Guillaume Gueguen

Claudia Senik

Adopting Telework. The causal impact of working from home on subjective wellbeing

Keywords: Work from Home, Life Satisfaction, Mental Health, Covid-19 Work from Home, Life Satisfaction, Mental Health, Covid-19 JEL codes: I31, M5

We study the impact of work from home on subjective wellbeing during the Covid period, where self-selection of individuals into telework is ruled out, at least part of the time, by stay-at-home orders. We use a difference-in-difference approach with two-way fixed-effects and identify the specific impact of switching to telecommuting, separately from any other confounding factor. In particular, our identification strategy avoids the influence of inter-personal heterogeneity by exploiting the multiple entries into telework, by the same individuals, at different times. On average over the period, switching to work from home -especially full-time, worsens mental health. We also distinguish a positive but imprecisely measured impact of part-time telework on life satisfaction. However, this hides a dynamic evolution, whereby the initial deterioration gives place to an adaptation process after a couple of months. We also uncover a particularly pronounced fall in subjective wellbeing of women with children's subjective, especially in the first months; this could be associated with home-schooling.

Introduction

One of the major legacies of the Covid-19 pandemic will certainly be the extension of IT-based distant interactions, in particular telework. In most countries, nonpharmaceutical interventions against the pandemics included a massive and forced use of telecommuting whenever it was possible to carry out one's job from home.

In the UK for instance, this concerned about one third of all jobs, mostly in the service sector. This shock has come as an acceleration of an ancient but slow ongoing evolution led by digital technology, that enabled work to be done outside the premises of the firm, at home, in remote offices, or in co-working spaces. Once the pandemic is over, a return to the statu quo ante is unlikely, as the potential stigma that was associated with remote work has disappeared, and workers and companies have made substantial investments in the equipment needed in order to work from home [START_REF] Barrero | Why Working from Home Will Stick[END_REF]. Although [START_REF] Dingel | How Many Jobs Can Be Done at Home?[END_REF] calculated that, on average, 37% of U.S. jobs could technically move to full telecommuting, this proportion could reach much higher levels in some sectors and occupations, such as managers [START_REF] Hensvik | Which Jobs Are Done from Home? Evidence from the American Time Use Survey[END_REF]. The stakes are high, as a massive and sustained shift to telework would set off a chain of far-reaching consequences, not only for work arrangements, but also for land use, the housing market, labour costs, employment levels and macroeconomic growth [START_REF] Bergeaud | Adjustment Costs and Factor Demand: New Evidence from Firms' Real Estate[END_REF]. Whether work from home (WfH) will stay eventually depends on its impact on productivity (from the labour demand side) and on the value that workers see in this possibility. We are interested here in the labour supply side: is telework conducive to workers' wellbeing?

We analyse the question through the lens of self-reported life satisfaction and mental health. In this literature, self-declared life satisfaction is considered as a synthetic over-arching concept that subsumes subdomains, such as job satisfaction, family satisfaction, satisfaction with leisure, etc. [START_REF] Van Praag | The Anatomy of Subjective wellbeing[END_REF].

Mental health indicators, on the other hand, are based on a clinical approach of subjective wellbeing.

We study the impact of work from home (WFH) due to the lockdown episode imposed by the Covid pandemics, although, once the pandemics is over, the workers may also consider the possibility of distant work outside the premises of their firm in other locations than home, such as shared working spaces or remote offices made available by the firm, for example. We discuss how this restricts the generality of the results.

The influence of work from home on subjective wellbeing is likely to transit principally through job satisfaction, but not exclusively, and its net impact is a priori ambiguous, although working from home has often been an unmet demand on behalf of workers, usually considered with suspicious by employers. Firstly, each of the main drivers of wellbeing at work that have been identified by the literature, i.e. autonomy (Csíkszentmihályi, 1990;Karasek and Theorell, 1990), social capital (Helliwell andHuang 2010, 2011), progression perspectives (Loewenstein andSicherman, 1991, Frank andHutchens, 1993;Senik, 2005), purpose (Cremer, 1993, Fehr andSchmidt, 1999;Cassar and Meier, 2018;Bailey et al., 2019;Henderson and Van den Steen, 2015;Yeoman et al. 2019), job security and work-life balance [START_REF] Warr | wellbeing and Theworkplace[END_REF](Warr , 2007;;[START_REF] Clark | What Really Matters in a Job? Hedonic Measurement Using Quit Data[END_REF][START_REF] Green | Demanding Work. The Paradox of Job Quality in the Affluent Economy[END_REF][START_REF] Gallie | Employment Regimes and the Quality of Work[END_REF]Gallie, , 2013)), could be either enhanced or attenuated by WFH. We hypothesize that distant working is likely to be favourable to autonomy and work-life balance, but detrimental to social capital, purpose, future perspectives, and job security, because of the impoverishment of inter-personal interactions, and the remoteness from the firm's locus of control. One can thus expect life satisfaction to be improved by telework thanks to the alleviation of commuting constraints [START_REF] Stutzer | Stress That Doesn't Pay: The Commuting Paradox[END_REF][START_REF] Bryson | Are You Happy While You Work?[END_REF] and a general increased freedom on one's time use, but that mental health would deteriorate for those who benefit from the firm as a social integration structure. We also expect these negative effects to be stronger for those who work entirely from home than for workers who split their time between home and the firm, and thus benefit from the continuation of "in person" social contacts. We are also interested in the dynamic effect of working from home: do people feel increasingly isolated as they spend more time in this arrangement, or do they adapt progressively? Overall, as Mas and Pallais (2020)'s survey illustrates, the net impact of telecommuting on subjective wellbeing is a priori ambiguous. We test for these different effects using the life satisfaction question included in the survey, as well as the twelve dimensions of the general health questionnaire (GHQ) of mental health, which address several of the aforementioned channels.

In terms of empirical evidence, pre-Covid and Covid episodes also offer ambiguous lessons. Prior to the health crisis, and despite the rarity of telework, which concerned 3% to 5% of workers in OECD countries (Flex Jobs 2017; ONS 2019), many empirical studies had examined the relationship between work from home and subjective wellbeing, without reaching consistent results [START_REF] Gajendran | The Good, the Bad, and the Unknown About Telecommuting: Meta-Analysis of Psychological Mediators and Individual Consequences[END_REF][START_REF] Bailey | A Review of Telework Research: Findings, New Directions, and Lessons for the Study of Modern Work[END_REF][START_REF] Oakman | A Rapid Review of Mental and Physical Health Effects of Working at Home: How Do We Optimise Health?[END_REF]. The meta-analysis led by [START_REF] Oakman | A Rapid Review of Mental and Physical Health Effects of Working at Home: How Do We Optimise Health?[END_REF] pointed to the less beneficial health effect of work from home on women, certainly due to the blurring of work-home boundaries. Famous experiments conducted within companies suggest a positive effect of telecommuting on wellbeing, but it is difficult to generalize the lessons drawn from these particular cases [START_REF] Bloom | Does Working from Home Work? Evidence from a Chinese Experiment[END_REF][START_REF] Mas | Valuing Alternative Work Arrangements[END_REF][START_REF] Delanoeije | Between-Person and Within-Person Effects of Telework: A Quasi-Field Experiment[END_REF].

