Measuring human capital in South Africa using a socioeconomic status human capital index approach

ABSTRACT

The Human Capital Index (HCI) developed by the [World Bank, 2018a. The human capital project. World Bank. https://hdl.handle.net/10986/30498 Accessed 26 February 2019] provides a measure which can be used to study human capital (HC) productivity gaps between countries. The HCI uses measures of survival, education and health to estimate, at a country level, the HC ‘a child born today can expect to attain by her/his 18th birthday, given the risks of poor health and poor education where she lives’ [World Bank, 2018a. The human capital project. World Bank. https://hdl.handle.net/10986/30498 Accessed 26 February 2019, 2]. The socioeconomic disaggregated human capital index (SES-HCI), an extension of the HCI, provides a means for analysing HC inequalities within countries. This study estimates SES-HCIs for South Africa by income quintiles, school quintiles, geographical area, gender and race. The main driver of HC inequalities in all the SES indicators is found to be the quality of schooling. Factors to address the inequalities and the limitations of the measuring instruments are identified.

KEYWORDS:

• Human capital
• inequality
• human capital index

1. Introduction

The Human Capital Project (HCP), of the World Bank (2018a) introduced a Human Capital Index (HCI) for all countries, in order to encourage better investments into human capital (HC) by identifying national productivity gaps. For the purpose of the HCI, the World Bank accepted the broad definition of HC, stated by the OECD (2001:18) as ‘the knowledge, skills, competencies and attributes embodied in individuals that facilitate the creation of personal, social and economic well-being’. The HCI did not measure all aspects contained in this definition. Instead, it used just three components, survival, education and health measured at a country level, to estimate the HC ‘a child born today can expect to attain by her 18th birthday, given the risks¹ of poor health and poor education where she lives’ (World Bank, 2018a:2). Proxies used to measure these three components were: for survival, the under-5 mortality rate (U5MR); for education, expected learning-adjusted years of schooling; and for health, adult survival and stunting rates.

The HCI results indicated that South Africans born today can, on average, expect to obtain 41% of their full potential health and education, by the age of 18. South Africa ranked 126th out of 157 countries measured (World Bank, 2018a), which confirms the need for further research for understanding the multidimensional nature of the low levels of HC in South Africa. South Africa is furthermore one of the most socioeconomically unequal countries in the world with a gini coefficient for income² of 0.63 in 2014 (World Bank, 2019a) and 0.95³ for wealth⁴ (Orthofer, 2017). Leibbrandt et al. (2012) demonstrated that income inequality in South Africa is driven by the labour market, and so to reduce income inequality policies to effectively grow skills and productivity are required. The bidirectional relationship between HC and income inequality (Chani et al., 2014), has thus resulted in policy commitments, as stated in the National Development Plan (NDP) 2030, to develop HC through increasing investments and furthermore move to a knowledge-intensive economy (NPC, 2012).

However, because of data and methodological challenges, analyses to date on the impacts on inequality of HC, measured using a multidimensional approach, have been limited. Most researchers in South Africa have used educational attainment to measure HC (Lam, 1999; Van der Berg, 2010; Pellicer & Ranchhod, 2012; Branson & Leibbrandt, 2013; Wanka, 2014). For a discussion on the problems of this narrow approach and alternative methods of measuring HC see Oxley et al. (2008) and Folloni & Vittadini (2010).

The World Bank’s (2018a) HCI does not provide any indication of the distribution of HC, or information needed to analyse the causes of national HC and productivity gaps and track progress made through policy intervention. The World Bank has begun to address this limitation by extending the HCI methodology to construct indices of HC disaggregated by socioeconomic status (SES) quintiles within countries (D’Souza et al., 2019). The SES-disaggregated human capital index (SES-HCI) has been estimated for 51 countries (of which South Africa is not one), approximately a third of the countries in the HCI study. The limitations of available data are cited as the main reason for the exclusion of the remaining countries.

The World Bank and the United Nations Development Programme (UNDP) provide complementary indices, including the Knowledge Economy Index (KEI), the Multidimensional Poverty Index (MPI) and the Human Development Index (HDI). Each index provides country-level information on progress made towards achieving related Sustainable Development Goals (SDGs). The measures of the HCI are aligned to SDG 2, SDG 3 and SDG 4 which are related to reducing hunger, ensuring good health and well-being and ensuring quality education for all, respectively (World Bank, 2019d).

Fransman & Yu (2018) derived a MPI disaggregated by gender, race and spatial location for South Africa, revealing that the MPI of Africans contributed more than 95% to multidimensional poverty. The three main indicators of the MPI driving poverty in South Africa were identified as the number of years of schooling, unemployment and disability. Within this context, this study aims to measure the education and health components impacting the development of a child’s potential and resultant productivity gaps in South Africa by SES indicators using the SES-HCI.

This allows recommendations to be made on how the SES-HCI can best be used to measure and monitor progress made by investments in HC, to ensure that all children reach their potential, in the South African context of very high inequality.

2. Materials and methods

2.1. Data and sample

Primary and secondary data used for this study are from Wave 5 of the 2017 National Income Dynamics Study (NIDS) dataset and the 2016 South African Demographic Household Survey (NDoH et al., 2019). The NIDS is a panel dataset compiled biennially by the South African Labour and Development Research Unit (SALDRU) based at the University of Cape Town (UCT). The first wave was released in 2008, administered to a nationally representative sample, and the most recent wave, Wave 5, was conducted in 2017 (see Brophy et al., 2018). It comprises a total of approximately 37 000⁵ individuals in 13 719 households as a cross-sectional dataset. Post-stratification weights as per SALDRU (2017) were applied.

