Estimating net child care price elasticities of partnered women with pre-school children using a discrete structural labour supply-child care model

Gong, Xiaodong; Breunig, Robert Working Paper Estimating net child care price elasticities of partnered women with pre-school children using a discrete structural labour supply-child care model Treasury Working Paper, No. 2012-01 Provided in Cooperation with: The Treasury, The Australian Government Suggested Citation: Gong, Xiaodong; Breunig, Robert (2012) : Estimating net child care price elasticities of partnered women with pre-school children using a discrete structural labour supplychild care model, Treasury Working Paper, No. 2012-01, ISBN 978-0-642-74844-7, The Australian Government, The Treasury, Canberra This Version is available at: https://hdl.handle.net/10419/210379 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/au/legalcode i ESTIMATING NET CHILD CARE PRICE ELASTICITIES OF PARTNERED WOMEN WITH PRE-SCHOOL CHILDREN USING A DISCRETE STRUCTURAL LABOUR SUPPLY-CHILD CARE MODEL Xiaodong Gong and Robert Breunig Treasury Working Paper 2012 — 01 [November 2012] Xiaodong Gong was with the Australian Treasury when the main part of this work was undertaken. He is now with the National Centre for Social and Economic Modelling at the University of Canberra. Robert Breunig is with the Research School of Economics at the Australian National University and is a consultant at the Australian Treasury. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Australian Treasury. We are grateful to Anthony King, Gordon Leslie and Rob Heferen for comments on an earlier draft of the paper. Guyonne Kalb and Stephan Whelan commented on a related paper and their insights are also reflected in this paper. We have further benefited from the comments of participants at three conferences where we presented this work in July 2011: the Econometric Society ii Australasia Meetings in Adelaide; the Australian Conference of Economists in Canberra, and the HILDA Survey ‘10th Anniversary’ Research Conference in Melbourne. Any omissions and mistakes are the sole responsibility of the authors. This paper uses unit record data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey. The HILDA Project was initiated and is funded by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs (FaHCSIA) and is managed by the Melbourne Institute of Applied Economic and Social Research (Melbourne Institute). The findings and views reported in this paper, however, are those of the author and should not be attributed to either FaHCSIA or the Melbourne Institute. iii © Commonwealth of Australia 2012 ISBN 978-0-642-74844-7 This publication is available for your use under a Creative Commons Attribution 3.0 Australia licence, with the exception of the Commonwealth Coat of Arms, the Treasury logo, photographs, images, signatures and where otherwise stated. The full licence terms are available from http://creativecommons.org/licenses/by/3.0/au/legalcode. Use of Treasury material under a Creative Commons Attribution 3.0 Australia licence requires you to attribute the work (but not in any way that suggests that the Treasury endorses you or your use of the work). Treasury material used ‘as supplied’ Provided you have not modified or transformed Treasury material in any way including, for example, by changing the Treasury text; calculating percentage changes; graphing or charting data; or deriving new statistics from published Treasury statistics — then Treasury prefers the following attribution: Source: The Australian Government the Treasury Derivative material If you have modified or transformed Treasury material, or derived new material from those of the Treasury in any way, then Treasury prefers the following attribution: Based on The Australian Government the Treasury data Use of the Coat of Arms The terms under which the Coat of Arms can be used are set out on the It’s an Honour website (see www.itsanhonour.gov.au) Other Uses Inquiries regarding this licence and any other use of this document are welcome at: Manager Communications The Treasury Langton Crescent Parkes ACT 2600 Email: [email protected] iv ABSTRACT Abstract: The purpose of this paper is to improve our understanding of the relationship between child care price and women’s labour supply. We specify and estimate a discrete, structural model of the joint household decision over women’s labour supply and child care demand. Parents care about the well-being and development of their children and we capture this by including child care directly in household utility. Our model improves on previous papers in that we allow formal child care to be used for reasons other than freeing up time for mothers to work (such as child development) and we allow mothers’ work hours to exceed formal child care hours. As informal and paternal care are important features of the data, this second relaxation of previous hour constraints is particularly important. We estimate the model using data from 2005 to 2007 from the Household Income and Labour Dynamics in Australia (HILDA) Survey. We find that on average a one percent increase in the net price of child care leads to a decrease in hours of labour provided by partnered women of 0.10 per cent and a decrease in the employment rate of 0.06 per cent. These estimates are statistically significant. Furthermore, we find that labour supply responses are larger for women with lower wages, less education, and lower income. JEL Classification Numbers: C15; C35; J22. Keywords: Child care demand; child care price; women’s labour supply; elasticities; discrete choice model Xiaodong Gong NATSEM, University of Canberra email: [email protected] tel: +61 (0)2 6201 2771 Robert Breunig Australian National University email: [email protected] tel: +61 (0)2 6125 2148 v EXECUTIVE SUMMARY • In this paper, we specify and estimate a model for partnered women’s simultaneous decisions about how much to work and how much child care to use. • The model is an improvement over previous research in that it allows for comparison of alternative policies which affect household budget constraints, such as policies which change child care costs, and also allows for analysis of the distributional effects of such policies. • The model is realistic in that labour supply and child care decisions are treated jointly and both hours worked and hours of child care demanded are chosen from a small set of commonly observed values. Hours can not be adjusted in arbitrarily small amounts but must respect the real-life constraints of the labour market and slots typically offered by child care providers. • The model includes constraints which require that children be cared for at all times by someone other than the mother while the mother is working. Such constraints are important