Re-estimating gender differences in income in South Africa: The implications of equivalence scales

ABSTRACT

Most studies of poverty and inequality in South Africa measure individual welfare by deflating total household resources, such as income, by household size. This per-capita method makes no adjustments for the different consumption needs of children or for household economies of scale. However, in addition to being more likely to live in households where average per-capita household income is lower compared with men, we show that women in South Africa also live in significantly larger households which include more children. These gendered differences in household composition are driven to a large degree by low rates of co-residency between men and women. We therefore investigate how adjusting household resources for the presence of children and economies of scale affects measures of the gender gap in income.

KEYWORDS:

• Gender
• household formation
• income
• equivalence scales

1. Introduction

South Africa has very high levels of poverty, and is also one of the most unequal countries in the world. As the availability of micro-data has increased over the post-apartheid period, so an extensive literature has developed which calibrates poverty and inequality and which evaluates the quality of the data that are used to generate these measures (cf. Meth & Dias, 2004; Ardington et al., 2006; Hoogeveen & Özler, 2006; Van der Berg et al., 2008; Leibbrandt et al., 2010a). However, little attention in this literature has been paid to how economic resources are compared across households of different size and composition. The poverty lines that are applied in South Africa are per-capita thresholds and almost all studies measure poverty and inequality in terms of per-capita household income or expenditure.

A few studies have examined how the profile of the poor changes when household resources are adjusted for the lower consumption needs of children and for the economies of scale that derive from living together rather than apart (Deaton & Paxson, 1997; Woolard & Leibbrandt, 1999, 2001; Klasen, 2000; Streak et al., 2009). These studies have found that, keeping the poverty rate fixed, equivalence scale adjustments make only a small difference to the profile of the poor. This finding perhaps helps to explain the reliance on per-capita measures in the South African literature on poverty and inequality.

In this study, we consider how household structure in South Africa affects measures of the distribution of income, focusing in particular on inequality in access to household resources between men and women. In contexts where most households consist of both men and women, we would not expect the application of equivalence scales to make a significant difference in the measurement of gendered access to household income. However, as we show in this article, many men and women in South Africa do not live with members of the opposite sex. This pattern is evident particularly among Africans, and is related to low levels of union formation between African men and women and the prevalence of labour migration in South Africa, where traditionally men settled elsewhere for purposes of employment (Hosegood et al., 2009; Posel & Rudwick, 2013). Moreover, rates of non-marital childbirth remain high in South Africa, and children live predominantly with their mothers (Posel & Devey, 2006; Hall & Wright, 2010), which means that the households in which women live tend to be larger and comprise a greater share of children.

These differences in household structure between men and women imply that the use of equivalence scales to adjust for household size and composition will make a difference to our measurement of income inequality between men and women. Significant disparities in access to resources have been found to exist between men and women in South Africa. Although based on per-capita measures, recent research, for example, provides evidence that women are more likely than men to live in income-poor households (where average per-capita household income is below the poverty line) and that the burden of extreme poverty is higher among women than men (Posel & Rogan, 2012). These findings are not surprising in light of far higher unemployment rates among women than men and a persistent gender gap in earnings (Casale, 2004; Bhorat & Goga, 2013).

In this article, we revisit gender differences in income in South Africa using nationally representative household survey data, collected in the first wave of the National Income Dynamics Study (NIDS 2008). We use these data first to describe differences in household size and household composition, and to highlight the relationship between household structure and income. We then investigate differences in household formation among women and men, and show how adjustments for child costs and economies of scale substantially narrow gender differences in income (although these differences remain significant). Because larger households which include children have fewer economic resources than smaller households with fewer children, our findings have implications more broadly for measuring inequality in South Africa.

In the next section we review studies of equivalence scales with a particular focus on South Africa, and in Section 3 we outline the data and methods used in the study. We describe the variation in household formation and income in South Africa in Section 4, and in Sections 5 and 6 we investigate the implications of scale adjustments for measures of gender differences in income and the gender poverty profile. We conclude with a discussion of our findings in Section 7.

2. Review

In measuring poverty and inequality, researchers typically aggregate all resources received in a household and then assign a share of these resources to each resident household member.

The most common approach is to calculate average per-capita household income (or expenditure). This method assumes that aggregate resources are equally shared among household members who all have the same weight (or the same consumption needs) regardless of their age or gender. It also assumes that the costs of maintaining a given standard of living do not decrease when individuals live together rather than apart.