Two main reasons for using the NIDS were the very comprehensive nature of the data and the fact that this paper forms part of a larger study which analyses HC using different measurements and the impact of HC on inequality. Using the same dataset will make future alternative HC measurements comparable. However, the Wave 5 NIDS data has insufficient observations for estimating the U5MR, which the HCI requires to calculate survival (only 26 observations of under-5 child deaths were recorded). Therefore, child mortality rates from a document by the NDoH, StatsSA, SAMRC and ICF (hereafter referred to as NDoH et al., 2019) on U5MRs from the 2016 SADHS⁶ dataset were used as part of the component of survival to supplement the NIDS data. The fact that the time periods of the two studies differ is acknowledged, but is unlikely to impact the results. The NDoH et al. (2019) results were concerned with the previous 5 or 10 years, whereas the NIDS measured observations over the previous 12 months. Also, the SADHS reference year was 2016 while that for NIDS was 2017.

2.2. Index framework and variables

The HCI and SES-HCI methodologies were published in Kraay (2018) and D’Souza et al. (2019) respectively. The SES-HCI followed largely the same method as the HCI, but at a subgroup level based on a variety of SES indicators, namely: income, race, gender, geographical area and school quality. Variables were included based on data availability as suggested in D’Souza et al. (2019).

The HCI index is formulated as (1) $\mathrm{H}\mathrm{C}\mathrm{I}=\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\times \mathrm{S}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l}\times \mathrm{H}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{h}$(1)

With the three components defined as (2) $\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}={\displaystyle \frac{1-\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}5\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{y}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}{1}}$(2) (3.1) $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l}={\mathrm{e}}^{\mathrm{\varnothing }\left(\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l}\times \frac{\mathrm{H}\mathrm{a}\mathrm{r}\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\mathrm{T}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}{625}-14\right)}$(3.1) (4.1) $\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{h}={\mathrm{e}}^{({\gamma }_{\mathrm{A}\mathrm{S}\mathrm{R}}\times (\mathrm{A}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{i}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}-1)+({\gamma }_{\mathrm{S}\mathrm{t}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}\times \left(\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}-1\right)/2)}$(4.1) where under-5 mortality rate (U5MR) is defined as the number of deaths under age 5 per 1000 births in the last year. ∅ is the rate of return to schooling which in the World Bank study (Kraay, 2018) is 8%.⁷ In Equation (3.1) the expected years of schooling (EYS) are adjusted for a harmonised test score (HTS) calculated from the international TIMSS⁸ https://mail.google.com/mail/u/0?ui=2&ik=04f70a3010&view=lg&permmsgid=msg-f:1685760991070096860-m_-2668106772879604077__ftn10 and PIRLS⁹ assessments (maximum score of 625 used to account for schooling quality), to calculate a learning-adjusted years of education. γ_ASR is the return to an additional unit of adult survival and γ_stunting the return to not being stunted, which Kraay (2018),¹⁰ for the purpose of estimating the HCI, https://mail.google.com/mail/u/0?ui=2&ik=04f70a3010&view=lg&permmsgid=msg-f:1685760991070096860-m_-2668106772879604077__ftn12 estimated as 0.65 and 0.35 respectively. The interpretation of the health return estimates is that when the health component improves to the extent that the adult survival rate (ASR) increases by one percentage point, then worker productivity increases by 0.65 percentage points (Kraay, 2018). Similarly, an improvement in overall health associated with a reduction in stunting rates of 10 percentage points raises worker productivity by 3.5% (D’Souza et al., 2019). Where data for both stunting rates and ASRs are available, the average of the improvements in productivity associated with both health measures is applied in the health component of the HCI, as noted in Equation (4.1). In Equation (3.1), 14 is the maximum number of years of school enrolled for from age 4–17. The reason for including the returns to education and health in the HCI calculation is that it allows one to estimate how much a reduction in full education or health reduces earnings and productivity (Kraay, 2018). The values selected for the returns to education¹¹ and health by Kraay (2018) are anchored in an extensive study of the empirical literature.

This study uses methodological elements from both the SES-HCI and HCI to estimate the best context-specific SES-HCIs for South Africa. EYS, in Equation (3.1), was also estimated using both educational attainment and enrolment (Woßmann, 2003). Education enrolment has become near universal in South Africa (StatsSA, 2011), thus both attainment and enrolment were used to provide comparable measures of EYS. Results are presented in Table 3 below. For education attainment, the definition for EYS is the mean years of schooling an individual could expect to obtain by and including the age of 18 years¹² https://mail.google.com/mail/u/0?ui=2&ik=04f70a3010&view=lg&permmsgid=msg-f:1685760991070096860-m_-2668106772879604077__ftn13.

Because income inequality in South Africa is largely driven by the labour market (Leibbrandt et al., 2012) and education attainment drives labour market outcomes (Taylor, 2019 and Kamanzi et al., 2021), when measuring the SES-HCI disaggregated by income, the school component was adjusted to account also for tertiary education. The age 25¹³ is used as the expected age at which education attainment will have been completed (see UNDP, 2020). To calculate mean years of education attainment by age 25, the NIDS highest education attainment variable was recoded as per Branson & Leibbrandt (2013) and 16 years the potential maximum attainment. For secondary schooling values, the years of schooling were adjusted by the relevant HTS per school quintile on a graded curve, to obtain learning-adjusted years of education, before applying the return to education. Years of tertiary education were not adjusted by the HTS. The school component for the SES-HCI adjusted to include tertiary education is presented as Equation (3.2) and the results are shown in Table 8. (3.2) $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l}={\mathrm{e}}^{\mathrm{\varnothing }\left(\left(\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{o}\mathrm{o}\mathrm{l}\times \frac{\mathrm{H}\mathrm{a}\mathrm{r}\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\mathrm{T}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}{425}\right)+\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{r}\mathrm{y}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}-16\right)}$(3.2)

