1 Introduction
In this paper, we revisit the estimation of equivalence scales taking into account the fact that expenditure shares on food, clothing (adult/child) or even housing may not represent household welfare, and, therefore, the scales calculated from those shares following, for example, Deaton (
1997), Pendakur (
1999), Yatchew et al. (
2003) or Dudel et al. (
2021b) could be biased. Nicholson (
1976), in particular, argues that child cost estimates from such data can be overstated, implying biased equivalence scales, because children primarily consume food and clothing.
Instead, we rely on self-assessed household food, clothing and housing “adequacy”, arguing that households not able to meet their basic needs are necessarily achieving lower levels of welfare than those who do meet those needs. Pradhan and Ravallion (
2000) suggest a similar approach to the estimation of subjective poverty lines, which they estimate for Jamaica and Nepal. Lokshin et al. (
2006) apply that thinking to compare subjective and objective poverty lines in Madagascar, where they specifically refer to consumption adequacy questions (CAQ), which are similar to those used in this analysis. We were only able to find one other paper, de Ree et al. (
2013), that uses CAQ to consider equivalence scales, although their primary focus is on price and utility dependence in the estimation of such scales, rather than the difference between objective and subjective scales, as is our focus here. For the most part, the literature has not used CAQ for the estimation of equivalence scales; instead, it has used other subjective queries, such as those related to life or income satisfaction or even minimum income needs, as we discuss in more detail, below.
Taking the concepts developed by Pradhan and Ravallion (
2000), we estimate the compensation required for households of different types to have an adequate supply of basic needs, which we translate into equivalence scales for different household types. For comparison purposes, we also estimate equivalence scales from expenditure shares on the same goods. The analysis is predicated on the South African 2014/15 Living Conditions Survey (Stats SA,
2017), because it is the most recent survey that captures the relevant information.
In summary, we find that basic needs security leads to subjective scales that are consistent across types of need, which is in sharp contrast to scales calculated from basic needs expenditure shares, at least in this analysis; this could be due to the removal of potentially discretionary expenditure (Daley et al.,
2020). Our subjective scales result in economies of scale and positive weights for both children and adults. We also find that scales for children tend to be larger in multiple-adult households than in single-adult households, and that is especially true for the first child. Our estimates are relatively consistent with a household scale economy of 0.5, and are generally lower than they would be if we had instead, applied the modified OECD scales. Finally, we find that scales, at least those we find to be more plausible, do not change all that much after including the control function.
2 Literature Review
It is common to estimate equivalence scales from microdata on consumption, especially food consumption, which is widely available in expenditure surveys around the world. Such estimates still tend to focus on developed countries as a recent series of papers focusing on Germany (Dudel et al.,
2021a,
b; Garbuszus et al.,
2021) and Canada (Pendakur,
2018) demonstrates. There is a related literature underpinned by time use data. Bradbury (
2008) uses both time and expenditure costs, finding relatively larger child costs than are underscored by consumption share analysis, alone. Borah (
2020) also incorporates time use data and subjective income satisfaction data, finding greater monetary equivalence weights for adults than for children, while household production increases are associated more with children than with adults. Combining these two leads to rather similar child and adult weights in the equivalence scales. On the other hand, Couprie and Ferrant (
2015), who focus on additional time needed, rather than full time costs, find that two singles living apart need about 2h15m additional free time to match their utility as a couple living together; however, the analysis did not consider children.
Not all consumption based estimation focuses on developed countries. Recent work, such as Daley et al. (
2020), includes a number of years and countries, including South Africa, which is our focus. South African focused studies also exist; see, for example, Yatchew et al. (
2003), Posel et al. (
2020) and Koch (
2022). Although Daley et al. (
2020) do not believe the square-root scale is appropriate, Koch (
2022) finds robust empirical support for it, when considering South African food shares. Therefore, we provide further clarity on the appropriateness of that scale in this analysis. Daley et al. (
2020) also find differences across countries and time, as well as across consumption bundles. In particular, they find larger economies of scale when considering necessities other than food, except for South Africa, where they suggest that consumption bundles for smaller families might include discretionary spending. We offer additional insight into commodity-based scale differences in the country, and, through the use of subjective measures of basic needs adequacy, we remove the potential for discretionary spending among all households, which we find yields more similarity in the underlying scales across goods types.
