Market work, housework and childcare: A time use approach

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Abstract

Raising children takes considerable time, particularly for women. Yet, the role of childcare time has received scant attention in the macroeconomics literature. We develop a life-cycle model in which the time dimension of childcare plays a central role. An important contribution of the paper is estimation of the parameters of a childcare production function using data on primary and secondary childcare time as reported in the American Time Use Survey (2003–2014). The model does a better job matching the observed life-cycle patterns of womens' time use than a model without childcare. Our counterfactual experiments show that the increase in the relative wage of women since the 1960s is an important factor in the increase in womens' work time; changes in fertility associated with the baby boom play a smaller role, and changes in the price of durables are found to have a negligible effect. We consider the effects of cheaper daycare. Not surprisingly, this experiment leads to greater use of daycare and more time allocated to market work. A knock-on effect of cheaper daycare is a substantial decline in primary childcare time.

Introduction

An important message in Becker's (1965) seminal paper is that in order to understand the full impact of policies on the economy, we should also examine their effects on non-market activities. Important, recent papers studying the allocation of womens' time include Greenwood et al. (2005), Attanasio et al. (2008) and Jones et al. (2015). However, most studies on womens' labor market decisions ignore the role of childcare, and those that do typically treat childcare as exclusively a monetary cost. The implications of childcare has received little, if any, attention in the literature exploring the allocation of womens' time in a life-cycle setting. Yet childcare requirements constitute a substantial constraint on how women with children allocate their time. This inattention seems surprising since most of the increase in female participation is from married women. Further, as Aguiar and Hurst (2007) note, “there are certain elements of child rearing for which market goods and parental time are not good substitutes. This proposition is supported by the fact that hardly anyone uses market substitutes to raise their children completely. For this reason, we feel it appropriate to analyze childcare separately.”

This paper develops a life-cycle model in which the time requirements of childcare are treated seriously. Since women often bear the brunt of childcare, the focus is on women – men are an exogenous source of income for the household. The data used to discipline our choices and to evaluate the model are from the American Time Use Survey (ATUS) which is available since 2003. The ATUS data distinguishes between two types of childcare time. The first is primary childcare time which corresponds to time during which the primary activity of the survey respondent is taking care of a child. Included among such activities is bathing, feeding and reading to children. The second type of childcare time is secondary childcare time during which another activity, like housework or leisure, is the primary activity, but the respondent is nonetheless caring for a child. In order to focus on the role of the childcare constraint on the allocation of time, we take the childcare requirement as exogenous. In the model, this constraint can be satisfied through the choice of primary childcare time, secondary childcare time, and daycare. One contribution of this paper is the estimation of the parameters of the childcare production function, including the elasticity of substitution between primary and secondary childcare time using data from the American Time Use Surveys between 2003 and 2014.

As shown in Section 5, childcare requirements differ markedly depending on both the number of children, and their age. So as to develop a reasonably parsimonious model, the length of a period is set to six years. Since older children can, to a large extent, take care of themselves, our focus, is on children under the age of twelve. Consequently, for the purposes of the childcare constraint, what matters is the number of children under the age of six, and the number of children six to eleven years of age. Since women in their 40s have very few children, there are four model periods during which a women can bear children (age groups 18–23, 24–29, 30–35 and 36–41). We categorize the number of children (in each of the two child age groups) as being: zero, one, or two or more. As a result, there are 81 (=34 where the 3 refers to the number of children that a woman can bear in each of her 4 model periods during which she is fertile) ‘types’ of women, depending on their fertility pattern. Women face no uncertainty over the timing of children: at the start of her life-cycle, each woman knows how many children she will bear, and at what ages she will bear them.

In the data, there are two chief sources of secondary childcare time: leisure and housework time. As is typical, households directly value leisure. Housework time is incorporated into the model by modeling home production as in Benhabib et al. (1991) and Greenwood and Hercowitz (1991). More specifically, home produced goods require both housework time and durables.

Finally, the model features a hump-shaped profile for wages, the particulars of which are borrowed from Gomme et al. (2005), and womens' wages are, on average, a fraction of mens' wages. Market wages are important since they help determine the opportunity cost of both primary childcare time, as well as that of housework time.

The model is evaluated on its ability to replicate the allocation of time between working in the market, housework, primary childcare, and leisure. While some of the model's parameters are calibrated to closely match the average allocation of time to these activities, the allocation of time over the life-cycle is not targeted and so constitutes an important test of the model. The model captures the way that time spent on primary childcare varies with a woman's age. In particular, primary childcare time is high when women have many children – up to their mid-30s – after which primary childcare time drops off. The model also does well in mimicking the life-cycle pattern of leisure and housework time. While not a tight fit, the model nonetheless captures the general life-cycle pattern on womens' market time. The model overstates womens' market time for women over the age of 65, likely due to omitting modeling retirement decisions in the model.

What is the role of childcare in this model? To answer this question, we look at the behavior of women in the model who never have children. In the model, the chief difference between these women and the averages reported across all women lies in the behavior of market time. The model predicts that women who never bear children have a profile for market time that is strictly declining with age, a pattern which simply does not match up with the hump-shaped profile observed in the ATUS data for all women. This observation shows that the role of childcare in the model is to cause a substitution of time out of market work into time activities to satisfy the childcare requirement – chiefly, primary childcare time. Childcare can also mute the effects of certain changes or policies. Secondary childcare, for example, can decrease the impact of an increase in wages.1 The latter would decrease leisure and time spent doing secondary childcare, which needs to be substituted by costly daycare which in turn decreases the benefits of higher wages.

