# 4. Results

Date

## 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 parametersAij and bi 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 ß2k implies a positive effect of xk 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 ß3kimplies a positive effect of xk 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
y2 (A11) -0.158[-1.34]
l2(A22) -1.472**[-4.53]
cm2(A33) 0.273**[2.96]
yl(A12) -0.016[-0.16]
ycm(A13) -0.005[-0.06]
lcm(A23) -0.542**[-5.28]
b1 5.079**[6.31]
b'c b2 b3
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]
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 (σp2) 0.014[0.05] 0.160**[3.62]
Covariance of unobserved preference for leisure and unobserved heterogeneity in wage (σwp) 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:
ional 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.

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 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]
Balance of SA -0.254**[-2.87]
Perth -0.171**[-3.49]
Balance of WA -0.203**[-3.38]
Tasmania -0.224**[-2.33]
Northern Territory -0.095[-0.50]
ACT -0.068[-1.30]
The mother was educated in Australia but was not born in Australia -0.040[-1.34]
The mother was educated and born outside of Australia -0.147**[-3.04]
Variance of the unobservables in the wage equation (σw2) 0.151**[63.62]

t-values are in the brackets. * Significant at 10 per cent level. ** Significant at 5 per cent level.

The parameter estimates for the wage equation are presented in Table 3. The parameter estimates are in line with a standard Mincer equation for Australia (see Breusch and Gray, 2004; Leigh, 2008; and Breunig et al., 2008 for a few examples). For example, higher education brings a wage premium of about 45 per cent for mothers of pre-school children, relative to their counterparts who only finished Year 12, and women who speak a language other than English earn less than those who do not.

## 4.2 Simulation results

Table 4 presents average elasticities of labour supply and child care demand with respect to mother's wage, other combined family income (partner's labour income and household non-labour income), gross child care price and net child care price for the full sample.

Labour supply and child care both have two components: the decision to participate and the decision of how much to participate. For the labour supply elasticities we report an employment (or participation) elasticity that addresses the question of whether or not people choose to work. The hours elasticity captures both changing hours for those who are already working and changing hours for those who decide to commence or cease working.

Similarly with child care, we provide an elasticity (use of formal care) which captures the decision to use child care or not. The hours elasticity captures both changing hours for those who are already using child care and changing hours for those who decide to commence or cease using child care.

Table 4. Elasticities: All partnered mothers with at least one pre-school child
With respect to Labour supply elasticity Child care demand elasticity
Hours Employment Hours of formal care Use of formal care
Gross child care price -0.106** (0.03) -0.070** (0.02) -0.294** (0.05) -0.166** (0.03)
Net child care price -0.096** (0.03) -0.059** (0.01) -0.246** (0.04) -0.132** (0.02)
Wage 0.427** (0.08) 0.274** (0.05) 0.281** (0.06) 0.176** (0.03)
Household Income (other than mother's earnings) -0.092* (0.05) -0.048 (0.04) -0.036 (0.04) -0.036* (0.02)

Standard errors are in the parentheses. ** Significant at 5 per cent level. * Significant at 10 per cent level.

### 4.2.1 Labour supply elasticities

First of all, it is worth noting that the estimates of wage and income elasticities of labour supply in Table 4 are in line with the literature (see for example, Breunig, et al., 2008 or Gong et al., 2010 which surveyed the estimates). For mothers with pre-school children, the average wage elasticities of hours worked and employment are 0.427 and 0.274 (significant at the 5 per cent level) and the income elasticities of hours worked and employment are -0.092 (significant at the 10 per cent level) and -0.048.

Secondly, the average labour supply elasticities of both gross and net child care price are statistically significant and negative. The average gross child care price elasticities of hours of work and employment for the mothers are -0.106 and -0.070, respectively, which means that for a one per cent increase in the gross child care price, on average, mothers' hours of work would decrease by about 0.11 per cent and their employment rate would decrease by 0.07 per cent.

The net price elasticities of hours of work and employment of the mothers with pre-school children are -0.096 and -0.059, respectively. As expected, they are slightly smaller than the gross price elasticities due to the means-testing of CCB.

### 4.2.2 Relationship to previous results

These findings confirm those of Gong et al. (2010) that there is a negative and statistically significant labour supply response of partnered women to child care price. The estimates reported in Table 4 and those reported by Gong et al. (2010) are not statistically different from one another. However, Gong et al. (2010) report a higher point estimate of the gross price elasticity of employment of -0.29.

There are five reasons why the point estimates between the two studies might differ. Firstly, the two papers use a different estimation approach. In this paper, we directly specify the utility function and the household budget constraint. In Gong, et al. (2010), a linear approximation of the labour supply function that is consistent with the utility maximisation process is estimated.12 Secondly, the two papers use different samples. This paper uses a sample of households which have at least one pre-school child whereas Gong, et al. (2010) use all households with children under the age of 13. Thirdly, the estimates reported in this paper are the 'average elasticity', which is the average of the elasticity across all observations. In Gong et al., the 'elasticity of the average' is reported, which is the elasticity calculated at the sample average. While it is clear that these three differences should result in different elasticity estimates, we have no a priori beliefs about whether this should make elasticity estimates larger or smaller.

Fourthly, and the biggest difference between the two papers, is the way that child care prices are treated in the estimation of elasticities. One reason why one might expect smaller elasticities in this paper is that they are calculated with respect to a change in the child care price for pre-school children. In Gong et al. (2010), elasticities are reported with respect to a change in average child care price which means that all child care prices are changing, not just those for pre-school children. This difference is expected to lead to smaller estimates in this paper than in Gong et al. (2010). To confirm this point, we calculated gross child care price elasticities specific to pre-school children using the results from Gong et al. (2010). The employment elasticity of the child care price of pre-school children is estimated to be about -0.15. Indeed, this is smaller than the estimate of -0.29 for the elasticity with respect to average (all) prices.

