Centre-Based Care and Parenting Activities*

We examine the relationship between parenting activities and centre-based care using time diary and survey data for mothers in Germany. While mothers using centre-based care spend signiﬁcantly less time in the presence of their child, we ﬁnd that differences in the time spent on speciﬁc activities such as reading, talking, and playing with the child are relatively small or zero. The pattern of results is more pronounced for lower education mothers. The lack of large decreases in activities is explained by two factors: (i) that centre care replaces time that parents spend with the child but are doing other things such as housework or leisure (a small direct effect), and (ii) that evenings become relatively more activity-rich (a compensating indirect effect). For the intensive margin (full-day vs. half-day), we ﬁnd more additional reductions in parenting activities, but these are compensated for by lower education mothers during non-centre hours. Our ﬁndings represent novel evidence that activities in the home environment are a complement to centre-based care, highlighting a credible additional mechanism for child development effects of centre-based care.


I. Introduction
Children in high-income countries spend more time in child care centres than ever before (OECD, 2017).Many studies find positive effects of centre-based care on child development, especially for children from less-educated parents, but some also show Bulletin zero or even negative effects. 1 The direction and size of the effect are most commonly thought to be related to the educational opportunities offered at the child care centre relative to the home environment, with some studies focusing specifically on the role of centre quality (e.g.Bauchmüller, Gørtz and Rasmussen, 2014).However, this institutional channel typically takes the educational environment at home as a fixed consideration. 2 A much less-explored channel is whether usage of centre-based care might impact child development by changing the home environment, for instance, by affecting parenting activities.
Our study asks: how do parenting activities differ when centre-based care is being used?Parental interactions play a key role in children's development, independent of the role of learning institutions, such as child care centres (Cunha et al., 2006; Todd  and Wolpin, 2007; Del Bono et al., 2016; Kim et al., 2018; Moroni, Nicoletti and  Tominey, 2019).Specific activities, such as reading to the child, are particularly valuable (e.g.Kalb and van Ours, 2014; Mayer et al., 2019; Price and Kalil, 2019).However, based on broad trends, it is far from obvious that the increasing usage of centre-based care has reduced parenting activities and, consequently, affected child development.Indeed, nowadays, parents spend more time on activities with their children than they did in the 1960s (Dotti Sani and Treas, 2016). 3ur main contribution is to use time diary data to estimate the relationship between centre-based care usage and parenting activities in Germany, a country with a universal child care system.We estimate conditional differences for (i) time spent together with the child (not necessarily interacting), (ii) time spent on parenting activities overall, and (iii) time spent on specific activities (e.g.reading or playing).These outcomes are created by summing the time spent on parenting activities as the main activity (or in the presence of a child) in 10-minute segments over the day.To account for potential selection on unobservables into centre-based care, we implement the coefficient stability approach of Oster (2019).Our estimates imply that mothers using centre-based care spend significantly less time in the presence of their child, but that differences in the time spent on specific activities like reading, talking, and playing with the child are relatively small or zero.The pattern of results is more pronounced for lower education mothers.As such, our results suggest that parents using centre-based care are concentrating similar amounts of educational activities into less overall time with their child.
We explore differences in parenting activities during care hours ('direct effects') and during evenings and weekends ('indirect effects').Direct effects may differ depending on how activity-rich parental care is in the counterfactual, for example, if parents are occupied with other things such as housework during the day spent with the child.Indirect effects may occur if parents see their parental activities as a complement or a substitute 1 Some examples are (Havnes and Mogstad, 2011; Datta Gupta and Simonsen, 2012; Havnes and Mogstad, 2015;  Blanden et al., 2016; Cornelissen et al., 2018; Felfe and Lalive, 2018; Felfe and Zierow, 2018; Baker, Gruber and  Milligan, 2019; Kuehnle and Oberfichtner, 2020). 2 One of the few economic studies not to take the home environment as given is Kuger, Marcus and Spiess (2019); it shows that the quality of centre-based care affects the quality of the home environment, using established quality measures for both environments. 3Moreover, the type of parents who see the largest increases in parenting activities -that is, higher educated parents, according to Dotti Sani and Treas (2016) -are those who have seen the largest increases in usage of centre-based care (e.g.see Jessen et al., 2018, for Germany).
for centre-based care, which may be due to positive or negative changes in motivation or time constraints, respectively.We find that the lack of a large decrease in activities is both due to the direct effect being relatively small and there being a compensating indirect effect in relative terms.Specifically, we see a decrease in time with child outside of centre hours due to an earlier bed time but no decrease in parenting activities implying more activity-rich evenings.
A further contribution of our paper is that we do not just focus on centre-based care usage, per se, but on the effect of the dosage as well: We complement our main analysis with an examination of the effects of full-day vs. half-day care.We do this using the same time-use data and additional survey data, the German Family Panel (pairfam).The dosage of centre-based care is an important margin since the literature finds quite different effects on child development by hours of centre-based care (e.g.Loeb et al., 2007; Datta Gupta  and Simonsen, 2010; Felfe and Zierow, 2018).We find that full-day care, in comparison to half-day care, is also associated with a decrease in parenting activities.We additionally find decreases in the frequencies of certain parenting activities such as playing or outdoor activities.This is in line with the literature that finds more limited child development effects at this margin in the German context (see Felfe and Zierow, 2018).
Our method involves regressing time spent on parenting (and non-parenting) activities on an indicator for centre-based care usage.We estimate an unconditional model and a conditional model with a rich set of controls for child, parent, and household characteristics.
To account for potential selection on unobservables into centre-based care, we implement the coefficient stability approach of Oster (2019).Selection on unobservables is accounted for by assuming it relates to the degree of selection on observables, which itself is measured based on coefficient movements (and changes in the R 2 ) that occur when including control variables.We present 'identified sets' that are estimate bounds based on assumed upper and lower limits for the degree of selection on unobservables.In general, we find that our coefficients are relatively stable to the inclusion of controls, thus suggesting fairly limited selection bias.
Ours is the first economic study to examine this question with detailed time-use data.Some existing studies look at related questions. Baker, Gruber and Milligan (2008) and Herbst and Tekin (2014) look at the effects of child care programmes (in Canada and the United States, respectively) on the style and quality of parental interaction (among other outcomes).However, while important, quality and style of parenting are not necessarily closely related to the time spent on parenting activities.Further studies focus on the impact of maternal employment on parenting activities showing that parental quality time with children does not need to decline with increases in maternal employment (e.g.Hsin and  Felfe, 2014; Del Bono et al., 2016; Bastian and Lochner, forthcoming).Kröll and Borck (2013) examine the same question (also for Germany) and find that centre-based care actually increases maternal interactions with children.However, this analysis is based on how often mothers report having undertaken activities with their children in the past fortnight, rather than precise time diary data.A few studies from other social sciences find that centre-based care is associated with decreases in parent-child interactions; however, these studies do not attempt to address potential selection on unobservables (e.g.Booth et al., 2002; Folbre and Bittman, 2004; Craig and Powell, 2013;  Habibov and Coyle, 2014).
Previous studies neither distinguish between direct and indirect effects, nor attempt to systematically explore adjustments in non-parenting activities. 4Through this, our study contributes to the literature on the economics of parenting that tries to explain parenting decisions as rational choices that may be affected by the institutional environment (e.g.Doepke and Zilibotti, 2017; Doepke, Sorrenti and Zilibotti, 2019).We also pay more attention than previous studies to differences in specific types of parenting activities such as reading and primary care.In doing so, we follow the child development literature, which distinguishes between activities that involve different levels of interaction (Kalil,  Ryan and Corey, 2012; Fort, Ichino and Zanella, 2020) and, thus, distinguish between activities according to their productivity with respect to child development.

