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Labor supply heterogeneity and demand for child care of mothers with young children

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Abstract

This paper presents a structural model of the labor supply and child care choices of partnered mothers with pre-school aged children. The father’s time-use decisions are taken as given. The main goal is to analyze the sensitivity of maternal time use to the price of child care, taxes, benefits and child care subsidies. To account for non-convexities in the budget sets, we specify a discrete choice model. We estimate the model on data on couples with young children from the HILDA survey representative of the Australian population, which contains detailed information on time use and bought-in child care. Simulations based on the estimated parameters show that the time decisions of mothers with pre-school children are highly sensitive to changes in wages and the cost of child care. Our results also suggest that lowering effective tax rates faced by partnered mothers as second earners, by switching from family payments that are targeted on joint incomes to payments that are universal and funded by a more progressive individual-based income tax, would lead to a substantial increase in their labor force participation and hours of work.

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Notes

  1. Applications using this approach include Ribar (1995), Doiron and Kalb (2005) and Kabátek et al. (2014).

  2. Several studies of female labor supply allow for more flexible treatment of the unobserved heterogeneity (Bernal 2008; Blau and Hagy 1998 and Tekin 2007), building on seminal works of Heckman and Singer (1984) and Mroz (1999). The latent-class approach can be considered a generalization of these models, allowing for additional flexibility.

  3. Every variable or function with subscript h can vary across households. Each of these is therefore in principle a contributor to across-household heterogeneity in choices.

  4. The fact that we restrict ourselves to the unitary framework and do not develop a collective model is essentially due to data limitations that constrain what we can estimate. Furthermore, non-convexity of budget constraints is a central aspect of the motivation of the modeling in this paper, and this non-convexity poses a problem for the possibility of the existence of a decentralized sharing rule, which is a central aspect of the collective approach.

  5. In principle, the distributional factors could also include the wage rates, but this will not be allowed for in the empirical model.

  6. For a detailed exposition of the economics of this type of household model, see Apps and Rees (2009), Ch 3.

  7. For example there may be tax offsets for expenditure on market child care.

  8. For detailed discussion and applications of the discrete approach adopted here see, for example, Van Soest (1995), Van Soest et al. (2002) and Pacifico (2012).

  9. In other empirical studies, additional household-specific restrictions are often needed to account for infeasibility of certain choices. Kornstad and Thoresen (2007), for example, constrain choice sets of selected households to account for high degree of rationing in Norwegian day care centers.

  10. A limitation of the HILDA time-use data is that only one activity is reported for each episode. In contrast, the Australian Bureau of Statistics (ABS) Time Use Surveys report a second activity when relevant. Child care is almost always a second activity during housework and related activities.

  11. Similar income-based exclusion restrictions are used by, e.g., Blundell et al. (2007b) and Sorensen (1993).

  12. The imputation of child care prices should be approached with caution because the observed prices can reflect variation in quality of the service. The quality of child care can be endogenous to the regressors used in the Heckman selection model and hence can distort reliability of the imputed prices. To address these concerns, we estimate an alternative specification of the model which uses imputed prices of child care for all families in the sample. Relative differences in the predictions made by the original model and the alternative specification can be used to assess whether the endogeneity is likely to play a role here.

  13. This helps to reduce the computational complexity of the problem. Given that the utility function is identified up to a monotonic transformation only, it does not seem overly restrictive.

  14. The penalized choices are identical to the standard choices in all respects other than household income, which is lower for penalized choices. Negative marginal utility would imply that penalized choices in the interior would be favored by the decision makers, but the observed choices are always on the budget frontier. Maximum Likelihood estimates maximize the probability of the observed outcomes and will therefore give parameters that make internal choices unlikely, that is, parameters that imply a positive marginal utility of income.

  15. “Full-time” employment is defined by the ABS as 35 hours or more per week.

  16. The time-use data are collected by questionnaire and reported as weekly time uses. Unlike diary data, questionnaire data are typically subject to larger reporting errors, and as a result the sum of individual time allocations to the various activities sometimes fails to satisfy the time constraint.

  17. As a robustness check, we also estimated the structural model excluding these 85 women. This gave virtually identical estimates of elasticities and policy effects.

  18. Leisure is computed as the remainder of the daily time endowment after subtracting market work and household production hours, which may be adjusted to satisfy the total time constraint. The 42-h per week threshold follows from assuming at least 6 h per day for sleep and personal care.

