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

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    
y2(A11) -0.165[-1.41]  
l2(A22) -1.460**[-4.52]  
cm2(A33) 0.278**[3.01]  
yl(A12) -0.027[-0.26]  
ycm(A13) -0.009[-0.10]  
lcm(A23) -0.514**[-5.03]  
b1 5.074**[6.22]  
b's
  b2 b3
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 (σp22) 0.013[0.05] 0.159**[3.11]
Covariance of unobserved preference for leisure and unobserved heterogeneity in wage (σwp) 0.037[0.91] 0.147**[5.98]
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.

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
Constant 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 (σw2) 0.151**[63.66]

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

Table A.1.3 Elasticities: partnered mothers with at least one pre-school child Alternative specification: child care for school-aged children is fixed and does not enter the household utility function
With respect to Labour supply elasticity Child care demand elasticity
  Hours employment Hours of formal care Use of formal care
Gross child care price -0.105** (0.03) -0.069** (0.02) -0.282** (0.05) -0.160** (0.03)
Net child care price -0.079** (0.02) -0.052** (0.01) -0.221** (0.04) -0.126** (0.02)
Wage 0.417** (0.09) 0.268** (0.05) 0.275** (0.06) 0.172** (0.04)
Household Income (other than mother's earnings) -0.087 (0.05) -0.045 (0.04) -0.038 (0.04) -0.032 (0.02)

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

Table A.1.4. Elasticities for selected sub-samples
Alternative specification: child care for school-aged children is fixed and does not enter the household utility function
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 -0.092** (0.03) -0.060** (0.01) -0.272** (0.04) -0.155** (0.03)
Without tertiary education -0.123**(0.04) -0.081**(0.02) -0.297**(0.05) -0.167**(0.03)
By father's education        
With tertiary education -0.092** (0.03) -0.060** (0.01) -0.272**(0.04) -0.155**(0.03)
Without tertiary education -0.130** (0.04) -0.088** (0.02) -0.315**(0.05) -0.178**(0.03)
By number of children        
One pre-school child -0.079** (0.02) -0.051** (0.01) -0.216** (0.03) -0.125** (0.02)
Multiple pre-school children -0.155**(0.05) -0.102** (0.03) -0.409** (0.07) -0.228** (0.04)
By mother's wage        
Above median -0.081**(0.02) -0.052**(0.01) -0.259**(0.04) -0.146**(0.03)
Below median -0.128**(0.04) -0.085**(0.02) -0.305**(0.05) -0.174**(0.03)
By household income (other than mother's earnings)    
Above median -0.076**(0.02) -0.049**(0.01) -0.225**(0.04) -0.133**(0.02)
Below median -0.134**(0.04) -0.089**(0.02) -0.339**(0.05) -0.187**(0.03)
Net child care price
By mother's education        
With tertiary education -0.079** (0.02) -0.048** (0.01) -0.213** (0.03) -0.115** (0.02)
Without tertiary education -0.091**(0.03) -0.056**(0.01) -0.210**(0.04) -0.111**(0.02)
By father's education        
With tertiary education -0.078**(0.02) -0.047** (0.01) -0.206**(0.34) -0.111**(0.02)
Without tertiary education -0.097** (0.03) -0.061** (0.02) -0.223**(0.04) -0.119**(0.02)
By number of children        
One pre-school child -0.064** (0.02) -0.039** (0.01) -0.168** (0.03) -0.092** (0.02)
Multiple pre-school children -0.121** (0.04) -0.075** (0.02) -0.294** (0.05) -0.154** (0.03)
By mother's wage        
Above median -0.067**(0.02) -0.043**(0.01) -0.218**(0.04) -0.124**(0.02)
Below median -0.092**(0.03) -0.061**(0.01) -0.223**(0.04) -0.128**(0.02)
By household income (other than mother's earnings)    
Above median -0.069**(0.02) -0.044**(0.01) -0.205**(0.04) -0.121**(0.02)
Below median -0.090**(0.02) -0.060**(0.01) -0.236**(0.04) -0.131**(0.02)
Wage
By mother's education        
With tertiary education 0.439** (0.09) 0.280** (0.05) 0.303** (0.07) 0.191** (0.04)
Without tertiary education 0.387**(0.08) 0.250**(0.05) 0.235**(0.06) 0.146**(0.03)
By father's education        
With tertiary education 0.400**(0.08) 0.252**(0.05) 0.268** (0.06) 0.168** (0.03)
Without tertiary education 0.458** (0.10) 0.303** (0.06) 0.291**(0.07) 0.183**(0.04)
By number of children        
One pre-school child 0.417** (0.08) 0.265** (0.05) 0.300** (0.07) 0.193** (0.04)
Multiple pre-school children 0.418** (0.09) 0.274** (0.06) 0.228**(0.05) 0.134**(0.03)
By mother's wage        
Above median 0.415**(0.08) 0.259**(0.05) 0.286**(0.06) 0.177**(0.03)
Below median 0.420**(0.09) 0.277**(0.05) 0.265**(0.07) 0.168**(0.04)
By household income (other than mother's earnings)    
Above median 0.356**(0.07) 0.227**(0.04) 0.240**(0.05) 0.150**(0.03)
Below median 0.479**(0.10) 0.308**(0.06) 0.310**(0.07) 0.195**(0.04)
Income
By mother's education        
With tertiary education -0.113** (0.06) -0.063** (0.04) -0.052 (0.04) -0.041 (0.03)
Without tertiary education -0.051 (0.04) -0.019(0.03) -0.019 (0.03) -0.019(0.02)
By father's education        
With tertiary education -0.107*(0.06) -0.060(0.04) -0.049(0.04) -0.041(0.03)
Without tertiary education -0.042(0.04) -0.009(0.03) -0.014(0.03) -0.013(0.02)
By number of children        
One pre-school child -0.089* (0.05) -0.042 (0.04) -0.043 (0.04) -0.033 (0.02)
Multiple pre-school children -0.084* (0.05) -0.050 (0.04) -0.028 (0.04) -0.032 (0.02)
By mother's wage        
Above median -0.125**(0.06) -0.071*(0.04) -0.055(0.04) -0.044(0.03)
Below median -0.050(0.04) -0.018(0.03) -0.021(0.03) -0.020(0.02)
By household income (other than mother's earnings)    
Above median -0.159**(0.08) -0.104**(0.06) -0.069(0.05) -0.057(0.04)
Below median -0.015(0.02) 0.014(0.02) -0.007(0.02) -0.007(0.01)