to avoid bias in the estimated effects of child care prices. • The paper improves the modelling of the relationship between hours of child care and mothers’ working time in two important ways: – The model allows for the use of child care for purposes other than freeing up mothers’ time to work. For example, child care may be used to improve children’s development. vi – The model allows hours worked by the mother to exceed hours of formal child care, with the difference being made up by informal and/or paternal care. This relaxation of hours restrictions imposed in previous research is important in that we observe in the data that over thirty per cent of working mothers work more hours than the hours spent by their children in formal care. • Both of these innovations are novel in the literature. • We model and include effects of the personal tax system and major transfer payments including New Start Allowance, Parenting Payment Partnered, Family Tax Benefits, and Child Care Benefit.1 • The model is estimated using data from Waves 5 through 7 (2005-2007) of the ‘in-confidence’ version of the Household Income and Labour Dynamics in Australia (HILDA) Survey. • The model is estimated for partnered women with pre-school children—that is children age five and under who are not attending school. This homogeneous sample reduces model bias from unobserved factors. This reduction in bias comes at a cost, however, as the results may not be applicable to other groups (partnered women 1 In estimation of the model, we do not include fringe benefits tax which may be related to child care if it is received as part of a compensation package. We also do not include Child Care Rebate (CCR) which was introduced (as the then Child Care Tax Rebate) during our analysis period but which was initially paid to families with a long delay. We argue that the rebate, in its form at the time, would have had only a minor effect on families' decisions about child care; and in the prices we construct from the data provided by families it appears that they did not include the rebate in their calculations at that time. vii with school-aged children or single parents of pre-school children, for example). • We focus on the estimation of net price elasticities, which provide an estimate of how labour supply or child care demand changes for a change in the net price of child care. 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. Economic theory tells us that net, not gross, prices should determine behaviour. Government policy in Australia is targeted at changing the actual out-of-pocket 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. The gap between the net and gross price elasticities is not constant across the population because of the means testing of subsidies. Net price elasticities are thus more useful to study the distributional effects of policy. • We confirm the findings of Gong et al. (2010) that the labour supply behaviour of partnered women with young children responds (negatively) to child care price; – we find that a one per cent increase in the net price of child care for pre-school children leads to a decrease in hours worked by partnered women of 0.10 per cent. Such a price change leads to a decrease in the employment rate of 0.06 per cent. These estimates are statistically different from zero. – the analogous gross child care price elasticities are similar. A one per cent increase in the gross pre-school child care price viii causes mothers’ hours of work to decrease by 0.11 per cent and mothers’ employment rate to decrease by 0.07 per cent. – both labour supply and child care demand are more responsive in families with lower income, with less educated parents, and with lower female wages. Poorer families, for whom child care expenses may take up a larger fraction of the household budget, are thus more affected by child care price changes than wealthier families. – Gong et al. (2010) found a gross child care price elasticity of employment of -0.29. The gross child care price elasticity from the approach of Gong et al. (2010) for the sub-group of pre-school children as considered in this paper is -0.15, which is not statistically different than the corresponding point estimate of -0.07 presented in this paper. The differences in the two papers can be explained by five factors: : the two papers estimate different models; : the two papers use different methods to calculate elasticities; : the two papers use different samples; : the price variable which is being changed in the elasticity calculation is different in the two papers; and : we impose a quantity constraint, in this paper, that total child care hours (formal, informal and paternal) be at least as great as a mother’s working hours which allows hours of 5 2. MODEL AND ESTIMATION 2.1 The discrete choice model of labour supply and child care We estimate a discrete, structural model of the joint decision regarding hours of labour supplied by partnered women and household-level child care demand for families with pre-school children. The model assumes that households maximise their utility. Households get utility from consumption, leisure, and child development. Households choose hours of work by the mother, taking into account the trade-off between additional consumption which is made possible by working more hours but reduced leisure and time with children. Hours of formal child care are chosen to maximise child development and to free up the mother’s time for work, but must be paid for at the market rate. We first discuss two important innovations in our paper: restricting the set of possible hours of work and child care to more realistically reflect labour market and child care conditions; and the relationship between hours worked, hours of formal care, and hours of paternal and informal care. We then discuss the technical implementation of our model. 2.1.1 More realistic labour and child care markets The theoretical framework in this paper assumes that the decision about whether or not to work and how many hours to work for partnered women is made simultaneously with the decision of whether or not to use child care and how much child care to use. Blau and Robins (1988); Blau and Hagy (1998); and Connelly (1992) pioneered this approach, but these early papers assumed that hours worked and hours of child care demanded adjusted exactly to families’ desires. For example, a partnered woman could choose to work 36 hours and if a 6 small change in circumstances made it preferable for her to work 36.5 hours, she could adjust her labour supply exactly. Our model is based on the standard discrete neo-classic labour supply model first developed by Van Soest (1995), but extended to include maternal child care as an explicit argument of the household utility function and to define the budget constraint over a small, discrete set of possible working hours and formal child care hours rather than over working hours alone. For example, an individual may choose to work 35 or 40 hours, but not a value in between these two points. (In practice, as described below, we allow eight different possibilities for working hours and six different possibilities for formal child care hours.) Families pick the combination of mother’s working hours and formal child care that maximises their well-being from this set of 48 possible combinations of hours worked and hours of child care demanded. Kornstad and Thoresen (2007) estimate a similar model in that households are constrained in their choice of work and child care hours to a discrete set of points. However, our paper differs in the treatment of the relationship between formal child care and hours worked by the mother, as described below. 