  19. An economic rationale for this would be that informal child care is quantity-rationed and has a lower cost than formal child care, the price of which determines demand for child care at the margin.

  20. The details of the tax rates, family payments and income thresholds on which the figure is based are set out in “Appendix 2”.

  21. For a graphical analysis of cases in which the second earner has lower income than the primary earner, see Apps and Rees (2009), Ch 6.

  22. This “tax penalty” on the second earner’s income under joint taxation explains why switching from a joint to a purely individual-based system stimulates the participation of the second earner (see, for example, Steiner and Wrohlich 2004).

  23. The latter is obtained by taking weighted means over all classes, where the weights are the class probabilities given the observed choice.

  24. Standard errors on the elasticities were computed through 199 Monte Carlo simulations, recomputing the percentage changes with simulated sets of parameters determining \(\mathbf {A}\) and \(\mathbf {b}\). These parameters were drawn from the estimated (multivariate normal) distribution of the ML estimates. See Ruud (1991).

  25. In absolute terms, the wage increase induces the average mother to spend about 0.55 h per week more on market work, 0.40 h less on household production, and 0.15 h less on leisure.

  26. This elasticity is well in line with that of Gong and Breunig (2011) but smaller than that in Breunig et al. (2012).

  27. On average mothers spend about 0.10 h per week longer on household production and reduce their market work by 0.10 h and bought-in child care by 0.05 h.

  28. It should be noted that these results are specific to the population of partnered mothers with preschool children. The revenue neutrality is also achieved by raising income taxes only for this group.

  29. The percentage changes presented in Table 8 use quartile-specific sample means of time-use allocations as a point of reference. If we would use unconditional means, the percentage change for female labor supply in the fourth quartile would be 1.26 %.

  30. In our sample, 65 % of mothers are predicted to increase their hours of formal child care (typically the mothers who increase their hours of market work). Once again, a key role is played by mothers with higher wages who reduce their market work hours and also their utilization of formal care. The relatively large fall in their claimed benefits is sufficient to offset most of the rise in benefit claims by other households.

  31. This allows us to examine direct substitution effects between maternal and formal child care.

  32. There is no clear consensus with respect to which form the working indicator should take on. Blundell et al. (2007a) put the employment dummy into the budget constraint, so that it represents fixed monetary costs of working. Donald and Hamermesh (2009) interact the dummy with time-use variables entering the utility function, referring to the corresponding parameters as shifters of time-use efficiency. We choose to add the employment dummy into the individual utility function in a non-interacted form, which allows us to model fixed disutility from work without substantially increasing the computational burden.

  33. Restricting the age range to women aged 48 and under hardly affects the results—the correlation coefficient between the two sets of wage predictions is 0.99.

  34. Despite its title, the ML is a tax on income and is not tied to funding any aspect of the health system.

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Author information

Authors and Affiliations

  1. Sydney University Law School, Sydney, Australia

    Patricia Apps

  2. IZA, Bonn, Germany

    Patricia Apps, Jan Kabátek & Arthur van Soest

  3. Melbourne Institute of Applied Social and Economic Research, University of Melbourne, Melbourne, Australia

    Jan Kabátek

  4. Netspar, Tilburg, The Netherlands

    Jan Kabátek & Arthur van Soest

  5. CES, University of Munich, Munich, Germany

    Ray Rees

  6. Department of Econometrics and OR, Tilburg University, Tilburg, The Netherlands

    Arthur van Soest

Authors
  1. Patricia Apps
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  2. Jan Kabátek
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  3. Ray Rees
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  4. Arthur van Soest
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Corresponding author

Correspondence to Jan Kabátek.

Additional information

This research was supported under the Australian Research Council’s Discovery Project funding scheme (Project ID: DP1094021). The authors thank seminar participants at Université Laval, University of Lausanne, University of Mannheim, Netherlands Bureau for Economic Policy Analysis (CPB), Tilburg University, the ESPE Annual Conference, the NATSEM International Child Care, Work, and Family Workshop, the Netspar Pension Day, and the Netspar International Workshop for their valuable comments.