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

A.2 Estimates using the sub-sample of mothers with pre-school children only

The following tables present the results using the sub-sample of mothers who only have pre-school children and no school-aged children.

Table A.2.1 Simulated maximum likelihood estimates--parameters of the utility function
Alternative sample: Partnered mothers with at least one pre-school child and no school-aged children, pooled estimates (2005-2007)
Variables    
y2(A11) -0.278**[-2.40]  
l2(A22) -1.714**[-3.91]  
cm2(A33) 0.069[0.54]  
yl(A12) -0.066[-0.45]  
ycm(A13) -0.120[-1.09]  
lcm(A23) -0.525**[-3.81]  
b1 6.186**[8.38]  
  b's b2 b3
Constant -0.761[-0.41] 4.995**[2.02]
Age of the mother 0.412**[2.03] 0.283*[1.70]
The mother speaks a language other than English -0.814*[-1.75] -0.064[-0.20]
The mother is Aboriginal or Torres Strait Islander -0.895[-0.87] 2.854**[2.43]
The mother was educated in Australia but was not born in Australia 0.113[0.29]  
The mother was educated and born outside of Australia 0.055[0.10]  
Age of the youngest child 0.451**[4.07] 0.068[0.29]
No. of children aged 0 to 4 0.837**[3.67] 0.399[1.47]
No. of children aged 5 to 12    
No. of children aged 13 to 15 -0.213[-0.57] -0.314[-0.86]
Presence of female adult (besides mother) in household 0.830[1.16] 0.724[1.25]
Dummy variables for highest level of education received:    
Father received higher education -0.306[-0.77] -0.132[-0.53]
Father received vocational education -0.090[-0.26] -0.128[-0.45]
Father did not finish year 12 -0.011[-0.03] -0.128[-0.48]
Father has Year 12 education    
The mother and the father were both educated in Australia but neither was born in Australia   0.061[0.32]
The mother and the father were both born and educated outside of Australia   -0.686**[-2.42]
Presence of children older than 12 in household   0.015[0.10]
Mean age of pre-school children   -0.279[-1.15]
% of child care staff with teaching experience (state average)   -0.042*[-1.64]
% of child care staff with teaching qualification (state average)   -0.007[-0.25]
Variance of the unobserved preference for leisure (σp22) 0.012[0.06] 0.118**[2.03]
Covariance of unobserved preference for leisure and unobserved heterogeneity in wage (σwp) 0.041[0.63] 0.132**[4.05]
Fixed benefit equation
Constant 1.424**[5.55]  
Age of the mother -0.266**[-4.10]  
The mother speaks a language other than English 0.193[1.46]  
The mother is Aboriginal or Torres Strait Islander -0.477**[-2.20]  
The mother was educated in Australia but was not born in Australia 0.104[1.08]  
The mother was educated and born outside of Australia 0.279**[2.17]  
Age of the youngest child -0.084**[-3.06]  
No. of children aged 0 to 4 0.021[0.37]  
No. of children aged 5 to 12
No. of children aged 13 to 15 0.404**[2.63]  
Presence of female adult (besides mother) in household -0.242[1.53]  
Dummy variables for highest level of education received:    
Father received higher education 0.025[-0.25]  
Father received vocational education -0.058[-0.65]  
Father did not finish year 12 0.157[1.42]  
Dummy, wave 6 (2006) 0.030[0.51]  
Dummy, wave 7 (2007) 0.051[0.86]  
Likelihood -1,979.49  
Observations 1,159  