2.1.2 Formal child care, informal child care, paternal care and mother’s working hours In our model, we assume the following: (1) During waking hours, children are cared for in one of four possible ways: by the mother; by the father; in a paid, formal child care setting; or in an informal child care setting. This last category will include care by other relatives or friends and may be paid or unpaid. 7 (2) In our model, we combine the father’s time caring for children with informal care. This is partially driven by data restrictions. We do not observe hours or price of informal care. Nor do we observe hours of care by the father. In our model of the time allocation for mothers and children, therefore, these two types of care appear interchangeable. The model does allow for fathers to spend time taking care of children and allows the amount of time which fathers spend taking care of children to vary across households, but this care is not explicitly modelled. (3) We assume that fathers’ hours worked do not respond to changes in the price of formal child care or to mothers’ wages. This is assumed for tractability of the model but also corresponds to evidence that mothers still bear a disproportionate share of time in taking care of children (Sayer, 2005; Kalenkoski et al., 2005). Kalenkoski et al. (2005) also confirmed a common finding that while women’s market work responds to the presence of children, men’s market work does not. Kimmel and Connelly (2007) modelled women’s time spent in a variety of activities including home production and childcare and similarly treated fathers’ behaviour as fixed. (4) The household may choose to use formal child care regardless of whether the mother is at work or not. Formal care may exceed mother’s working hours and may be used for purposes such as child development or freeing up time for the mother for activities other than paid work. (5) We impose the restriction that total child care hours are at least as great as the hours of paid work by the mother and model informal and paternal child care as the difference between mother’s working hours and 8 formal child care hours. If formal child care hours equal or exceed mother’s working hours, we assume that informal and paternal child care are zero. Otherwise, we set combined paternal and informal child care equal to mother’s hours worked less hours in formal child care.3 Families will face different costs and benefits of informal care depending upon the proximity of grandparents or other relatives or the presence of other potential care-takers at home and we account for this in the model. Our approach is an improvement over Duncan et al. (2001) and Kornstad and Thoresen (2007) who assume, unrealistically, that formal child care hours must be greater than or equal to mother’s hours of work. In our data, see below, about one-third of households report formal child care exceeding mother’s working hours. Figure 1 presents the household’s decision over the allocation of the child’s time. Sleep (the darkest shaded area) is treated as fixed and the family decides over the allocation of the remaining parts--how to split the remaining time into care by the mother, formal child care and informal/paternal child care. Figure 2 presents the mother’s time allocation. After sleeping time, which is treated as fixed, mother’s remaining time (the three most lightly shaded sections of Figure 2) is allocated between working, taking care of children, and leisure. Two `adding-up’ constraints implied from (1) — (4) above must hold: 3 An alternative approach would be to use reported hours of informal care and to simultaneously model demand for formal and informal care alongside mother's labour supply. One immediate problem is that there is no information on price for informal care (in our data, only 10 per cent report paying for informal child care) even though families may incur non-pecuniary costs. 9 Mother’s time taking care of child = child’s time being taken care of by mother Child’s time in informal/paternal care = mother’s working hours — child’s time in formal care (or zero if this is negative) Figure 1: Child’s time Figure 2: Mother’s time 10 We further assume that, for mothers with both pre-school and school–aged children, the primary consideration of the mother when she makes her labour supply and child care usage decisions is the well-being of the pre-school child(ren). That is, we assume that when school-aged children are present together with pre-school children in the same household, child care of the school-aged children outside school hours is assumed to mirror that of the pre-school children. Again, this is for tractability. For example, if formal hours of child care for the pre-school child are 40 and the school-age child is in school 30 hours per week then we assume that the school-age child is in before- and/or after-school care for 10 (40 less 30) hours per week. We test this assumption in two ways. First, we replace this assumption with an assumption that formal child care of school-aged children is fixed and does not enter the utility function. Secondly, we estimate the model using households with pre-school children only. We present these results in the Appendix and discuss them in section 4.2.3. None of the conclusions of the paper are sensitive to this assumption. 