in large-scale surveys (Goodman 1997). The SDQ is conceptualised around two broad classifications of how children react to stressors: internalising and externalising symptoms. Internalising behaviour problems primarily occur within the person and include anxiety and depression. Because of the lockdown conditions, in Elfe-SAPRIS, only emotional symptoms (i.e., '[child] cries often') were included, while the peer relationship problems subscale was not included (i.e., '[child] is rather solitary, tends to play alone'), as children were cut off from their peer networks. Externalising behaviour problems occur in interactions with other people and include aggression and attention problems, such as hyperactivity/inattention symptoms (i.e., '[child] is easily distracted, concentration wavers'). The conduct problems subscale (i.e., '[child] often fights with other children or bullies them') is excluded, as it mostly relates to children's relationships with peers. The reduced form used 10 of the 20 items. We tested the validity of this reduced score by correlating it to the full difficulties score available in the Elfe 5.5 year wave. The correlation was very high (0.91), making us confident that the reduced form is a good proxy for the full SDQ score and suitable to the specific context of the lockdown situation, which featured fewer peer interactions. We only used reduced form of the SDQ hereafter. SDQ is scored such that higher scores indicate more difficulties.
The SDQ is not directly comparable to our other outcomes, as we are able to observe it at two data points: once before and again during the lockdown; we therefore calculate change in child well-being by comparing these two scores. On the other hand, our others outcomes are only collected during the lockdown survey and question the parent directly about the change in family well-being, by questioning whether relationships improved or deteriorated. Therefore, in order to construct a child well-being outcome that is comparable with our other outcomes, we first build a continuous indicator of the variation in SDQ scores at the two time points available (Figure 1 bottom right panel shows the distribution). We then class children according to whether their well-being appears to have improved (children whose SDQ score is lower during lockdown than at age 5.5), remained stable (no change in SDQ score), or worsened (higher SDQ during the lockdown than at age 5.5).

Description of children's well-being during lockdown
The first lockdown had positive effects on family life for half of the respondents. One-third reported no change, and 14% of the families reported negative effects (see Figure 1). Most children and their families navigated the lockdown period with relatively little impact on family well-being. Most parents reported that their relationships with their children did not change (62%) or even improved (24%). Only a small proportion (15%) felt that their relationships were more strained than usual. The same pattern was found for relationships between siblings: 64% of parents having multiple children declared that the relationship between siblings did not change; 23% said that they improved; and 13% reported that the relationships deteriorated during lockdown.
As concern socio-emotional difficulties experienced by children (such as feeling fearful, having recurrent headaches or stomach aches, or having difficulties concentrating and completing tasks), the first lockdown does not seem to have been responsible for a massive increase or decrease in children's socio-emotional problems, at least among this group of primary-school-aged children; the average SDQ values measured during lockdown are similar (if slightly higher) to the average values observed before, when the child was 5.5 years old. However, the correlation is not so strong (0.38), meaning that score changes are quite frequent and go in both directions. There is almost the same proportion of children whose socio-emotional problems decrease (42%) and increase (45%), while for a small proportion, the score is exactly the same (13%). Within the top quintile of children that presented the most socio-emotional problems at age 5.5 (belonging to quintile 5), one-third has roughly the same level of difficulties during the lockdown, one-third has a high level but not as high as those observed during the lockdown (see Appendix Table A2 for the cross-tabulate distribution of the two scores). The remaining third had low levels of socio-emotional problems during the lockdown. It is rather difficult to attribute the changes in SDQ score to the lockdown since the premeasurement of the SDQ occurred four years beforehand. That is why we will not comment much descriptive results but will concentrate further on multivariate regressions that include specific variables about lockdown to see whether they might have affected the changes in SDQ. Moreover, because some children have more to lose than others (those with few socioemotional problems before the lockdown), it is important to control for the initial level as recommended by Dalecki and Willits (1991) when examining change in regression analysis.