Early empirical studies of the massive telework episode due to Covid-19 often conclude to the negative effect of telework, especially for women [START_REF] Lyttelton | Gender Differences in Telecommuting and Implications for Inequality at Home and Work[END_REF][START_REF] Xiao | Impacts of Working from Home During Covid-19 Pandemic on Physical and Mental wellbeing of Office Workstation Users[END_REF]), but do not really disentangle the impact of telework per se from that of the health crisis [START_REF] Gibbs | Work from Home & Productivity: Evidence from Personnel & Analytics Data on It Professionals[END_REF][START_REF] Etheridge | Worker Productivity During Lockdown and Working from Home: Evidence from Self-Reports[END_REF][START_REF] Barrero | Why Working from Home Will Stick[END_REF]. The fall in subjective wellbeing due to the context has been abundantly documented (e.g. [START_REF] Pierce | Mental Health Before and During the Covid-19 Pandemic: A Longitudinal Probability Sample Survey of the UK Population[END_REF][START_REF] Pelly | Worker wellbeing Before and During the Covid-19 Restrictions: A Longitudinal Study in the UK[END_REF][START_REF] Sibley | Effects of the Covid-19 Pandemic and Nationwide Lockdown on Trust, Attitudes Toward Government, and wellbeing[END_REF][START_REF] Anaya | Locked down in Distress: A Causal Estimation of the Mental-Health Fallout from the COVID-19 Pandemic in the UK[END_REF][START_REF] Banks | The Mental Health Effects of the First Two Months of Lockdown and Social Distancing During the Covid-19 Pandemic in the UK[END_REF][START_REF] Brodeur | COVID-19, Lockdowns and wellbeing: Evidence from Google Trends[END_REF][START_REF] Schmidtke | The Effects of the Covid-19 Pandemic on the Mental Health and Subjective wellbeing of Workers: An Event Study Based on High-Frequency Panel Data[END_REF]), but while in the early days of the lockdown, increased symptoms of depression and anxiety were often attributed to telecommuting, with the easing of restrictions, many surveys revealed that the vast majority of workers do not want to return to the office 5 days a week (e.g. [START_REF] Felstead | Homeworking in the UK: Before and During the 2020 Lockdown[END_REF].

Only a few studies are able to disentangle the pure effect of work from home from that of the Covid context, thanks to longitudinal panel data, especially when they cover pre-Covid and Covid periods. Close to our work, a report by [START_REF] Felstead | Homeworking in the UK: Before and During the 2020 Lockdown[END_REF], based on the same British data, documents the fall in mental health indicators of newly home-centered workers, as compared to pre-Covid time, especially in April and May 2020. Our paper complements this report, whose ambition is to describe more broadly the extent, composition and impact of telework on several outcomes, but not life satisfaction, and who only uses 3 early Covid waves of the survey. Another recent study is that of [START_REF] Bertoni | Remote Working and Mental Health During the First Wave of Covid-19 Pandemic[END_REF] who use longitudinal data from the SHARE survey of senior Europeans and estimate the causal effect of switching to remote work during the COVID-19 pandemic on mental health. The paper uncovers negative effects of telework for respondents with children at home, but a positive effect for men and for respondents with no co-residing children. The limitation of that study is imposed by the data, which is restricted to senior workers and only contains mental health outcomes, but not life satisfaction. A study by [START_REF] Schifano | Well-Being and Working from Home During Covid-19[END_REF] tracks self-declared wellbeing measures of individuals across five European countries, using four waves of a longitudinal survey covering the period May-November 2020. They find no effect of switching into working at home, except for a small drop in anxiety. This could be due to the small size of their sample, which only contains 9700 observations for 5 countries and 4 waves, as well as the fact that the survey does not cover a pre-Covid benchmark period; it could also be due to the fact that they measure the average impact of switching to telework, whereas it is likely that the impact unfolds over time, as we will show.

In this paper, we identify the specific impact of switching to telework on subjective wellbeing, separately from a set of confounding factors such as the context of the health crisis (fear of contagion, recession, stress), potential heterogeneity between people who hold teleworkable jobs versus not, and unobserved individual heterogeneity in general. This is allowed by the long panel dimension and the high frequency of the data during the pandemic, as we use the United Kingdom Household Longitudinal Survey (UKHLS), which is usually run on a yearly basis, but has developed an additional Covid-19 module with frequent waves since April 2020, and contain both life satisfaction and mental health measures.

The fact that teleworking was imposed overnight by stay-at-home orders rules out the usual problem of self-selection of individuals into telework, at least during the most stringent lockdown periods. In the UK, the legal obligation to work from home whenever possible, was enforced during the entire period under study, with a particular strength during the lockdown episodes, i.e. between March 26th and June 23rd, 2020, as well as between November 5th and December 2nd, 2020. But, as there was no explicit legal list of service jobs that were obliged to switch to telework, some firms could keep or call their employees back on site when they considered it as "absolutely necessary". We thus assume that during the Covid-19 episode, a person was working from home if this had been decided by the government or their employer. We also discuss the possibility some degree of self-selection into WfH. Figure 1 illustrates the massive switch to telework starting in March 2020.

As many people have alternatively been telecommuting and working on site, and as we observe people at eight different points of times during Covid, between April 2020 and March 2021, we can identify the specific impact of working from home for these people, (i.e. those who hold a teleworkable job), hence exploit the intra-individual variations in a person's working arrangement during the Covid episode. We thus follow a difference-in-difference approach with individual and time fixed-effects, and estimate the impact of switching to telework on subjective wellbeing measures. Hence, within the group of people who did not use to telework before the Covid crisis, we compare the subjective wellbeing of those who work at home at some point during the Covid episode in 2020 and 2021 to that of people who are not teleworking at that time (including themselves at times they do not telework). In the language of difference-in-difference analysis, we consider the situation of being working at home during Covid as a "treatment", we call "intention to treat" (ITT) people who did not telework before 2020 and do telework at least once during the eight waves of 2020 and 2021. Hence "treated" people are ITT individuals who are actually working from home in a given wave of the special Covid survey;

and not ITT are people who never telework in 2020 or 2021.

We also identify the impact of the duration of working from home. In this regard, one can potentially expect two opposite effects: positive adaptation to new social, technological and organisational constraints, or an increasingly negative desocializing impact of distance to firm and colleagues. We expect the results to be different from the ones uncovered by other studies that only contrast work from home and work on site during the Covid period because their data do not cover the pre-Covid time or because they do not have panel data.

But we also expect to find different results from studies that only have one point in time for the Covid period, hence cannot observe the subjective wellbeing of the same workers depending on whether they are working from home or not during Covid times: these studies cannot distinguish the effect of switching to WfH from the differential impact of the crisis on workers depending on whether they hold a teleworkable job.