An alternative approach still assumes that all household resources are pooled and then shared, but it recalibrates household size so as to recognise both the different consumption needs of household members and the economies of scale that arise when people live together in the same household. When this recalibration assumes a parametric form, two adjustments are typically made. First, household members are converted into ‘adult equivalents’, to identify the effective size of the household. The most common adjustment is to assume that children only consume a fraction of the resources of adults. Second, to incorporate the effects of economies of scale, effective household size is weighted by an exponential parameter that is smaller than one (thereby assuming that the cost-savings from living together do not change with household size) (Deaton & Paxson, 1997).

The appropriate adjustments for the costs of children and for economies of scale are likely to vary across countries, depending for example on the costs of schooling and healthcare, and how much households allocate to food consumption or spending on household ‘public goods’. Because food consumption is private, it might be expected that in developing countries, where food forms a large share of the household’s budget and there is less spending on household public goods, the extent of economies of scale will be small (Deaton & Paxson, 1997; Streak et al., 2009). However, for poorer households there may be considerable economies of scale in being able to buy food and cooking fuel (such as paraffin) in bulk, and in sharing the costs of housing and utilities.

There is a large literature which estimates equivalence scales across a range of countries (cf. Danzinger et al., 1984; Deaton & Muellbauer, 1986; Deaton & Paxson, 1998; Lancaster et al., 1999). While there is also a sizeable literature on poverty and inequality in South Africa, particularly in the post-apartheid period, very few studies have estimated equivalence scales for South African households. The exceptions include studies by Woolard (2002) and Woolard & Leibbrandt (1999, 2001) who use data from 1995 and 1993 respectively. These studies estimate equivalence scales for African households with the Engel method, which derives the scales by comparing the share of income that households, of different size and composition, spend on food. The researchers find high costs for children, although they acknowledge that the Engel method may over-estimate child costs, and they find relatively large variation in the economies of scale estimates (the parameter for adult equivalence ranges from 0.81 to 0.99, while that for economies of scale ranges from 0.62 to 0.85).

A bit more attention has been paid to whether poverty profiles in South Africa are sensitive to equivalence scale adjustments (cf. Deaton & Paxson, 1997; Woolard & Leibbrandt, 1999, 2001; Streak et al. 2009). Because poverty lines in South Africa are typically per-capita thresholds, these studies do not consider how poverty rates change with the application of equivalence scales. Rather, they fix the poverty rate using a relative poverty line, and investigate how the profile of the poor changes when the equivalence scale parameters are varied to adjust for economies of scale and for the lower cost of children compared with adults.

A focus in these studies has been whether the poverty rankings among children, adults and the elderly are modified with equivalence scale adjustments. A common finding is that the poverty share of children and the elderly changes with lower child costs and larger economies of scale (which reduce the share of children among the poor and increase the share of the elderly) (Deaton & Paxson, 1997; Woolard & Leibbrandt, 2001; Streak et al., 2009). But these changes are typically small, and the general conclusion, as expressed by Streak et al. (2009:184), is that ‘poverty profiles at the aggregate level are not highly sensitive to the (adult equivalent scale) used’.

These findings perhaps explain why the convention in South Africa has been to measure poverty and inequality by applying per-capita scales. A few of the earliest post-1993 studies tended to follow May et al. (1995) in assuming an economies of scale parameter of 0.9 and that children require half the resources of adults¹ (May et al., 1995, 1998; Woolard & Leibbrandt, 2001). But almost all of the more recent studies, including poverty reports by the central statistical office (Statistics South Africa), measure poverty or inequality using per-capita income or expenditure (cf. Ardington et al., 2006; Hoogeveen & Özler, 2006; Bhorat et al., 2009; Leibbrandt et al., 2010a, 2010b; Statistics South Africa, 2012).²

In this study, we revisit the implications of equivalence scale adjustments by focusing on how these adjustments affect gender differences in income. When an individual’s resources are measured as a share of total household resources, we would only expect to find gender differences in income (or expenditure) when there are also gender differences in household size and composition (because a sizeable share of men and women do not co-reside). We show that this is the case in South Africa where, in comparison with African men, African women on average live in households that are significantly larger and more likely to include children. In contrast to earlier studies for South Africa, we consider not only whether scale adjustments alter the profile of the poor for a given relative poverty line, but also how these adjustments affect women’s income (or the income of households in which women live) relative to men’s income.

3. Data

To estimate gender differences in income in South Africa, we use data collected in a nationally representative household survey from 2008, the NIDS. Conducted by the Southern Africa Labour and Development Research Unit at the University of Cape Town, the survey collected information on a range of socio-economic variables in just over 7300 households, consisting of around 28 000 individuals.