To account for education quality in the disaggregated SES indicators, average HTS per school quintile¹⁴ (using PIRLS (2016), TIMSS Mathematics (2015) and TIMSS Science (2015)) from Reddy et al. (2016) and Howie et al. (2017) are used and shown in Table 1. Quintile 5 schools have a mean HTS of 425 (68% of 625) and quintile 1 schools 315 (50% of 625). With an average mean score of 343 (54.9%) and 345 (55.2%) out of 625 calculated using World Bank (2018b) and NIDS data respectively, South African HTSs are low overall in the global context. The country with the highest HTS was Singapore with 581 (World Bank, 2019c). Singapore also had the highest HCI score: 0.88. Patrinos & Angrist (2018) note that the large difference between the scores of Singapore and South Africa is more than 2 standard deviations and is equivalent to a generation of lost schooling. To investigate the distributions differences in HC in South Africa, the HTS is also graded on a curve to illustrate the difference within the country as per the SES-HCI. Results using a maximum HTS of 425 will therefore also be presented, thus applying the quintile 5 schools mean HTS as the maximum score. The calculated HTSs for the different SES indicators are presented below when discussing the results for the SES-HCI by geographical area, gender and race.

Table 1. South African harmonised test score per school quintile.

School Quintile	PIRLS (2016)	TIMSS MAT (2015)	TIMSSSCIE (2015)	Avg/avg student*
1	288	341	317	315.33
2	299	341	317	319
3	303	341	371	338.33
4	328	423	425	392
5	426	423	425	424.67

Source: Reddy et al. (2015) and Howie et al. (2017).

*This is the average score across the PIRLS (2016), TIMSS MAT (2015) and TIMSSSCIE (2015) per student and school quintile.

To measure stunting, the NIDS provides height for age z-scores for children under-5. Stunting is measured as being 2 standard deviations below the median height for age scores, as used by studies on stunting based on NIDS data (see Otterbach & Rogan 2017). To estimate the health component, the probability of not being stunted per subgroup was adjusted by the return to reduced stunting provided in Kraay (2018).

Following D’Souza et al. (2019), this study omits adult survival from the health component when calculating the SES-HCI.¹⁵ Thus, the health component presented in Equation (4.1) is adjusted to: (4.1) $\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{h}={\mathrm{e}}^{{\gamma }_{\mathrm{S}\mathrm{t}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}\times \left(\mathrm{N}\mathrm{o}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{u}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}-1\right)}$(4.1) SES indicators used to disaggregate HCI in this study are income quintile¹⁶ (the NIDS derived household income variable was divided by household size to calculate HH income per capita), school quintile (Q1–Q5, as categorised in the NIDS dataset), geographical region (urban versus rural¹⁷), gender and race. Each of these elements is related to earnings inequalities in South Africa (StatsSA, 2019). Details of the different proxies and data applied for each of the components of the SES-HCI indicators are presented in Table 2. Note that when disaggregating by school quintile it is not possible to calculate an under-5 stunting or mortality rate because most children under 5 years of age are not in school yet and therefore cannot be allocated to a school quintile. Instead, and because higher school quintiles require higher fees, the relevant income quintile values were used as indicators for the U5MRs and health components. Changes in under-5 mortality and stunting rates are expected to move in the same direction.

Table 2. Study variations by data and survival, education and health components.

Component	Data	Survival*	Education				Health
			Age category	Expected years of schooling (EYS)	Harmonised test score (HTS)	Rates or return	Stunting	ASR***
HCI (Kraay, 2018). (World Bank, 2019c)	National Administrative data^a	Under-5 mortality rate (U5MR)	4–17	Enrolment rates	TIMSS and PIRLS	8%	Under-5 stunting rate (U5SR)	ASR***
SES-HCI (D’Souza et al., 2019)	Household data (DHS; MIC)	U5MR	6–17	Enrolment rates	TIMSS and PIRLS	8%	U5SR	–
SA SES-HCI by income. Tables 4–7	Household data (NIDS; DHS).	U5MR	4–17	Enrolment rates	Table 6	8%	U5SR	–
SA SES-HCI by income (with tertiary education). Table 8.	Household data (NIDS; DHS)	U5MR	4–25	Education attainment	Table 6	8%	U5SR	–
SA SES-HCI by race. Tables 10–12.	Household data (NIDS; DHS)	U5MR	4–17	Enrolment rates	Table 9	8%	U5SR	–
SA SES-HCI by region. Tables 10–12	Household data (NIDS; DHS)	U5MR	4–17	Enrolment rates	Table 9	8%	U5SR	–
SA SES-HCI by gender. Tables 11–13	Household data (NIDS; DHS)	U5MR	4–17	Enrolment rates	Table 9	8%	U5SR	–
SA SES-HCI by school quintile.** Table 13	Household data (NIDS; DHS)	U5MR proxy**	4–17	Enrolment rates	Table 1		U5SR	–

^a See Kraay (2018) footnote on page 1 for all the contributors to the data collection process.

*For the SES-HCI estimates, the total number of observed under-5 deaths using the NIDS was only 26. Thus SES-HCI disaggregated indicators were in addition calculated using the SADHS U5MRs (NDoH et al., 2019).

**With regards to disaggregation by school quintile the U5MR per income quintile were used as a proxy in the case of the NIDS data and wealth quintile (calculated using wealth indices estimated by means of Principal Component Analysis) for the SADHS data. Under-5 stunting rates per income quintile was used as a proxy for under-5 stunting per school quintile.

***Adult survival rate.

Lastly, D’Souza et al. (2019) noted that, since different datasets were employed, interpreting and comparing HCI results using different data sources, as in Kraay (2018) and D’Souza et al. (2019), should be undertaken with caution.