We show that in average over the Covid period, work from home exerts a positive, but imprecisely measured impact on self-declared life satisfaction, but a rather negative effect on mental health (GHQ score), depending on the intensity of distant work: In average, "always" working from home is detrimental to mental health, but there is no effect of "often" WFH. The average negative impact of full telework on workers' global score of mental health hides a dynamic evolution, as the initial deterioration disappears after a period of adaptation of several consecutive months of WfH. we also observe a stronger negative effect of telework on women with children under 15 years old, especially over the April-July 2020 period -an effect that is likely to be related to home-schooling. Our identification strategy relies on the assumption that workers have not had the choice whether to work from home or not. Inasmuch as this assumption is correct, our results suggest that working entirely from home is prone to have a detrimental effect on mental health, but that people can adapt to this arrangement, both psychologically and by taking the necessary practical adjustments. However, we also consider the possibility that some workers have had the possibility of choosing their working arrangement, especially at the end of the period. In June 2020, September 2020, and January 2021, surveyed workers were asked: "Once social distancing measures are relaxed and workplaces go back to normal, how often would you like to work from home? (Always, often, sometimes, never)". We do find a small correlation between declaring a desire to work "often" or "always" from home in the future and the likelihood that one is actually teleworking in the subsequent waves of the survey. Hence, although this cannot be interpreted as causal, we cannot exclude a certain degree of self-selection. We thus refrain from concluding to the possibility of enforcing generalized full work from home as the norm without psychological harm.

We are aware of the limits of this study, as it relies on the Covid-based lockdown episode which had two specific features: The first one is that people had to work from home in the literal sense, with the specific implications of this arrangement, such as possible confusion between private and professional life, especially for women. After Covid, distant work may persist, but it can also take place in tier-places such as co-working spaces or distant offices, with potentially different effects on mental health. The second one is that distant work was explicitly extended to its furthest possible limits, thus excluding stigma or any other feeling of particular exclusion, privilege, or guilt by those who were concerned. After the end of the Covid crisis, the effect on people's mental health will depend on the general coordination among workers and firms, and on the specific arrangement chosen by each firm, in particular whether they treat distant work as an objective or as a privilege. Keeping these limitations in mind, we proceed to studying the impact of work from home on subjective wellbeing in the context of the Covid crisis in 2020 and early 2021.

Data and Identification Strategy

We use the UK Household Longitudinal Survey (UKHLS), a rich yearly panel survey, which allows to track the same individuals over time and covers a wide range of topics, including self-reported wellbeing measures. An additional Covid-19 module was added, with waves in April, May, June, July, September and November 2020 as well as January, March and September 2021 (Understanding Society 2020b, 2020a). We use four pre-Covid waves (2016-2019) and eight of the aforementioned Covid waves (we leave September 2021 out of the sample, as it is too distant in time from the previous wave).

Our sample comprises employed people with a positive number of working hours in each wave. After dropping individuals for whom information on telework is missing from the Covid module, or who changed place between 2019 and 2020, it contains 9284 different individuals.

We run our analysis on the entire unbalanced panel formed by the individuals who are surveyed in the pre-Covid waves as well as in some Covid waves. For robustness, we considered using a strictly balanced panel, but this would leave us with roughly 1/13th of the initial sample size (727 observations), which would obviously induce a selection large bias and lower precision of the results. We chose to follow an intermediate approach, which consists in constructing a "quasi-balanced" panel, where we keep people who are observed in at least four out of the eight Covid waves, i.e. 4346 individuals. We also experiment with other variants of "quasi-balanced panel", i.e. keeping people who are observed in at least three (5255 individuals), or five (3416 individuals) times out of the total eight waves of the Covid panel.

Our main dependent variables are the standard measures of subjective wellbeing: self-declared life satisfaction and the GHQ12 scores (OECD, 2013). Life satisfaction is scaled on a 1-7 scale. It was measured at each wave, except in April and June 2020. As is classic in this research domain, we analyse it as a cardinal measure [START_REF] Ferrer-I-Carbonell | How Important Is Methodology for the Estimates of the Determinants of Happiness?[END_REF]. The GHQ module (included in all waves) contains 12 questions related to different dimensions of mental health, i.e. concentration, loss of sleep, the feeling of playing a useful role, being capable of making decisions, feeling constantly under strain, problem overcoming difficulties, enjoying day-to-day activities, ability to face problems, feeling unhappy, feeling depressed, losing self-confidence, feeling worthless. For each of the 12 questions, for example "Have you recently been able to concentrate on whatever you are doing? ", respondents must tick an answer out of four modalities: much less than usual (0), less than usual (1), same as usual (2), better than usual (3). We also create a synthetic variable by summing the answers to the 12 questions (dropping observations for which one dimension is missing). The obtained global (recoded) GHQ score runs from 0 (the most distressed) to 36 (the least distressed). These measures of subjective wellbeing address most of the potential impacts of working from home, as discussed in Section 1.

Over its thirty years of development, the subjective wellbeing literature has questioned the validity and reliability of these outcome measures. One of their drawbacks is that they may reflect two types of unobserved individual heterogeneity: first, the way people transform the circumstances of their life into wellbeing, and, second, the way they express their latent level of wellbeing on a discrete scale. However, provided that these are time-invariant personality traits, these problems can be surmounted by using longitudinal panel data, such as the UKHLS, that allow controlling for individual fixed-effects. Other criticisms have pointed to the difficulties of using a subjective discrete scale (Bond and Lang 2019), but in practice these measures have proven their consistency and their predictive power, and are now considered as mainstream tools [START_REF] Frey | Happiness and Economics[END_REF][START_REF] Kahneman | Developments in the Measurement of Subjective wellbeing[END_REF][START_REF] Layard | Happiness: Lessons from a New Science[END_REF][START_REF] Christopher | Trends in conceptions of progress and wellbeing[END_REF]. In view of our specific exercise, it is particularly important to be able to follow the same individuals before and during Covid, as well as to observe them several times during Covid. This is because it allows controlling for individual heterogeneity in the way people (in different occupations for instance) react to the Covid crisis, and to distant work itself. Other analyses of the impact of telework on subjective wellbeing that are based on data that do not cover the pre-Covid data, or only observe individuals once during the Covid period, are unable to avoid these problems.

The regular main module of the UKHLS asks "Do you work mainly at...", where a possible answer "At home" is available. We use this to identify people working from home between 2016 and 2019. The Covid-19 module of the UKHLS contains the following question: "During the last four weeks how often did you work at home? ", with four response modalities: Always, Often, Sometimes, and Never. We consider separately the "always" and "often" modalities as different intensities of WfH and "sometimes" and "never" as not WfH [START_REF] Felstead | Homeworking in the UK: Before and During the 2020 Lockdown[END_REF]. We understand "always" as a situation where people work fully from home, and "often" as one where they sometimes work within the premises of the firm. We verify that the WfH intensities ("often" versus "always" or not WfH) are roughly the same over the different Covid waves (Appendix Table A1), hence are not driven by time-effects.

We use difference-in-difference estimates with two-ways (individual and wave) fixed-effects. We assume that the obligation to work from home during lockdown episodes was an exogenous shock imposed by the government or by their firm on individuals who held a teleworkable job. We will discuss this assumption latter.

We define an individual bimodal variable that takes value 1 if we see a person working from home at least once in 2020 or 2021 but not before 2020, and 0 otherwise. In the language of Randomized Experiments, this variable identifies "Intention To Treat" individuals (ITT). We then define a binary variable "Treated", which

T reatedi,t = Covidt * IT Ti * T eleworki,t (1)
For example, consider ITT individuals who work from home in April, May and June 2020, go back to work on site in July, September and November 2020 and work again from home in January and March 2021: these people are identified as "ITT" in all periods, but their "Treated" variable will take values 1 -1 -1 -0 -0 -0 -1 -1 respectively during our 8 Covid waves. Note that in the sample, a small number of individuals declared that they were working from home in pre-Covid waves. As we are interested in the impact of exogenously switching to telework, we are not considering these people as part of the ITT group. ITT identifies people who hold a teleworkable job but did not telework before 2020. Alternative specification where we drop these individuals from the sample leave the results essentially unchanged. The descriptive statistics of the regression sample appear in the Appendix Table A1 .