In particular, emphasis was placed in the NIDS on collecting information on income from each individual in the household (rather than relying on a single respondent), and from both employment and non-employment sources of income. The income measure which we use in this study includes net income from wage and self-employment as well as income from government grants (namely, the old age pension, disability grant, child grant, foster child grant and care dependency grant), social insurance (unemployment insurance and worker compensation), private pensions, dividends, interest, rental income, remittances and income from subsistence agriculture (derived from both sales and own-consumption). An implied rental value is also included. (Further details on the construction of the income variable can be found in Argent [2009].)³

The NIDS collected basic demographic information on all individuals who were identified as being members of the household, even if they lived physically in the household for only 15 days of the previous year. However, when measuring household size in this study, we consider only resident household members (those who usually spend at least four nights a week in the household).

To estimate the sensitivity of gender differences in income to adjustments for child costs and economies of scale, we use the parametric form of the adult equivalence scale (AES):where A is the number of adults (16 years and older), C is the number of children (15 years and younger), α is the relative cost of a child and Θ is the economies of scale parameter.

The per-capita scale implies a child cost parameter of α = 1 and an economies of scale parameter of Θ = 1. We consider six different adult equivalent scale adjustments, listed in the following, also distinguishing between the cost of young children aged zero to 10 years (α₁) and older children aged 11 to 15 years (α₂):⁴

• AES1: α₁ = 0.5, α₂ = 0.9, Θ = 1

• AES2: α = 0.5, Θ = 1

• AES3: α₁ = 0.5, α₂ = 0.9, Θ = 0.9

• AES4: α = 0.5, Θ = 0.9

• AES5: α₁ = 0.5, α₂ = 0.9, Θ = 0.7

• AES6: α = 0.5, Θ = 0.7

The range of parameters chosen subsumes most of the parametric adjustments tested in the poverty studies discussed earlier in Section 2 and the scales estimated in the early post-1993 poverty studies.⁵ Using these adjustments, we describe the gender gap in income at the mean and along the length of the income distribution for adult men and women. We also consider whether poverty profiles are sensitive to adjustments for household size and composition. We preface our findings with a discussion of household formation and income in South Africa, and a description of differences in the size and composition of the households in which men and women live.

4. Household structure, income and gender in South Africa

4.1. Household size and composition, and income

There is considerable variation in both household size and household composition in South Africa. Tables 1 and 2 show that approximately 7% of the total population lived alone in 2008, while 25% lived in households with seven members or more. Almost one-quarter of the population were resident members of households with no children (younger than 16 years), while almost one-fifth lived in households where at least half of all household members were children.

Table 1. Household size, per-capita income and poverty rates, 2008

Household size	Percentage of the population	Average per-capita household income	Income ratio (relative to a single-person household)	Percentage poor
1	6.86 (0.29)	3 726.64 (328.82)	1	17.64 (1.67)
2	11.28 (0.33)	2 853.31 (157.93)	0.77	29.33 (1.28)
3	14.78 (0.36)	2 999.16 (253.09)	0.80	42.13 (1.27)
4	16.94 (0.36)	2 043.79 (87.63)	0.55	46.81 (1.13)
5	14.49 (0.32)	1 375.99 (56.57)	0.37	57.17 (1.22)
6	10.49 (0.26)	870.02 (31.78)	0.23	65.19 (1.26)
7 or more	25.15 (0.36)	473.66 (7.92)	0.13	83.09 (0.59)

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses. The poverty line is R664 per month in 2008 prices.

Table 2. Share of children, per-capita income and poverty rates, 2008

Share of children in the household	Percentage of the population	Average per-capita household income	Income ratio (relative to a childless household)	Percentage poor
0	24.83 (0.45)	3 348.44 (152.34)	1	24.17 (0.86)
>0 and ≤0.25	12.56 (0.29)	1 528.64 (75.49)	0.46	46.16 (1.20)
>0.25 and ≤0.5	43.99 (0.46)	1 403.12 (69.46)	0.42	61.91 (0.71)
>0.5 and ≤0.75	17.34 (0.30)	762.52 (82.78)	0.23	83.51 (0.84)
>0.75	1.27 (0.09)	315.36 (21.90)	0.09	92.72 (1.73)

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses. The poverty line is R664 per month in 2008 prices. Children are aged 15 and younger.

