1. Introduction


The purpose of this paper is to increase our understanding of the relationship between the price of child care and the labour supply behaviour of partnered women. Many governments, including Australia, subsidise child care to encourage female labour force participation and also to promote child development. A large part of the effectiveness of these subsidies thus depends crucially upon the labour supply responsiveness of women to child care costs. In this paper we build a model that can be used to understand and compare the labour supply effects of alternative tax and subsidy policies which affect child care prices.

In a previous paper, Gong et al. (2010) showed that there is a negative relationship between child care price and partnered women's labour supply. They showed that measurement error in child care price is a problem and they addressed the problem by constructing local area prices using detailed, child-level data. However, they used a linear labour supply model which does not correspond to the actual work choices which partnered women face. They also estimate their model in a way that embeds the current tax system and child care subsidy policies making the model inappropriate to use for evaluation of alternative policies. In this paper, we use their improved method of price construction but address these two limitations through a more realistic labour market model combined with an approach which can be used to evaluate competing policy proposals.

In this paper we focus on the estimation of the net price elasticity, which measures how labour supply or child care demand changes for a change in the net price of child care. Gong et al. (2010) only provided estimates of gross price elasticities. The gross price is the posted price at a child care centre. The net price is what families actually pay out of pocket after accounting for any subsidies or rebates. It is this latter price that economic theory tells us should determine behaviour. Government policy on the cost of child care in Australia is targeted at changing the actual out-of-pocket child care costs that families face (rather than, for example, fixing prices) and thus the net price elasticity is more appropriate for understanding the effect of policy. It is important to note that the gap between the net and gross price elasticities is not constant across the population because of the means testing of subsidies. For some demographic groups, net and gross price elasticities may be quite similar whereas for others they may be quite different. Since we also care about the distributional effects of policy, this provides another argument for the importance of net price elasticities.

In order to estimate these net price elasticities, we specify and directly estimate the household's utility function. In this respect, our paper is similar to those of Blau and Robins (1988); Ribar (1992, 1995); Blau and Hagy (1998); Duncan et al. (2001); and Kornstad and Thoresen (2006, 2007). We construct and estimate a joint discrete structural model of labour supply and child care demand for partnered women with pre-school children.2 We focus on mothers with pre-school children because they are the group for whom the relationship between labour supply and child care is strongest. We assume that women choose work hours and hours of formal child care from a small set of realistic values which reflect typical work hour patterns and typical time slots which are available through child care providers. The framework may be used to estimate the effects of policy changes which affect the household budget constraint, such as child care price subsidies, wage subsidies or cash transfers.

Our paper offers two important methodological innovations. First, to the best of our knowledge, this is the first paper that explicitly includes child care as an argument of the utility function of similar discrete choice models. Previous papers have incorporated child care into such models in very restrictive ways. Kalb and Doiron (2005) included child care costs in the budget constraint of a standard discrete labour supply model but child care did not enter the utility function. Kornstad and Thoresen (2006, 2007) allowed the possible labour supply choices to depend upon mode of child care but restricted the utility function to depend only upon leisure and consumption. Since parents derive utility from the well-being of their children and since child care can be an input into children's educational development, it is important to allow child care to enter the utility function.

Second, our modelling of the relationship between hours worked by the mother and hours of child care improves upon the previous literature by allowing formal child care to be used for reasons other than allowing the mother to work and by accounting for the role of informal and paternal care in freeing up time for mothers to work. Children must be cared for at all times. Duncan et al. (2001) showed that it is important to constrain the number of child care hours to be at least as large as the hours of labour supplied by the mother. They showed that failure to do so can bias child care price effects. But Duncan et al. (2001) then constrained the number of paid (or formal) child care hours to be greater than the number of hours worked by the mother, ignoring the possible contribution of paternal and informal care. Kornstad and Thoresen (2006, 2007) also impose an hours constraint, specifically that the mother's work hours must be exactly equal to paid child care hours. In our view, this is too restrictive. We observe in the data (see below) that over thirty per cent of households use less hours of formal child care than the number of hours worked by the mothers. This clearly violates the constraints imposed by Duncan et al. (2001) or Kornstad and Thoresen (2006, 2007). Our model requires that the number of total child care hours (formal, informal and paternal) be at least as large as the number of hours worked by the mother. Formal child care hours may be greater or smaller than hours worked by the mother. Thus, our approach improves on both of these previous attempts to model quantity constraints.

The rest of the paper is organised as follows. In the next section (Section 2) we discuss the model, the estimation method, and the simulation approach we use to estimate elasticities. Section 3 describes the data. In Section 4, we present the estimation results of the model coefficients and the elasticities simulated from those estimates. This includes discussion of the relationship between the results in this paper and earlier results. Section 5 concludes.

2 In this paper, partnered women with young children include married women and women in de facto relationships. These women are also referred to as `mothers' and their spouses/partners are referred to as `fathers'.