Empirical analysis
To test our hypotheses, we first present some descriptive statistics for each outcome, as well as their distribution according to the parents' level of education, the family's income level, and pre-COVID socio-emotional status. Because families potentially cumulate both socio-economic and pre-COVID child socio-emotional difficulties, we consider these dimensions simultaneously by performing multivariate regressions on each of the four items considered.
To provide a synthetic view, we consider the binary version of each indicator: either positive change versus negative or stable, or negative change versus positive or stable. We also tested multinomial regressions using improvement, worsening and stability of each outcomes, but as the results were both very similar and much complex to present in a synthetic way for four dimensions, we kept logistic regressions. Analyses of the detailed indicators were also performed and are available upon request (OLS regression on the continuous form of the SDQ change). We estimated a stepwise series of logistic regressions with our four well-being indicators as dependent variables, but present the regression with all covariates only.
Our main variables of interest are each parent's level of education, the evolution of the professional and financial situation during lockdown, and type of housing. Mothers' and fathers' educational levels were measured in three groups: secondary school or less, some tertiary education (a 1-year or 2-year degree, such as post-secondary school vocational degrees), and bachelor's degree or more. For the descriptive analysis, we used each parent's education level, but for the regression models, we keep only the mother's educational level in order to consider single mothers. For employment, five situations were distinguished for each parent: did not work before the lockdown, stopped working because of the pandemic, worked on-site only, teleworked only, and had mixed types of work situations. For the financial situation, we control for household income using the income quintile measured in the pre-COVID wave of the Elfe cohort and a dichotomous variable indicating whether or not the household's financial situation worsened after the start of the pandemic. This allows us to distinguish between the household's usual living standards of the households and financial changes due to the COVID crisis. For housing conditions, we distinguish between flats without external space, flats with external space, and houses; we also include a variable indicating whether the child can isolate himself/herself easily, with difficulty, or whether this is impossible. The control variables included are the child's sex and family structure (whether the child lives in a two-parent family, with a single parent, or in a shared custody arrangement; also whether the child has siblings or is an only child). Finally, the longitudinal nature of the data allows for us to control for pre-lockdown SDQ, measured at 5.5 years of age. 4

The SES gradients
The family's well-being during lockdown is correlated with the socioeconomic conditions of the household (see Figure 2). For each of our well-being indicators except SDQ, there is a clear gradient according to each parent's level of education, which is more or less pronounced according to the indicator observed. The proportion of children whose parents declared having a negative experience during the lockdown was much larger among the least educated compared to the most educated groups, there is also a clear gradient according to mother's level of education. With regard intra-household relationships, a deterioration of the parent-child relationship or siblings relationship were less likely among the most educated group compared to the least educated group. Previous results are based on mother's education but are similar for father's education, except that there is no visible gradient for the family's experience during the lockdown (see Appendix Figure A2). Since initial level of SDQ is not controlled for in this descriptive graph, the interpretation of raw percentage is limited. We observe than children presenting fewer socio-emotional problems initially such as those having a high educated 4 Other explanatory variables were taken into account, such as the age of the parents, the child's school work time, his or her daily leisure time or the number of outings in the last 7 days. These variables have not been retained because they were too highly correlated with the other variables of interest or because of potential problems of reverse causality.
mother are more likely to know a degradation of their score than others, with no difference between having a bachelor's degree or less.

Figure 2:
Four outcomes (binary negative version) by mother's education level Similar trends are observed when looking at family incomes. As shown in Figure 3, there seems to be a gap between the families in the first two income quintiles who are more likely to have negative experience of lockdown, or worse family relationship. They were more likely to have a negative experience during the lockdown; and both the parentchild and siblings relationships were worse on average compared to families with higher household income.

Figure 3:
Four outcomes (binary negative version) by mother's education level

The importance of past child outcomes
Children with pre-COVID socio-emotional difficulties may encounter specific challenges during the lockdown that can potentially affect the family experience with the lockdown and the relationships between family members. Their difficulties may be exacerbated by the disruption of their regular routines and the lack of interactions with their peers. Lockdown conditions may therefore trigger intra-familial conflicts. As expected, Figure 4 shows that socio-emotional difficulties were exacerbated in children with previous difficulties. Intra-family relationships, especially between parents and children and to a lesser extent between siblings, were clearly worse when the child had previous socioemotional difficulties. The share of those reporting negative family experiences during the lockdown increased with the level of child socio-emotional problems and was especially high for children with the most socio-emotional difficulties pre-lockdown (belonging to the top quintile SDQ score). As previously mentioned, the worsening of socioemotional difficulties is more likely when the initial score was low. This supports and confirms the idea that it is essential to control for the initial level when analysing change.

Figure 4:
Four outcomes (binary negative version) by quintiles of previous SDQ Table 1 shows the results of the regressions models predicting the likelihood of our four outcomes: parents considering the lockdown a negative family experience, worse parentchild relationships, worse sibling relationships, and worse child SDQ score. 5 While mothers' level of education was significant when no additional controls were included, it was not statistically significant when working status and financial situation are added (the coefficients for mothers with low and middle levels of education are always positive but do not indicate significant differences between these education levels and high education levels). Alternative specifications using the highest level education of parents or fathers' education levels give similar results. The penalty previously observed in descriptive analysis for those with lower educational level appears therefore to be related to their material conditions during the lockdown. Regarding employment and economic factors, we observe a small effect of parents' work status on some of the outcomes. When the mother worked outside home during the lockdown, the parent respondent (in most cases, the mother) was more likely to declare the lockdown a negative experience for family life. Parent-child and sibling relationships were also significantly worsened when the father worked outside the home. Thus, it seems that the absence of one parent, even temporarily when he or she worked outside the home, was detrimental to family life in this specific context. The level of household income did not significantly impact any of the four outcomes considered, once all controls are included. However, financial deterioration increased the likelihood of viewing the lockdown negatively, having worse intra-family relationships (the direction is similar but not significant for the parent-child relationships), and children worsened socio-emotional score.