II. Institutional background
In 2020, 35% of children in Germany under three and 93% of those aged 3-5 were enrolled in centre-based care.For both age groups, just over half of the enrolled children were in full-time care, defined as 35 hours or more per week.The child care system in Germany can be characterized as a virtually universal, strongly state-subsidized system.For-profit providers play a very limited role, with only 2.6% of institutions in 2017 being private and non-charitable (Destatis, 2017).Parental fees are mostly income-dependent and relatively low compared with most other OECD countries (OECD, 2020), with many states having even abolished fees altogether for older age groups and some also for younger age groups (Huebener, Pape and Spiess, 2020).In 2012, average fees amounted to 144 Euros per month and family, on average (Schroeder, Spiess and Storck, 2015).In general, parents cannot obtain higher quality by paying higher fees, which weakens the link between family income and centre-based care quality compared with countries using a market-based system (Stahl, Schober and Spiess, 2018).In our analysis, we make no assumptions regarding centre-based care quality, as the goal of this study is to assess how parenting activities respond to centre-based care usage and not the overall activities that children are exposed to (in centre-based care and at home).
Figure 1 shows enrolment rates in centre-based care for under and over 3-year-olds separately for East and West Germany over the time period covered by our analysis.For over-threes, the majority of the expansion in child care centre slots took place in the 1990s in response to the 1996 introduction of a legal entitlement to a place for children 3 years and older, and a general trend in Europe to expand centre-based care for children 3 years and older (see e.g.Spiess, 2008).In both East and West Germany, enrolment rates for over-threes have been above 80% since before 2000.Despite a strong increase in full-day enrolment in West Germany in the 2010s (Jessen et al., 2018), full-day rates remain below 50%.In East Germany, full-day enrolment rates are much higher, covering 74% of over-threes children in 2018.
In contrast, for under 3-year-olds, enrolment rates were very low well into the mid-2000s, particularly in West Germany.In 2008, a federal law (KiföG) was passed, extending the legal claim to a place at a child care centre to children of at least 1 ), which is a long-running household survey containing information on about 15,000 households per year (Goebel et al., 2019).For precision, data are pooled in 2-year bins.Annual statistics since 2007 from the German Federal Statistical Office (starting that year, official administrative data contain the share in full-day care) year of age, coming into effect in August 2013.The legal change and the accompanied increased provision came in response to a long-lasting over-demand for centre-based care, in particular by parents with infants and toddlers (i.e.Spiess and Wrohlich, 2005;  Wrohlich, 2008).However, while enrolment rates for under-threes subsequently climbed, demand increased further, still resulting in a continuation of shortages (Jessen et al., 2018).
Parents in Germany make frequent use of informal care, especially by grandparents.In 2017, between 50% and 60% of all children from 6 months old until the age of 6 years had grandparents as caregivers; for older children, grandparents were mainly used in addition to centre-based care.Other private caregivers looked after between only 10 and 30% of children, depending on child age.Nevertheless, informal care, such as that offered by grandparents, is typically for only a few hours per week and complementary to formal care (Barschett, Spiess and Ziege, 2021).This is shown in Appendix Tables B4 and B5: informal care is higher for children who attend a child care centre, suggesting that informal care may have been used to extend hours of formal care, rather than to substitute for it.
Parental care in Germany is characterized by a strong gender divide, with mothers acting as the primary caregivers (Schober, 2014).Parenting activities (and housework), therefore, are carried out to a much larger degree by mothers despite a slight narrowing of the gender gap since the 1990s, as illustrated in Appendix Figure B1.Consistent with the 'primary-male-breadwinner' model, evidence shows that the roll-out of centre-based care, as described above, had an employment effect for mothers but made no difference for fathers (Müller and Wrohlich, 2020).For this reason, we focus our main analysis on mothers and report additional results for fathers in the Appendix.