The tables show also that household structure is strongly correlated with per-capita household income. First, there is a significant inverse relationship between household size and per-capita household income (Table 1). For example, compared with households with at least seven members, average per-capita household income is eight-fold higher in single-person households, and four-fold larger in households with four members. Consequently, and as is commonly found in a wide range of countries (Lanjouw & Ravallion, 1995), the percentage of households measured as poor increases sharply as household size increases. Poverty rates in the tables are calculated using the rebased upper poverty threshold for South Africa, of R664 per capita per month (2008 prices) (Statistics South Africa, 2015:10). Whereas only 18% of people living alone were poor in 2008, more than 80% of those living in households with at least seven members were poor.

Second, average per-capita household income falls and per-capita poverty rates rise as the share of children in the household increases (Table 2). For example, whereas 24% of individuals living in households without children were poor in 2008, over 80% living in households with a child share greater than 0.5 were poor.

Per-capita measures of income, however, will overstate the relationship between household structure and economic resources. This is illustrated in Table 3, which reports average adjusted household income by household size and the share of children in the household, using one of the six AES measures outlined earlier – the scale used by May et al. (1995) and a number of others in the early poverty literature, where α = 0.5 and Θ = 0.9. Although the decline in average adjusted income by household size and the share of children is still clearly evident, it is far less precipitous. For example, rather than an eight-fold difference in average individual income between single-person households and households with seven members or more, as measured with the per-capita scale, there is a five-fold difference using the equivalence adjustment. Similarly, the income ratio of individuals living in households with no children, and individuals in households in which more than half of all members are children, falls from approximately 4.6 to 3.

Table 3. Average adjusted individual income by household size and share of children in the household

Household size	AES4: α = 0.5, Θ = 0.9	Income ratio (relative to a single-person household)	Share of children in the household	AES4: α = 0.5, Θ = 0.9	Income ratio (relative to a childless household)
1	3 726.64 (328.82)	1	0	3 585.90 (162.74)	1
2	3 123.81 (169.50)	0.84	>0 and ≤0.25	1 989.94 (97.64)	0.55
3	3 820.10 (324.23)	1.02	>0.25 and ≤0.5	1 981.73 (93.14)	0.55
4	2 787.90 (121.69)	0.75	>0.5 and ≤0.75	1 259.71 (133.13)	0.35
5	1 915.00 (73.93)	0.51	>0.75	595.25 (40.68)	0.17
6	1 272.79 (46.28)	0.34
7 or more	723.96 (11.48)	0.19

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses.

Average incomes increase following adjustments for child costs and economies of scale, but the income increase is larger in bigger households with more children, which are also households with the lowest income. As we might expect, this compression of the income distribution leads to a decrease in inequality in South Africa. This is illustrated in Table 4, which shows that the Gini coefficient falls significantly from 0.682 using per-capita income to 0.647 using the last scale adjustment (AES6).⁶

Table 4. Inequality measures using per-capita and adjusted income, 2008

	Gini coefficient
Per-capita scale	0.682 (0.007)
AES1: α1 = 0.5, α2 = 0.9, Θ = 1	0.669 (0.007)
AES2: α = 0.5, Θ = 1	0.668 (0.007)
AES3: α1 = 0.5, α2 = 0.9, Θ = 0.9	0.662 (0.007)
AES4: α = 0.5, Θ = 0.9	0.660 (0.007)
AES5: α1 = 0.5, α2 = 0.9, Θ = 0.7	0.648* (0.006)
AES6: α = 0.5, Θ = 0.7	0.647* (0.006)

Source: NIDS (2008).

Notes: The data are weighted. Bootstrap standard errors are in parentheses.

*Inequality measure is significantly different from the per-capita measure at the 95% confidence level.

4.2. Household structure and gender

If men and women typically co-reside, for example because rates of union formation are high, then we would not expect significant gender differences in household structure or in per-capita household income, and equivalence scale adjustments would not be expected to affect differentially the income of households in which women and men live. Even if women are less likely than men to be employed or they have far lower earnings capacity, these differences will be offset when men and women co-reside, because the calculation of adjusted (and per-capita) household income assumes that all income in the household is pooled. In this case, gender differences in income would derive more from how resources are allocated within households, which equivalence scale adjustments do not reveal, than from differences between households.

However, where many men and women do not live together, there are more likely to be gender differences in household structure; and gender differences in access to the labour market and other resources will be more apparent. In this case, accounting for the size and composition of households may also differentially affect the income of households in which women and men live.

In South Africa, substantial shares of women and men do not live with members of the opposite sex, and this pattern is more pronounced among Africans, the majority population group, than non-Africans. Table 5 shows that among Africans in 2008, approximately 30% of adult women lived in households where there are no adult men, and 29% of adult men lived without any adult women (the corresponding figures are 18% and 11% among non-Africans).