Regression models
Regarding housing conditions, the type of housing (house or flat with or without an external space) had little significant effect. Parents living in a flat, whether they had access to an external space (yard, balcony) or not, were more likely to have a bad experience of the lockdown than those living in a house, all else being equal. Whether the child could isolate themselves at home was highly significant, and this strongly affected all four outcomes. When children were less able to isolate themselves, the outcomes were worse.
Apart from the material living conditions, the family structure little affected wellbeing during lockdown. Single parent families (captured by both the family structure variable "being lone parent" and the item "mother/father not in household" from the mother's and father's employment statuses) suffered more and were more likely to have a negative lockdown experience. Since the data used consist of a cohort of children, the sample is homogenous in age but differs by sex and number of siblings. Being a single child increases the risk of deterioration of the SDQ. Children with more socio-emotional difficulties are more likely to have negative experience of lockdown or worse relationship with parents or with other siblings.
As pointed out in our descriptive results, the lockdown provided some families an opportunity to spend more pleasant time together. If we consider the opposite outcomes, the probability that the lockdown has been our positive dummies (i.e. that intra-family relationships were improved, or improved score of SDQ), most of the determinants perform as expected, in the opposite direction of the negative outcomes, with a few interesting exceptions that deserve attention (see Table 2).
Our results suggest that working outside the home for the mother during lockdown is the only professional situation that really penalises families, since it also reduced the likelihood of having improving outcomes, and for two of them significantly. They also suggest that the possibility of the child isolating him/herself was often a prerequisite for having a positive experience of lockdown. We also note that the relationship between parents and children benefited from a shared custody arrangement. In contrast to what was found for the negative outcomes, where education was not significant once other controls were added, we found that the lower education group was less likely to have a positive experience of the lockdown than high education group. Finally, the reduction of incomes had little effect on the positive outcomes, except for the child's socio-emotional score, where an income drop decreased the probability of having improved SDQ score.
The children having more difficulties are more likely to have better relationships with parents and other siblings. This result shows a large heterogeneity in children reactions to lockdown, as previous ones showed worse relationships, especially for children having the most difficulties (belonging to top quintile of SDQ 6 ). We did observe that parents of boys were less likely to report an improvement of the SDQ. Note: When the mother worked on-site, the parent respondent was more likely to declare the lockdown a negative family experience than when the mother was teleworking on a full-time basis. *** p<0.001, ** p<0.01, * p<0.05. Note: When the mother has a lower educational level, the parent respondent is more likely to declare the lockdown a positive family experience or improved sibling relationship than when the mother is highly educated. *** p<0.001, ** p<0.01, * p<0.05.