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

Table A.2.2 Simulated maximum likelihood estimates– wage equation
Alternative sample: Partnered mothers with at least one pre-school child and no school-aged children, pooled estimates (2005-2007)
Variables Mothers of the pre-school children
Constant 2.405**[6.19]
Age of the mother 0.186[0.79]
Age-squared of the mother 0.002[0.06]
Dummy variables for highest level of education received:  
Mother received higher education 0.429**[10.67]
Mother received vocational education 0.155**[3.68]
Mother did not finish year 12 -0.088[-1.58]
Mother has Year 12 education  
The mother speaks a language other than English -0.093[-1.61]
The mother is Aboriginal or Torres Strait Islander -0.084[-0.46]
The mother was not with both parents at the age of 14 -0.103**[-2.38]
Sydney  
Balance of NSW -0.052[-0.98]
Melbourne -0.123**[-2.66]
Balance of VIC -0.059[-0.98]
Brisbane -0.093*[-1.79]
Balance of QLD -0.147**[-2.53]
Adelaide -0.142**[-2.06]
Balance of SA -0.144[-1.21]
Perth -0.198**[-2.58]
Balance of WA -0.361**[-2.88]
Tasmania -0.162[-0.88]
Northern Territory -0.167[-0.76]
ACT -0.151**[-2.11]
The mother was educated in Australia but was not born in Australia 0.023[0.54]
The mother was educated and born outside of Australia -0.009[-0.15]
Variance of the unobservables in the wage equation (σw2) 0.150**[45.85]

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

Table A.2.3 Elasticities Alternative sample: Partnered mothers with at least one pre-school child and no school-aged children, pooled estimates (2005-2007)
With respect to Labour supply elasticity Child care demand elasticity
  Hours employment Hours of formal care Use of formal care
Gross child care price -0.107** (0.03) -0.072** (0.02) -0.284** (0.07) -0.159** (0.03)
Net child care price -0.081** (0.03) -0.054** (0.02) -0.223** (0.03) -0.126** (0.02)
Wage 0.432** (0.11) 0.278** (0.07) 0.304** (0.06) 0.189** (0.04)
Household Income (other than mother's earnings) -0.029 (0.05) 0.002 (0.03) -0.012 (0.04) 0.001 (0.03)