Table 5. Co-residence of adult men and women, 2008

	African		Non-African
	Women	Men	Women	Men
Percentage living without other adult men	30.31 (0.74)	50.07 (0.97)	17.59 (1.66)	55.27 (2.07)
Percentage living without other adult women	37.76 (0.82)	28.63 (0.98)	51.91 (2.00)	11.38 (1.58)
N	7768	5818	2267	1929

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses. Adults are aged 16 years and older.

These living arrangements are explained partly by continuing patterns of temporary labour migration in post-apartheid South Africa (Posel & Casale, 2003; Collinson et al., 2007; Posel, 2010). Although regulations preventing the permanent settlement of Africans in urban areas were lifted by the late 1980s, many individuals continue to migrate to places of employment, leaving partners and children behind, and returning ‘home’ for only a few weeks a year. A further important factor accounting for these patterns of co-residence is the low rate of union formation among Africans in particular. In 2008, over 60% of African women and men had never married, or were widowed or divorced. In contrast, the majority (over 55%) of non-African women and men were married or living together with a partner.

Even though a large share of African women and men live in households without adults of the opposite sex, they do not necessarily live without other adults. However, Table 5 shows that African women are more likely to live with other adult women than African men are to live with other adult men.

These differences help explain why African women live in significantly bigger households, with more adults, than African men (shown in Table 6). However, a more important reason concerns the presence of children. African women are far more likely than African men to co-reside with children: almost 44% of African men live in households without children, compared with only 23% of African women. The average number of children, and particularly young children, is therefore significantly greater in women’s households than in men’s households, and the share of children in total household size is also considerably larger (32% compared with 21%). These gendered patterns in co-residence with children are explained in part by male-dominated patterns of labour migration in South Africa, but also by high rates of non-marital childbirth, with children being far more likely subsequently to reside with their mother than their father (cf. Posel & Devey, 2006; Hall & Wright, 2010).

Table 6. Household size and composition of adult men and women, 2008

	African		Non-African
	Women	Men	Women	Men
Household size
Average household size	5.34* (0.057)	4.54 (0.065)	3.93 (0.081)	3.78 (0.077)
Average number of adults (>15 years old)	3.31* (0.034)	3.14 (0.040)	2.92 (0.052)	2.95 (0.056)
Average number of young children (0 to 10 years old)	1.42* (0.023)	0.93 (0.023)	0.67 (0.038)	0.54 (0.036)
Average number of older children (11 to 15 years old)	0.61* (0.013)	0.46 (0.013)	0.33 (0.021)	0.29 (0.021)
Percentage living with
No other adults (>15 years old)	11.60* (0.57)	19.01 (0.87)	8.48 (1.08)	8.54 (1.48)
No young children (0 to 10 years old)	32.60* (0.80)	52.91 (0.95)	60.14 (1.90)	65.95 (1.92)
No older children (11 to 15 years old)	57.12* (0.80)	67.06 (0.85)	74.27 (1.66)	76.51 (1.73)
No children (0 to 15 years old)	22.96* (0.76)	43.81 (0.99)	47.97 (2.01)	53.21 (2.11)
Share of children in household (number of children/household size)	0.322* (.004)	0.211 (0.004)	0.198 (0.008)	0.167 (0.008)
N	7768	5818	2267	1929

Source: NIDS (2008).

Notes: The data are weighted. Adults are aged 16 years and older. Standard errors are in parentheses.

*Means or shares between men and women are significantly different at the 95% confidence level.

Given gender differences in household size and composition, we would expect equivalence scale adjustments to have more effect on African women’s income (or the income of households in which African women live) than on African men’s income. In contrast, there are no significant differences in the size or composition of households in which non-African women and men live. Although women live in households that are slightly larger and include more children, none of the descriptive characteristics presented in Table 6 is significantly different for non-African women and men.⁷ Consequently, in the remainder of the article we restrict our analysis of gender differences in income to Africans, who constitute 80% of the South African population.

5. Re-estimating the gender gap in income

To illustrate how adjusting for household size and composition affects the gender gap in income⁸ among Africans, we start by comparing the mean incomes of men and women when the per-capita scale is applied, and when the six equivalence scale adjustments are made, as detailed in Section 3.

 Table 7 describes a large and significant gap in average per-capita household income between men and women of almost 38%. In addition to differences in household structure, households in which African women live include significantly fewer employed members on average (0.34 compared with 0.53 among men), and lower levels of earned income (the unadjusted gender gap in average earned income among employed African women and men is 33%).