Figure 2 offers a clear picture of the evolution of life satisfaction for four groups of workers (excluding those who teleworked before Covid-19): people who never telework (red line), people who are not teleworking at the time they are interviewed (ITT not teleworking, purple line), people who "always" telework at the time they are interviewed ( blue line), and people who "often" telework (green line). Before May 2020, all ITT are in the same group (ITT, purple). From May 2020 onwards, the ITT group splits in two parts: treated (blue and green lines) or untreated (purple). Pre-Covid-19, the trends in life satisfaction and GHQ are the same whether people hold a teleworkable job or not.

The figure shows that during Covid, life satisfaction is higher among people who are working from home, Except in the first Covid wave, people who "often" WfH report a higher level of life satisfaction than any other group. People who are not teleworking, whether they hold a teleworking job or not, report a lower level of life satisfaction.

The dynamics of the GHQ score (Figure 3) is different, as people who do not hold a teleworkable job almost always report a higher score of mental health (red curve). Starting in June 2020, those who work from home (green and blue) fare better than those who hold a teleworkable job but work on site (purple).

In order to go beyond this descriptive approach, we run econometric estimates of the causal impact of WfH on subjective wellbeing. We use a difference-in-difference estimation with two-way fixed-effects (individual and wave level), following equation (2) :

Yi,t = α + β * Covidt + γ * IT Ti + ϕ * Covidt * IT Ti + δ * TreatedALWAYS i,t + λ * TreatedOFTEN i,t + θ * Xi,t + ψ * Xi,t * Covidt + Wt + µi + ϵi,t (2)
with:

T reatedALW AY Si,t = Covidt * IT Ti * T eleworki,t[ALW AY S]
and:

T reatedOF T ENi,t = Covidt * IT Ti * T eleworki,t[OF T EN ]
where Yi,t is alternatively the GHQ (0 -36 Our parameters of interest are δ and λ, which, under the assumptions that ITT individuals did not have the choice to telework or not, identifies the causal effect of working from home during Covid, either "always"

)
or "often". They compare the difference in wellbeing of individuals who are "always" teleworking at time t (δ)

or "often" teleworking at time t (λ) versus ITT individuals who are not teleworking at time t (control group).

By construction, all these individuals hold a teleworkable job. Note that parameters δ and λ capture a mix of between-individuals and within-individual effects, as they estimate the wellbeing difference between ITT individuals who are currently teleworking and ITT who are not, including themselves in other Covid waves.

Xi,t is a vector containing the usual socio-demographic controls, i.e. the logarithm of net monthly household income, size of the household, gender, age and age squared of the respondent, 1-digit ISCO occupational codes, highest diploma completed, number of worked hours, dummy variables for living with a 0-15 years old child, and in a rural area. We interact all these controls with the Covid-19 dummy (Xi,t * Covidt) in order to account for the possibility that reactions to the crisis differed across groups of the population (as in [START_REF] Pierce | Mental Health Before and During the Covid-19 Pandemic: A Longitudinal Probability Sample Survey of the UK Population[END_REF]. Suppose, for instance, that men were more negatively affected by the health crisis than women, and were also more likely to be teleworking, then not controlling for the interaction would lead to underestimate parameter δ. These controls and interactions enable to purge parameter δ from individualspecific reactions to Covid-19 shock. We include all these controls in all our estimates, even when not displayed in the tables for space reasons. µi stands for individual fixed-effects. This specification controls for unobserved individual heterogeneity, in particular any trait that could have oriented people towards a teleworkable versus non teleworkable job (education, skills, taste, etc.). Finally ϵi,t is the error term.

Dynamic analysis

We also study the dynamic effect of the duration of telework. This evolution is a priori ambiguous, as workers could feel increasingly disconnected from their colleagues, or, alternatively, could adapt to their new work arrangement both psychologically and by taking the necessary logistic adjustments. We are interested in the impact of consecutive months of telework on subjective wellbeing. We thus estimate the impact of "always" (resp. "often") working from home for one month, i.e. 1 wave (δ1, resp. λ1), for the second consecutive month (λ2), the third consecutive month (λ3), the fourth consecutive months (λ4 ), and so on. Our estimates follow the structure of equation ( 3):

Yi,t = α + β * Covidt + γ * IT Ti + ϕ * Covidt * IT Ti + n=8 n=1 δn * TreatedALWAYS * [n th W ave] + n=8 n=1 λn * TreatedOFTEN * [n th W ave] + θ * Xi,t + ψ * Xi,t * Covidt + Wt + µi + ϵi,t (3)
For each wave, this specification operates a partition of ITT individuals in groups characterized by the wave and the telework intensity, with "not currently working from home" as the reference category. Each parameter δn and λn measures the wellbeing impact of being in one's n th consecutive wave of WfH, as opposed to not being currently working from home.

Heterogeneity

We also run tests of the heterogeneity of the effects, asking whether work from home was more beneficial or detrimental to women or men, younger or older persons, people with or without children, living in cities or the countryside, etc. We are particularly interested in the presence of children, which is likely to have caused work-family tensions when home-schooling was in order. This may have impacted teleworkers more, as they were home with their children, or on the contrary, created more organizational difficulties for parents who had to leave their children at home, unattended. When running these treatments, we follow the logic of equation

(2) , separating the pure effect of WfH from the Covid context, and interacting the Treated variable with the hypothesized source of heterogeneity, as in equation ( 4).

Yi,t = α + β * Covidt + δ1 * Treated i,t + δ2 * Treated i,t * couple i,t + θ * Xi,t + ψ * Xi,t * Covidt + Wt + µi + ϵi,t (4)
We also estimate equation ( 2) on the sub-samples of women and men, with and without children under 15.

Self-selection

Although the identification of a causal impact of working from home relies on the assumption that this arrangement was imposed on people rather than chosen, one cannot be totally sure that there was absolutely no decisional latitude on behalf of workers. To enquire, we use a question that was included in the questionnaire at three points of time-June 2020, September 2020, and January 2021, and asked respondents: "Once social distancing measures are relaxed and workplaces go back to normal, how often would you like to work from home?

Always, often, sometimes, never ". We then estimate the correlation between the answer to this question and the likelihood of being actually working from home in later points of time following equation (5).

T reatedi,t+n = α + W F Hf uturei,t + θ * Xi,t + ϵi,t

We interpret this correlation as the maximum possible self-selection, i.e. assuming that any association between wishing to work from home and actually doing so is due to the person's decision, which of course is far from the truth. We cannot go further than this exercise because of two data limitations: first, the question was only asked in three out of eight the waves of the Covid survey; second, it was only asked to people who were actually working from home, and these are not the same at all waves. Hence, the information is missing for a large number of individuals. This precludes using this question as a control in the estimates of equation

(2) or equation (3).

3 Results

Average effects of working from home

Table 2 displays the estimates of life satisfaction and a selection of GHQ scores following equation ( 2). (For space reasons, we display the results for the remaining GHQ questions in Appendix Table A3). Switching to working from home, whether "often" or "always" is positively associated with life satisfaction, but the effect is imprecisely measured and not statistically significant. By contrast, being "always" in distant work negatively impacts people's global score of mental health. This is true of most of the GHQ dimensions, i.e. concentration, usefulness, enjoyment, decision, self-confidence, overcoming problems, and depression. By contrast, "often" working from home exerts no precisely measured impact on mental health.