The literature has also developed equivalence scales from other subjective measures of well-being, including income satisfaction, minimum income needs and life satisfaction. van Praag and van der Sar (
1988) show that income evaluation questions like those in van Praag (
1971) may be used without assuming cardinal utility. Income evaluation questions request survey respondents to declare net income amounts that they would regard as very good, or sufficient or even very bad. A similar approach makes use of minimum income questions, which attempt to extract “the smallest amount of income that would be needed by the household to make ends meet each month” (Goedhart et al.,
1977). In much of this analysis, the reported minima increase with actual income, which Goedhart et al. (
1977) suggest is related to the need to make additional fixed payments, such as mortgages, although other interpretations are also offered. Since these survey questions require respondents to generally address hypothetical scenarios, the answers may not accurately reflect what is being requested (Bradbury,
1989; Melenberg and van Soest,
1996). Steiger et al. (
1997) suggest that the cognitive tasks in answering these seemingly simple survey queries are, in fact, quite complex.
The hypothetical nature of the queries has been addressed in at least two different ways. One approach focuses on finding individuals whose minimum income matches their actual income. At the intersection of needs and actual (Goedhart et al.,
1977), one can explicitly focus on households in poverty and avoid preference restrictions. Hartog (
1988) specifically argues that welfare cardinality is not necessary; rather, we only need assume that there is a “common, interpersonally comparable feeling of welfare” of enough to get along. This argument is formalized as ordinal local comparability by Grodner et al. (
2022), and leads to local equivalence scales. Essentially, ordinal local comparability is the ability to make comparisons only at a specific point, mininum needs income, and offers further support to the intersection method that is generally applied in that literature; see Goedhart et al. (
1977), Kapteyn et al. (
1987), Bishop et al. (
2014) and Mysíková et al. (
2022), for example. Kapteyn et al. (
1987) find that the subjective evaluations lead to implausibly low family cost parameters, which imply very flat equivalence scales across household structure measures. Bishop et al. (
2014) and Mysíková et al. (
2022), present comparisons of subjective equivalence scales (from minimum income questions) across Europe. The former finds that there are greater economies of scale in developed welfare states, while the latter suggests that there is an East–West divide in the economies of scale. Both argue that subjective scales are different from modified OECD scales, lead to poverty rate differences, and that child costs are not as low as those in Kapteyn et al. (
1987).
The second approach uses income or life satisfaction for scale estimation. Doing so has yielded lower economies of scale than those arising from the preceding minimum income questions, with life satisfaction leading to some of the lowest scales (Melenberg and van Soest,
1996; Charlier,
2002; Schwarze,
2003; Biewen and Juhasz,
2017). Charlier (
2002) finds that satisfaction with income scales increase with household size, and, therefore, are somewhat reasonable. Despite potentially addressing the hypothetical nature of minimum income questions, subjective well-being depends heavily on perceptions; Bradbury (
1989) offers a relatively early review arguing that reference group effects are important in these analyses and may be systematically related to family type. In the literature, reference effects are underscored by a benchmark relative to oneself or even to others (Clark et al.,
2008), income aspirations (Stutzer,
2004) and other features. Stutzer (
2004) finds that subjective well-being depends on the gap between income aspirations and actual income, not on the income level as such; the higher the gap, the less satisfied. In other words, respondents are likely to conflate both their own views and societal references (Stutzer,
2004; Clark et al.,
2008). Ferrer-i-Carbonell (
2005), for example, consider three separate measures—own income, reference income and the gap between own and reference.
Given the possible confounding factors, extracting equivalence scales from subjective measures requires researchers to estimate appropriate reference groups; otherwise, the subjective view may not reflect what is required for equivalence scales (Borah et al.,
2019). The literature suggests that a variety of comparisons, such as reference income from similar individuals (Ferrer-i-Carbonell,
2005) or from Mincerian earnings equations (Senik,
2008; Borah et al.,
2019) are relevant. However, (Boyce et al.,
2010) find that income rank is more important for life satisfaction than absolute income. Income gaps (D’Ambrosio and Frick,
2012) are also relevant, because households feel better off when they are relatively richer and worse off when they are relatively poorer. Furthermore, there may be a dynamic component with respect to relatively newer rich and poor households in the comparison group. This dynamic aspect might have two effects, one that is negative—due to relative deprivation - and another that is positive, as it suggests anticipatory possibilities (Senik,
2008). A simpler descriptor is “jealousy” and “ambition”, the former of which underscores old European sentiments, while the latter is uncovered in America and the former eastern bloc of Europe (Senik,
2008). Even though these subjective approaches do not require utility cardinality, and, therefore, ought to be relatively straightforward, the applied literature suggests that, empirically, it is anything but straightforward.
