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School entry, afternoon care, and mothers’ labour supply

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Abstract

The availability of childcare is a crucial factor for mothers’ labour force participation. While most of the literature examines childcare for preschool children, we specifically focus on primary school-aged children, estimating the effect of formal afternoon care on maternal labour supply. To do so, we use a novel matching technique, entropy balancing, and draw on the rich and longitudinal data of the German Socio-Economic Panel (SOEP). We show that children’s afternoon care increases mothers’ employment rates and their working hours. To confirm the robustness of our results, we conduct a series of sensitivity analyses and apply a newly proposed method to assess possible bias from omitted variables. Our findings highlight how childcare availability shapes maternal employment patterns well after school entry.

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Notes

  1. In the states of Berlin, Brandenburg, and Mecklenburg-Vorpommern, the transition to secondary school occurs after grade 6.

  2. Less than 5% of primary schools are all-day schools in the strict sense of operating an all-day schedule for all the children enrolled (Marcus et al. 2013).

  3. We use the user-written programme “ebalance” (Hainmueller and Xu 2013) in Stata to implement entropy balancing.

  4. More specifically, entropy balancing solves equations of the following form for \(\omega _1- \omega _n\):

    $$\begin{aligned} \bar{x}_1^T = \omega _1 \cdot x_{11} + \omega _2 \cdot x_{12} + \cdots + \omega _n \cdot x_{1n} \\ \bar{x}_2^T = \omega _1 \cdot x_{21} + \omega _2 \cdot x_{22} + \cdots + \omega _n \cdot x_{2n} \\ \vdots \nonumber \\ \bar{x}_j^T = \omega _1 \cdot x_{j1} + \omega _2 \cdot x_{j2} + \cdots + \omega _n \cdot x_{jn} \end{aligned}$$

    \(\bar{x}_j^T\) denotes the mean of variable \(x_j\) in the treatment group, \(x_{jn}\) is the value of the n-th control group observation in the j-th conditioning variable, and \(\omega _n\) denotes the weight of the n-th control group member. Note that while this discussion focuses on the first moments (means), the argument for the second moment (variance) follows analogously. Entropy balancing imposes the restriction that all \(\omega _n\) must be non-negative (i.e. no observation receives a negative weight). While there are generally more control group observations than restrictions, i.e. N > J, usually more than one weighting scheme \(\omega _1- \omega _n\) solves this set of equations. Out of the many possible weighting schemes that fulfil these conditions, entropy balancing selects the weighting scheme in which the weights deviate as little as possible from equal weights—where distance is measured by the eponymous entropy divergence (Kullback 1959).

  5. As the treatment indicator is almost orthogonal to the control variables after entropy balancing (treatment and weighted control groups have the same means in all control variables), the inclusion of control variables in the regression step does not change the estimated treatment effect substantially but rather increases its precision.

  6. More specifically, we not only control for the economic situation in the mother’s region, for state- fixed effects, and for the degree of urbanisation, but we also include variables that capture preferences for childcare policies (e.g. the child’s care arrangements before school entry) and maternal work preferences (e.g. maternal work intentions and labour market history).

  7. Although starting to observe children from 1999 onward precedes the expansion of afternoon care, we still observe children in both treatment and control groups between 1999 and 2003. Few children receive afternoon care between 1999 and 2003; this increases from 2003 onwards. Therefore, we also conduct a sensitivity analysis and look only at mothers and children observed from 2003 onward. The results remain very similar.

  8. The results are also robust to using cases with an interview between August and December; see Sect. 6.

  9. Before 2009 the question reads “Which of the following institutions do [your] children currently attend?” and lists both primary school and after-school programme as category leaving parents the possibility to give multiple answers.

  10. We include binary variables for each answer (see Table 10 in Appendix) to the questions “Do you intend to engage in paid employment (again) in the future?”, “When, approximately, would you like to start with paid employment?”, “Are you interested in full-time or part-time employment, or would both suit you?”, “Is it or would it be easy, difficult or almost impossible to find an appropriate position?”, “Could you start working within the next 2 weeks?”, and “Have you actively looked for work within the last 4 weeks?”.

  11. Table 10 in Appendix provides a full list of control variables.

  12. In Table 10, we show that propensity score matching also works well in reducing the differences between treatment and control groups. None of the standardised biases are larger than 20% after propensity score matching, although several values are greater than 5%, which is considered to be a threshold for low values (see Caliendo and Kopeinig 2008). However, the standardised bias is clearly smaller for the entropy balancing specification than for the propensity score specification. For some variables, such as child’s gender, the standardised bias in the propensity score specification is even larger than in the unweighted control group.

  13. For the analyses in Table 6, we split our sample according to different characteristics of mother and child and run separate regressions in each subsample. This analysis includes control variables only in the regression step and not in the matching step as cell sizes in some subgroups become too small for the matching procedure.

  14. This is partly due to smaller sample size.

  15. This rule applies to “open all-day schools” only. These are those where participation to afternoon activities is voluntary and they constitute the large majority of all-day schools among primary schools (Marcus et al. 2013). In the 5% of schools, where participation in all-day schooling is compulsory for all the pupils, parents do not have the choice option at the beginning of the school year.

  16. This specification is not our preferred one as the restriction might be overly conservative: mothers know their child’s treatment status before school start and, hence, can adapt their employment pattern in anticipation of the treatment.

  17. Note that in the published article, Oster (2017) suggests a value of \(R_{\mathrm{max}}^2 = \mathrm{min}\{1.3 \cdot \tilde{R^2}, 1\}\). Nevertheless, we rely on the working paper version, which is more conservative as it generally generates higher values of \(R_{\mathrm{max}}^2\).

  18. Similarly the adjusted \(R^2\) increases from 0.03 to 0.33.

  19. We use the Stata command psacalc provided by Oster (2013) to calculate the estimates of \(\delta \) and the lower bound.

  20. Note that the \({\tilde{\delta }}\) found for the outcome “working” in Panel B is negative as the treatment effect moves away from zero rather than towards zero when including control variables. The large and negative value of \({\tilde{\delta }}\) implies that any bias in the estimated effect due to omitted variables would have to be not only substantially larger than the bias generated by omitting observable variables, but it would also have to be in the opposite direction of the bias from omitting observable variables.

  21. For the propensity score matching, we rely on kernel matching with a Gaussian kernel and a bandwidth of 0.06 (see Heckman et al. 1997; Marcus 2014). We rely on the user-written programme “psmatch2” in Stata (Leuven and Sianesi 2003).

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Acknowledgements

We gratefully acknowledge support by the College for Interdisciplinary Educational Research (CIDER). Moreover, we thank C. Katharina Spieß, Adam Lederer, Janina Nemitz, seminar participants at the University of Chicago and DIW Berlin, as well as participants of the GEBF 2016 and the 2016 ESPE conferences for valuable comments.

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Authors and Affiliations

  1. DIW Berlin, Berlin, Germany

    Ludovica Gambaro, Jan Marcus & Frauke Peter

  2. UCL Institute of Education, London, UK

    Ludovica Gambaro

  3. Universität Hamburg, Hamburg, Germany

    Jan Marcus

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  1. Ludovica Gambaro
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  2. Jan Marcus
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Correspondence to Jan Marcus.

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Appendix

Appendix

See Tables 10 and 11.

Table 10 Descriptive statistics of reduced and full set of \(t_0\) controls—before and after matching
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Table 11 Tobit and hurdle regression
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Gambaro, L., Marcus, J. & Peter, F. School entry, afternoon care, and mothers’ labour supply. Empir Econ 57, 769–803 (2019). https://doi.org/10.1007/s00181-018-1462-3

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