Table 7. Average income (Rand) and the gender gap among African adults, 2008

Adjustment	Women’s income	Men’s income	Women/men	Gender gap in income
Per-capita scale	918* (30.2)	1470 (78.0)	62.5	37.5
AES1: α1 = 0.5, α2 = 0.9, Θ = 1	1015* (31.6)	1538 (78.1)	66.0	34.0
AES2: α = 0.5, Θ = 1	1057* (33.6)	1573 (78.8)	67.2	32.8
AES3: α1 = 0.5, α2 = 0.9, Θ = 0.9	1141* (35.2)	1665 (80.8)	68.6	31.4
AES4: α = 0.5, Θ = 0.9	1184* (37.2)	1701 (81.5)	69.6	30.4
AES5: α1 = 0.5, α2 = 0.9, Θ = 0.7	1458* (44.2)	1981 (88.1)	73.6	26.4
AES6: α = 0.5, Θ = 0.7	1502* (46.4)	2019 (89.0)	74.4	25.6

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses.

*Means between men and women are significantly different at the 95% confidence level.

With allowances for the lower costs of children, and for economies of scale, average incomes for both women and men increase, but the increase is considerably larger among women. When adjusting only for adult equivalence in AES1 and AES2, average income for women increases by 10% and 15% respectively compared with the per-capita measure. For men, the increases are considerably smaller (4% and 7% respectively) because, as shown earlier, men are far less likely than women to live with children.

Adjustments for economies of scale have an even larger relative effect on women’s income. Holding child costs constant at α₁ = 0.5 and α₂ = 0.9 (an income of R1015), average income for women increases by 12% (to R1141) when adjusting for household size with an economies of scale parameter of 0.9 (i.e. moving from AES1 to AES3). Using the more generous economies of scale parameter of 0.7, women’s mean income increases by 44% (from AES1 to AES5). For men, the economies of scale adjustments result in smaller increases of 8% and 28% respectively (from a base of R1538), because men live in smaller households on average.

These different adjustments have implications for the size of the average gender gap, which falls from 37.5% using the per-capita scale to 25.6% when the largest adjustments are made, namely α = 0.5, Θ = 0.7 (AES6). Although the average gender gap in income remains significant even at this scale, adjusting for child costs and economies of scale reduces the size of the gap considerably, by almost one-third of the per-capita value.

Table 8 compares the average gender gap along the length of the respective income distributions for African men and women, using the per-capita scale, and four of the adjusted income measures. For per-capita household income, for example, household income per person at the 10th percentile of the income distribution for women is R150 and at the 10th percentile of the income distribution for men is R183. The ratio of women’s income to men’s income at this point in their respective income distributions is 82%, with a corresponding gender gap of 18%. The gender gap widens steadily as per-capita household income increases, such that at the 90th percentile the gender gap is nearly 40%.

Table 8. Per-capita and adjusted household income (Rand) by gender, Africans 2008

Income percentile	Women	Men	Gender gap	% change in gap – per-capita base
Per-capita income
10th	150	183	18.0	–
30th	300	387	22.4	–
50th	474	651	27.2	–
70th	801	1 197	33.1	–
90th	1 956	3 250	39.8	–
AES1: adjusted income (α1 = 0.5, α2 = 0.9, Θ = 1)
10th	177	212	16.5	−8.3
30th	355	432	17.8	−20.5
50th	550	725	24.1	−11.4
70th	888	1 266	29.9	−9.7
90th	2 148	3 417	37.3	−6.3
AES2: adjusted income (α = 0.5, Θ = 1)
10th	191	228	16.2	−10.0
30th	381	450	15.3	−31.7
50th	574	750	23.4	−14.0
70th	915	1 306	29.9	−9.7
90th	2 238	3 503	36.1	−9.3
AES3: adjusted income (α1 = 0.5, α2 = 0.9, Θ = 0.9)
10th	206	249	17.2	−4.4
30th	413	495	16.6	−25.9
50th	630	828	23.9	−12.1
70th	993	1 400	29.1	−12.1
90th	2 418	3 617	33.1	−16.8
AES5: adjusted income (α1 = 0.5, α2 = 0.9, Θ = 0.7)
10th	278	328	15.2	−15.5
30th	558	658	15.2	−32.1
50th	830	1 049	20.9	−23.2
70th	1 296	1 736	25.3	−23.6
90th	3 124	4 098	23.8	−40.2

Source: NIDS (2008).