2.1.3 Technical specification of the model The household is assumed to maximise a trans-log utility function by choosing consumption y mother’s working hours h and formal child care hours fi c of each of her K children (indexed by i) from a set of discrete options: 1 ,, , , ( ) ' ' , (log ,log ,log )' f fK mm yhc c MaxUvvAvbvv y l c=+≡  (1) 01 s.t. ( , ) ( , ). K i fi i y y wh X p c X τϕ = ≤+ − ∑ (2) y is general consumption net of child care costs which is determined through the budget constraint (2) by asset income and father’s income (both captured in 11 0 y ), the mother’s wage ( w ) and working hours, and the tax and transfer system which is captured by the function τ and which depends upon household characteristics, X .4 The function ϕ captures child care subsidies which depend upon child care costs (price, which may vary by the age of the child, i p multiplied by usage) and household characteristics. In addition to requiring that formal care of school-aged children be determined by the care needs of the pre-school children as described in 2.1.2 above, we also assume that all pre-school children use the same amount of formal care and pay the same price. This can be alternatively viewed as allowing differences in hours and price of care for pre-school children, but modelling the family’s average demand. m l is the leisure of the mother which is specified as the difference between her time endowment ( m T ) and time spent either working or caring for children as in Figure 2 above , mm m l T hc= −− (3) m c is the time spent on maternal care which is specified as min{ , }, m c cf c T hT c= −− (4) where c T is the time during which children need to be cared for either by the mother, by the father, through the formal market or informally. c T represents the three most lightly shaded sections of Figure 1. The parameters of the utility function are summarised in A , a symmetric 33× parameter matrix with entries ij A , ( , 1, 2, 3ij= ), and 123 ( , , )'b bbb= , a vector 4 In τ , we include Newstart Allowance (NSA), Parenting Payment Partnered (PPP), Family Tax Benefits A and B, together with personal income tax, Medicare levy, and Low Income Tax Offset (LITO). Tables 2 and 3 list the variables that are contained in X. 12 with three parameters. 1 b is a constant, but 2 b and 3 b are specified to allow both observed and unobserved individual and household characteristics to affect utility: , (k=2,3) (5) where are exogenous characteristics including the age of the mother and the children, number of children in each age group, and other characteristics that describe the family composition such as the presence of extra female adults. In the case of multiple children, maternal child care is measured as the average number of maternal care hours for all pre-school children in the household and the impact of the number of children on utility is through 3 b . That is, the number of children affects the marginal utility of maternal care by shifting 3 b . (This explains why 23 bb≠ in equation (5) above. The k subscript on S allows for different characteristics to enter the two equations.) Moreover, the potential impact of informal child care is also allowed for by the inclusion of a dummy in 3 b equal to one if f hc> . This dummy controls for which condition in equation (4) determines maternal child care hours and equals one if the family makes recourse to informal child care (as calculated by our residual measure of informal child care usage). The error terms k p ε may be interpreted as random preferences due to unobserved characteristics. Working hours and formal child care hours may take the following values: {0,8,16,24,32,40,48,56}h∈ , (6) and {0,10,20,30,40,50}, fi c∈ (7) 13 These can be chosen in any of the possible 48 combinations, allowing a wide range of part-time and half-day possibilities for both work and formal care. To estimate the model, we add random disturbances j µ (as in Van Soest, 1995) to each alternative in the choice set, as in the multinomial logit model (Maddala, 1983): ( , , ) ( 0,...,48) j j j mj mj j U Uyl c j µ = += (8) where j µ ‘s are independently and identically distributed with a type I extreme value distribution, and are independent of all observable and unoberservable terms in the model. The mother chooses alternative j if it is the alternative (out of m*g=48) from which she derives the most utility, i.e. if j U is the largest among all the alternatives. Conditional upon k p ε , X , and w , the probability that j is chosen is , , , 1 exp( ( , )) Pr[ for all ] . exp( ( , )) j mj mj ji mg i mi mi i Uyl c UU i Uyl c ∗ = ≥= ∑ (9) To predict the wage rates of non-workers and workers whose wages are missing in the data and to allow for correlation between wage rates and unobserved utility preferences ( k p ε ), a wage equation is simultaneously estimated with (1) and specified as a standard Mincer wage equation: log ' w wz πε = + (10) where z is a vector of individual characteristics of the mother. Her education level, current area of residence measured by capital city and state, and a variable equal to one if the mother lived with both of her parents when she was 14 (to 14 capture stability while growing up) are included in the wage equation but not in the utility function and serve the role of exclusion restrictions. π is a vector of parameters to be estimated. w ε is an unobserved term, assumed to be normally distributed with mean zero, independent of z , but is allowed to be correlated with k p ε . As in similar models (for example, Gong and Van Soest, 2002), unobserved fixed benefit of not working ( FB ) is added to the income at zero hours of work. Thus the utility of all alternatives at zero hours of work are replaced by 0 0, ( ,) mm U y FB l c+ . FB is specified as 'FB t δ = (11) where t is a vector of exogenous variables (which are listed in Table 2) and δ is a vector of parameters. Positive fixed benefits increase the probability of not working by increasing the utility of non-participation. They can be interpreted equally as fixed costs associated with working. 2.2 Estimation If all the wages were observed and there were no unobserved preferences, the model could be estimated by maximum likelihood with the likelihood contribution given by Equation (9). With unobserved wages, the wage Equation (10) also needs to be estimated. This is done simultaneously with the joint labour supply-child care model. With the presence of unobserved preferences in leisure and maternal child care, maximum likelihood estimation would require evaluation of the three-dimensional integral defined over the distribution of the error terms w ε , 2 p ε , and 3 p ε . Numerical integration in more than two dimensions can be difficult to solve. 