Discussion
This article explored the consequences of France's first COVID-19 lockdown in the spring of 2020 on intra-family relationships and children's socio-emotional well-being. During that period, most workplaces, schools, and extra-curricular activities were closed, and all activities outside the home were strictly limited. Given the disruption of all family routines and living in a vacuum, we expected family resources to be key factors shaping the experience of lockdown restrictions. Using national longitudinal data from a sample of around 4,500 families with a child aged around 9 and focusing on four indicators of family and child well-being, we found that primary school children and their families adapted relatively well to the change. However, this period was challenging for a small but significant proportion of families.
As expected, we found that families with children experiencing challenges prior to lockdown were most affected, as it is more difficult for parents to handle them without outside support. We found a negative relationship between pre-COVID socio-emotional problems and family well-being during lockdown. However, children who had the most difficulties before lockdown were not necessarily the most affected by the stay-at-home measures, showing a strong heterogeneity in child's reaction. Indeed, school requirements and timetables were lightened; the children with the most difficulties also benefited more from this relaxation of constraints. This result echoes other studies on adolescents that have shown that those with the most academic difficulties are those who reported the best experiences of lockdown (Buzaud et al., 2021).
If we go back to our theoretical assumptions, we find that parental education is positively associated with better intra-family relationships and experiencing the lockdown positively as a family. However, parent's level of education was much less significant once employment and financial situation were taken into account. This therefore only partially verifies our first hypothesis (H1), which assumes fewer difficulties for families with higher levels of education. This mixed result may be linked to the various ways that parents invested in childcare and the pressure they put on themselves to parent during this context. During the lockdown, one of the main challenges was ensuring the continuation of school work and keeping children busy. Qualitative research showed that parents were very concerned about schooling. Schoolwork was a struggle, particularly for less educated parents because they had to manage homework with little equipment, more constraints on their time and fewer cultural, financial and social resources. Inversely, monitoring school work might have been easier for more educated parents (Garbe et al. 2020;CAFC 2021), especially as their children have fewer school difficulties on average. In highly educated families, parents who normally have extended working hours may have taken advantage of the stay-at-home period to spend more time with their children, which is why we observe a more positive lockdown experience for this group.
However, 13% of these highly educated families reported negative lockdown experiences. One possible explanation is related to active parenting (Lareau 2011). Highly educated parents might have felt particularly compelled to increase their parenting activities and strictly control children's screen time (Garbe et al. 2020;Berthomier and Octobre 2020;Thierry et al. 2021), which may have also generated tensions in some families. The inability to outsource domestic and childcare activities as during normal times may have led to an overload of childcare efforts, especially for mothers. This unequal sharing of parental work in more equality-sensitive families may also have led to tensions.
We also hypothesised greater difficulties for families whose financial and/or professional situations deteriorated during the lockdown (H2a). This was found to be particularly the case for parents who worked outside their homes during this period. Those working outside the home during the first peak of the pandemic were mostly frontline employees in essential activities, often in contact with other people at work or in public transportation. This may have been very stressful, particularly for parents with a 9year-old child. Parent stress might have affected the ability to provide effective parenting and may have spread to other family members, leading to strained family relationships or increasing children's socio-emotional problems. An additional stressor is related to the evolution of family income. Despite strong public policy support, including the introduction of paid furloughs and financial support for self-employed people, some families reported drops in their incomes. Our results highlight that it is not so much the level of income per se that affected family well-being as much as its evolution. Thus, traditional SES stratifiers (such as education and income) were not strongly correlated with family well-being during lockdown. On the other hand, factors related to the exceptional situation, whether the deterioration of financial situation or having to work outside the home while most people stayed at home, had a particularly negative effect on family relationships and children's socio-emotional well-being. Adults' concerns may have indirectly affected children. When lockdowns limit children's interactions largely to their families, there is little to mitigate the negative impact of parents' worries and anxieties on their children's well-being.
Our findings are in line with our hypothesis H2b and many other studies that have shown that housing conditions appear to be crucial for the lockdown experience (Lambert et al. 2020). This shows that for families, it was not so much the type of accommodation that was important as whether it provided the child with a place to be alone when needed. Having a place of their own enabled children to carry out their school work in a calm environment without distractions, but also to enjoy other activities away from the parental gaze and allowed them to isolate themselves in case of tensions. In total, these results confirm that material conditions were a strong determinant of family well-being during confinement, and that those with fewer material resources, notably resources linked to housing, have been penalised.
The present study has some limitations. First, our results are descriptive and our data and methods do not allow for a causal identification of a "real" effect of the lockdown on family functioning or on child well-being. This is notably the case for our child well-being outcome, where our construction of the variable identifying a "change" in well-being relies on a pre-lockdown measurement taken about four years before the Elfe-Sapris survey. We are not able to causally attribute changes in the child well-being scores between these two data points to lockdown. Second, due to social distancing measures, the Elfe-SAPRIS survey was implemented online, which have led to response bias. Families who had enough time to complete the questionnaire may have had the best experience of lockdown. Moreover, the poorest families, without access to the Internet or being less reachable by email (which was the way used for contacting parents), were not covered by our survey. However, these families have been the hardest hit by the economic consequences of the pandemic and have the poorest living conditions. In addition, the child's experience of confinement and well-being was reported from the perspective of the parent responding to the survey, in most cases the mother, and not from the perspective of the children themselves, which can positively bias the results if parents do not perceive their children's difficulties.
Our results show that, for most households, families' experience of France's first lockdown was on the whole relatively positive. However, this unprecedented period has exacerbated existing difficulties for families with poor living conditions and those facing deteriorating financial conditions. Despite the extreme uncertainty and concentration of family and professional activities in a single space for some, it was in a majority of cases an enchanted interlude, during which parents and children were able to spend time together and share activities. These results occurred during a particular period when everything was new, and within a context of relatively strong governmental safety nets for households. Subsequent lockdowns were quite different, as children returned to school and the workload on working parents increased while for others did not work. Further research is needed to monitor long-term consequences of the Covid crisis for family wellbeing.