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

ABSTRACT

In this paper, we explore the use of covariate balancing propensity scores (CBPS) in estimating the impact of the South African child support grant (CSG) on the height-for-age score of benefiting children. CBPS is a different approach to estimating propensity score, under CBPS the scores are estimated such that the estimation incorporates covariate balancing condition. This approach is therefore relatively robust to misspecification of the propensity score model which makes it ideal for this case study. We show that utilising the CBPS leads to treatment effect estimate that is larger and more precisely estimated than estimates that have been reported in the literature because the method exploits the dual function of propensity score. The effect of CSG under CBPS is as large as 44% of standard deviation on average. This implies that the effect of the grant cannot be regarded as small as previously reported in the literature.

KEYWORDS:

• Covariate balancing propensity score
• stunting
• height-for-age score
• malnutrition

JEL:

• I38
• H53
• D13

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See http://www.statssa.gov.za/?p=2564.

2 Coetzee (2011) reports an insignificant effect of 7% of a standard deviation. Footnote 15 in Aguero et al. (2006) reported that no significant effect was found in the binary treatment case.

3 Note that Aguero et al. (2006) use the KwaZulu-Natal Income Dynamics Study while Coetzee (2011, 2013) use the National Income Dynamic Study.

4 Namely children’s height-for-age, progress through the school system and expenditure on food, negative effect was found for probability of repeating a school year.

5 This variable influences the treatment effect because more motivated caregiver apply earlier than other caregivers. This increased dosage for children with motivated caregivers will have effect on the inference even in the binary treatment case. Details on the construction of this variable is provided latter.

6 Popularly known as DW algorithm

7 Means test is such that the primary caregiver must have a monthly income below R800 in urban areas or R1,100 in rural areas.

8 Besides the fact that blacks are most affected by poverty and inequality (in percentage terms), children from other race groups are relatively small and this may create balancing problem for the CBPS algorithm.

9 See Appendix B section 3.1 in Coetzee (2011)

10 Weight equals 1 for treatment group members and $p/1-p$ for control units where $p$ is the propensity score.

11 Perhaps the large difference between our PSM result and the one reported in Coetzee (2011) is due to the changes we made. For example our sample did not drop children below 2 years old and our motivation equation includes the caregiver relationship.

12 Also note that the highest point of the control density is 6 under CBPS while it is 8 under the conventional propensity scores.

13 See https://www.who.int/nutgrowthdb/about/introduction/en/index4.html for some explanation.