21 defacto relationships, there are 12,109 observations on 4,754 women. Excluding those families with no pre-school children further reduces the sample to 2,601 observations on 1,198 women. Pre-school children are defined as children age five and under who are not attending school. We exclude a further 131 observations on 92 women who live in multiple-family households and 219 observations on 156 women who are studying full-time. This leaves us with an estimation sample of 2,251 observations on 1,069 women across the three waves. After discarding observations with missing values for any variables used in our model (excepting wage), the sample consists of 2,023 observations on 978 partnered mothers with at least one pre-school child. Note that households with school-aged children, but without pre-school children, are omitted from our analysis sample. Our rationale for this is that the labour supply and child care issues faced by those households may be quite different from those with pre-school children. Importantly, school-aged children attend school for around 30 hours per week, which makes their need for maternal or non-maternal child care much less than that of younger children. This sample of households with pre-school children, for these reasons, will be a more homogeneous sample which should reduce the influence of unobserved preferences on observed outcomes. This sample homogeneity allows for a simpler model and provides a reduction in bias. We present sample statistics in the second column of Table 1. In the third column of Table 1 we present the sample statistics for a sub-sample of 1,159 mothers of pre-school children in households in which there are no school-aged children present. This sub-sample is used for sensitivity analysis as described below. From the second column of Table 1, about 43 per cent of households with pre-school children use formal child care. Hours spent in child 22 care for the pre-school children are about 18 hours per week. About 56 per cent of the mothers were employed and the average working mother works 25 hours per week at an hourly wage of $25 (at the June 2005 price level). The characteristics of the mothers in the sub-sample are broadly similar to those of the whole sample except they are younger and slightly better educated. Many households use less formal child care than the mother’s hours of work. To see how mothers’ working hours and formal child care hours are related, Figure 3 presents the distribution of the difference between the two. Figure 3 shows that in about more than thirty per cent of households with pre-school children, the average reported hours of formal child care per pre-school child are less than the mothers’ reported hours of work. This indicates that the quantity constraint (that formal child care hours are greater than or equal to hours worked by the mother) imposed by Duncan et al. (2001) and Kornstad and Thoresen (2007) is probably too restrictive. Table 1 Sample statistics: mean values. Pooled data from 2005 — 2007 Variables Partnered mothers with at least one pre-school child Partnered mothers with pre-school children but with no school-aged children Hours worked per week (for those mothers who are working) 24.8 (13.7) 25.6 (13.5) Employment rate (mothers) 0.56 0.60 Average hours of formal child care (per child) for children using formal care 18.8 (12.9) 19.0 (13.2) Proportion of families using formal care 0.43 0.45 Hourly wage rate of the mother (at June 2005 price) 25.3 (22.5) 26.6 (22.1) Weekly household income from father’s earnings and unearned private income 1238 (1242) 1305 (1289) Median hourly child care price (at June 2005 price) 4.67 (0.92) 4.73 (0.98) Age of the mother 32.9 (5.9) 31.8 (5.8) Dummy variables for highest level of education received: Mother received higher education 0.34 0.41 Mother received vocational education 0.25 0.24 Mother finished Year 12 only 0.21 0.21 Mother did not finish Year 12 0.21 0.14 Father received higher education 0.27 0.30 23 Table 1 Sample statistics: mean values. Pooled data from 2005 — 2007 (continued) Variables Partnered mothers with at least one pre-school child Partnered mothers with pre-school children but with no school-aged children Father received vocational education 0.42 0.40 Father finished Year 12 only 0.14 0.16 Father did not finish Year 12 0.17 0.14 Dummy, mother did not live with both parents at the age of 14 0.22 0.22 Dummy, equals one if the mother was not born in Australia, but was educated in Australia 0.14 0.15 Dummy, equals one if the mother was educated and born outside of Australia 0.05 0.06 Dummy, the mother speaks a language other than English 0.12 0.11 Dummy, the mother is Aboriginal or and Torres Strait Islander 0.02 0.02 Dummy, equals one if mother and the father both educated in Australia and both born outside of Australia. 0.19 0.20 Dummy, equals one the mother and the father are both born and educated outside of Australia 0.10 0.08 Number of children aged 0 to 4 1.3 (0.6) 1.4 (0.6) Number of children aged 5 to 12 .60 (0.8) - Number of children aged 13 to 15 .09 (0.3) 0.05 (0.25) Age of the youngest child 1.5(1.5) 1.1 (1.2) Dummy, presence of female adult in the household other than the mother 0.03 0.03 Dummy, presence of children older than 12 in the household 0.87 0.78 Mean age of children 1.9 (1.4) 1.5 (1.2) Dummy variables equal to one if current state of residence is: NSW 0.28 0.27 VIC 0.25 0.26 SA 0.08 0.07 WA 0.10 0.11 TAS 0.03 0.02 NT 0.01 0.01 ACT 0.03 0.03 % of child care staff with teaching experience (state average) 15.7% (4.4%) 15.7% (4.4%) % of child care staff with teaching qualification (state average) 66.9% (5.0%) 66.9% (5.0%) Observations (number of partnered mothers) 2,023 1,159 Note: Standard deviations are in the parentheses. 24 Figure 3 Hours worked by mothers less average formal child care hours of pre-school children 0% 10% 20% 30% 40% 50% 60% 0% 10% 20% 30% 40% 50% 60% -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 Per cent Per cent Hours worked by mother less average hours of formal child care of preschool children 3.2 Child care price Gong et al. (2010) show that measurement error in the child care price can have large effects on results in labour supply and child care demand models. In this paper, we follow their method to construct the child care price. The model is designed to evaluate how families respond to changes in child care price in terms of their demand for child care and mothers’ labour supply. We thus need a price that reflects a `typical’ amount that a household will have to pay if they choose to increase hours of formal child care (or an amount they will save if they decrease formal hours of child care). There are two problems that arise. The first is that we need a child care price that applies to families who are not currently using any child care. As price changes, these families may begin to use child care and we need a price to evaluate this possibility. When families purchase child care they are purchasing a bundle of attributes. They are paying the cost of having their children cared for at some basic standard. But they are also paying, perhaps at additional cost, for other 25 attributes such as quality and location. This quality component which makes up part of the observed price that is being paid by families who already use child care creates a modelling problem. The family’s choice of how much quality to purchase (that is the choice of what child care price to pay) is likely to be