Child disability, welfare payments, marital status and mothers’ labor supply: Evidence from Australia

Figures & data

Table 1. Sample information with standard deviation in parenthesis for mothers, including those having an own disability

Variable	Definition	Sample proportion/mean
		weighted	unweighted
Employment	1 if in labor force, 0 otherwise	0.663	0.671
Hourswk	Hours worked per week	25.562 (14.201)	25.453 (14.148)
Welfare	1 if the mother receives a welfare payment, 0 otherwise	0.323	0.334
ChildDisis1	1 if the child disability is profoundly limited in core activities, 0 otherwise	0.033	0.034
ChildDisis2	1 if the child disability is severely limited in core activities, 0 otherwise	0.037	0.036
ChildDisis3	1 if the child disability is moderately/mildly limited in core activities, 0 otherwise	0.022	0.021
ChildDisis4	1 if the child disability is not limited in core activities, 0 otherwise	0.038	0.040
Age	Age of the observation minus 45	$-7.770$ (6.567)	$-7.513$ (6.476)
Degree	1 if the highest education is degree or above, 0 otherwise	0.221	0.219
Diploma	1 if the highest education is certificate, diploma or advanced diploma, 0 otherwise	0.289	0.280
Year12	1 if the highest education is year 12, 0 otherwise	0.164	0.164
IncomeMis	1 if income gap (unit income minus personal income) is not available, 0 otherwise	0.196	0.188
LnIncome	Natural log of income that is unit income minus	4.534	4.558
	Personal income and is set as 0 if it is missing	2.878	2.856
Ykidage	Age of the youngest dependent child	6.100 (4.268)	6.238 (4.268)
NoChildren	Number of children under 15 in the family	1.869 (0.857)	1.866 (0.859)
OwnDis1	1 if own disability is severely limited in core activities, 0 otherwise	0.022	0.025
OwnDis2	1 if own disability is moderately/mildly limited in core activities, 0 otherwise	0.049	0.053
OwnDis3	1 if own disability is not limited in core activities, 0 otherwise	0.046	0.047
NoPersonWel	Number of persons in the household other than mother and partner receiving welfare payments	0.112 (0.421)	0.112 (0.426)

Table 2. Sample information with standard deviation in parenthesis for mothers, excluding those having an own disability

Variable	Definition	Sample proportion/mean
		weighted	unweighted
Employment	1 if in labor force, 0 otherwise	0.679	0.688
Hourswk	Hours worked per week	25.658 (14.069)	25.544 (14.015)
Welfare	1 if the observation receives any government welfare benefit payment, 0 otherwise	0.303	0.313
ChildDisis1	1 if the child disability is profoundly limited in core activities, 0 otherwise	0.028	0.029
ChildDisis2	1 if the child disability is severely limited in core activities, 0 otherwise	0.029	0.029
ChildDisis3	1 if the child disability is moderately/mildly limited in core activities, 0 otherwise	0.020	0.019
ChildDisis4	1 if the child disability is not limited in core activities, 0 otherwise	0.033	0.034
Age	Age of the observation minus 45	$-7.903$ (6.516)	$-7.629$ (6.430)
Degree	1 if the highest education is degree or above, 0 otherwise	0.226	0.226
Diploma	1 if the highest education is certificate, diploma or advanced diploma, 0 otherwise	0.285	0.276
Year12	1 if the highest education is year 12, 0 otherwise	0.170	0.170
IncomeMis	1 if income gap (unit income minus personal income) is not available, 0 otherwise	0.197	0.191
LnIncome	Natural log of income that is unit income minus personal income and is set as 0 if it is missing	4.590 (2.878)	4.608 (2.863)
Ykidage	Age of the youngest dependent child	5.959	6.109
		$-4.250$	$-4.256$
NoChildren	Number of children under 15 in the family	1.878 (0.854)	1.875 (0.852)
NoPersonWel	Number of persons in the household other than mother and partner receiving welfare payments	0.101 (0.409)	0.101 (0.413)