The opposite effect of "always" working from home on life satisfaction versus mental health (GHQ) reveals that the channel from WfH to these two dimensions of subjective wellbeing are not the same. For example, people may be happy because they do not have to commute to work, and are able to spend more time in their home, which is usually seen as a private and comfortable place (gemutlich), but have more mixed emotions concerning their work situation, such as feeling disorganized or demotivated by distant work. Note also that the dimensions of the GHQ that are obviously related to the work domain, such as ability to concentrate, selfconfidence, and feeling useful, are the most negatively affected by telework. This interpretation is compounded by the fact that working "often" from home does not have a negative impact on mental health. Partial work from home corresponds to a situation where the contact with the firm is maintained, which preserves the social integration and identity dimensions of work. Life satisfaction initially slightly increases for those who always work from home, in May and July 2020 (as well as those who "often" WfH, but the coefficients are imprecisely measured) but these effects wither afterwards. Concerning mental health, the transition to working from home is initially detrimental for those who "always" work from home, but this negative effect disappears after June 2020. Figures 6and 7 plot the same coefficients for specific components of the GHQ12, namely concentration and feeling useful. The patterns are similar: these outcomes are initially negatively affected by WfH, especially for those who "always" telework, but this negative impact disappears after a few consecutive months.

Dynamic effects

This dynamic evolution, also noted by [START_REF] Felstead | Homeworking in the UK: Before and During the 2020 Lockdown[END_REF], sheds light on the result found by other studies, such as [START_REF] Schifano | Well-Being and Working from Home During Covid-19[END_REF], who find no intra-individual effect of switching to telework. This could be due to the progressive adaptation to telework, which cannot be captured by a single average measure.

Attrition

One could worry that the dynamic improvement in mental health that we observe is due to attrition, whereby people whose mental health continues to deteriorate because of distant work end up dropping out from the panel. To enquire, we estimate equation ( 2) using a "quasi-balanced" panel, where we keep people who are observed in at least in four out of the eight Covid waves, i.e. 4346 individuals. As shown by Appendix Tables A7 andA8, the results are essentially unchanged as concerns mental health, i.e. the GHQ score deteriorates for those who "always" work from home. Concerning life satisfaction, the positive effect is more precisely measured,

Self-selection

Dynamic analysis shows that the average impact of work from home over the period under study is essentially driven by the two first waves of observation, i.e. April and June 2020. These are also the months of the first lockdown, which may have been particularly strict. Hence, we tend to trust these results as revealing of the causal effect of WfH. In July 2020, people seem happy to work from home, both in terms of life satisfaction and GHQ, but this is the time when the lockdown was lifted (although not the social distancing strategy), and possibly the beginning of summer holidays for some of them. Starting in September, no statistically significant impact of having been working from home since the start of Covid is distinguishable. This suggests that people have adapted to work from home, both psychologically and as in terms of logistical and ergonomic organization.

However, the fact that mental health improves over time for people who keep working from home could also reflect some degree of self-selection.

In our difference-in-difference setting, perfect identification of the causal effect of telework would require that workers have absolutely no say on whether they work at home at any point of time, which we are unable to verify. It is true that the gravity of the health situation, the successive stringent lockdown measures and the omnipresence of the slogan "stay at home, protect the NHS, save lives" provided strong civic incentives for firms and workers to abide. Nonetheless, there might have been some degree of self-selection in and out of telework when the lockdown was less stringent. Unfortunately, the UKHLS data is not precise enough to allow ruling out this suspicion by isolating the episodes and regions of strict lockdown, because the timing of data collection for each wave, and the period to which the question about telework refers ("During the last four weeks how often did you work at home?").

As explained in Section 1.4, we use a question about the willingness to work from home when the Covid is over in order to detect possible signs of self-selection. Using equation ( 5), we uncover a small correlation with the probability of being actually working from home in subsequent months. As displayed in table A4, A5 and, A6, the correlation between declaring in June 2020 that one wants to WfH when the pandemics is over (either "often" or "always") and being actually working from home in the subsequent months, is of about 0.08. It increases to about 0.10 to 0.12 for those who declare so in September 2020 or January 2021. However, there seems to be no self-selection in the intensity of the correlation between wishing to work from home "always" in the future and the probability of being actually "always" working from home in the subsequent months:

the correlation, if any, is negative. Identically, there is a weak (0.04) or no statistically significant correlation between wishing to "often" WfH at a given point of time, and being actually "often" working from home in subsequent periods.

As noted, the question was only asked to people who were currently working from home when the question was included in the survey, i.e. in three of the eight Covid waves. The small number of observations that are concerned precludes any further use of this variable, such as using it as a control or a selection variable.

Overall, we tend to be confident that the results for the period April to June reflect causality, and to interpret the subsequent period as a mix of adaptation and self-selection. But we also consider the possibility that distant schooling, which was more widespread before September 2021, may have weighted differently on parents depending on their workplace. We address this issue in the next section.

Heterogeneity

We finally ask whether our results depend on the specific situation of workers in terms of gender, family situation, place of residence, etc. We first estimate equation ( 4) and look at the interaction term between each of these categories and being working from home (Treated). We uncover a statistically significant negative impact of telework on the life satisfaction of parents (Table 3). To explore this finding, we successively run estimates of equation ( 2) on the sub-samples of women and men, with and without children under 15 (Table 4). It turns out that the influence of telework (both often and always) is particularly negative for women's life satisfaction and mental health when they have children. by contrast, we detect no specific effect of children for men who telework. Because of the dynamic adaptation phenomenon that we uncovered, and because we suspect that part of this negative effect is due to the burden of home-schooling, which predominantly accrued to women, and was more prevalent before the summer 2020, we split the sample into two sub-periods: April-July 2020, and September 2020-March 2021. As expected, we observe that the impact of children is essentially concentrated in the first sub-period. It also seems that women without children benefit more from telework in the second period.

Conclusions and Discussion

With the health crisis, the sudden and unexpected obligation to work from home and the massive extension of this arrangement create the condition for identifying the causal effect of telework on subjective wellbeing, in the way of a "natural experiment". Overall, our results suggest that in average over the period, working entirely from home has deteriorated workers' mental health, in particular concentration, self-confidence, or feeling useful. We also detect a small and imprecisely measured positive effect on life satisfaction. However, after a couple of months, these effects withered for those who remained in telework for several consecutive months.

Can the dynamic effects that we uncover be interpreted as pure adaptation? The fact that mental health improves over time for people who keep working from home could also reflect some degree of self-selection.

In our difference-in-difference setting, perfect identification of the causal effect of telework would require that workers have absolutely no say on whether they work at home at any point of time, which we are unable to verify. It is true that the severity of the health situation, the successive strict lockouts and the ubiquitous slogan "stay at home, protect the NHS, save lives" have created strong incentives for companies and workers to comply. Nonetheless, might have been some self-selection in and out of telework when the lockdown was less strict. Unfortunately, the timing UKHLS data collection is not precise enough to allow ruling out this suspicion by isolating the episodes and regions of strict lockdown. De facto, we document a small correlation between the willingness to work from home in the future when the pandemics is over, as declared by respondents when the question is included in the survey (in three out of eight waves), and the probability of being actually in that work arrangement in subsequent months. Note however, that we do not find a positive correlation between the desired intensity ("often" or "always") of WfH and the actual situation in which respondent were observed in subsequent months.