correlated with unobservable components in the utility function and in the labour supply equation. This correlation between actual price paid and unobservable effects creates bias in estimated coefficients and elasticities. To solve both of these problems, we calculate a local average (median9) price for each Labour Force Survey Region (LFSR)10 in Australia. We apply this price to families that do not currently use child care and to families that currently use child care. In this way, the component that is specific to families’ current choice of child care is at least partly ‘averaged out’. The `in-confidence’ version of HILDA allows us to implement this solution as it contains information on the postcode in which respondents live. This version of HILDA also provides child care usage by age groupings of children, gross family income, child and family characteristics, and eligibility rules for Child Care Benefit. We construct separate prices for pre-school and school-aged children. In the HILDA survey, we have the number of hours kht h spent in child care for each child (k) in the household (h) for each of three types of child care (t)--long day care, family day care, and other formal paid care.11 Households in the data 9 We use the median since it is less vulnerable to outliers than the mean. 10 Labour Force Survey Regions are described in ABS, 2005. 11 This last category is mostly in-home care at the home of the carer or the home of the child. 26 report hours of child care used. We calculate hours paid by rounding up to multiples of five hours for not-yet-in-school-aged children and multiples of three hours for school-aged children to reflect typical lengths of paid sessions. Long day care centres and family day care centres typically operate 50 hours per week, and typical part-time arrangements are at least in units of half-days. For school-aged children, typical after-school care sessions are three hours. Net cost of child care sht c  is not provided for each child but is provided for each type of care and is split by school-aged (s=1) and not-yet-in-school (s=0) aged children. For families who have one child in the not-yet-in-school-aged category, we know the cost of child care for each type of care for that child. For families that have more than one child in the not-yet-in-school-aged category, we only know the total amount spent on that group of children for each type of care. Since we know the hours that each child is in care for each type of care, we split the cost in proportion to the hours spent in that type of care. We assume that families are spending the same amount per hour on each child within the same age range for each type of care. We calculate the net child care cost per child as 1 kht kht sht K kht k h cc h = = ∑  (16) We combine this with the hours of child care information to calculate a gross per-child price for each type of care. We take all of these individual child prices and calculate two median prices for each Labour Force Survey Region (LFSR): one for children who are not yet in school and one for school-aged children. We impute this median price to each household in the LFSR. For pre-school children, we have sixteen observations 27 per LFSR on average. There is substantial variation across LFSRs. Table 5 in Gong et al. 2010 shows that this method of constructing prices does well in matching state-level average prices from administrative data. By using local area averages, we are essentially using a quality-adjusted price. Our modelling assumption is that households react to the average price level irrespective of the quality they choose. This is akin to assuming that shifts in median prices affect all quality levels. We control for child care quality by adding variables from administrative data which capture the average number of qualified staff per child in formal day care centres. These variables are only available at the state level however. Finally, we note that the main variable of interest in this study is the price of child care for children who are not yet in school. We calculate the price for school-aged children and this price enters into the family budget constraint (and thus it affects the decision to work), but we do not analyse how changes in this price affect behaviour. We focus on how mothers’ behaviour changes as the price for pre-school children changes. 4. RESULTS 4.1 Estimation results The Simulated Maximum Likelihood results are based upon 30 draws per household. We present the parameter estimates of the utility function in Table 2. The parameters ij A and i b determine the shape of the utility function but their interpretation is not straightforward. The signs of the parameters in b determine the direction in which characteristics affect preferences. A positive 2k β implies a 28 positive effect of k x on the marginal utility of leisure. However, unlike in a standard discrete labour supply model where leisure is specified as the residual of labour supply from the mother’s total endowment, it cannot be interpreted readily as a negative effect on labour supply in this model. In this model, leisure is the residual of labour supply and maternal care so that a positive effect on leisure can be a negative effect on either labour supply or maternal care, or both. Similarly, a positive 3k β implies a positive effect of k x on maternal care but may represent either a negative effect on labour supply or a negative effect on formal child care, or both. Table 2. Simulated maximum likelihood estimates — parameters of the utility function Partnered mothers with at least one pre-school child, pooled estimates (2005-2007) Variables 211 ()yA -0.158[-1.34] 222 ()lA -1.472**[-4.53] 2 m 33 c ( )A 0.273**[2.96] 12 ()yl A -0.016[-0.16] 13 () m yc A -0.005[-0.06] 23 () m lc A -0.542**[-5.28] 1 b 5.079**[6.31] 'bs 2 b 3 b Constant -0.854[-0.66] 2.952[1.55] Age of the mother 0.333**[2.20] 0.397**[2.90] The mother speaks a language other than English -0.925**[-2.67] 0.004[0.02] The mother is Aboriginal or Torres Strait Islander -1.365[-1.33] 1.372[1.29] The mother was educated in Australia but was not born in Australia 0.025[0.08] The mother was educated and born outside of Australia -0.012[-0.03] Age of the youngest child 0.406**[5.62] 0.048[0.25] No. of children aged 0 to 4 0.857**[5.08] 0.331[1.44] No. of children aged 5 to 12 -0.184*[-1.76] 0.078[0.91] No. of children aged 13 to 15 0.248[1.17] -0.646**[-2.80] Presence of female adult (besides mother) in household 0.135[0.31] 0.468[1.05 ] Dummy variables for highest level of education received: Father received higher education -0.219[-0.78] -0.154[-0.68] Father received vocational education -0.038[-0.15] 0.027[0.13 ] Father did not finish Year 12 -0.176[-0.60] -0.126[-0.51] 29 Table 2. Simulated maximum likelihood estimates — parameters of