Inequality in South Africa: what does a composite index of well-being reveal?

Abstract

In this paper, we construct a multidimensional composite well-being measure for South Africa at a micro-level. This allows us to compare the inequalities in well-being in 2008 and 2017. Additionally, we determine the factors, which are significantly related to the inequality in well-being at these two points in time, using recentered influence function (RIF) regressions. Lastly, we use the Blinder–Oaxaca decomposition technique to determine if the change in well-being inequality, is mainly due to an endowment – or a coefficient effect. The RIF results show factors increasing well-being inequality are demographic but also extends to knowledge and skills in the technology sector, access to financial markets, transport and living outside of urban centres. Blinder–Oaxaca decomposition results indicate the difference in well-being inequality is mainly due to the coefficient effect. Policies should not only endeavour to attain a more equal spread of endowments but should also consider the elasticities of these endowments.

KEYWORDS:

• Composite index
• well-being
• inequality
• decomposition
• South Africa

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

Source: Authors’ calculations from NIDS (2018).

Note: * refers to the reference group. Income inconsistencies between waves 1 and 5 in time-invariant variable is an indication of missing data.

Source: Authors’ calculations from NIDS (2018).

*Note: CWI = composite well-being index with min-max normalisation, equal weighting and linear aggregation, CWI (stand) composite well-being index with standardised normalisation, equal weighting and geometric aggregation, CWI (PCA) composite well-being index weighted using PCA. CWI (geometric) is a composite well-being index with min-max normalisation, equal weighting and geometric aggregation (excluding dimensions = 0, missingness = 6%).

Source: Authors’ calculations from NIDS (2018). Note all calculations, including design weights.

Note: Standard errors in parentheses.

* p < 0.10, ** p < 0.05, *** p < 0.01.

Source: Authors’ calculations from NIDS (2018).

Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01.

1 Genuine Progress Index, Index of Economic Well-being, Index of Sustainable Economic Well-being and the Sustainable Societal Index.

2 The Min-Max method normalise an index to have an identical range [0, 1] by subtracting the minimum value and dividing by the range (Arellano & Bover, 1995; Tabachnick & Fidell, 2007; OECD, 2008).

3 As the minimum-maximum method is our preferred method of normalisation, it implies that some indicators do have a value of zero, which can result in a dimension with a value of zero, which has implications if geometric aggregation is used. However, in the complete data set there are very few dimensions of individuals that have a value of zero. In the instance where a dimension is equal to zero, the whole observation is deleted. Nonetheless, the rate of missingness is very low and the results are comparable to that of the linear aggregated index.

4 The range, average deviation from the mean, variance and its square root, the standard deviation, relative standard deviation, interquartile range, mean pair distance, the Gini-coefficient, Lorenz curves, Theil’s measure of entropy and the Atkinson’s class of inequality measures.

5 See Alaimo and Solivetti (2019) and Ferrari and Cribari-Neto (2004) for fractional – (the former study) and beta models (the latter study) used for bounded variables [0,1].

6 For a detailed discussion of ‘recentered influence functions’ (RIF) see Firpo et al., (2009).

7 The error term is a combination of the reweighting error and the specification error.

8 The construction of the ‘quality of housing index’ follows the same method (equal weighting and linear aggregation) as is used to construct the education component of the HDI (UNDP, 2010).

9 See Table A2 in the Appendix for the RIF results, using the Gini-coefficient.

10 We remind the reader that the reweighting is done similar to a normal Blinder-Oaxaca decomposition, for example, if there are two groups: A and B. In this instance, we have waves 1 and 5, and the group differences in the predictors are weighted by the coefficients of group B to determine the endowments effect. The endowment component measures the expected change in group B’s mean outcome (variance) if group B has group A’s predictor levels. Similarly, for the coefficient component (the coefficients effect), the differences in coefficients are weighted by group B’s predictor levels. That is, the coefficient component measures the expected change in group B’s mean outcome (variance) if group B had group A’s coefficients.

11 We do not discuss the interaction effect in itself, as much of the discussion coincides with that of the coefficient- and endowment effects.

12 Please note that certain of the variables are ordinal of nature, but we assume it to be continuous, in line with the findings of Frey and Stutzer (2000).