As highlighted at the outset, we focus on (self-assessed) food, clothing and housing adequacy—in other words, a respondent in the household replies that the household has “less than adequate”, “adequate” or “more than adequate” food, clothing or housing available. Similar to self-assessed life satisfaction or income adequacy, the responses are ordinal, and, therefore, do not require cardinality assumptions. Although it is beyond the scope of this research to compare equivalence scales derived from basic needs consumption adequacy to those derived from minimum income or life satisfaction questions (and we are not aware of any research attempting to do so), Pradhan and Ravallion (
2000) argue that one advantage of CAQ is that individuals, especially the poor, may struggle to understand what income is, and, therefore, will not be in a position to define their income needs. It also seems that answering a CAQ question for the entire household is likely to be an easier task than answering a life satisfaction question for that household; it is likely that hungry members of the household will voice their hunger, for example, which might require less interpretation with respect to adequate food consumption than with an exact location on a scale of life satisfaction or income satisfaction. However, because CAQs are self-assessed, we remain concerned that respondents will conflate their views with reference effects. As noted so far, the literature suggests a range of potential reference options. In practice, since the exact choice of reference is not known, the application of any reference effect will necessarily be measured with error. Therefore, rather than applying a specific reference effect, we apply a control function method accounting for the expectation that the suggested reference offers a noisy measure of the true reference effect.
We contribute to the literature in numerous ways. We offer one of the few studies of subjective equivalence scales that is available for developing countries, and the first of which we are aware for Africa. The only developing country studies applying subjective approaches that we could uncover are for Mexico (Rojas,
2007), which finds that an increase of 40% in household income is required to keep a person’s economic satisfaction constant when a second member is added, and Indonesia (de Ree et al.,
2013), which are found to be larger than those derived from a modified OECD scale (Hagenaars et al.,
1994). We diversify the literature away from subjective well-being, defined either by minimum income evaluations, life or income satisfaction, focusing on more fundamental basic needs, such as the adequacy of food, clothing and shelter. This diversification in subjective measures affects the choice of reference measures. We do not use income gaps or Mincerian earnings to underscore reference group proxies, which is rather common in the literature, because we need to proxy for needs adequacy rather than income adequacy; thus our focus will be on needs expenditure, which we assume is a noisy measure of reference effects. We also offer further insight into the apparent disagreement in the literature on the square-root scale in South Africa (Daley et al.,
2020; Koch,
2022). Through the use of basic needs (in)security, we remove the potential concern that smaller households have relatively larger discretionary expenditures. Finally, we present a formal comparison of the plausibility of the shares arising from both the subjective analysis and the more traditional share-based analysis, which has not received previous attention in the estimation of scales in developing countries.
4 Data
The preceding methods are applied to data taken from the South African Living Conditions Survey (LCS) 2014/2015 (Stats SA,
2017), which is collected to help understand living conditions and poverty in South Africa. Although a similar survey was conducted in 2008–09, the LCS is cross-sectional. It is useful for our analysis, because it captures all of the relevant data, including the adequacy of consumption on food, clothing and housing, as well household expenditure, expenditure on particular types of goods, household size and structure and some information on gender, ethnicity and household location. We defined children to be 15 years and under, which is also the age at which individuals are allowed to leave school, according to Republic of South Africa (
1996). The survey covered 23,380 households containing 88 906 individuals (which is limited to individuals residing in the household at least four nights per week); the reported response rate for the survey was 84.9%.
The adequacy questions were asked at the household level, thus answers come from only one individual. The question was asked in the following format, “During the month prior to the survey period, what was your household’s standard of food consumption/housing/clothing?”.
4 Expenditure and income information follows classification of individual consumption by purpose (COICOP) categories. Food expenditures lie in Category 01, clothing expenditures lie in Category 03, while housing expenditures are in Category 04. These expenditure categories match the basic needs categories, and, thus are appropriate for the analysis. Every subcategory of expenditure is summed within a household; however, we do not include food purchased away from home in the food expenditure. Although our focus is on consumption adequacy and expenditure shares for the calculation of scales, the data includes an income satisfaction question, a minimum income question and a living standards question, which could also be used for the estimation of equivalence scales.