3. Results

With high levels of income inequality in South Africa, inequality between fee and non- or low-fee paying education and healthcare services (Spaull, 2019 and StatsSA, 2019) and the bidirectional relationship between HC and earned income (Chani et al., 2014), it is expected that SES-HCI calculations per socioeconomic indicator should show large variations. According to StatsSA (2019), higher income quintiles, quintile 5 schools and urban regions have higher earnings and are thus expected to have higher SES-HCI measures than low-income quintiles, quintile 1 schools and rural regions, respectively. Furthermore, based on the results from the World Bank’s (2018a) measure of HCI for South Africa, women (HCI of 0.41) are expected to have only a slightly higher SES-HCI score than men (HCI of 0.36). However, StatsSA (2019) reported that men have higher levels of employment and earnings and thus it appears that factors other than expected HC at the age of 18 affect labour market outcomes with respect to gender. The SES-HCI will thus be disaggregated by gender using the NIDS to further investigate the distribution of HC between men and women by the age of 18. With regards to race, and due to the country’s history of racial segregation, it is expected that White South Africans would have the highest SES-HCI in comparison to the other race groups (StatsSA, 2019).

To contextualise the results obtained using the NIDS household data, the national HCI calculation using the NIDS dataset is compared to the World Bank’s (2019b) estimates in Table 3. The impact of substituting the survival to age 5 estimate with SADHS data is also shown. The impact of using education attainment as opposed to enrolment is also demonstrated.

Table 3. HCI, South Africa: NIDS data versus World Bank (WB) data calculation.

Component	WB	NIDS	NIDS/SADHS	NIDS
	Enrolment*	Enrolment*	Enrolment*	Attainment**
Survival to Age 5 (A)	0.96	0.97	0.96	0.97
Expected years of school	9.4	12.4	12.4	10.1
HTS	343	345	345	345
School (B)	0.49	0.56	0.56	0.60
Not stunted	0.73	0.79	0.79	0.79
Adult Survival Rate (ASR)	0.68	–	–	–
Health (C)	0.86	0.93	0.93	0.93
HCI (A x B x C)	0.41	0.51	0.50	0.54

Source: NDoH et al. (2019), World Bank (2019b) and authors own calculations.

*Expected years of schooling estimated using repetition adjusted enrolment rates with a potential maximum of 14 years.

**Expected years of schooling estimated using education attainment, with a potential maximum of 12 years.

The HCI estimates, as per the NIDS data, are all higher than the World Bank’s results. The main contributors to this higher measure are the EYS measures and the calculated probability of not being stunted. These result in a seven percentage point increase in both the school component (when using enrolment, but 11 percentage point when using attainment) and the health component.

The difference between the estimates of the probability of not being stunted can simply be attributed to dataset differences. The NIDS under-5 sample is smaller than the World Bank’s datasets and thus the health component of the HCI calculated by the World Bank (2018b) is likely to be more accurate. Moreover, the World Bank also includes the ASR which could not be calculated from the NIDS dataset. The large difference between the World Bank (2018b) and the NIDS data estimates for EYS, using repetition adjusted enrolment rates, of 9.4 years and 12.4 years respectively, is more difficult to explain unless it is seen as also being due to dataset differences. Which measure is more accurate is unclear. The EYS value for the attainment variable is 10.1 years and is lower than the NIDS enrolment figure. Attainment has a potential maximum of 12 years, versus enrolment, which has a maximum of 14 years, so the values calculated using the NIDS are similar (88.6% for enrolment and 84.2% for attainment). Because the results are similar, enrolment is used to measure the SES-HCI estimates below, the same method used by the World Bank (2018b). Furthermore, with school attendance almost universal, the differences in HC educational outcomes in South Africa are likely to come from school quality (measured by the HTS) and tertiary education attainment, rather than lower than tertiary education attendance or attainment.

3.1. Disaggregated index scores by income quintile

The results from the SES-HCI estimates disaggregated by income quintile in Table 4 show quintile 1 with an SES-HCI of 0.48 and quintile 5 with an SES-HCI of 0.60, a 12 percentage point difference. Using the HCI definition, this would thus mean that, by the age of 18, the productivity of children born and raised in income quintile 5 households could expect to be 12 percentage points greater than that of children in income quintile 1 households, as a result of the different health and education services received. Surprisingly, quintile 4 has a lower probability of survival to age 5 than quintile 3. While the number of under age 5 deaths decreases consistently from quintile 1 to 5, so do the number of births. This results in a lower survival rate for quintile 4.

Table 4. SES-HCI, South Africa: Income quintiles.

Component	Overall	1	2	3	4	5
Survival to Age 5 (A)	0.97	0.97	0.97	0.98	0.95	1.0000
Expected years of schooling	12.4	12.0	12.0	12.5	12.7	13.2
Harmonised test score	345	331	340	345	361	386
School (B)	0.56	0.54	0.55	0.57	0.59	0.62
Not stunted	0.79	0.72	0.79	0.82	0.86	0.88
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.91	0.93	0.94	0.95	0.96
HCI (AxBxC)	0.51	0.48	0.50	0.52	0.53	0.60

Source: Authors own calculations.

The results of the SES-HCI recalculated using the survival to age 5 rates provided by the larger SADHS dataset, are shown in Table 5 (NDoH et al., 2019). SADHS results confirmed increasing under-5 survival rates per wealth quintile, with the exception of the under-5 survival rate for quintile 4 being higher than quintile 5. The under-5 deaths per 1000 births from poorest to the richest quintile were noted as 67, 52, 51, 37 and 41 (NDoH et al., 2019).

Table 5. SES-HCI, South Africa: Income quintiles (using survival to age 5 estimates from the SADHS per wealth quintile as a proxy).