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

Table A.2.4 Elasticities for selected sub-samples
Alternative sample: Partnered mothers with at least one pre-school child and no school-aged children, pooled estimates (2005-2007)
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) -0.063** (0.02) -0.271** (0.06) -0.152** (0.03)
Without tertiary education -0.131**(0.04) -0.088**(0.03) -0.310**(0.08) -0.171**(0.04)
By father's education        
With tertiary education -0.095**(0.03) -0.062** (0.02) -0.271** (0.06) -0.151** (0.03)
Without tertiary education -0.135** (0.05) -0.093** (0.03) -0.314** (0.07) -0.177** (0.04)
By number of children        
One pre-school child -0.077** (0.02) -0.052** (0.01) -0.211**(0.05) -0.122**(0.02)
Multiple pre-school children -0.147** (0.05) -0.097** (0.03) -0.382**(0.10) -0.208**(0.04)
By mother's wage        
Above median -0.081**(0.03) -0.053**(0.02) -0.255**(0.06) -0.142**(0.03)
Below median -0.133**(0.04) -0.090**(0.03) -0.314**(0.07) -0.175**(0.04)
By household income (other than mother's earnings)        
Above median -0.079**(0.03) -0.051**(0.02) -0.223**(0.06) -0.129**(0.03)
Below median -0.135**(0.04) -0.092**(0.03) -0.345**(0.08) -0.188**(0.04)
Net child care price
By mother's education        
With tertiary education -0.076** (0.02) -0.051** (0.01) -0.223** (0.06) -0.126** (0.03)
Without tertiary education -0.091**(0.03) -0.061**(0.02) -0.224**(0.06) -0.124**(0.03)
By father's education        
With tertiary education -0.075** (0.02) -0.049** (0.01) -0.221** (0.06) -0.124** (0.03)
Without tertiary education -0.095** (0.03) -0.066** (0.02) -0.228** (0.06) -0.130** (0.03)
By number of children        
One pre-school child -0.060** (0.02) -0.040** (0.01) -0.167**(0.02) -0.097**(0.01)
Multiple pre-school children -0.110**(0.04) -0.073** (0.02) -0.299**(0.09) -0.164**(0.04)
By mother's wage        
Above median -0.068**(0.02) -0.045**(0.01) -0.216**(0.06) -0.121**(0.03)
Below median -0.095**(0.03) -0.064**(0.02) -0.231**(0.06) -0.130**(0.03)
By household income (other than mother's earnings)        
Above median -0.071**(0.02) -0.046**(0.01) -0.203**(0.06) -0.117**(0.03)
Below median -0.092**(0.03) -0.063**(0.02) -0.244**(0.06) -0.134**(0.03)
Wage
By mother's education        
With tertiary education 0.437** (0.11) 0.281** (0.07) 0.322** (0.07) 0.207** (0.04)
Without tertiary education 0.421**(0.11) 0.274**(0.07) 0.270**(0.06) 0.167**(0.03)
By father's education        
With tertiary education 0.401** (0.09) 0.253** (0.06) 0.293**(0.06) 0.128**(0.04)
Without tertiary education 0.502** (0.13) 0.336** (0.09) 0.330** (0.07) 0.207** (0.04)
By number of children        
One pre-school child 0.440** (0.10) 0.285** (0.07) 0.342**(0.07) 0.223**(0.04)
Multiple pre-school children 0.420**(0.11) 0.269**(0.08) 0.253** (0.05) 0.144** (0.03)
Above median 0.412**(0.10) 0.258**(0.07) 0.308**(0.06) 0.189**(0.04)
Below median 0.451**(0.11) 0.298**(0.08) 0.300**(0.07) 0.189**(0.04)
By household income (other than mother's earnings)        
Above median 0.352**(0.09) 0.221**(0.06) 0.255**(0.05) 0.158**(0.03)
Below median 0.511**(0.13) 0.336**(0.09) 0.353**(0.08) 0.221**(0.04)
Income
By mother's education        
With tertiary education -0.051 (0.05) -0.014 (0.04) 0.002 (0.04) -0.005 (0.03)
Without tertiary education 0.013 (0.04) 0.034(0.03) 0.031 (0.04) 0.012(0.03)
By father's education        
With tertiary education -0.055 (0.06) -0.021 (0.04) -0.003 (0.04) -0.011 (0.03)
Without tertiary education 0.032(0.03) 0.055 (0.03) 0.045 (0.03) -0.028 (0.02)
By number of children        
One pre-school child -0.043(0.05) -0.003(0.04) 0.000(0.04) -0.003(0.03)
Multiple pre-school children -0.010(0.04) 0.010(0.03) 0.028(0.04) 0.006(0.02)
By mother's wage        
Above median -0.075(0.06) -0.036(0.04) -0.013(0.04) -0.017(0.03)
Below median 0.017(0.04) 0.040(0.03) 0.037(0.036) 0.018(0.03)
By household income (other than mother's earnings)        
Above median -0.069(0.07) -0.040(0.05) 0.003(0.05) -0.010(0.04)
Below median 0.012(0.03) 0.045**(0.02) 0.021(0.03) 0.012(0.02)

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

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