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Empirical Economics

Erschienen in:

04.01.2016

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

verfasst von: Patricia Apps, Jan Kabátek, Ray Rees, Arthur van Soest

Erschienen in: Empirical Economics | Ausgabe 4/2016

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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.

Vorheriger Artikel Dynamic labor supply adjustment with bias correction

Nächster Artikel Measuring the US NAIRU as a step function

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

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.

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.

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.

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

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

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

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).

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.

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.

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

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.

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.

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.

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

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.

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

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.

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.

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

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.

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).

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

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).

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.

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

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.

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.

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 %.

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.

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

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.

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.

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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Titel: Labor supply heterogeneity and demand for child care of mothers with young children
verfasst von: Patricia Apps
Jan Kabátek
Ray Rees
Arthur van Soest
Publikationsdatum: 04.01.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 4/2016
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1046-4

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