Table 3. Employment for mothers including and excluding those having an own disability

	ChildDis1	ChildDis2	ChildDis3	ChildDis4	able children
Mothers including those having an own disability
Mothers with a partner receiving welfare
In labor force	31	17	9	17	243
Not in labor force	39	23	12	10	265
Participation rate	44	43	42	62	48
Mothers with a partner not receiving welfare
In labor force	10	32	21	51	1488
Not in labor force	8	14	9	15	487
Participation rate	57	70	71	77	75
Single mothers receiving welfare
In labor force	8	12	13	15	248
Not in labor force	23	28	11	20	230
Participation rate	27	30	54	43	52
Single mothers not receiving welfare
In labor force	5	9	6	11	266
Not in labor force	6	6	4	4	82
Participation rate	44	59	62	72	76
Mothers excluding those having an own disability
Mothers with a partner receiving welfare
In labor force	23	12	6	16	216
Not in labor force	29	17	10	6	232
Participation rate	44	41	39	72	48
Mothers with a partner not receiving welfare
In labor force	9	22	19	46	1376
Not in labor force	4	13	7	8	441
Participation rate	66	63	74	85	76
Single mothers receiving welfare
In labor force	5	10	9	12	207
Not in labor force	19	15	8	13	182
Participation rate	20	41	55	46	53
Single mothers not receiving welfare
In labor force	4	8	5	9	242
Not in labor force	3	3	3	2	65
Participation rate	52	73	63	81	79

Table 4. Estimates of the RF of BiProbit models for mothers, including those having an own disability

	Mothers with a partner				Single mothers
	Work decision		Welfare		Work decision		Welfare
	Coeff.	Std. err	Coeff.	Std. err	Coeff.	Std. err	Coeff.	Std. err
Constant	$-0.01$	0.21	$-0.14$	0.21	$-0.50$	0.24	1.29	0.25
ChildDis1	$-0.46$	0.15	1.52	0.17	$-0.63$	0.25	0.32	0.25
ChildDis2	$-0.22$	0.18	0.65	0.16	$-0.43$	0.23	0.02	0.22
ChildDis34	$-0.07$	0.12	0.34	0.13	$-0.13$	0.18	0.20	0.18
Age	$-0.04$	0.01	0.00	0.01	$-0.02$	0.02	$-0.02$	0.02
Age-square	$-3\times {10}^{-3}$	$1\times {10}^{-3}$	$2\times {10}^{-4}$	$5\times {10}^{-4}$	$-5\times {10}^{-4}$	$9\times {10}^{-4}$	$-2\times {10}^{-3}$	$9\times {10}^{-4}$
Degree	0.58	0.09	$-0.57$	0.09	1.06	0.16	$-0.74$	0.15
Diploma	0.41	0.07	$-0.09$	0.08	0.46	0.11	$-0.13$	0.11
Year12	0.26	0.08	$-0.11$	0.09	0.29	0.14	$-0.29$	0.14
IncomeMis	$-0.40$	0.19	$-0.63$	0.17	$-0.18$	0.16	$-1.40$	0.17
LnIncome	0.02	0.03	$-0.09$	0.02	0.04	0.02	$-0.23$	0.03
YChildAge	0.11	0.01	$-0.05$	0.01	0.10	0.02	$-0.03$	0.01
No.Children	$-0.18$	0.03	0.13	0.04	$-0.13$	0.06	0.13	0.06
No.PersonWel	$-0.41$	0.07	0.24	0.08	$-0.31$	0.11	0.08	0.10
OwnDis1	$-0.72$	0.22	0.59	0.18	$-1.17$	0.43	$-0.01$	0.29
OwnDis2	$-0.64$	0.16	0.20	0.16	$-0.64$	0.19	0.56	0.19
OwnDis3	0.23	0.15	0.15	0.15	$-0.14$	0.19	0.04	0.20
$\mathit{\tau }$	$-0.32$	0.04			$-0.34$	0.06
Log-likelihood	$-2781.139$				$-1112.869$