Component	Overall	1	2	3	4	5
Survival to Age 5 (A)	0.96	0.93	0.95	0.95	0.97	0.96
Expected years of schooling	12.4	12.0	12.0	12.5	12.7	13.2
Harmonised test score	345	331	340	345	361	385
School (B)	0.56	0.54	0.55	0.57	0.59	0.62
Not stunted	0.79	0.72	0.79	0.82	0.86	0.88
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.91	0.93	0.94	0.95	0.96
HCI (AxBxC)	0.50	0.46	0.48	0.51	0.54	0.57

Source: Authors own calculations and NDoH et al. (2019).

The impact on the HCI results of using the different survival to age-5 estimates is very small. While the SES-HCI calculations in Table 5 are slightly lower for all income quintiles, with the exception of quintile 4, when using the SADHS data (NDoH et al., 2019), the difference between income quintiles 1 and 5 changes by only 1 percentage point. This is because the NIDS survival to age-5 estimates, despite the small sample size, are very close to those calculated from the 2011 Census data (StatsSA, 2011)

The HTSs for income quintiles in Tables 4 and 5 are calculated using the mean HTS per school quintile in Table 1 and the percentage of scholars attending the different school quintiles in each income quintile. This is shown in Table 6.

Table 6. Average harmonised test score (HTS) calculated using percentage of learners from each school quintile in each income quintile.

School quintile	HTS	Income quintile
		1	2	3	4	5	National
Quintile 1	315.33	29.88	23.41	20,28	12.58	9.79	22.08
Quintile 2	319	32.43	27.6	24,95	17.37	6.24	24.69
Quintile 3	338.33	28.03	29.75	29,99	27.45	20.8	29.03
Quintile 4	392	7.09	13.25	16,83	23.24	13.27	13.20
Quintile 5	424.67	2.56	5.99	7,94	19.36	49.91	11.01
TOTAL		100	100	100	100	100	100
Average score		331	340	345	361	385	345

Source: Authors own calculations.

According to the NIDS data, only 49.91% of children in income quintile 5 households attend fee-paying (Quintile 5) schools. This surprising result is probably explained by the fact that because of South Africa’s high income inequality, income quintile 5 starts with households whose per capita income is as low as R4 600 per month¹⁸ https://mail.google.com/mail/u/0?ui=2&ik=04f70a3010&view=lg&permmsgid=msg-f:1685760991070096860-m_-2668106772879604077__ftn22. Fees for quintile 5 schools may therefore be unaffordable to many households classified as income quintile 5. This mix of school attendance reduces the differences in HTSs per income quintile. To show greater HC distributional differences of school quality, the HTSs are graded on a curve, with 425 set as the maximum grade in Table 7.

Table 7. SES-HCI, South Africa: Income quintiles, using a graded curve.

Component	Overall	1	2	3	4	5
Survival to Age 5 (A)	0.97	0.97	0.97	0.98	0.95	1.0000
Expected years of schooling	12.4	12.0	12.0	12.5	12.7	13.2
Harmonised test score	345	331	340	345	361	385
School (B)	0.85	0.69	0.71	0.74	0.78	0.85
Not stunted	0.79	0.72	0.79	0.82	0.86	0.88
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.91	0.93	0.94	0.95	0.96
HCI (AxBxC)	0.66	0.60	0.64	0.67	0.71	0.81

Source: Authors own calculations.

As expected, the difference in the HCI between the income quintiles is now greater, with a 21 percentage point difference between income quintile 1 and 5 compared with 12 percentage points in Table 4. To contextualise this adjusted result: if South Africa had a national HCI estimate 21 percentage points greater than its current value (i.e. 0.62 instead of 0.41) it would rise to approximately 54 out of 157 countries from its current rank of 126 (World Bank, 2018b). This would place South Africa in approximately the top 40% of countries, instead of the current rank of the lowest 20%. Such is the advantage of income quintile 5 over quintile 1 households within South Africa.

The SES-HCI is adjusted in Table 8 to include tertiary education disaggregated by income quintile. Equation (3.2) replaces Equation (3.1) to estimate the schooling component, as explained above.

Table 8. SES-HCI, South Africa: Per income quintile, using a graded curve and mean education attainment at age 25.

Component	Overall	1	2	3	4	5
Survival to Age 5 (A)	0.97	0.97	0.97	0.98	0.95	1.0000
Expected years of schooling	11.3	10.6	10.7	11.2	11.6	12.5
Harmonised test score	345	331	340	345	361	385
School (B)*	0.58	0.54	0.55	0.57	0.61	0.69
Not stunted	0.79	0.72	0.79	0.82	0.86	0.88
Adult survival rate	–	–	–	–	–	–
Health (C)	0.93	0.91	0.93	0.94	0.95	0.96
HCI (A x B x C)	0.52	0.47	0.50	0.53	0.56	0.66

Source: Authors own calculations.

*Rate of return of 8% per additional year of education applied as per Kraay (2018).

The difference in HCI between income quintiles 1 and 5 is now 19 percentage points and the HCI measure is lower for all quintiles. Thus, although tertiary education was included because of its importance for labour market inequality, the uptake of tertiary education in South Africa is so small that the mean attainment of education is still only just over 12 years for quintile 5. If the SES-HCI was disaggregated further to income deciles, the difference would be greater, because the gap between mean years of attainment by age 25 jumps from the 10.22 and 13.7 for income deciles 1 and 10 respectively, compared with 10.68 and 12.50 for income quintiles 1 and 5. Calculating the SES-HCI by income decile would therefore more accurately reflect HC inequalities. The difficulty of disaggregating the data further into income deciles is due to the lower number of observations for each decile from the NIDS data, which raises questions of their validity. Furthermore, the impact of increasing rates of return to education in South Africa on SES-HCI estimates is recommended for future research given that authors including Van Broekhuizen (2011),¹⁹ Branson & Leibbrandt (2013) and Lam et al. (2015) estimated high and increasing earnings returns from tertiary education. Despite the conclusion by Kraay (2018) that a consistent rate of return should be applied, given that income inequality originates in the labour market in South Africa, when disaggregating data to estimate a HCI for different SES indicators, it is recommended that future research applying different rates of return per education category, gender, race and geographical location should be conducted. The suggested research could furthermore be extended to estimating and applying economic rates of return to health outcomes specific to South Africa.