Notes: The data are weighted. The percentiles are derived from the income distribution for Africans.

Equivalence scale adjustments reduce the size of the gender gap along the income distribution. However, adjustments for child costs reduce the size of the gap by more at the lower to middle end of the distribution, while economies of scale adjustments have a more variable effect across the distribution. The reduction in the gender gap is also illustrated in the kernel densities shown in Figures 1 and 2, for per-capita income and adjusted income AE5 (α₁ = 0.5, α₂ = 0.9, Θ = 0.7) respectively. The gap between the distributions for African men and women narrows visibly as adjustments are made for child costs and economies of scale.⁹ Nonetheless, as shown also in Table 8, the gap still widens along the income distribution and remains substantial especially at higher levels of income, across all measures of adjusted income.

Figure 1. Per-capita household income. Source: NIDS (2008).

Figure 2. Adjusted household income (AE5). Source: NIDS (2008).

6. Gender and poverty with scale adjustments

The official poverty thresholds for South Africa are per-capita lines, and if these lines are not adjusted then the application of equivalence scales in the estimation of individual income will automatically decrease poverty rates. Studies which explore the implications of equivalence scale adjustments for measuring poverty in South Africa therefore use a relative poverty line, set at 40% of the national income distribution, and they investigate how the profile of the poor changes with scale adjustments (Woolard & Leibbrandt, 1999, 2001; Streak et al., 2009). We adopt the same approach here and consider how the gender composition of African adults in poverty changes, with a poverty rate set at 40% of each of the national income distributions.

Although scale adjustments narrow the gender gap in income significantly, they have a far smaller effect on the ordering or ranking of African women and men in the bottom four income deciles. Table 9 shows that among African adults in poverty the percentage who is female declines marginally, from 60% using per-capita income to 58.4% using the most generous adult equivalent adjustment (AES6), and the decline is not statistically significant. This finding is consistent with the small changes in poverty profiles found in the earlier studies which focused on children and the elderly.

Table 9. Gender composition of poverty using a 40% relative cut-off, African adults, 2008

Adjustment	Poverty line at 40% (Rand)	Percentage of poor African adults who are women
Per-capita scale	441	60.0 (0.84)
AES1: α1 = 0.5, α2 = 0.9, Θ = 1	519	58.5 (0.85)
AES2: α = 0.5, Θ = 1	548	58.7 (0.84)
AES3: α1 = 0.5, α2 = 0.9, Θ = 0.9	600	58.8 (0.85)
AES4: α = 0.5, Θ = 0.9	632	58.7 (0.84)
AES5: α1 = 0.5, α2 = 0.9, Θ = 0.7	802	58.4 (0.84)
AES6: α = 0.5, Θ = 0.7	834	58.4 (0.85)

Source: NIDS (2008).

Notes: The data are weighted. Standard errors are in parentheses. Adults are aged 16 years and older.

There is a small amount of churning in which women and men, identified as poor using per-capita income, are identified as non-poor when scale adjustments are applied, with 5 to 7% of women and 3 to 7% of men moving above the 40% threshold. As we would expect, those who switch out of poverty come from significantly larger households with more children (and conversely for those moving below the threshold).

7. Discussion

Most studies of poverty and inequality in South Africa do not adjust for differences in household composition or the possibility of economies of scale in the household, and simply deflate household income by household size. This approach is adopted both for reasons of convenience and because of research which shows that when the poverty rate is fixed, the profile of the poor is mostly not sensitive to scale adjustments.

In our study of gender differences in income among Africans, we find similarly that with scale adjustments there are only small changes in the gender composition of the poorest 40% of the population. However, we find sizeable changes in the gender gap in income: differences in the income of households in which African women and men live narrow considerably with larger adjustments for economies of scale and for the consumption needs of children.

Differences in income are not significant among non-African women and men, who are more likely than Africans to live in households with members of the opposite sex. These differing patterns of co-residence are explained partly by very low rates of union formation among African men and women and also by persistent patterns of ‘temporary’ labour migration enforced under apartheid, where for reasons of employment African migrants continue to live apart from family members for most of the year. Because of this low co-residency there are significant overall differences in the size and composition of the households in which African women and men live, while this is not the case among non-African women and men.

African women live in households that are larger, mostly because African women are considerably more likely than African men to live in households with children. These gendered patterns in living arrangements in South Africa have been documented widely from the perspective of children: with low rates of union formation, high rates of non-marital childbirth and male-dominated patterns of labour migration, African children are far more likely to live in households with their mother than with their father. Because African women overall live in larger households than African men, where children also comprise a larger share of household members, scale adjustments reduce the effective size of households by more among women than men. Consequently, the application of these adjustments increases the income of households in which women live by more than the income of households in which men live, significantly reducing the size of the gender gap in income along the length of the respective income distributions.