In this data, there are few differences between total consumption and total consumption in-kind. For the analysis, we use household consumption expenditure capturing both monetary and in-kind payment for all goods and services, as well as the money metric value of the consumption of home services. The primary service captured is rent, which is set at 7.5% of the reported value of the building. The LCS data is collected for 12 months, with different samples in different provinces; in other words, we do not have repeated observations for any household. We inflate/deflate expenditure values to April 2015, the midpoint of the survey year, using the consumer price index.
5
8 Discussion
With this research, we have presented the first, of which we are aware, subjective equivalence scales for Africa, based on consumption adequacy. It is also one of the few studies of subjective equivalence scales that is available for developing countries – we are only aware of Rojas (
2007), who estimates subjective scales for Mexico and de Ree et al. (
2013), who consider the potential for price and utility dependence in equivalence scales using Indonesian data. Rojas (
2007) finds that an increase of 40% in household income is required to keep a person’s economic satisfaction constant when a second member is added, while a 20% increase is required to keep a person’s economic satisfaction constant when a sixth person is added to a five-member household. Although we follow a different approach, our estimates are not directly comparable to the linear 40% estimate. However, our food share equivalence estimates imply a required income increase of 35–40%, while our adequacy scale estimates imply a required income increase of 25–40% for the first additional adult. However, if the second member of the household is a child, the figures are closer to half of that. On the other hand, we report a range of estimates for five-member and six-member households. For example, if the sixth additional member is an adult that has been added to a three-adult and two-child household, the scale estimates (using endogenous food shares) increase from 2.20 to 2.24 or 1.96 to 2.08 (implying only a few percentage points). If we look across food, housing and clothing adequacy scales, the implied required percentage point increase in income ranges from 1.2% (2.617–2.650, exogenous housing adequacy) to 15.1% (2.371–2.736, exongeous food adequacy). Thus, our approach offers a wider number of scales, and, therefore, a less simplistic interpretation.
de Ree et al. (
2013) do not present scales in as much detail as we do here, and, therefore, an across the board direct comparison is more difficult to make. However, they suggest that their scales for Indonesia are larger than those implied by the OECD-modified scales. The modified OECD scale (Hagenaars et al.,
1994) suggests equivalence weights of 1.0 for the first adult, 0.5 for the second and each person over the age of 14, and 0.3 for each child under 14. Despite the fact that our child/adult threshold is 15, and, therefore, not identical, our most plausible scales—those from food shares, as well as those derived from consumption adequacy—are everywhere below the implied modified OECD adjustment that would be computed for the household. Thus, our consumption adequacy scales are also smaller than those estimated for Indonesia.
Previous literature has presented a range of scale estimates (focusing on expenditure data) for South Africa. Two of the most recent disagree on the appropriateness of the square-root scale (Daley et al.,
2020; Koch,
2022). Our adequacy-based scales suggest economies of scale within the square-root region, and, therefore, is in agreement with Koch (
2022); however, these same estimates suggest child costs much less than one (nearer 0.5). Thus, when combined, our subjective-based equivalence scales are relatively smaller than any scales previously estimated for South Africa (including the square-root scale). That conclusion is not entirely dissimilar to what has been uncovered by other subjective-scale research. Although Charlier (
2002), for example, does find that satisfaction with income yields scales that increase with household size, Kapteyn et al. (
1987) find that the subjective evaluations lead to implausibly low family cost parameters. In our view, our estimates are not implausibly low, although they may represent a lower bound. Additional subjective scales comparisons are necessary to offer further insight.
Our basic needs security subjective scales are consistent across types of need, which we did not find with expenditure shares on the same types of need. Possibly, the difference arises, because subjective needs remove any discretionary expenditure that might be incorporated into objective expenditure share measures (Daley et al.,
2020). Furthermore, across the board, we find smaller equivalence scales for housing adequacy, compared to food and clothing adequacy. Such differences are not entirely surprising, due to the fact that both clothing and housing are less private than food; clothing has some durability (across generations, for example), and, is widely available used, while space within a house can be reallocated. For example, although Frazer (
2008) focuses on the manufacturing reduction associated with charitable clothing donations, the reduction is extensive and arises from reduced demand. Therefore, at any level of clothing adequacy, we would expect reduced clothing expenses. Such donations, especially if they are not recorded as ‘in-kind’ expenditure, and their impact on clothing expenditure (shares) offers one explanation for the observation that clothing share equivalence scales are not entirely plausible, at least in this analysis.