3.2. Disaggregation by geographical area, gender and race

In Table 10 the SES-HCI is disaggregated by geographical area, gender and race. First, the indices for schooling quality, based on the percentage of learners which attend the different school quintiles are presented in Table 9. This is done because of the importance of schooling in explaining SES-HCI differences. Schooling quality is better in urban than rural areas, is similar for females and males, but differs greatly between races, with Whites having an average HTS of 413 versus 340 for Africans. This difference is explained because 84.08% of Whites and only 7.30% of Africans attend quintile 5 schools. It should be noted, however, that approximately 90% of learners in South Africa are African, and 681801 African learners were enrolled at quintile 5 schools as compared with 251 012 White learners (using NIDS weighted data). Thus, 57% of learners attending Quintile 5 schools are African and 21% are White.

Table 9. Harmonised test score (HTS) by area, gender and race.

School quintile	HTS	Percentage school quintile attendance by area, gender and race*
		Area		Gender		Race
		Urban	Rural	Male	Female	African	Coloured	Asian/Indian	White
Quintile 1	315.33	12.86	32.18	21.16	22.34	23.80	6.00	4.16	1.96
Quintile 2	319	15.85	35.64	25.35	24.56	26.84	13.31	2.08	2.14
Quintile 3	338.33	30.06	25.9	29.31	26.97	30.03	16.61	1.16	6.57
Quintile 4	392	21.73	4.34	13.01	14.45	12.02	37.03	29.31	5.26
Quintile 5	424.67	19.5	1.95	11.16	11.69	7.30	27.05	63.29	84.08
TOTAL		100	100	100	100	100	100	100	100
Average score		361	328	345	346	340	378	407	413

Source: Authors own calculations.

*The calculation is based on individuals aged 4–17 enrolled in an educational institution.

In Table 10, Whites have an SES-HCI score of 0.64 compared with 0.58 for Asians/Indians, 0.54 for Coloureds and 0.50 for Africans. The schooling components and health components have 10 and five percentage point differences respectively between Africans and Whites. Coloureds have a six percentage point difference in the health component compared to Whites. It is important to note that stunting is the only indicator included in the health component and differences between races would likely increase if data were available to also include ASRs. According to Marandu (2011) the adult mortality rates of Africans, Coloureds, Asians/Indians and Whites were 0.613, 0.414, 0.311 and 0.260 respectively by the age of 60. Although the schooling component is the main influencer of HC difference in Table 10, survival and the health components are also important contributory factors. It is also important to note that the distribution of HC when measured by quintiles is more unequal according to race than according to income. The percentage point difference between income quintiles 1 and 5 is 12 percentage points (Table 4), whereas the difference between Africans and Whites is 14 percentage points.

Table 10. SES-HCI, South Africa: area, gender and race, using educational enrolment.

Component	Overall	Urban	Rural	Male	Female	African	Coloured	Asian/ Indian	White
Survival to Age 5 (A)	0.97	0.974	0.967	0.975	0.969	0.972	0.98	1.00	1.00
Expected years of schooling	12.4	12.5	12.2	12.1	12.6	12.3	12.5	12.1	13.2
Harmonised test score	345	361	328	345	346	340	378	407	413
School (B)	0.56	0.58	0.54	0.56	0.57	0.56	0.60	0.61	0.66
Not stunted	0.79	0.81	0.77	0.77	0.89	0.79	0.77	0.85	0.93
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.94	0.92	0.92	0.96	0.93	0.92	0.95	0.98
HCI (A x B x C)	0.51	0.53	0.49	0.50	0.53	0.50	0.54	0.58	0.64

Source: Authors own calculations.

The SES-HCI scores are also calculated using survival to age 5 (Table 11) (NDoH et al., 2019) and HTSs graded on a curve (Table 12).

Table 11. SES-HCI, South Africa: area, gender and race, using educational enrolment (using SADHS (2016) U5MRs).

Component	Overall	Urban	Rural	Male	Female	African	Coloured	Asian/Indian*	White
Survival to Age 5 (A)	0.96	0.96	0.95	0.95	0.97	0.95	0.96	–	0.97
Expected years of schooling	12.4	12.5	12.2	12.1	12.6	12.3	12.5		13.2
Harmonised test score	345	361	328	345	346	340	378		413
School (B)	0.56	0.58	0.54	0.56	0.57	0.56	0.60		0.66
Not stunted	0.79	0.81	0.77	0.77	0.89	0.79	0.77		0.93
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.94	0.92	0.92	0.96	0.93	0.92		0.98
HCI (AxBxC)	0.50	0.52	0.48	0.49	0.53	0.49	0.53	–	0.62

Source: Authors own calculations, NDoH et al. (2019) and Victoria et al. (2020).

*There were no results published by Victoria et al. (2020) for Asians and Indians thus excluded.

Table 12. SES-HCI, South Africa: area, gender and race, using graded curve for HTS.

Component	Overall	Urban	Rural	Male	Female	African	Coloured	Asian/ Indian	White
Survival to Age 5 (A)	0.97	0.974	0.967	0.975	0.969	0.972	0.98	1.00	1.00
Expected years of schooling	12.4	12.5	12.2	12.1	12.6	12.3	12.5	12.1	13.2
Harmonised test score	345	361	328	345	346	340	378	407	413
School (B)	0.73	0.77	0.69	0.72	0.74	0.72	0.80	0.82	0.91
Not stunted	0.79	0.81	0.77	0.77	0.89	0.79	0.77	0.85	0.93
Adult stunting rate	–	–	–	–	–	–
Health (C)	0.93	0.94	0.92	0.92	0.96	0.93	0.92	0.95	0.98
HCI (A x B x C)	0.66	0.70	0.62	0.64	0.69	0.65	0.72	0.78	0.89

Source: Authors own calculations.

