Optimising balance using covariate balancing propensity score: The case of South African child support grant

Figures & data

Table 1. Summary statistics.

Variable	Mean	SD	Mean	SD	Mean	SD
	All (3451)		Treated(2415)		Control(1036)
w1_zhfa	−0.98	1.49	−0.96	1.51	−1.02	1.44
Delay(yrs)	5.08	4.6	3.46	3.34	8.84	4.92
motivation	0.03	1.01	0.44	0.88	−0.92	0.57
employed	0.25	0.44	0.25	0.43	0.26	0.44
married	0.37	0.48	0.35	0.48	0.42	0.49
PC edu	6.57	4.59	6.97	4.5	5.64	4.67
PC age	41.53	15.59	39.62	14.33	45.97	17.41
Hh head gen	0.36	0.48	0.37	0.48	0.35	0.48
Child gender	0.5	0.5	0.5	0.5	0.51	0.5
electricity	0.63	0.48	0.62	0.49	0.64	0.48
water	0.17	0.37	0.16	0.36	0.19	0.4
telephone	0.03	0.17	0.03	0.17	0.03	0.18
toilet	0.2	0.4	0.19	0.39	0.23	0.42
Ae food expenditure	187.92	125.64	184.33	115.03	196.29	147.15
Informal dwelling	0.07	0.25	0.07	0.26	0.06	0.24
Child age	7.89	4.27	7.4	3.87	9.04	4.88
rural	0.75	0.43	0.76	0.43	0.72	0.45
PC relationship	0.64	0.48	0.71	0.45	0.47	0.5
low birthweight	0.03	0.16	0.03	0.18	0.01	0.12

*PC edu Primary Caregiver education (years); PC Age Primary Caregiver’s age (yrs); HH head gen Gender of head of household; Ae food expenditure Adult equivalent food expenditure; PC relationship Child’s relationship with primary caregiver

Table 2. Censored regression to predict caregiver motivation.

Variables	(1)
	Delay in years
Child age	0.877***
	(0.019)
rural	−0.820***
	(0.164)
Caregiver relationship	−1.662***
	(0.170)
Constant	0.740***
	(0.242)
Observations	3,451

Standard errors in parentheses ***p < 0.01.

Figure 1. Standardised difference in means before and after weighing under CBPS.

Figure 2. Standardised difference in means before and after weighing under conventional propensity score.

Table 3. Treatment effect estimate with matching and balancing weights.

	WLS with balancing weights		WLS with Matching weights
	CBPS	PS	CBPS	PS
treatment	0.397	0.186	0.444	0.295
standard error	(0.049)***	(0.057)***	(0.083)***	(0.089)***
robust standard error	(0.165)**	(0.1472)	(0.2050)***	(0.1663)*
other covariates	yes	yes	yes	yes

Standard errors in parentheses ***p < 0.01, **p < 0.05, *p < 0.1.

Table 4. CBPS model and conventional logit model.

	CBPS		PS
	Estimate	Std. Error	Estimate	Std. Error
(Intercept)	4.88	0.478***	3.913	0.287***
motivation	2.02	0.134***	3.254	0.125***
employed	0.586	0.147***	−0.025	0.129
married	−0.234	0.126*	−0.025	0.135
pc_edu	−0.0148	0.12	−0.007	0.016
pc_age	−0.0657	0.112	−0.037	0.004***
hh_head_gen	0.0592	0.107	0.248	0.133*
child_gender	−0.602	0.122***	−0.118	0.11
electricity	−0.567	0.153***	−0.166	0.122
water	−0.229	0.131*	−0.171	0.174
telephone	1.34	0.0941***	−0.054	0.319
toilet	−0.667	0.0978***	−0.554	0.166***
ae_food_expenditure	0.000527	0.132	−0.0004	0.0004
informal_dwelling	1.07	0.138***	0.324	0.214
low_bw	1.01	0.142***	0.044	0.355

***p < 0.01, *p < 0.1.

Table 5. Covariate influence under CBPS and logit model.

	CBPS	PS
(Intercept)	0.365674	0.437676
motivation	0.151365	0.363966
employed	0.043911	0.002796
married	0.017534	0.002796
pc_edu	0.001109	0.000783
pc_age	0.004923	0.004139
hh_head_gen	0.004436	0.027739
child_gender	0.04511	0.013199
electricity	0.042487	0.018567
water	0.01716	0.019127
telephone	0.10041	0.00604
toilet	0.04998	0.061966
ae_food_expenditure	3.95E−05	4.47E−05
informal_dwelling	0.080178	0.03624
low_bw	0.075682	0.004921

Figure 3. Propensity score density before and after CBPS matching.

Figure 4. Propensity score density before and after conventional propensity score matching.

Figure A1. Standardised difference in means before and after matching under CBPS weighting.

Figure A2. Standardised difference in means before and after matching under conventional