III. Adjustment mechanisms
This section discusses ways in which centre-based care usage might affect parenting activities.We focus on the amount of time spent on activities as an outcome rather than any measure of parenting quality or style, or directly observed parenting quality.We define direct effects as changes that occur during the time that children commonly spend at child care centres, and indirect effects as changes that occur outside of centre hours as a result of parental adjustments.
The direct effect (i.e. during centre hours) of centre-based care on parenting activities will be negative if centre-based care usage reduces the time that a parent spends with their child, when they would have otherwise engaged in some parenting activities in the counterfactual.No effect is only possible if centre-based carefully crowds out informal care arrangements, by grandparents, for instance, or if despite being with the child, no parenting activities are done in the counterfactual.Despite being partly mechanical, the magnitude of direct effects varies depending on how concentrated parenting activities are during centre hours.
Indirect effects (i.e.outside of centre hours) could go in either direction.They may be positive if centre-based care is a complement to parenting activities.This could be if centre-based care reduces parental time constraints or increases parental motivation to interact with their child.Time constraints may be reduced if parents use the centre-based care hours to complete other tasks, such as paid work or housework, thereby freeing up non-centre hours for parenting activities.Furthermore, not being at home with a child may mean there might be less cleaning and tidying to be done in the evening. 5Motivation may be increased if spending less time with the child overall means that parents try to ensure that they do more activities with the child in the remaining time.Further, it could be that centre-based care inherently encourages parents to interact with their child, for example, through teacher recommendations (see e.g.Cornelissen et al., 2018;  Kuger et al., 2019). 6Moreover, if centre-based care has a direct effect on children's cognitive or socio-emotional development, parents could adjust their inputs in response to this and increase their time spent on specific parenting activities (see Nicoletti and  Tonei, 2020).
Indirect effects may be negative if centre-based care is a substitute for parenting activities.This could be the result of a decrease in parental motivation, for example, if parents feel that certain activities are no longer necessary since they are already done with their child in centre-based care.This might specifically be the case if there is a notable positive effect of centre-based care on child development.Furthermore, substitution could occur through a worsening of parental time constraints, for example, if parents use centre-based care hours to take on significant extra activities, such as paid work, meaning they have more tasks to do in the evenings instead of parenting activities.No effect might arise if centre-based care is neither a substitute nor a complement, that is, if there are no motivation and time-constraints effects or if they are counterbalanced.We aim to shed light on adjustment processes to understand the effects on parenting activities by looking at a set of non-parenting activities.
While we have priors for the direct effects, there is little evidence on which to base hypotheses regarding the direction of the indirect effects.A separate question is what direction the overall effect might be (i.e.direct and indirect together).There might be positive indirect effects on parenting activities that are large enough to overcompensate for a negative direct effect.Again, we have little guidance to form any priors in this regard.In Appendix section A, we provide stylized examples to illustrate the specific cases.