The SADHS mortality rates result in the SES-HCI indicator for each measure being lower than the NIDS estimates. However, the inequalities of HC when calculated in this manner are not much different from the NIDS estimates.

As shown in Table 12, the graded curve education estimates accentuate the difference between the different SES indicators. The urban indicator is eight percentage points higher than the rural; female is five percentage points higher than male, and the gaps between Africans and other race groups and Whites increase even further. This is because schooling becomes the determining factor of differences between race groups. Adjusted for school quality, there is now a 19 percentage point difference in the schooling estimate between Africans and Whites.

3.3. SES-HCI disaggregated by school quintile

Because of the importance of schooling quality in HC differences, HC according to school quintile is shown for HTSs on a graded curve in Table 13. It is difficult to estimate under-5 mortality and stunting rates by school quintile since children have to be four or older to be in school. Thus, income quintiles are used as proxies for school quintile indicators because of the expectation that school quintile, survival and health indicators will be positively correlated to income quintiles, given the fact that higher quintile schools are fee-paying.

Table 13. SES-HCI, South Africa: Per school quintile.

Component	1	2	3	4	5	1	2	3	4	5
	Max HTS* 625					Graded curve (max HTS 425)
Survival to Age 5 (A)	0.97	0.97	0.98	0.95	1.00	0.97	0.97	0.98	0.95	1.00
Expected years of schooling	13.1	12.9	13.1	13.2	13.6	13.1	12.9	13.1	13.2	13.6
Harmonised test score	316	319	338	392	425	316	319	338	392	425
School (B)	0.55	0.55	0.58	0.63	0.68	0.71	0.71	0.75	0.86	0.97
Not stunted	0.79	0.72	0.79	0.82	0.86	0.79	0.72	0.79	0.82	0.86
Adult stunting rate	–	–	–	–	–	–	–	–	–	–
Health (C)	0.91	0.93	0.94	0.95	0.96	0.91	0.93	0.94	0.95	0.96
HCI (A x B x C)	0.48	0.50	0.53	0.57	0.66	0.62	0.64	0.69	0.78	0.93

Source: Authors own calculations.

The SES-HCI difference between quintile 1 and quintile 5 schools is 18 percentage points, but 31 percentage points when applying the graded curve. The difference between quintile 1 and 2 schools is minimal, the largest difference being between quintiles 4 and 5. This is particularly evident for the graded curve where the difference between quintiles 4 and 5 is 15 percentage points. It is again evident that differences in the schooling component are driven by schooling quality rather than EYS.

4. Conclusions and considerations

Based on household incomes, gender, geographical area, school quality and race, the estimated SES-HCI scores for South Africa highlight large inequalities in HC. The main determinant of this inequality is school quality. Children attending quintile 1 schools have a 17 percentage point lower SES-HCI score than those attending quintile 5 schools. The NIDS data suggest that only 11% of children attend quintile 5 schools. Thus, improving schooling quality, especially in quintile 1–4 schools, would reduce productivity differences and income inequality in South Africa.

These findings are supported by authors such as Leibbrandt et al. (2010), van der Berg (2010) and Spaull (2019). Emphasising the inequalities in education, Spaull (2019) found that 3% of high schools in South Africa produced more mathematics distinctions than the remaining 97% of high schools put together. It is evident that educational inequalities begin from a young age, with children from poorer households not obtaining basic skills and thus remaining perpetually disadvantaged when compared to children from wealthier households who attend better quality schools (Spaull, 2015). The cycle of poverty is thus perpetuated by the schooling system. As Taylor (2019) emphasised, it is clear that improved education and the quality thereof is the most likely way of improving the life-chances of children, regardless of race, language, gender, or geographical location. Furthermore, the improvement in educational quality is also required to drive the growth of a knowledge economy, as set out in the NDP 2030 (NPC, 2012), and has been identified by Asongu & Nwachukwu (2018) as required to ensure inclusive human development.

When applying a graded curve for HTSs, inequalities between the different SES indicators were exacerbated further. The large impact of using the graded curve on the HCI results illustrates how poorly South Africa performs globally in terms of schooling quality. Thus, in order to empower South Africans, improved learning and skills, rather than time spent at school, should be emphasised.

Gender inequality is also highlighted in the findings. Despite the SES-HCI estimates showing that women have higher HC than men, women have poorer employment prospects and earn less than men (StatsSA, 2019). Characteristics other than HC, such as additional penalties due to motherhood, thus negatively impact the labour market outcomes of women (Casale & Posel (2005) and Magadla et al. (2019)).

These findings are aligned to the plans of the African Human Capital Project, which aims to increase productivity in Africa by 13% by 2023. The challenges highlighted as negatively affecting productivity in Africa as compared to other regions include girls and women who are born into a region experiencing the highest fertility rates, the percentage of girls who drop out of schools, maternal mortality rates and adolescent fertility rates. Increasing the learning-adjusted years of schooling and reducing adolescent birth rates by approximately 20% and 18% respectively have thus been identified as requirements to achieve the productivity improvements required (World Bank, 2019d).