Table 5. Estimates of the RF of BiProbit models for mothers, excluding those having an own disability

	Mothers with a partner				Single mothers
	Work decision		Welfare		Work decision		Welfare
	Coeff.	Std. err.	Coeff.	Std. err.	Coeff.	Std. err.	Coeff.	Std. err.
Constant	$-0.02$	0.05	$-0.17$	0.04	$-0.67$	0.07	1.03	0.08
ChildDisis1	$-0.53$	0.03	1.64	0.05	$-0.92$	0.09	0.58	0.07
ChildDisis2	$-0.40$	0.03	0.66	0.03	$-0.23$	0.08	$-0.07$	0.08
ChildDisis34	0.05	0.02	0.37	0.02	$-0.17$	0.04	0.26	0.05
Age	$-0.05$	$1\times {10}^{-4}$	$3\times {10}^{-3}$	$1\times {10}^{-4}$	$-0.03$	$4\times {10}^{-4}$	$-0.04$	$3\times {10}^{-4}$
Age-square	0.00	0.00	0.00	0.00	0.00	0.00	1$\times {10}^{-4}$	1$\times {10}^{-6}$
Degree	0.54	0.01	$-0.54$	0.01	1.14	0.03	$-0.76$	0.02
Diploma	0.38	0.01	$-0.08$	0.01	0.49	0.02	$-0.18$	0.02
Year12	0.24	0.01	$-0.07$	0.01	0.21	0.02	$-0.37$	0.03
IncomeMis	$-0.41$	0.03	$-0.55$	0.03	$-0.09$	0.03	$-1.60$	0.04
LnIncome	0.02	0.00	$-0.09$	0.00	0.06	0.00	$-0.24$	0.00
YChildAge	0.12	0.00	$-0.05$	0.00	0.12	0.00	$-0.03$	0.00
No.Children	$-0.19$	0.00	0.13	0.00	$-0.18$	0.00	0.20	0.00
No.PersonWel	$-0.41$	0.01	0.22	0.01	$-0.27$	0.01	0.29	0.01
tau	$-0.33$	0.00			$-0.37$	0.00
Log-likelihood	$-2470.694$				$-891.759$

Table 6. Estimated marginal effects of child disability on the probability to work with the variance and covariance in parenthesis

	ChildDis1	ChildDis2	ChildDis34	2*$\left(\begin{array}{cc}{\mathrm{\Sigma }}_{12}\hfill & {\mathrm{\Sigma }}_{13}\hfill \\ \hfill & {\mathrm{\Sigma }}_{23}\hfill \end{array}\right)$
	(${\mathrm{\Sigma }}_{11}$)	(${\mathrm{\Sigma }}_{22}$)	(${\mathrm{\Sigma }}_{33}$)
Mothers including those having an own disability
Mothers with a partner
Conditional on receiving welfare	$-0.0521$ (0.0028)	$-0.0254$ (0.0030)	0.0024 (0.0018)	$\left(\begin{array}{cc}0.0002\hfill & 0.0002\hfill \\ \hfill & 0.0001\hfill \end{array}\right)$
Conditional on not receiving welfare	$-0.0454$ (0.0024)	$-0.0317$ (0.0024)	$-0.0049$ (0.0013)	$\left(\begin{array}{cc}0.0002\hfill & 0.0001\hfill \\ \hfill & 0.0001\hfill \end{array}\right)$
Single mothers
Conditional on receiving welfare	$-0.1859$ (0.0051)	$-0.1386$ (0.0043)	$-0.0288$ (0.0028)	$\left(\begin{array}{cc}0.0002\hfill & 0.0003\hfill \\ \hfill & 0.0004\hfill \end{array}\right)$
Conditional on not receiving welfare	$-0.1737$ (0.0064)	$-0.1298$ (0.0045)	$-0.0219$ (0.0021)	$\left(\begin{array}{cc}0.0003\hfill & 0.0003\hfill \\ \hfill & 0.0004\hfill \end{array}\right)$
Mothers excluding those having an own disability
Mothers with a partner
Conditional on receiving welfare	$-0.0749$ (0.0036)	$-0.0859$ (0.0036)	0.0540 (0.0022)	$\left(\begin{array}{cc}0.0003\hfill & 0.0003\hfill \\ \hfill & 0.0001\hfill \end{array}\right)$
Conditional on not receiving welfare	$-0.0615$ (0.0033)	$-0.0866$ (0.0033)	0.0352 (0.0014)	$\left(\begin{array}{cc}0.0002\hfill & 0.0002\hfill \\ \hfill & 0.0001\hfill \end{array}\right)$
Single mothers
Conditional on receiving welfare	$-0.2627$ (0.0059)	$-0.0764$ (0.0071)	$-0.0394$ (0.0034)	$\left(\begin{array}{cc}0.0002\hfill & 0.0003\hfill \\ \hfill & 0.0004\hfill \end{array}\right)$
Conditional on not receiving welfare	$-0.2444$ (0.0089)	$-0.0664$ (0.0057)	$-0.0282$ (0.0025)	$\left(\begin{array}{cc}0.0002\hfill & 0.0003\hfill \\ \hfill & 0.0003\hfill \end{array}\right)$