German time-use survey
We use diary data from three waves of the German Time-Use Survey, which is a repeated cross-section of around 5,000 households per survey wave taken in 1991/92, 2001/02, and 2012/13 (Maier, 2014; Destatis, 2015).The diary data record the main and (optional) secondary activity of each adult household member in 5-or 10-minute slots over 2 or 3 days using a 3-digit classification. 7An example of a 3-digit activity is 'reading to child', which is from the 2-digit activity of 'child care', which belongs to the 1-digit category of 'work in the household'.We use the activities recorded under 'child care' as our parenting activities.In Appendix Table B2, we show the full list of 3-digit categories contributing to parenting activities.
In addition to recording specific activities, the survey also indicates for each time slot whether it was spent with a child under the age of 10 years present.Importantly, the parent need not necessarily record a parenting activity as the main or secondary activity while spending time with the child.For example, a parent may record ironing as the main activity and watching television as the secondary activity, while also indicating that their child was present.The data also include information on households -such as usage of centre-based care, age of youngest child, number of children, single-parent household, and location in East or West Germany.At the respondent level, the data include information on age, gender, education, marital status, and economic activity.

Bulletin
We use parent-days as the unit of observation for our analysis.We define two main measures of parental involvement: (1) time with child, as the number of minutes that a parent spends together with their child; and (2) parenting activities, as the minutes spent on child care activities as the main activity.We think of time with child as capturing a more basic form of child care with often no dedicated interactions.In contrast, parenting activities involve specific interactions with the child, which likely better foster child development (see e.g.Kalil et al., 2012; Hsin and Felfe, 2014).Thus, we think of parenting activities as being the relevant measure of the educational potential of the home environment and thus also a measure of home quality.We also distinguish between particular types of parenting activities: reading to the child, playing with the child, talking with the child, and primary care. 8We also estimate effects on non-parenting activities, like 'paid work', 'housework', and 'leisure', to investigate adjustments by time of the day.9Those broader categories are classified consistently across survey waves and, thus, we pool all survey waves.The coding for the specific 3-digit parenting activities changed after the 1991/92 wave, so to ensure that our results are not artefacts of the change in classification, we only consider the last two survey waves for those outcomes.
In our analysis, we focus on mothers as they are commonly the main caregivers in Germany. 10Appendix Figure B1 shows the average daily duration of our main parenting and non-parenting activities, indicating that mothers spend more time on parenting by a factor of two to three.In the Appendix, we also present main results for fathers, with -as expected -much smaller effects.We split our analysis sample by educational background, which is defined as higher if the mother holds an 'Abitur' secondary school certificate from the upper educational track in Germany and, thus, is eligible for university.The education split is motivated by differential effects of centre-based care on child development found in the literature and well-established differences in parenting activities by education (see e.g.Bradley et al., 2001; Guryan, Hurst and Kearney, 2008; Kalil et al., 2012; Gimenez-Nadal  and Molina, 2013; Dotti Sani and Treas, 2016).We also differentiate by the time of the day (centre hours or non-centre hours) in specifications that aim to estimate direct and indirect effects.In these specifications, the outcomes are the sum of minutes dedicated to each activity during either centre hours or non-centre hours in a day.
We restrict our sample to parents whose youngest child is of the enrolment age for centre-based care (i.e.under 6 years old).Furthermore, we drop all parents who have more than one child under 10 years old.This restriction reduces the sample by 59% but ensures that time with child measures effects on the enrolled child and not any potential indirect effects on time with an older child (who is also under 10 years).We do not expect the effects to be dramatically different for the dropped households (with further children under 10) since it is enrolment of the youngest child in centre-based care that usually makes the key difference in terms of the child care responsibilities of parents.We corroborate this point in Appendix section C2.We use the household survey data (pairfam), which reports activities on a child level allowing to contrast effects estimated using the same restriction for one child under 10 using the entire estimation sample without this restriction.All estimates for parenting activities for the two samples are statistically indistinguishable.
After imposing these restrictions (and focusing on mothers), our analysis sample comprises 2,453 parent-days and 995 person observations.Table 1 presents summary statistics of the main sample, split by enrolment in centrebased care.11Differences between the samples are apparent as seen in column (3); mothers of children enrolled are on average older, have obtained higher education, are more likely to be full-or part-time employed, and more live in East Germany, where overall enrolment is higher (see section II).Children in centre-based care also are older: the age difference between survey waves is relatively constant as children of all age groups increasingly attend.Due to those described differences between the groups, in the empirical analysis, it is paramount to control for those factors, as these are also likely to correlate with parenting behaviour.
To illustrate the diary data, Figure 2 plots the number of minutes per hour of the day spent doing different activities by usage of centre-based care.In these descriptive plots, we focus on weekdays, since this demonstrates the clearest differences in terms of direct and indirect effects.However, in our analysis, the baseline specifications pools weekdays and weekend days, to give a clearer picture of effects on parenting activities overall.The descriptive plots show that centre-based care is associated with mothers spending less time with their children on weekdays during regular care centre hours (08:00-16:00), especially in the morning.There are also fewer parenting activities, although this pattern is less pronounced and followed by an apparent increase in the late afternoon and evening (16:00-20:00).Time in paid work is higher for centre-based care users, while both housework and leisure are lower during centre-based care hours.Finally, we see that mothers with their child in centre-based care wake up earlier.