To investigate the driving forces in the model, we run several counterfactuals: lower relative wages for women, a higher price of durables, and higher fertility. To ground these counterfactuals in reality, we look back roughly 50 years to the 1960s. At that time, women earned about 60% of what men earned, compared to 80% in the early 2000s. Not surprisingly, our model predicts that lowering womens' wages leads them to allocate less time to the market, and more time to housework, primary childcare, and leisure. This result is in accord with Jones et al. (2015). As described below, in the 2000s, the relative price of durables is normalized to one; in the 1960s, this relative price is roughly 2.8. Greenwood et al. (2005) find that when durables are more expensive, households use fewer of them, substituting into housework time at the expense of market time. In contrast, our model finds virtually no effect of the price of durables on womens' market time – despite our use of an elasticity of substitution between durables and housework time that makes this substitution relatively easy. Finally, higher fertility, as in the 1960s, increases childcare requirements. However, this change has little effect on market time, housework time or leisure. Instead, the chief effect of increased fertility is to increase both primary childcare time and the use of daycare. Evidently, women find it efficacious to maintain the amount of time allocated to market activity and purchase market daycare inputs.

In the public policy sphere, there has been some concern over the lower allocation of time to the market by younger women relative to men. One way to potentially boost the market time of younger women is to subsidize daycare. This public policy issue is addressed in the model by lowering the price of daycare. In response to a 25% decline in the price of daycare, the model predicts more than a three-fold increase in the use of daycare. This experiment also raises the time spent by young women on market activity. One potential downside to this policy: the model predicts sharply lower primary childcare time. This last prediction is troubling in light of the documented importance of primary childcare time in child development. The recent empirical literature shows ambiguous effects of the expansion of subsidized child care. Baker et al. (2008), for example, find that the expansion of universal subsidized child care in Québec increased aggressiveness and decreased social and motor skills of children.

The remainder of the paper is organized as follows. The related literature is discussed in Section 2. In Section 3 we examine data from the American Time Use Survey; in Section 4, we describe the model; in Section 5 we discuss the calibration of the model. Solving the model is difficult owing to the number of potentially non-binding constraints; see Section 6. In Section 7 we examine the results of the simulations. Section 8 concludes.

Section snippets

Related literature

As previously mentioned, we are not the first to look at the time allocations of women. Broadly speaking, there have been two approaches. The first looks at the roles of relative wages and the price of durables, excluding the effects of childcare and fertility. Greenwood et al. (2005) build a life-cycle model with home production and a durables adoption decision. They find that the durable goods revolution is the prime driver of changes in womens' market time and that its effects are roughly

Historical facts: female labor force, housework and childcare

This section uses data from U.S. time use surveys to examine trends in married womens' market work, housework, childcare and leisure. The term married woman is used as a shorthand to include not only married women but also women with a domestic partner.

Fig. 1(a) reports the observed changes in the allocation of time of married women to market work over the second half of the twentieth century. The data come from the 1965 Time Use Survey (TUS) and the American Time Use Survey (ATUS) where we use

Households

The economy is populated by overlapping generations of households. As discussed in the Introduction, households differ with respect to their fertility patterns. There is no uncertainty with regards to fertility: a household knows how many children it will have, and when. The index j is used to distinguish between households of different fertility patterns; for a given fertility pattern, households are otherwise identical.

Households are comprised of a married couple which splits its time among

Calibration

Functional forms are given by Eqs. (2), (3), (5) and (7). The model's parameters are summarized in Table 2.

To start, a model period is set to 6 years. This choice is motivated by the observation that children tend to start school at age 6, and that their childcare requirement may change upon entering school. The household ‘lives’ for 10 periods, or 60 years. In data terms, we are looking at households for which the respondent is aged between 18 and 78.

A number of the model's parameters are

Solving the model

There are a number of features in the model that make it difficult to solve using standard techniques, meaning solving sets of non-linear Euler equations and constraints. First, the fact that secondary childcare time and daycare services are perfect substitutes means that the non-negativity constraint on daycare sometimes binds. Second, there is sufficient substitutability between primary childcare time and secondary childcare that the non-negativity constraint on primary childcare time

Results of the simulations

In this section we examine how well the model performs with regards to the life-cycle profiles for the allocation of time as reported in the ATUS.

Conclusions

This paper constructed a life-cycle model of the allocation of womens' time that includes the time cost of childcare. While the calibration matched the average allocation of time to the market, housework and primary childcare, households within the model were free to determine the life-cycle patterns of their time allocations. The paper made a number of contributions. First was the estimation of the parameters of the childcare production function, including: the weight on primary versus

Acknowledgements

Angelo Melino, the editor and two referees provided helpful comments. Bryan Breguet provided excellent research assistance. This work was funded, in part, by the Fonds Québécois de la Recherche sur la Société et la Culture (2012-SE-144688). This paper draws on material from our earlier paper, “The Household Revolution: Childcare, Housework, and Female Labor Force Participation.” Gomme also acknowledges the financial support of the Social Sciences and Humanities Council (410-207-1171).

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