the utility function Partnered mothers with at least one pre-school child, pooled estimates (2005-2007) (continued) Variables Father has Year 12 education The mother and the father were both educated in Australia but neither was born in Australia -0.006[-0.04] Mother and father were both born and educated outside of Australia -0.458**[-2.00] Presence of children older than 12 in household 0.172[1.45 ] Mean age of pre-school children -0.180[-0.92] % of child care staff with teaching experience (state average) -0.039**[-1.96] % of child care staff with teaching qualification (state average) -0.009[-0.39] Variance of the unobserved preference for leisure ( 2 p σ ) 0.014[0.05] 0.160**[3.62] Covariance of unobserved preference for leisure and unobserved heterogeneity in wage ( wp σ ) 0.038 [0.93] 0.149**[6.05] Fixed benefit equation Constant 1.168**[7.25] Age of the mother -0.207**[-5.17] The mother speaks a language other than English 0.230**[2.95] The mother is Aboriginal or Torres Strait Islander -0.075[-0.44] The mother was educated in Australia but was not born in Australia 0.051[0.84] The mother was educated and born outside of Australia 0.148*[1.79] Age of the youngest child -0.081**[-4.79] No. of children aged 0 to 4 0.017[0.46] No. of children aged 5 to 12 0.101**[3.48] No. of children aged 13 to 15 0.280**[3.72] Presence of female adult (besides mother) in household 0.003[0.03 ] Dummy variables for highest level of education received: Father received higher education -0.010[-0.16] Father received vocational education -0.043[-0.73] Father did not finish year 12 0.076[1.09 ] Father has Year 12 education Dummy, wave 6 (2006) 0.026[0.72 ] Dummy, wave 7 (2007) 0.058[1.56 ] Likelihood -3347.96 Observations 2,023 t-values are in the brackets. * Significant at 10 per cent level. ** Significant at 5 per cent level. From the estimates, we see that family structure and the mother’s characteristics all play important roles in determining preferences. The number of children, age of the mother, and the mother’s immigration background (as indicated by speaking a language other than English) all have significant effects on preferences. However, the direction and magnitude of the impacts of the variables on labour supply or maternal care can not be ascertained directly from the parameter values, but rather need to be calculated through simulation. 30 The parameters in the fixed benefit equation can be linked more directly to the labour force participation of the mother—a positive parameter indicates that the corresponding variable increases the benefits of not working and thus a negative impact on participation. For example, the older the youngest child is, the lower the fixed benefit of not working. Mothers with older children are therefore more likely to participate in the labour force than those with younger children. The number of school-aged children also plays a significant role in this fixed benefit --more young children (including school-aged) leads to a higher fixed benefit of staying at home and a lower participation rate. It is worth noting that unobserved preferences for maternal care play a significant role and they are positively correlated with the unobserved heterogeneity in the wage equation. The variance of the unobserved preference for leisure, however, is imprecisely estimated. Table 3. Simulated maximum likelihood estimates –wage equation Partnered mothers with at least one pre-school child, pooled estimates (2005-2007) Variables Constant 1.994**[7.53 ] Age of the mother 0.476**[3.02 ] Age-squared of the mother -0.049**[-2.07] Dummy variables for highest level of education received: Mother received higher education 0.445**[14.91] Mother received vocational education 0.118**[3.82 ] Mother did not finish year 12 -0.091**[-2.57] Mother has Year 12 education The mother speaks a language other than English -0.097**[-2.46] The mother is Aboriginal or Torres Strait Islander -0.016[-0.11] The mother did not live with both parents at the age of 14 -0.026[-0.97] Sydney Balance of NSW -0.136**[-3.65] Melbourne -0.137**[-4.29] Balance of VIC -0.113**[-2.65] Brisbane -0.123**[-3.29] Balance of QLD -0.122**[-3.21] Adelaide -0.048[-0.89] 37 wage, and household income are all strongly correlated. Lower responsiveness from women with higher wages and income may be partly because child care costs are a smaller part of the household budget for these women. Similar to the results for labour supply elasticities, child care demand elasticities are also slightly smaller for women with higher wage/education or with a more educated partner (or higher income from household sources other than the mother’s earnings) than those with lower wage/education or with lower educated partners (other household income). Child care price elasticities also differ by family type. In households with multiple children, labour supply elasticities of child care price are larger than those in single child households. In multiple children households, child care costs form a larger part of the budget and the household response to a change in child care price is thus larger. 38 5. CONCLUSIONS In this paper, we construct and estimate a model of labour supply and child care demand for partnered women with pre-school children. The model extends the standard discrete structural labour supply model by explicitly including child care as a separate argument of the utility function. This model enables us to analyse labour supply and child care demand simultaneously. We expect this approach to correspond more closely to how households actually make decisions about work and child care. We introduce an important methodological innovation in this paper in that we impose a quantity constraint that the number of total child care hours (formal, informal and paternal) is required to be at least as large as the number of hours worked by the mother. However, unlike previous papers, we allow formal child care to exceed mother’s work hours to account for other possible uses of child care such as child development. Unobserved heterogeneity in time allocation preferences is included and is allowed to be correlated with unobservable factors which influence wages. The model is estimated using Simulated Maximum Likelihood with data drawn from the fifth to seventh waves (covering the period 2005 — 2007) of the ‘in-confidence’ version of the Household, Income, and Labour Dynamics in Australia (HILDA) Survey. Utility function, child care demand, and wage equation estimates are used to simulate estimates of the gross and net child care price elasticities for partnered women with children. This framework can also be used to estimate the effects on 39 labour supply, child care demand, income distributions, and public expenditure of possible future policy changes. We find statistically