Appendices

Appendix 1: Heckman selection models

In Tables 10 and 11 below we present details of the Heckman selection models used to predict missing wages and child care prices. The models are estimated on a sample of partnered women aged 55 years and under, with those reported as full-time students or disabled excluded.Footnote 33 The exclusion restrictions used in the participation equation are non-wage income and number of children.

The child care price equations are estimated on a sample limited to mothers with pre-school children. This subsample is larger than the sample used for estimating the structural time-use model because the time-use data in HILDA was collected for a randomized subsample only. The exclusion restrictions in the child care participation equation are number of adults in the household (excluding the spouses) and residential distance from grandparents (the base group represents families without grandparents).

Table 10 Mothers’ wage estimation, Heckman selection model
Full size table
Table 11 Child care price estimation, Heckman selection model
Full size table

Appendix 2: Australian family income taxes and child care subsidies

Net household income is calculated as gross income net of tax liabilities and family payments. We compute tax liabilities under the Personal Income Tax (PIT), Low Income Tax Offset (LITO), Medicare Levy (ML),Footnote 34 and family payments under Family Tax Benefit Part A (FTB-A) and Family Tax Benefit Part B (FTB-B). The calculation of the net price of formal child care takes account of the two main subsidies for child care, Child Care Benefit (CCB) and the Child Care Rebate (CCR). Each of these components of the overall system is described below. We also report details of the tax-benefit system used to construct Figs. 6 and 7 for a family with two children under 13, with one under 5, in the 2007–2008 financial year.

1.1 Personal Income Tax and LITO

The 2007–2008 marginal rate scale of the PIT begins with a zero rated threshold of $6,000, followed by rates of 15, 30 and 40 % up to an income of $150,000, and thereafter a top rate of 45 %. The LITO in the same financial year provided a tax offset of $750, phased out at 4 cents in the dollar on individual incomes above $30,000. The resulting effective rate scale was therefore a zero rated threshold of $11,000 and a higher rate of 34 cents in the dollar on incomes from $30,001 to $48,750, as depicted in Fig. 6. Because the

1.2 Medicare Levy

A Medicare Levy (ML) applies at a rate of 1.5 % of income, with exemptions defined on family income and varying with the number of children. In 2007–2008 the family income limit for a full reduction for a two-parent family was $29,207, plus $2,682 for each dependent child. The exemption was withdrawn at a rate of 8.5 cents in the dollar above this limit, with the effect of raising the marginal rate above that limit to 44 cents in the dollar. Thus the ML introduces a further nonconvexity in the effective rate scale and also shifts the tax base toward joint income.

1.3 FTB-A and FTB-B

FTB-A provides a payments for each dependent child. The size of the payment varies with the age of the child. The “Maximum Rate” of FTB-A in 2007–2008 for a child under 13 years was $4,460.30. This maximum payment was withdrawn at 20 cents in the dollar on a family income over $41,318 up to the “Base Rate” of $1,890.70 per annum. The Base Rate was withdrawn at 30 cents in the dollar at a higher family income threshold that depends on the number of dependent children. For a family with two dependent children, the income threshold for the Base Rate was $95,192. Given the size of the payments and withdrawal rates of 20 and 30 cents in the dollar, married mothers can face effective marginal rates on earnings that are well above the top rate of the PIT scale, as illustrated in Fig. 7.

FTB-B provides an annual payment of $3,584.30 in 2007–2008 for a family with a child under 5 years. The payment was withdrawn at a rate of 20 cents in the dollar on a second income above $4,380. It can therefore be classified as a “gender based tax” (see Alesina et al. 2011) with, paradoxically, the higher rate applying to the income of the mother as second earner.

1.4 Child Care Benefit and Child Care Rebate

Child Care Benefit depends (among other things) on the ages of children, number of children, type of child care and the hours of child care used. The benefit is phased out with rising family income according to the age of the child and the number of children receiving child care.

The Child Care Rebate reimburses families for their claimed child care expenses. It can cover up to 50 % of the net child care expenses (that is, after subtracting CCB). The CCR rate is not income-tested, but it has an upper cap on the amount of expenses which can be reimbursed. For the year 2008, this cap was $4,354 per year.

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Apps, P., Kabátek, J., Rees, R. et al. Labor supply heterogeneity and demand for child care of mothers with young children. Empir Econ 51, 1641–1677 (2016). https://doi.org/10.1007/s00181-015-1046-4

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