Although scale adjustments reduce the size of the income gender gap by up to one-third of its size, large gender differences in income remain, particularly at the upper end of the income distribution. This is because the gender gap in income derives not only from differences in household structure, but also from differences in the employment probabilities and earnings potential of men and women in the labour market.

Exploring the implications of household structure for the gender gap in household income is an important exercise in trying to better approximate differences in economic welfare. However, there are a number of limitations that also need to be recognised in the application of simple equivalence scales to money-metric measures of welfare. Adult equivalent parameters are not sensitive to variation in consumption needs among children of a particular age, or to variation among adults. Some children may require more resources to sustain them than other children, just as some adults may require more resources than other adults (depending on illness, pregnancy or the level of physical activity, for example). More generally, money-metric measures of welfare based on the household’s access to resources do not consider the actual use of the resources in the household and their distribution. These measures therefore would not be sensitive to an inequitable distribution of resources within the household, by gender or by age for instance. Moreover, although the direct economic costs of sustaining children may be smaller than the consumption needs of adults, the care of children also involves indirect costs (such as earnings foregone), which money-metric measures of gender differences will not reflect. Nonetheless, our study suggests that given the large variation in household structure in South Africa, and the association between household structure and economic resources, more attention should be paid both to the estimation and to the application of equivalence scales in studies of inequality in South Africa.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹May et al. (1995) based these values on a generalised scale for developing countries, suggested in a draft version of Deaton (1997).

²Some studies state explicitly that they do not apply equivalence scales because of research which shows that equivalence scale adjustments do not affect the identification of vulnerable households in South Africa (Bhorat et al., 2009). Two recent exceptions are studies by Tregenna (2012) and Tregenna & Tsela (2012). Tregenna (2012) uses the 2005/06 Income and Expenditure Survey data and shows that the income poverty gap falls substantially, by about 80% (or four billion Rand) when income is adjusted by equivalence scales. Using the same data, Tregenna & Tsela (2012) find that income and expenditure inequality measured with adjusted income is significantly lower than per-capita inequality measures.

³The income measure in the NIDS that we use (and that is commonly used in studies which analyse the NIDS data) includes imputed values for missing observations. We tested the sensitivity of our results to these imputations and found that, when using a measure of income without the imputed values, our overall findings on the implications of equivalence scale adjustments remain robust.

⁴For illustrative purposes, a child cost parameter of 0.5 assumes that a child will need 50% of the resources of an adult for the same level of welfare. An economies of scale parameter of 0.9 assumes that doubling the household size (from one to two adults) requires an increase in household income of 87% (2^0.9= 1.87) in order to maintain the same level of welfare. A value of 0.7 implies even greater economies of scale because the same household would need an increase in income of only 62% (2^0.7 = 1.62) to maintain its standard of living.

⁵In trying to contextualise the scales commonly adopted in South Africa, Woolard & Leibbrandt (1999) note that the World Health Organisation recommendation for the caloric requirements of a child seven or eight years old is 64% that of an adult male. In determining a Household Subsistence Level for South Africa, Potgieter (1995) estimated that a 10-year-old child would require 68% of the resources of an adult male for food and clothing. However, any choice of scale will ultimately involve an element of arbitrariness, which is why it is useful to consider a range of plausible scales.

⁶According to Atkinson (2003), a change in the Gini coefficient of three percentage points or more can be considered ‘economically significant’. The fall in the Gini coefficient shown here, of approximately 3.5 percentage points (from 0.682 to 0.647), therefore is not only statistically significant, but also economically significant. To contextualise this further for South Africa, Anand et al. (2015) estimate that to achieve a two percentage point reduction in the Gini coefficient would require reducing unemployment in South Africa by 10 percentage points or increasing government transfers by 40% (based on data from the 2012 NIDS).

⁷In addition to not finding significant differences in household size and composition by gender for non-Africans, we also do not find significant differences in per-capita or adjusted income between non-African men and non-African women (not shown here).

⁸We present only income data in this study, but our findings are robust to using expenditure as the measure of economic resources.

⁹The reduction in inequality between African women and men helps to explain why inequality among Africans falls, with scale adjustments, from a Gini coefficient of 0.6 with per-capita income to 0.55 when adjusted-income AES5 and AES6 are used.