The german family panel
For an additional analysis of the effects of full-day vs. half-day centre-based care, we use the German Family Panel (pairfam), which is a longitudinal household survey collected annually since 2008 and used for researching partnership and family dynamics. 12The survey records the frequency of specific parenting activities, but only for older children (three years and above) and since 2013.Therefore, we restrict our sample to data between 2013 and 2019 for children between 3 and 6 years of age.While the survey does not collect precise diary data, it gives us around seven times as many observations compared with the time-use sample for the full-day vs. half-day care analysis, allowing for greater precision in estimation.We cannot use pairfam to examine day care vs. no day care since the activity-questions are only available for children aged 3 and above who nearly all attend centre-based care.For each child of a parent, the survey asks: How often have you done the following things with your child during the past 3 months?An overview of frequencies of shared activities for mothers with children in half-day and full-day centre-based care is shown in Appendix Figure B2.We code indicator variables for whether each activity is carried out at least daily as outcome variables.The data also include information on the type of care each child uses, as well as parent, child, and household characteristics.We code children as being in full-day care if they are in centre-based care in the morning and afternoon and half-day if they are at centre-based care in the morning or afternoon. 13Appendix Table B1 shows summary statistics for children attending half-day or full-day care and for their mothers and households.

Empirical approach
We start our analysis with an unconditional model, whereby we regress parenting activities on centre-based care usage controlling only for a set of indicators of child age in years.Given near-zero usage rates in the first year of centre-based care in this age range and near full usage in the last 2 years before entering school at age 6, the relationship between child age and usage has a relatively large deterministic component.Therefore, we include it in the unconditional model.This unconditional model corresponds to the daily sum of the differences plotted in Figure 2. Next, we estimate a conditional model that accounts for selection into centre-based care based on observable characteristics: child age indicators, plus child gender, parent age, parent age squared, parental education indicators for secondary school track (upper, middle, or lower) and for university degree, marital status, single-parent status, number of children in household, as well as an indicator for weekday observations.We also include indicators for survey wave × region (East or West Germany) to control for the different institutional settings described in section II.Despite having a fairly rich set of controls, it remains plausible that selection into usage of centre-based care is driven to some degree by unobservable maternal characteristics that are also correlated with parenting activities.Due to this, the estimates ought to be interpreted as conditional correlations rather than as causal effects.
In an additional step, we account for possible selection on unobservables by examining coefficient stability across unconditional and conditional models.We follow Oster (2019) in making assumptions regarding (i) the maximum achievable R 2 , that is, R 2 max , and (ii) the extent of selection on unobservables relative to selection on our set of included controls, that is, δ.Our main specification assumes R 2 max = 1.3 R2 where R2 is the R 2 of the conditional model. 14We assume that δ is bounded such that δ ∈ [0, 1].At the most 'optimistic' bound of δ = 0, there is no selection on unobservables.At the most 'pessimistic' bound of δ = 1, selection on unobservables plays an equal role to selection on the included controls.This seems a reasonable upper bound given we have a fairly rich set of controls.The corresponding identified set of estimates gives us the upper and lower bound for the true effect, assuming that the real δ falls between the two extremes.
Whereas the bounds presented assume that selection on unobservables follows the same direction as selection on unobservables, we also provide the δ that would be required based on the coefficient movements and R 2 max for the true coefficient to be zero.A large absolute value of δ here indicates that the true coefficient is zero only if selection on unobservables is very large relative to selection on our controls.Relative selection on unobservables may go in the same or opposite direction as selection on observables.

Differences in parenting activities
Table 2 reports our estimates for the full sample of mothers and for sample splits by educational attainment. 15Each coefficient represents the difference in time with child (i.e.child present but not necessarily interacting) or time spent on parenting activities (i.e.interacting with child) when using centre-based care.Column (1) shows that mothers using centre-based care spend significantly less time per day together with the enrolled child.In the conditional model, the coefficient of −95.5 minutes equates to around −22.1% of the mean time with child in the sample.To some extent, this decrease is to be expected as a mechanical impact of centre-based care usage.Column (2), however, reveals a key result: the decrease in time spent on specific interaction with the child (parenting activities) is relatively small at only 13 minutes per day, just −9.8% of the sample mean.Thus, while mothers using centre-based care do spend less time in the presence of their child, this does not show up as much in terms of reduced interactions with their child.When we split the sample by educational attainment, we see that this result is more pronounced for mothers with lower education.Although lower education mothers reduce their time with child by more than higher education mothers (P-value for the difference is 0.079), their reduction in time spent on parenting activities is roughly the same (P-value is 0.803).
Comparing the conditional and unconditional models shows that the coefficients do not change by much upon adding control variables.For time with child, R 2 increases strongly by around 0.1 on average, indicating that the controls explain a relatively large share of variation in the dependent variables. 16The R 2 increase is lower for parenting activities, but coefficient movements are also smaller.As the identified sets for this outcome just include zero, we cannot reject the hypothesis that parenting activities remain similar in this pooled specification.Overall coefficients are fairly stable to the inclusion of these important controls and we end up with identified sets that suggest relatively tight ranges when accounting for potential selection on unobservables.While centre-based care usage is related to certain observable characteristics (evident in Table 1), the stability of the coefficients in Table 2 suggests that these differences are not, on average, associated with very different patterns of parental time use.