We thus acknowledge two possible interpretations of our findings, especially concerning the impact of the duration of WfH, i.e. the initial deterioration in SWB, and its later recovery for people who remain in full telework for several consecutive months. The first interpretation is adaptation to an exogenous switch into telework: people are initially demotivated and unable to concentrate, but they progressively adjust to their new working conditions, both psychologically, and by investing in the needed equipment, logistics and ergonomics.

The second interpretation is self-selection: people are initially forced into telework by the lockdown, but they later on enjoy some leeway about how long to keep working from home, so that the rebound in SWB is driven by workers for whom telework is beneficial and who actually choose to remain in that work arrangement. De facto, the negative impact of telework on mental health disappears in July 2020, which is the time when the first and strictest lockdown is lifted.

In view of the negative impact of WfH that we estimate, at least in the first months, it is surprising that many employees around the world manifest the desire to continue working from home, as documented by many surveys. This is probably because most of them aspire to work partly from home, as in our "often" category, rather than fully from home, or because they have adapted to this arrangement over time, as found in our section 3.2. Alternatively, this could be a case of misperception, as they keep associating the idea of home to a pleasant state, and fail to acknowledge the negative consequences of that arrangement on their mental health. This interpretation is consistent with the positive partial correlation coefficient between WfH and life satisfaction. The latter is positive in the first months of telework, although it is imprecisely measured in average over the period.

With respect to this last point, let us remark again that this study applies to work from home in the literal sense, with all the consequences that stem not only from working away from the firm's premises, but also from working in one's house, which is usually the domain of family and privacy, and in that case also a place where the blurring of the boundaries between private and professional life is likely to create tensions. In the future, distant work can take several other forms, such as co-working spaces or remote offices, which may not have the same drawbacks as being "home" in the literal sense.

In the same vein, as discussed, the greater negative impact of telework on women with children is likely to be due to the burden of having to take care of homeschooling -a feature that has no reason to be tied to work from home in the future. However, it reveals the greater porosity of work and family constraints for women, which rejoins previous findings of the literature.

Another limitation to the generality of the study is that it assesses the impact of working from home in a time when this arrangement was as pervasive as possible. When things are back to normal, the consequence of working from home may not be the same depending on the context, i.e. whether it remains a widespread practice, or turns back into an exception, and whether it is considered by a person's firm as a privilege or an obligation. In sum, the general coordination in terms of work arrangements will matter to their impact on subjective wellbeing.

Keeping these qualifications in mind, our results bear several possible implications in terms of policy conclusions. Absent self-selection, they suggest that, in average, everybody will be able to adjust without psychological harm to this work arrangement, after an initial stage of adaptation. On the other hand, in case the improvement in workers' mental health is partly due to self-selection, it follows that this possibility should be offered rather than imposed on them.

Because both interpretations certainly contain some truth, we conclude that telework cannot be judged universally good or bad for workers' wellbeing if it is imposed on them without any decisional latitude, but will be beneficial if it is offered as a possibility, a new degree of freedom, after a period of trial.

Attrition

Figure 1 :

 1 Figure 1: Fraction of people working from home (UKHLS)

Figure 2 :

 2 Figure 2: Evolution of life satisfaction over time by telework intensity

  or the life satisfaction (1 -7) score; Covidi,t is a dummy indicating whether the survey takes place during Covid time (after March 2020), so that β catches the impact of the health crisis on life satisfaction and mental health Wt are waves fixed effects. Parameter γ on IT Ti captures the difference in subjective wellbeing of ITT individuals, as compared to non ITT. Parameter ϕ on Covidt * IT Ti identifies the specific reaction of ITT individuals to the Covid-19 crisis, compared non ITT individuals.

Figures 4

 4 Figures 4 and 5 plot the coefficients δn with and λn with n ∈ [1, 8] in the estimates of life satisfaction and the global GHQ score following equation (3).

Figure 4 :

 4 Figure 4: Estimates of the dynamic effect of work from home on Life Satisfaction

Figure 6 :

 6 Figure 6: Eq (3) -GHQ: Have you recently been able to concentrate on whatever you're doing?

Figure 7 :

 7 Figure 7: Eq (3) -GHQ: Have you recently felt that you were playing a useful part in things

Table 1 :

 1 Description of the different populations of interest

	Year	Waves N	On Site WFH ITT ITT not Treated Treated %WFH
	2016	1	6811 6575	236	2996 2996	0	3
	2017	2	7043 6772	271	3087 3087	0	4
	2018	3	7142 6852	290	3085 3085	0	4
	2019	4	7778 7463	315	3375 3375	0	4
	2020-04 5	7682 4412	3270	3403 489	2914	43
	2020-05 6	4311 1807	2504	2589 321	2268	58
	2020-06 7	4292 1977	2315	2507 414	2093	54
	2020-07 8	3708 1921	1787	2098 486	1612	48
	2020-09 9	3473 2015	1458	1894 602	1292	42
	2020-11 10	3315 1860	1455	1782 493	1289	44
	2021-01 11	3163 1575	1588	1774 356	1418	50
	2021-03 12	3303 1725	1578	1873 474	1399	48
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(5)/(3)

takes value 1 if, at a given Covid time, an ITT individual is actually teleworking. This "Treated" variable is constructed as:

Table 1

 1 describes our regression sample, which contains about 50,200 observations for 9216 different individuals. As one can see, before the pandemic, roughly 3% of the sample declared working from home. Following the Covid-19 outbreak, this percentage peaks to roughly 58% in May 2020 and remains above 42% afterwards.

Table 2 :

 2 Impact of telework on life satisfaction and mental health

					Dependent variable:
		Lsat	GHQ	concentration	useful	enjoy	confidence depressed
		(1)	(2)		(3)	(4)	(5)	(6)	(7)
	Treated Always	0.049 *	-0.247 * * *	-0.061 * * *	-0.031 * * * -0.031 * *	-0.036 * * *	-0.039 * * *
		(0.029)	(0.091)		(0.011)	(0.011)	(0.012)	(0.013)	(0.014)
	Treated Often	0.054	0.009		-0.021	0.013	0.001	-0.017	-0.010
		(0.036)	(0.109)		(0.013)	(0.013)	(0.015)	(0.016)	(0.017)
	Log income	0.067 * * *	0.193 * *		-0.006	0.008	0.002	0.039 * * *	0.024 *
		(0.024)	(0.081)		(0.010)	(0.010)	(0.011)	(0.012)	(0.013)
	ITT*Covid	-0.026	-0.069		-0.013	-0.022 *	0.002	-0.003	0.008
		(0.031)	(0.100)		(0.012)	(0.012)	(0.014)	(0.015)	(0.016)
	Log income*Covid -0.037	-0.032		0.013	0.024 * *	-0.001	-0.019	-0.003
		(0.025)	(0.085)		(0.010)	(0.010)	(0.011)	(0.012)	(0.013)
	Observations	46,410	54,746		54,844	54,838	54,845	54,833	54,844
	R 2	0.003	0.005		0.004	0.005	0.002	0.003	0.003
	Adjusted R 2	-0.233	-0.188		-0.189	-0.187	-0.190	-0.190	-0.190
	Note:

* p<0.1; * * p<0.05; * * * p<0.01 Controls include the following variables and their interactions with Covid: income, education dummies, occupation dummies, household size, age, age squared, sex, living in a rural area, hours worked, being in couple, having a child, ITT.