significant gross and net child care price elasticities of labour supply for partnered women with young children. In particular the net child care price elasticities of hours of work and employment are about -0.10 and -0.06, respectively. These estimates are not statistically significantly different than those in Gong et al. (2010) and they re-confirm that the labour supply behaviour of partnered women with young children does respond to the price of child care. We explore how different demographic groups may respond differently to child care price changes. Labour supply and child care demand responses to child care price changes are highest amongst women with lower wages, lower household income, and lower education. Here we focus only on partnered mothers with pre-school children and we treat fathers’ work decisions as fixed. This provides two future extensions which could be considered: the analysis could be extended to households with only school-aged children (and without pre-school children) and to single-parent households; and the behaviour of fathers in couple-headed households could be included in the model. Both extensions involve additional model complexity but could potentially enrich the results of this paper. 40 REFERENCES Australian Bureau of Statistics (2005) ‘Australian Standard Geographical Classification (ASGC)’, catalogue number 1216.0, Technical Report, ABS, Canberra. Available at http://www.abs.gov.au/ausstats/[email protected]/mf/1216.0. Last viewed 21 July 2011. Australian Bureau of Statistics (2010) ‘Consumer Price Index, Australia, Sep 2010’, catalogue number 6401.0, ABS, Canberra. Available at http://www.abs. gov.au/AUSSTATS/a[email protected]/DetailsPage/6401.0Sep%202010?OpenDocument. Last viewed 21 July 2011. Bhat, C. 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Mimeo, (revised version of IZA Discussion Paper No. 2053), DIW, 43 Germany. 44 APPENDIX A.1 ESTIMATES OF AN ALTERNATIVE SPECIFICATION The following tables present the results of an alternative model specification where child care of the school-aged children is assumed to be fixed and does not enter the utility function explicitly. Table A.1.1 Simulated maximum likelihood estimates--parameters of the utility function Alternative specification: child care for school-aged children is fixed and does not enter the household utility function Variables 211 ()yA -0.165[-1.41] 222 ()lA -1.460**[-4.52] 2 m 33 c ( )A 0.278**[3.01] 12 ()yl A -0.027[-0.26] 13 () m yc A -0.009[-0.10] 23 () m lc A -0.514**[-5.03] 1 b 5.074**[6.22] 'bs 2 b 3 b Constant -0.895[-0.69] 2.910[1.53] Age of the mother 0.346**[2.29] 0.398**[2.90] The mother speaks a language other than English -0.938**[-2.72] -0.001[0.00] The mother is Aboriginal or Torres Strait Islander -1.371**[-1.34] 1.355[1.25] The mother was educated in Australia but was not born in Australia 0.039[0.13] The mother was educated and born outside of Australia 0.001[0.00] Age of the youngest child 0.399**[5.53] 0.047[0.25] No. of children aged 0 to 4 0.867**[5.16] 0.346[1.50] No. of children aged 5 to 12 -0.212**[-2.01] 0.110[1.28] No. of children aged 13 to 15 0.285[1.34] -0.650**[-2.83] Presence of female adult (besides mother) in household 0.140[0.31] 0.456[1.02] Dummy variables for highest level of education received: Father received higher education -0.220[-0.79] -0.150[-0.66] Father received vocational education -0.034[-0.13] 0.028[0.14] Father did not finish year 12 -0.191[-0.65] -0.132[-0.53] Father has Year 12 education The mother and the father were both educated in Australia but neither was born in Australia -0.020[-0.14] The mother and the father were both born and educated outside of Australia -0.459**[-2.01] Presence of children older than 12 in household 0.163[1.38] Mean age of pre-school children -0.176[-0.90] % of child care staff with teaching experience (state average) -0.038*[-1.95] % of child care staff with teaching qualification (state average) -0.009[-0.37] Variance of the unobserved preference for leisure ( 2 2 p σ ) 0.013[0.05] 0.159**[3.11] Covariance of unobserved preference for leisure and unobserved heterogeneity in wage ( wp σ ) 0.037[0.91] 0.147**[5.98] 45 Table A.1.1 Simulated maximum likelihood estimates--parameters of the utility function Alternative specification: child care for school-aged children is fixed and does not enter the household utility function (continued) Fixed benefit equation Constant 1.222**[7.26] Age of the mother -0.218**[-5.22] The mother speaks a language other than English 0.239**[2.96] The mother is Aboriginal or Torres Strait Islander -0.067[-0.38] The mother was educated in Australia but was not born in Australia 0.053[0.84] The mother was educated and born outside of Australia 0.154*[1.80] Age of the youngest child -0.083**[-4.75] No. of children aged 0 to 4 0.014[0.35] No. of children aged 5 to 12 0.108**[3.56] No. of children aged 13 to 15 0.288**[3.67] Presence of female adult (besides mother) in household 0.004[0.04] Dummy variables for highest level of education received: Father received higher education -0.009[-0.13] Father received vocational education -0.045[-0.74] Father did not finish year 12 0.079[1.10] Father has Year 12 education Dummy, wave 6 (2006) 0.027[0.72] Dummy, wave 7 (2007) 0.059[1.54] Likelihood -3350.86 Observations 2,023 t-values are in the brackets. * Significant at 10 per cent level. ** Significant at 5 per cent level. 46 Table A.1.2 Simulated maximum likelihood estimates– wage equation Alternative specification: child care for school-aged children is fixed and does not enter the household utility function Variables Mothers of the pre-school children Constan 1.992**[7.52] Age of the mother 0.477**[3.02] Age-squared of the mother -0.049**[-2.08] Dummy variables for highest level of education received: Mother received higher education 0.449**[15.01] Mother received vocational education 0.121**[3.92] Mother did not finish year 12 -0.089**[-2.51] Mother has Year 12 education The mother speaks a language other than English -0.097**[-2.46] The mother is Aboriginal or Torres Strait Islander -0.014[-0.10] The mother was not with both parents at the age of 14 -0.027[-1.00] Sydney Balance of NSW -0.138**[-3.69] Melbourne -0.139**[-4.34] Balance of VIC -0.114**[-2.67] Brisbane -0.125**[-3.34] Balance of QLD -0.123**[-3.21] Adelaide -0.049[-0.91] Balance of SA -0.256**[-2.91] Perth -0.172**[-3.50] Balance of WA -0.207**[-3.45] Tasmania -0.223**[-2.31] Northern Territory -0.094[-0.50] ACT -0.068[-1.30] The mother was educated in Australia but was not born in Australia -0.039[-1.28] The mother was educated and born outside of Australia -0.147**[-3.04] Variance of the unobservables in the wage equation ( 2 w σ ) 0.151**[63.66] t-values are in the brackets. * Significant at 10 per cent level. ** Significant at 5 per cent level.