Direct and indirect effects
Our main results show large reductions in time spent in the presence of the child with relatively small reductions in parenting activities.This finding can be explained either if (a) not much interaction with the child occurs during this centre hours in the counterfactual of no centre-based care usage (i.e. a small direct effect) or (b) lost interactions during centre hours are compensated for outside of care hours (indirect effect).We explore this issue in Figure 3. Panel (a) plots estimates (identified sets and 90% confidence intervals) by time of the day and educational attainment for parenting outcomes.17The differences during typical care centre hours (8am-4pm on weekdays) aim to capture direct effects, whereas changes during non-centre hours (all remaining hours, i.e. 4pm-8am on weekdays, and full weekend days) reflect indirect effects.During centre hours, both higher and lower education mothers decrease their time with child by a roughly similar amount, but for lower education mothers, the decrease in parenting activities is smaller. 18Outside of centre hours, there is an additional reduction in time with child for lower education mothers but not for higher education mothers.This reduction is consistent with an earlier bedtime. 19owever, despite the reduced time with their child in the evenings, lower education mothers do not reduce any parenting activities.Thus the time spent with children in the evening is more activity-rich.As such both direct and indirect effects play an important role in explaining the differences in effects between households with lower and higher maternal education.
Panel (b) presents the differences in three non-parenting activities: paid work, housework, and leisure by time of day and education in an effort to explore explanations for differences in parenting activities.The figures show that paid work increases during centre hours (a direct effect) with differences that are a little larger for lower education mothers.At the same time, there are decreases in housework that presumably would have been done during time with the child had it been at home.This is consistent with evidence that mothers use day care to take up paid work (Müller and Wrohlich, 2020) instead of multi-tasking child care and housework.Mothers from lower education households also experience a reduction in leisure during centre hours, which helps to explain their smaller direct reduction in parenting activities. 20Outside of centre hours, there is also a small increase in paid work, which appears to reflect early or late shifts. 21For lower education mothers there is also decrease in housework outside of centre hours, which may help explain how evenings are kept to be relatively activity-rich for the child.
In Appendix Figure C4, we explore heterogeneities and we briefly summarize those results here.We find that parenting activities during non-centre hours increase when the child is a girl while time with them is held constant. 22For boys, in contrast, time with child is reduced and parenting activities are held constant during non-centre hours; that is, mothers do not overcompensate for the reduced time during centre hours.The direct  effect for parenting activities is smaller for children older than 3 years and, similarly, we identify a positive indirect effect for this group, but not for younger children.We identify no heterogeneities by region (East or West Germany) and no conclusive effects by survey wave; while the point estimates for the direct effects are larger for later waves, consistent with increasing time spent in centre-based care, the differences are not statistically significant.