Furthermore, although we do not have a statistical criteria for judging the following comment, our simple counting approach suggests that clothing and housing share based estimates are implausible. In no case do we find plausibility scores better than 50%. On the other hand, the food share, food need, clothing need and housing need all have similar plausibility scores. As implied from the preceding discussion, the similarity of the scales derived from these different approaches, lends further credence to their plausibility. However, there is an obvious caveat: improved plausibility does not necessarily equate with correct.
Our results also suggest that endogeneity matters, although not enough to yield big differences in the scales, especially when it comes to subjective-based scales. We did find rather large differences in the scale estimates between endogenous and exogenous clothing and housing expenditure share models, however. For clothing and housing expenditure share, controlling for endogeneity increased the estimated scales; in some cases that increase was implausibly large. On the other hand, for food and clothing adequacy, endogeneity led to small increases in the share—the endogeneity effect was also small, but in the opposite direction for housing adequacy.
In the adequacy models, there are two potentially endogenous components. The first is associated with household expenditure, where the endogeneity correction was always negative, and was larger in absolute value for food adequacy than clothing, which was also larger in absolute value than it was for housing. The second was the reference effect correction, which led to the inclusion of the household’s expenditure share, as well as a control function to address the possibility that the expenditure share, as a proxy for reference effects, is measured with error. The sign of the expenditure share effects varied, although the control function component was always positive. Due to the multiple endogeneity components, as well as the signs of the endogeneity corrections, the exact direction of the endogeneity effect was not obvious.
As we have seen, all of the results suggest a non-monotonic pattern to marginal equivalence costs for both adults and children. Although this non-monotonic pattern may simply be a feature of South African households, or this particular data, additional research is needed. Such research can consider other developing countries and non-linearities associated with income/expenditure, the latter of which could even be utility or price dependent.
9 Conclusion
In this research, we have examined equivalence scales in South Africa making use of relatively standard approaches that rely on expenditure shares, as well as on self-assessed basic needs adequacy. Under the assumption that adequate food, clothing and shelter are needed for survival, the adequacy of these basic needs are plausible measures of welfare. Furthermore, they have the potential to be used to determine the required increase in income/expenditure that would allow an average household to reach adequate access to these basic survival needs. We exploit that thinking, and estimate categorical outcome models, which we use to indirectly estimate the aforementioned required increase, and, thus, equivalence scales for different types of households. We present those scales in a series of tables for each of our different measures: (1) actual expenditure shares on basic needs, and (2) self-assessed adequacy of basic needs.
Our approach has offered some diversification to the literature, in the sense that our subjective measures focus on perceived adequacy of basic needs (food, clothing and shelter), rather than on minimum income needs, income satisfaction or general life satisfaction. When using minimum income or life satisfaction, researchers have paid attention to potential reference groups. It was expected that self-assessed adequacy also suffers from reference effects, and, therefore, our diversification was not undertaken to eliminate such effects. Our results also suggest that these effects matter, although they do not materially influence the resulting scales. Approaching the problem via an estimate of the ability of an individual to meet their basic needs has a long history in psychology, however. It has been argued that being on the bottom rung of a hierarchy of needs is an important component of the psyche, and, therefore, welfare (Maslow,
1943); in this research, inadequately met food, housing and clothing represents that bottom rung.
Our results suggest that both housing and clothing expenditure shares are inappropriate welfare indicators, and that scales resulting from such models are more likely implausible than plausible, at least in South Africa. On the other hand, food expenditure shares, as well as food, clothing and housing (in)adequacy, appear to be better candidates. They yield similar scales and similar plausibility scores, regardless of whether we control for potential endogeneity. The adequacy scales are generally less than the food share scales, regardless of household structure, and for the exogenous and endogenous scales. Once controlling for endogeneity, the scale differences across goods are generally lower. Finally, the endogeneity/exogeneity differences between scales tend to be relatively small compared to the overall estimated scale variability across the scales.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.