Table 3 :

 3 Heterogenous impact of telework on life satisfaction and GHQ score

					Dependent variable:
			Lsat					GHQ
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Treated	0.105 * *	0.115 * * *	0.057	-0.018 -0.115 -0.058 -0.038	0.037
		(0.051)	(0.039)	(0.035)	(0.062) (0.159) (0.120) (0.108)	(0.191)
	Female	-0.460	-0.449	-0.451	-0.457 -2.982 -2.915 -2.917	-2.857
		(0.598)	(0.598)	(0.598)	(0.598) (1.993) (1.993) (1.993)	(1.993)
	Parent	0.082 * *	0.098 * *	0.082 * *	0.085 * * 0.028	0.054	0.033	0.034
		(0.033)	(0.043)	(0.033)	(0.034) (0.114) (0.147) (0.114)	(0.114)
	Couple	0.032	0.030	0.031	0.081 * * 0.089	0.088	0.084	0.114
		(0.029)	(0.029)	(0.029)	(0.040) (0.096) (0.096) (0.096)	(0.130)
	Treated * Female -0.077				0.061
		(0.064)				(0.197)
	Treated * Parent	-0.150 * *				-0.021
			(0.063)				(0.193)
	Treated * Rural			0.004				-0.117
				(0.072)				(0.223)
	Treated * Couple			0.099				-0.142
					(0.071)				(0.218)
	Observations	46,410	46,410	46,410	46,410	54,746 54,746 54,746	54,746
	R 2	0.003	0.003	0.003	0.003	0.005	0.005	0.005	0.005
	Adjusted R 2	-0.233	-0.233	-0.233	-0.233	-0.188 -0.188 -0.188	-0.188
	Note:	* p<0.1; * * p<0.05; * * * p<0.01
		Controls include the following variables and their interactions with Covid: income, education
		dummies, occupation dummies, household size, age, age squared, sex, living in a rural area,
		hours worked, being in couple, having a young child, ITT.

Table 4 :

 4 Heterogenous Effects of Telework by Sub-Period

		Always WfH LS Often WfH LS Always WfH GHQ Often WfH GHQ
	Entire sample	+		-
	Women w. children t1		-	-	-
	Women w. children t2		-
	Childless women t1	+
	Childless women t2	+	+		+
	Men with children t1
	Men with children t2		+
	Childless men t1	-
	Childless men t2		+
	Notes : T1 refers to April 2020-July 2020; T2 refers to September 2020-March 2021

Table A2 :

 A2 Workplace location of the regression sample

Table A3 :

 A3 Impact of telework on other GHQ dimensions p<0.1; * * p<0.05; * * * p<0.01 Controls include the following variables and their interactions with Covid: income, education dummies, occupation dummies, household size, age, age squared, sex, living in a rural area, hours worked, being in couple, having a child, ITT.

					Dependent variable:
		problem overcome decision sleep happiness worthless	strain
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Treated Always	-0.001	-0.013	-0.014 -0.0004 -0.002	-0.002	-0.008
		(0.009)	(0.013)	(0.009) (0.014) (0.011)	(0.011)	(0.014)
	Treated Often	-0.002	0.012	0.008	0.017	0.012	-0.010	0.012
		(0.011)	(0.016)	(0.011) (0.016) (0.014)	(0.014)	(0.017)
	Log income	0.011	0.039 * * * -0.002	0.023 * 0.005	0.043 * * *	0.005
		(0.008)	(0.012)	(0.008) (0.012) (0.010)	(0.010)	(0.012)
	ITT*Covid	-0.013	-0.023	0.004	0.005 -0.001	-0.011	-0.005
		(0.010)	(0.014)	(0.010) (0.015) (0.013)	(0.013)	(0.015)
	Log income*Covid -0.004	-0.016	0.013 -0.018	0.006	-0.019 *	-0.004
		(0.009)	(0.012)	(0.008) (0.013) (0.011)	(0.011)	(0.013)
	Observations	54,843	54,846	54,847 54,850 54,840	54,836	54,850
	R 2	0.003	0.004	0.005	0.003	0.002	0.004	0.005
	Adjusted R 2	-0.190	-0.189	-0.187	-0.190	-0.190	-0.188	-0.188
	Note:

*

Table A4 :

 A4 Wants to WFH in the future, JUNE p<0.1; * * p<0.05; * * * p<0.01

				Dependent variable:
			TW t8	TW t9	TW t10	TW t11	TW t12
			(1)	(2)	(3)	(4)	(5)
	wfhfut01		0.091 * * *	0.082 * * *	0.072 * * *	0.081 * * *	0.088 * * *
			(0.023)	(0.023)	(0.022)	(0.023)	(0.022)
	Constant		0.708 * * *	0.430 * *	0.324	0.386 *	0.454 * *
			(0.221)	(0.215)	(0.214)	(0.219)	(0.215)
	Observations	2,385	2,385	2,385	2,385	2,385
	R 2		0.042	0.045	0.044	0.032	0.046
	Adjusted R 2	0.033	0.036	0.034	0.022	0.036
	Note:

*

Table A5 :

 A5 Wants to WFH in the future, SEPTEMBER p<0.1; * * p<0.05; * * * p<0.01

		Dependent variable:
		TW t10	TW t11	TW t12
		(1)	(2)	(3)
	wfhfut01	0.037	0.127 * * *	0.105 * * *
		(0.028)	(0.028)	(0.028)
	Constant	0.572 * *	0.297	0.380
		(0.248)	(0.247)	(0.246)
	Observations 1,673	1,673	1,673
	R 2	0.029	0.042	0.042
	Adjusted R 2 0.015	0.028	0.028
	Note:

*

Table A6 :

 A6 Wants to WFH in the future, January

			Dependent variable:
			TW t12
	wfhfut01		0.112 * * *
			(0.027)
	Constant		0.879 * * *
			(0.237)
	Observations	1,743
	R 2		0.060
	Adjusted R 2	0.047
	Note:	* p<0.1; * * p<0.05; * * * p<0.01
	7.3 Balanced panel

Table A7 :

 A7 Impact of telework on life satisfaction and mental health. Quasi-balanced panel. p<0.1; * * p<0.05; * * * p<0.01 Controls include the following variables and their interactions with Covid: income, education dummies, occupation dummies, household size, age, age squared, sex, living in a rural area, hours worked, being in couple, having a child, ITT. Individuals observed at least in four out of the eight Covid waves.