Specific parenting activities
The specific type of parenting activity is at least as relevant for child development as the total time spent on activities overall (Fiorini and Keane, 2014).Therefore, in Figure 4, we explore which specific parenting activities comprise the overall reductions so far reported. 23We focus on differences during centre hours since no differences were found outside of centre hours for either lower or higher education mothers.The largest decreases come from playing and primary care, the latter of which perhaps represent the activity with the least educational content, comprising general supervision and basic hygiene.There are no decreases for reading or talking for either lower or higher education mothers.Reading and talking are activities that may help improve language skills, and it is interesting to notice that parents of both education levels do not compromise on these activities despite spending less time with their child.While the decreases are larger for higher education mothers, these are proportional with the larger overall decrease Bulletin in activities, thus suggesting no particular differences in focus between the educational groups.
Full-day vs. half-day centre-based care Thus far, the analysis has focused on the differences in parenting activities of using centrebased care compared with not using it, irrespective of the number of hours of care used per day.The full-day vs. half-day margin may have different implications for parenting activities, which we explore in this section.The intensive margin of day care is important since this has become the relevant decision for many parents (i.e.children over 3 years and older in Germany, nearly all of which use centre-based care -see Figure 1).Differences in parenting activities may also help explain the child development effects for full-day care, which tend to be differently beneficial for children from disadvantaged households depending on the skills examined (e.g.Loeb et al., 2007; Felfe and Zierow, 2018)  The 2012/13 wave of the German Time-Use Survey contains information on the hours of centre-based care normally used.Figure 5 plots the full-day vs. half-day estimates (i.e.conditional on usage of centre-based care) on parenting (panel a) and non-parenting activities (panel b).As before, we plot coefficients by time of day and education.Both mothers with higher and lower educational attainment see additional decreases in parenting activities during centre hours, but for lower educated mothers we identify a compensating increase during non-centre hours as an indirect effect, which is not found for higher educated mothers.
The decreases in time with child during centre hours for higher education mothers coincide with changes to paid work and housework, as before.However, in contrast to usage vs. non-usage, the increases in paid work are similar in size to the reductions in time with child suggesting worsening time constraints.We find no statistically significant differences for lower education mothers during centre hours, but suggestive evidence for less paid work and housework during non-centre hours facilitating the increase in parenting activities.
In order to investigate the full-day margin with greater precision, along with differences in specific parenting activities, we turn to the German Family Panel (pairfam). 24Using these data, we estimate differences for full-day vs. half-day usage of centre-based care in the probability of carrying out specific parenting activities on at least a daily basis.Table 3 shows the effects of full-day care on specific parenting activities (panel a).We think of the first four activities (reading, music, art, and playing) as educational activities and the last three (outdoors, sports, and watching television) as recreational activities.
For mothers with lower education, daily playing is lower by nine percentage points (pp) and there is weaker evidence for a lower frequency in reading when the child is in full-day care.Looking at higher educated mothers, we see stronger negative differences for playing and for art activities, but the regularity of reading holds constant.For recreational activities, daily outdoor activities become less likely with full-day care for all mothers, but sports and TV are unchanged.Consistent with the time-use data, full-day care is also associated with more paid work, especially for mothers with higher educational attainment.We also find that mothers with higher education are more likely to feel stressed and feel that they spend too little time with their child when full-day care is used -this difference is smaller for mothers with lower education.These findings point to greater time constraints faced by mothers whose children are in full-day care compared with half-day care, potentially reducing the capacity to be involved in parenting activities, particularly for mothers with higher educational attainment.The last three rows of Panel B look at child outcomes.We see Bulletin evidence for a reduction in children's nightly sleep.Looking at two measures of children's well-being, as reported by mothers, we find no differences in irritability but a lower prevalence in perceived happiness of children of lower educated households.This is in line with evidence of negative effects on socio-emotional behaviour of full-day care on disadvantaged children (Loeb et al., 2007; Felfe and Zierow, 2018).

VI. Conclusion
This paper asks how parenting activities respond to the usage of centre-based care.Our analysis shows that differences in parenting activities are relatively small, despite the fact that mothers using centre-based care spent significantly less time in the presence of their child.We find that the lack of large decreases in activities can be explained both by the fact that the direct effect is small (since day care replaces less activity-rich hours of the day) and since there is a compensating indirect effect making evenings more activity-rich.These results are more pronounced for lower education mothers.A specific analysis of the full-day vs. half-day margin finds that using centre-based care for 31 hours or more is associated with decreases in parenting activities that are proportionally compensated for during non-centre hours.Further analyses using survey data show small reductions in the frequency of certain activities (e.g.8-12 pp reduction of daily playing) as a result of using full-day care over half-day care, as well as increases in maternal stress and some evidence for reduced happiness for children from households with lower maternal education.Thus, with respect to full-day care, the potential benefits through the home environment channel are less clear.
Our findings imply a need for greater awareness that development effects of centrebased care may come through changes in the home environment, not just through the usage of centre-based care per se or through quality of this care.Policymakers may want to consider strengthening the home environment channel.One way this might be done is to encourage/enable the usage of centre-based care by households with lower educational backgrounds.Our findings imply that the home environment channel is strongest for these households; however, these households are less likely to be enrolled in centre-based care with children younger than 3. Research suggests that enrolment gaps with respect to maternal education are best addressed in Germany by improving the availability of places reducing (or abolishing) parental fees (Jessen, Schmitz and Waights, 2020).Another way is for centre-based care policy to be designed to allow for an easing of parental time constraints.Our analysis covers a period when usage of centre-based care was expected to facilitate paid employment and, in the earlier years, this was even the condition for a place.While such conditions may increase the employment effects of centre-based care, they may do so at the expense of child development by shutting out one of the mechanisms, that is, the easing of parental time constraints.