Table 7. p-values of testing hypotheses (2.9) and (2.10) for mothers including those having an own disability

Testing $H_q:h_q=0$ or $H_{\mathbf{Q}}:{\cap }_{\forall q}{H}_q$
EMaxT				MaxT			LR	D-$W_{\infty }$	Wald
$H_e$	$H_1$	$H_2$	$H_3$	$H_1$	$H_2$	$H_3$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$
Proposition: More severe child disability has higher negative impacts on mothers’ employment
Mothers with a partner conditional on receiving welfare
0.508	0.856	0.834	0.980	0.849	0.824	0.980	0.277	0.180	0.767
Mothers with a partner conditional on not receiving welfare
0.471	0.917	0.814	0.938	0.915	0.802	0.938	0.274	0.168	0.756
Single mothers conditional on receiving welfare
0.004	0.787	0.277	0.760	0.772	0.238	0.742	0.002	0.001	0.013
Single mothers conditional on not receiving welfare
0.016	0.812	0.269	0.791	0.804	0.234	0.780	0.008	0.004	0.045
Proposition: Child disability has higher negative impacts on single mothers than mothers with a partner
Conditional on receiving welfare
0.435	0.192	0.257	0.669	0.182	0.247	0.667	0.115	0.068	0.278
Conditional on not receiving welfare
0.187	0.242	0.319	0.748	0.231	0.310	0.748	0.167	0.100	0.380
Proposition: Child disability has higher negative impacts on mothers receiving welfare than mothers not receiving welfare
Mothers with a partner
0.974	0.454	0.994	0.994	0.449	0.994	0.994	0.461	0.682	0.403
Single mothers
0.123	0.438	0.229	0.459	0.431	0.218	0.452	0.151	0.077	0.353

Table 8. p-values of testing hypotheses (2.12) and (2.13) for mothers including those having an own disability

Testing $H_q^I:h_q<0$ or $H_{\mathbf{Q}}^I:h\le 0$
$Q^{\ast }=2$					$Q^{\ast }=1$	$Q^{\ast }=3$	$Q^{\ast }=2$	$Q^{\ast }=1$
EMaxT			MaxT		t	LR	LR	LR
$H_e$	$H_1^{\ast }$	$H_2^{\ast }$	$H_1^{\ast }$	$H_2^{\ast }$	$H_1^{\ast }$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$
Proposition: More severe child disability has higher negative impacts on mothers’ employment
Mothers with a partner conditional on receiving welfare
0.432	0.681	0.657	0.668	0.641		0.547	0.339
Mothers with a partner conditional on not receiving welfare
						0.532
Single mothers conditional on receiving welfare
						0.006
Single mothers conditional on not receiving welfare
						0.021
Proposition: Child disability has higher negative impacts on single mothers than mothers with a partner
Conditional on receiving welfare
						0.102
Conditional on not receiving welfare
						0.149
Proposition: Child disability has higher negative impacts on mothers receiving welfare than mothers not receiving welfare
Mothers with a partner
0.778	0.974	0.347	0.974	0.336	0.188	0.477	0.350	0.217
Single mothers
						0.137