Race was also identified as an important determinant of HC, which is unsurprising considering the Apartheid-era policies which practised racially biased expenditure on public services such as education. The discriminatory education system in the previous ‘homelands’ meant that black schools not only received fewer resources than white schools but also had different education curricula, receiving a poorer quality of education (Timaeus et al., 2013). While the post-Apartheid government has aimed to eliminate inequalities in public resource allocation to schools, education quality remains unequal and this inequality is identified in this study as perpetuating productivity gaps between population groups. As a result, earnings inequalities are particularly visible along racial lines in South Africa (StatsSA, 2019). The SES-HCI results confirm that labour market policies alone are insufficient to reduce racial income inequalities in South Africa. Improved education and health services are the key to reducing such inequalities.

While extending available research on HC distribution in South Africa by using the SES-HCI, this study has revealed several issues which need further consideration. Firstly, a SES-HCI which incorporates tertiary education would provide valuable information for estimating HC linked to the labour market. But for the results to be meaningful the data need to be disaggregated into income deciles rather than quintiles. Data availability is a challenge as was revealed in the NIDS data where only 26 deaths of under-5 children were evident from 870 births. Although the small number of observations in the NIDS data did not greatly impact the results in this study, disaggregating the data further, for example by income quintile to income decile, the more the estimates will become skewed and unreliable. In addition, further research accounting for higher and increasing earnings returns to higher levels of education and applying returns to education and health, specific to different subgroups in South Africa, should be explored. It is expected that greater inequalities would be identified.

Despite data limitations, estimating the SES-HCI for a number of indicators has provided important insights into the extent and causes of HC inequalities in South Africa. The SES-HCI estimates furthermore facilitate the monitoring of changes in HC gaps in South Africa.

Disclosure statement

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

Notes

1 It is the risks faced based on an assumption that ‘they experience currently-prevailing risks of poor health and poor education faced by children aged 0–17’ (D’Souza et al., 2019)

2 The National Income Dynamics Study (NIDS) calculates household income as the sum of labour market income (net of taxes), government grants, other government income, investment income, remittances received, subsistence agriculture income and imputed rent for owner-occupied housing (Chinhema et al., 2016). For the purpose of calculating inequality, the household income is divided by the number of household residents to obtain a household per capita income, which is assigned to each household member (Leibbrandt et al., 2012).

3 HC was not included in the measure of wealth (Orthofer, 2017)

4 Wealth (also known as ‘net worth’) is calculated as the difference between the market value of all assets and liabilities (Orthofer, 2017) and in NIDS household wealth is calculated by summing net financial wealth, net business equity, net real estate equity, value of vehicles, total value of pension/retirement annuities and livestock wealth (Chinhema et al., 2016).

5 The total numbers of individuals successfully interviewed in Wave 1 and Wave 5 were 26776 and 37 368 respectively (Brophy et al., 2018).

6 The Demographic Household Survey (DHS) program has fielded over 400 surveys across 90 countries, collecting household demographic data including birth histories. In South Africa, three surveys have been conducted: in 1998, 2003 and 2016. The SADHS reviewed 11 083 households (NDoH et al., 2019).

7 In the South African context, a standard 8% earnings return to education may underestimate the returns, with Depken et al. (2019) highlighting approximately 18% as an accurate estimate of returns per year of education attained in South Africa. The estimation approach included by Depken et al. (2019) included ordinary least squares (OLS) and instrumental variables (IV). Furthermore, in comparison to primary school attainment, van Broekhuizen (2011) estimated high and increasing rates of return to higher education, noting that secondary schooling, matric, bachelor’s degree and post-graduate degree attainment had 13%, 35%, 115% and 180% average earnings returns relative to primary schooling respectively.

8 Trends in International Mathematics and Science Study (TIMSS) is an IEA assessment which was administered to Grade 9s in South Africa in 1995, 1999, 2003, 2011 and 2015 (van der Berg and Gustafsson, 2019). To calculate harmonised test scores, TIMSS 2015 results available from Reddy et al., 2016, were used.

9 Progress in International Reading Literacy Study (PIRLS) is an IEA assessment which was administered to Grade 4s in South Africa in 2006, 2011 and 2016 (van der Berg and Gustafsson, 2019). To calculate the harmonised test scores, PIRLS Literacy 2016 results available from Howie et al. (2017) were used.

10 See Kraay (2018: 41–42) for details on the literature used to calculate the returns used for health, and Kraay (2018: 34–36) for education.

11 The 8% rate of return to schooling suggested by Kraay (2018) is deliberately chosen to be on the lower range, given a vast majority of the returns to education estimated do not control for health.

12 Age 18 is the expected age at which a child will complete grade 12 (Matric) in South Africa. Enrolment is measured until age 17 for the HCI but, given that enrolment at age 17 would result in attainment at age 18, age 18 is included when using the attainment approach.

13 The HCI definition would need to be adjusted from expected HC at age 18 to age 25.

14 School quintile (1 to 5) is the school quality variable used in the NIDS data. For each income quintile, gender, race and geographical area a harmonised test score was calculated using a score per school quintile calculated by averaging the values for the TIMSS Maths and Science scores and PIRLS scores to provide a score per school quintile as found in Reddy et al. (2016) and Howie et al. (2017). Thereafter the percentage of the school going population per disaggregated variable attending that particularly school quintile (available from the NIDS data) was calculated and a test score estimated. See the results in Table 1. The national figure obtained calculated from this method was 345 and the figure provided by the World Bank (2018b) for South Africa was 343. Thus the scores calculated are expected to provide a reliable estimate given the available data.

15 Kraay (2018) defined ASR as the fraction of 15-year olds surviving until age 60.

16 The NIDS dataset provides a derived household income variable which was divided by household size to calculate a household income per capita which was used to create 5 data samples, one for each quintile.

17 Traditional and farm options were combined to generate a rural variable.

18 The descriptive statistics for household income per capita quintile 5 are: Observations (5761), mean (13 512.55); Standard deviation (25 101.16), minimum value 4600 and maximum 868 507.80.

19 Van Broekhuizen (2011) used the wave 1 2008 NIDS dataset.