Data Availability Statement
Main analyses are based on the German Time-Use Survey.Access to scientific use files for all three waves was granted by the Research Data Centre of the Federal Statistical Office.
Further analyses in this paper are based on data from the first 11 waves of the German Family Panel (pairfam), release 11.0 (Brüderl et al., 2020).A detailed description of the study can be found in Huinink et al. (2011).
Final Manuscript Received: November 2020

Figure 1 .
Figure 1.Share of children enrolled in centre-based care by region, age group, and time Notes: Figure shows the share of children aged 0-6 years enrolled in centre-based care and in full-day care by region (West vs. East Germany) and age group over time.Enrolment includes formal child care centres and care by qualified publicly funded family day care.Data for 1991/92-2005/06 from the German Socio-Economic Panel (SOEP v35), which is a long-running household survey containing information on about 15,000 households per year(Goebel et al., 2019).For precision, data are pooled in 2-year bins.Annual statistics since 2007 from the German Federal Statistical Office (starting that year, official administrative data contain the share in full-day care)

Figure 2 .
Figure 2. Mothers' activities on weekdays by usage of centre-based care Notes: Circles denote mothers with a child in centre-based care, squares those without.Differences and averages are estimated in weighted regressions with indicators for child age and evaluated at mean values.Light grey triangles indicate the difference and whiskers are 95% confidence intervals.Data consist of time slots in 10-minute intervals (5 minutes in the first survey wave), which then are aggregated by hour of day.Source: German Time-Use Survey(1991/92, 2001/02 and 2012/13) table shows coefficients from OLS regressions of the outcome variables on an indicator variable for usage of centre-based care.Unconditional coefficients are from a regression that includes only indicators for child age in years.The conditional coefficients are from regressions that include the child age dummies, and, additionally, child gender, parent age (linear/squared), parent gender, parental education indicators for upper, middle, or lower secondary school track, and for university degree, marital status, single-parent status, number of children in household, a weekday indicator, and wave × region indicators.The identified set shows coefficients obtained using the method developed by Oster (2019), where R 2 max = min 1.3 × R2 , 1 assuming selection on unobservables is between zero (δ = 0) and a level equal to selection on observables (δ = 1).The δ for 0 coefficient row shows for each outcome variable how large the relative selection on unobservables must be to obtain a coefficient of 0. R 2 (unc., con.) shows the R 2 of the unconditional and conditional regressions.Mothers are defined as having obtained higher education when they have a degree from the upper secondary school track (required to enroll in university).Robust standard errors reported in parentheses.*P < 0.1, **P < 0.05, ***P < 0.01.† Denotes that the identified set excludes zero.Source: German Time-Use Survey (1991/92, 2001/02 and 2012/13).

Figure 3 .Figure 4 .
Figure 3. Mothers' differences in activities by time of day and education (a) Parenting activities (b) Other activitiesNotes: Centre hours are from 8 am to 4 pm on weekdays, non-centre hours are the remaining hours on weekdays (12 am-8 am and 4 pm-12 am) and the entire weekend days.Education level is defined based on whether mother has a secondary school degree from the higher track (Abitur).The plots show the conditional difference in outcome variables by centre-based care usage.Each estimate is based on a separate regression of the outcome summed over centre hours or non-centre hours on an indicator for usage of centre-based care and controls (see notes to Table2for details) using all three waves of the time-use survey (1991/02, 2001/02, and 2012/13).The hollow shapes and whiskers indicate the conditional coefficient (δ = 0) and 90% confidence intervals.The filled shapes indicate estimates under the assumption of δ = 1, that is, equally large selection on unobservables as on observables.The filled and hollow shapes together indicate the identified set.Appendix TableC2reports coefficients along with means of the outcome variables, and the δ required for zero coefficient, as well as separating out effects occurring at 'night' (which we define as 8 pm-8 am).Source: German Time-Use Survey(1991/92, 2001/02, and 2012/13)

Figure 5 .
Figure 5. Full-day vs. half-day care differences by time of day and education, wave 3 only (2012/13) (a) Parenting (b) Other activities Notes: Each estimate is based on a separate regression of the outcome summed over centre hours or non-centre hours on an indicator for usage of full-day centre-based care (>30 vs. 10-30 hours per week) and controls (as in Table 2) using the sample of centre-based care users.The filled and hollow shapes together indicate the identified set.See Figure 3 for further notes.Appendix Table C4 reports coefficients along with means of the outcome variables, and the δ required for zero coefficient.Source: German Time-Use Survey (2012/13)

TABLE 1
Sample characteristics by enrolment in centre-based care

Table 2
) using the sample of centre-based care users.The filled and hollow shapes together indicate the identified set.See Figure3for further notes.Estimates exclude the first survey wave (1991/92) as parenting activities are only compared consistently in the last two waves.Appendix TableC3shows detailed regression coefficients, including for other times of day.Source: German Time-Use Survey(2001/02 and 2012/13)

TABLE 3
Differences in parenting and non-parenting activities using full-day care This table shows conditional coefficients from OLS regressions of the outcome variables on an indicator variable for full-day care (defined as attending centre-based care in the morning and afternoon) for the sample of centre-based care users.Additional controls: dummies for child age, number of children in family, child gender, age of mother, indicator for migrant status, single-parent indicator, and an indicator for higher secondary schooling track.See Appendix FigureC5identified sets.