A fifth important difference between the two papers is that the model in this paper incorporates the quantity constraint on total child care hours equaling or exceeding mothers' work hours while allowing formal child care hours to be less than the mothers' work hours.

### 4.2.3 Child care demand elasticities

As expected, child care demand is negatively impacted by its own price. From Table 4, the average net child care price elasticity of formal child care hours is -0.246; for a one per cent increase in the net child care price, child care hours decrease, on average, by about 0.25 per cent. The net elasticity of formal child care use with respect to its own price is -0.132, which means that a one per cent increase in the net child care price would lead to 0.132 per cent decrease in child care use.

The results in Table 4 show that both child care demand and labour supply elasticities with respect to wage are positive and they are both negative with respect to child care price. The two cross-price elasticities have the same sign as the own price elasticities (wage elasticity of labour supply and child care price elasticity of child care) which implies that labour supply and child care are complements.

As mentioned above, the assumption that child care of school-aged children mirrors that of pre-school children is quite strong. Estimation results and elasticities for an alternative specification, in which child care for school-aged children is assumed to be fixed and does not enter the utility function, are presented in Tables A.1.1 through A.1.4 of the Appendix. The simulated elasticities are quite similar to the original specification. We conclude that this restriction does not matter for the substantive results.

### 4.2.4 Elasticities of subsamples

The response of both labour supply and child care demanded might differ for households with different characteristics. For families where mothers' participation in the labour market is more valuable (where the mother has higher wages) or for families which are more able to afford child care, we might see smaller responses to price changes. To better understand these effects, we split the samples in numerous ways related to mother's wage (by education and directly by mother's wage), household income (father's education and household income other than the mother's earnings) and number of children. We present elasticities for these various sample partitions in Table 5.

Table 5. Elasticities for selected sub-samples
With respect to Labour supply elasticity Child care demand elasticity
Hours Employment Hours of formal care Use of formal care
Gross child care price of pre-school children
By mother's education
With tertiary education -0.094**(0.03) -0.061**(0.01) -0.283**(0.04) -0.161**(0.03)
Without tertiary education -0.125**(0.04) -0.083**(0.02) -0.310**(0.05) -0.174**(0.03)
By father's education
With tertiary education -0.095** (0.03) -0.062** (0.01) -0.279** (0.04) -0.158** (0.03)
Without tertiary education -0.132** (0.04) -0.089** (0.02) -0.328** (0.05) -0.185** (0.03)
By number of children
One pre-school child -0.079** (0.02) -0.052** (0.01) -0.225** (0.03) -0.130** (0.02)
Multiple pre-school children -0.158** (0.05) -0.105** (0.03) -0.427** (0.07) -0.236** (0.04)
By mother's wage
Above median -0.083**(0.02) -0.053**(0.01) -0.270**(0.04) -0.152**(0.03)
Below median -0.130**(0.04) -0.087**(0.02) -0.318**(0.05) -0.180**(0.03)
By household income (other than mother's earnings)
Above median -0.077**(0.02) -0.050**(0.01) -0.236**(0.04) -0.138**(0.02)
Below median -0.136**(0.04) -0.090**(0.02) -0.353**(0.05) -0.194**(0.03)
Net child care price
By mother's education
With tertiary education -0.088** (0.02) -0.054** (0.01) -0.243** (0.04) -0.130** (0.02)
Without tertiary education -0.106** (0.03) -0.066** (0.02) -0.250** (0.04) -0.133** (0.02)
By father's education
With tertiary education -0.089** (0.02) -0.054** (0.01) -0.240** (0.04) -0.128** (0.02)
Without tertiary education -0.110** (0.03) -0.071** (0.02) -0.260** (0.04) -0.139** (0.02)
By number of children
One pre-school child -0.077** (0.02) -0.047** (0.01) -0.206** (0.03) -0.112** (0.02)
Multiple pre-school children -0.131** (0.04) -0.082** (0.02) -0.332** (0.05) -0.169** (0.03)
By mother's wage
Above median -0.080**(0.02) -0.051**(0.01) -0.258**(0.05) -0.127**(0.02)
Below median -0.109**(0.03) -0.069**(0.02) -0.252**(0.05) -0.145**(0.03)
By household income (other than mother's earnings)
Above median -0.080**(0.02) -0.051**(0.01) -0.242**(0.05) -0.143**(0.03)
Below median -0.109**(0.03) -0.073**(0.02) -0.353**(0.05) -0.194**(0.03)

Standard errors are in the parentheses. ** Significant at 5 per cent level. * Significant at 10 per cent level.

The first conclusion from Table 5 is that labour supply response clearly differs by demographic group. The labour supply of women with higher wages or in households with higher income levels is slightly less responsive to child care price than those with lower wages or from households with lower income. For example, the average employment elasticity of the net child care price for women with wages above the median is -0.05, while for those whose wages are below the median, it is -0.07.13 Comparing women above and below median non-labour income, with high and low education, or with partners with high and low education produces similar results. This is not surprising, as education, 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.

12 Gong et al. (2010) contains a lengthy discussion of the contrast between the `direct' approach of this paper and the `indirect' approach of that paper.

13 We can reject that these differences are zero at the 5 per cent level using the bootstrapped confidence intervals.