Table 9. p-values of testing hypotheses (2.9) and (2.9) for mothers excluding those having an own disability

Testing $H_q:h_q=0$ or $H_{\mathbf{Q}}:{\cap }_{\forall q}{H}_q$
EMaxT				MaxT			LR	D-$W_{\infty }$	Wald
$H_e$	$H_1$	$H_2$	$H_3$	$H_1$	$H_2$	$H_3$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$
Proposition: More severe child disability has higher negative impacts on mothers’ employment
Mothers with a partner conditional on receiving welfare
0.358	0.989	0.116	1.000	0.989	0.094	1.000	0.060	0.071	0.151
Mothers with a partner conditional on not receiving welfare
0.431	0.997	0.139	1.000	0.997	0.114	1.000	0.078	0.094	0.216
Single mothers conditional on receiving welfare
0.001	0.149	0.852	0.686	0.122	0.843	0.656	0.000	0.000	0.004
Single mothers conditional on not receiving welfare
0.013	0.202	0.806	0.742	0.172	0.797	0.726	0.009	0.005	0.047
Proposition: Child disability has higher negative impacts on single mothers than mothers with a partner
Conditional on receiving welfare
0.130	0.075	0.887	0.282	0.068	0.887	0.272	0.061	0.053	0.162
Conditional on not receiving welfare
0.239	0.133	0.917	0.396	0.123	0.917	0.388	0.122	0.102	0.290
Proposition: Child disability has higher negative impacts on mothers receiving welfare than mothers not receiving welfare
Mothers with a partner
0.937	0.239	0.888	1.000	0.229	0.888	1.000	0.228	0.432	0.101
Single mothers
0.182	0.529	0.482	0.341	0.524	0.475	0.330	0.220	0.111	0.485

Table 10. p-values of testing hypotheses (2.12) and (2.13) for mothers excluding those having an own disability

Testing $H_q^I:h_q<0$ or $H_{\mathbf{Q}}^I:h\le 0$
$Q^{\ast }=2$					$Q^{\ast }=1$	$Q^{\ast }=3$	$Q^{\ast }=2$	$Q^{\ast }=1$
EMaxT			MaxT		t	LR	LR	LR
$H_e$	$H_1^{\ast }$	$H_2^{\ast }$	$H_1^{\ast }$	$H_2^{\ast }$	$H_1^{\ast }$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$	$H_{\mathbf{Q}}$
Proposition: More severe child disability has higher negative impacts on mothers’ employment
Mothers with a partner conditional on receiving welfare
0.070	0.899	0.085	0.899	0.064	0.032	0.082	0.036	0.000
Mothers with a partner conditional on not receiving welfare
0.115	0.949	0.102	0.949	0.077	0.039	0.119	0.056	0.000
Single mothers conditional on receiving welfare
						0.002
Single mothers conditional on not receiving welfare
						0.022
Proposition: Child disability has higher negative impacts on single mothers than mothers with a partner
Conditional on receiving welfare
0.033	0.204	0.053	0.191	0.046		0.056	0.030
Conditional on not receiving welfare
0.073	0.291	0.094	0.280	0.084		0.113	0.066
Proposition: Child disability has higher negative impacts on mothers receiving welfare than mothers not receiving welfare
Mothers with a partner
0.371	0.784	0.174	0.784	0.162	0.087	0.267	0.178	0.032
Single mothers
						0.210