					Dependent variable:
		Lsat	GHQ	concentration	useful	decision confidence	depressed
		(1)	(2)		(3)	(4)	(5)	(6)	(7)
	Treated Always	0.047	-0.277 * * *	-0.068 * * *	-0.043 * * * -0.015 *	-0.038 * * *	-0.041 * * *
		(0.031)	(0.095)		(0.012)	(0.011)	(0.009)	(0.014)	(0.015)
	Treated Often	0.068 *	0.033		-0.019	0.003	0.007	-0.012	-0.006
		(0.037)	(0.113)		(0.014)	(0.014)	(0.011)	(0.016)	(0.018)
	Log income	0.039	0.145		-0.015	0.004	-0.009	0.040 * * *	0.023
		(0.030)	(0.099)		(0.012)	(0.012)	(0.010)	(0.014)	(0.016)
	ITT*Covid	-0.040	-0.167		-0.010	-0.048 * * * 0.005	-0.021	-0.005
		(0.033)	(0.108)		(0.013)	(0.013)	(0.010)	(0.016)	(0.017)
	Log income*Covid -0.015	-0.009		0.017	0.023 *	0.017 *	-0.021	-0.004
		(0.030)	(0.101)		(0.012)	(0.012)	(0.010)	(0.015)	(0.016)
	Observations	31,714	38,675		38,721	38,720	38,721	38,710	38,718
	R 2	0.003	0.006		0.005	0.006	0.005	0.004	0.003
	Adjusted R 2	-0.178	-0.138		-0.138	-0.137	-0.138	-0.139	-0.140
	Note:

*

Table A8 :

 A8 Impact of telework on life satisfaction and mental health. Quasi-balanced panel. * p<0.05; * * * p<0.01 Controls include the following variables and their interactions with Covid: income, education dummies, occupation dummies, household size, age, age squared, sex, living in a rural area, hours worked, being in couple, having a child, ITT. Individuals observed at least in four out of the eight Covid waves.

					Dependent variable:
		problem overcome	enjoy	sleep happiness worthless	strain
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Treated Always	-0.005 -0.018	-0.031 * * -0.004	0.0003 -0.005	-0.002
		(0.010) (0.014)	(0.013) (0.014) (0.012)	(0.012)	(0.015)
	Treated Often	-0.005	0.017	0.005	0.021	0.014	-0.012	0.023
		(0.011) (0.016)	(0.016) (0.017) (0.014)	(0.014)	(0.017)
	Log income	0.006	0.026 *	0.003	0.017 -0.002	0.047 * * *	0.002
		(0.010) (0.014)	(0.014) (0.015) (0.013)	(0.012)	(0.015)
	ITT*Covid	-0.015 -0.033 * *	0.003 -0.006 -0.011	-0.024 *	-0.008
		(0.011) (0.015)	(0.015) (0.016) (0.014)	(0.013)	(0.017)
	Log income*Covid -0.002 -0.008	0.003 -0.011	0.007	-0.021 *	-0.002
		(0.010) (0.014)	(0.014) (0.015) (0.013)	(0.012)	(0.016)
	Observations	38,716	38,720	38,719	38,723 38,714	38,709	38,722
	R 2	0.003	0.005	0.003	0.003	0.002	0.005	0.005
	Adjusted R 2	-0.141	-0.139	-0.140	-0.140	-0.141	-0.139	-0.138
	Note:

* p<0.1; *

We are grateful for financial support from the French National Research Agency, through the Investissements d'avenir framework ANR-17-EURE-0001; through the AAPG2021 (WRKCOV19). We also benefitted from funding by CEPREMAP. We thank Andrew Clark, Sarah Flèche, Dylan Alezra, Elizabeth Beasley, Mathieu Perona and particularly David Margolis for their comments on an early version of this paper, as well as participants in seminars at Higher School of Economics (Moscow), London School Economics, as well as Ox

The data used for this paper is freely and publicly made available by UK data services.


Palash Kanwar
email: palash.kanwar@student.uva.nl

Vilma Mesa
email: vmesa@umich.edu

Mapping student real-time viewing of dynamic textbooks to their utilization schemes of questioning devices

Keywords: Real-time textbook viewing data, questioning devices in textbooks, utilization schemes, undergraduate students, knowledge graphs, mathematics textbooks

We seek to map real-time viewing data of dynamic textbooks with student utilization schemes of questioning devices, an interactive feature that collects student responses to questions that promote reflection. An instrumental approach (Rabardel, 2021) suggests that knowledge of students' utilization schemes can provide useful information to textbook designers and authors (Quiroz et al., 2021). This information supports instructors' reflection on how students utilize textbook features designed to engage them with the content, so that they can adapt instruction. However, identifying utilization schemes requires intensive qualitative analysis of data collected via observations, interviews, or students' self-reports. As these analyses are time consuming, finding alternative ways of reliably identifying utilization schemes in a short period of time when many students are using a particular feature is beneficial. We present exploratory work that uses real-time viewing data of features in dynamic textbooks to identify viewing patterns that could be reliably mapped to student utilization schemes, possibly automatically. The textbooks we study are written in PreTeXt (https://pretextbook.org/) a markup language that precisely identifies every element in a textbook; when opened in a browser, it is possible to collect student responses to questioning devices and information about when individual users view specific textbook elements and for how long. These textbooks allowed us to gather large amounts of data from many students (over 400) who used the same textbooks across many states. The textbooks are used in calculus, linear algebra, or abstract algebra courses.

We provide here only a brief description of how we used knowledge graphs [START_REF] Hamilton | Representation learning on graphs: Methods and applications[END_REF] with tracking data (date and time of viewing, the sections that were viewed, and the total time in minutes spent viewing the section) to map viewing patterns of questioning devices to their utilization schemes using about 4,000 viewings of questioning devices collected over five semesters from 492 consenting students from 27 teachers in the U.S. Knowledge graphs are graphical representations of information that capture interactions between individuals and entities. The viewing data are represented in a network of nodes and edges to establish the occurrence of consistent and repetitive viewing behavior across the same student or several unique students. Each node contains the name of the section viewed and the amount of time spent in minutes viewing that section. Directed edges denote a jump to the next section, undirected edges denote possible concurrent viewing sections within a minute of viewing during the viewing period. Each knowledge graph is unique to each day of viewing for a particular student. An algorithm created to automate this process generates combinations of nodes and edges to create unique knowledge graphs facilitating the identification of common patterns that occur while viewing the textbook. The evidence needed to support our study is hypothesized to be of three types (1) Knowledge graphs for different students following the same utilization scheme should be consistent; (2) Knowledge graphs for the same student following the same utilization scheme should be consistent; and (3) Each utilization scheme should lead to a network of knowledge graphs representative of a community of unique students with similar viewing patterns. We used the three utilization schemes identified by [START_REF] Quiroz | Student utilization schemes of questioning devices in undergraduate mathematics dynamic textbooks[END_REF]: Familiarizing with Content Before Class (US1), Studying by Practicing and Doing Homework (US2), and Self-Evaluating and Understanding of Content (US3). With this technique we were able to identify three types of knowledge graphs with unique features that map them to each utilization scheme. We show a case, the first network of knowledge graphs represented in Figure 1, which always follows a linear viewing trajectory. The student views the sections in the textbook in the order they appear. This type of knowledge graph was mapped to the first utilization scheme, familiarizing with content. The other two networks of knowledge graphs were mapped to the other two utilization schemes (not shown for space reasons). The accuracy of the algorithm is high, 91%,86%, and 89% for US1, US2 and US3 respectively. We will study the nature of the networks for the 18% of unmapped viewings, to see what they reveal about use of questioning devices. This problem mostly occurs when students view the textbook multiple times on the same day, deploying different utilization schemes each time, and thus the algorithm has difficulty making the classification.

Figure 1 :

 1 Figure 1: Representative knowledge graphs for viewing data mapped to US1: Calculus student 50 (Teacher 35); 29% of students, 91% accuracy

Acknowledgment

Funding provided by the National Science Foundation (DUE 1624634, 1821509). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.