Issues in inequality in non-income dimensions

Achin Chakraborty

Institute of Development Studies Kolkata
1, Reformatory Street, 5th Floor
Calcutta University Alipore Campus
Kolkata 700 027
India
achinchak@rediffmail.com

Abstract
There are two basic approaches to measuring inequality in non-income dimensions. One views inequality as variation of an outcome indicator across individuals and the other views inequality as essentially disparities across socioeconomic groups. While the latter view now dominates the inequality measurement in health, measurement of education inequalities has so far taken the first view. In this paper, we have argued the importance of reckoning inequality in socio-economic group terms and advocated use of an ‘education concentration index’ exactly in the same way as the health concentration index measures socio-economic inequalities in health. The index has been applied to the Indian data to reckon two kinds of inequalities in educational attainment (years of education) – one across economic classes and the other across socially identified groups such as the Scheduled Tribes, Scheduled Castes and others. We find a strong correlation between the two types of inequalities across the states of India. We also find, as one would expect, that the inequality index values are negatively correlated with the average years of education. However, in actual policy context, analysis of the outliers might be more illuminating than studying the general pattern.

1. Introduction
Inequalities in the specific dimensions of human functioning, such as health and education, have been drawing increasing attention of researchers and policy analysts in recent years. What is behind this growing attention is perhaps the view – which James Tobin introduced as ‘specific egalitarianism’ – that certain specific scarce commodities should be distributed less unequally than the ability to pay for them. As Tobin observed, the ‘social conscience is more offended by severe inequality in nutrition and basic shelter, or in access to medical care or to legal assistance, than by inequality in automobile, books, clothes, furniture, boats’ (Tobin, 1970). Although Tobin’s focus was on egalitarian distribution of certain specific scarce commodities, there is no automatic connection between egalitarianism in the space of commodities and that in the space of human functionings, as Amartya Sen has long been pointing out (Sen, 1980).

While concerns for inequality in specific dimensions are now common, attempts to measure such inequalities have not been matched by thorough discussions of the ethical underpinnings of such measures. Even when income inequality increases within a country, for example, as average income increases, inequalities measured in terms of certain indicators of human development, such as life expectancy or gross enrolment ratio across population sub-groups may decrease for the obvious reason that the commonly-used indicators of health or education are fundamentally different from income in one very important respect. It is always true that as the average value of an indicator like literacy rate, mean years of schooling, or ‘average life span’ for the whole population increases, inequality among sub-groups of population decreases. This happens because unlike income all these indicators have a natural upper limit. Does it then mean that instead of worrying about disparity in human development indicators we should focus only on income inequality? We argue in this paper that there is a variety of specific aspects that are ethically relevant in the context of non-income dimensions of well-being, and these ethically relevant aspects are not deducible in a straightforward way from the moral arguments against income inequality that we are familiar with. This has important implications for the ways we measure inequality in non-income dimensions.

2. ‘Pure’ inequality versus socio-economic inequality
Measures of inequality suitable for a particular dimension of achievement may not be equally suited to measure another, primarily because underlying any measure of inequality is certain notion of justice. The choice of an inequality measure should in fact be regarded as a choice among alternative definitions of inequality rather than as a choice among alternative ways of translating a single conceptualization into some measure. The properties of the most popular measure of income inequality – the Gini coefficient – for instance, conform to a certain notion of distributive justice. Application of the Gini measure in other contexts may require suitable modifications of the measure, and interpretations of the results also have to be made carefully. The ethical properties of a measure would determine how ideal it would be for a given measurement task.

If we treated inequality in the distribution of a non-income attribute in the same way as we do in the case of income, we could apply the Gini to measure ‘pure inequality’ in a population. There had been some earlier attempts to adjust some average achievement level for inequality. Hicks (1997) proposed to calculate Gini coefficient for the distribution of what he called the ‘life-span achievement’, and with the Gini coefficient thus calculated adjust life expectancy for inequality. The distribution of age-at-death, he argued, reflected the inequality of life-span achievements, since life-spans range from infants who die at birth or before age one, to persons who die at ages over 100 years. Hicks’ approach is fraught with a number of problems. First, from the age-at-death statistics one can obviously calculate some descriptive measure in inequality, but the normative implications of such an exercise remain unclear. In the case of income inequality, the Lorenz curve in terms of income has meaningful interpretation as far as our shared egalitarian values go. Bottom 10 per cent of the population enjoying, for example, 10 per cent of total income has immediate egalitarian connotation. This is not the case with age-at-death distribution, since in this case the so-called ‘line of perfect equality’ has little intuitive meaning. Second, a general application of Gini measure would ignore the biological asymmetries in survival chances between groups of people. It is well-known that, given equal care, women tend to have lower age-specific mortality rates than men do. A society which treats its people equally irrespective of their gender may produce a higher value of Gini coefficients compared to the other where the survival chances have been ‘equalised’ through unequal treatment of men and women. Thus it makes little sense to treat actual death distribution independent of the distribution of potential life in the biological sense[1].

Apart from the specific problems that the indicator of life expectancy confronts while reckoning inequality, the general issue is whether we should go for ‘pure’ inequality measures, such as the coefficient of variation or the Gini coefficient for the distribution of ‘life-span achievements’ among individuals, or we should measure the inequality in the distribution of a health indicator across socio-economic groups. The Gini coefficient had been applied earlier by others to measure pure health inequality (Le Grand, 1987). However, in much of the literature since the 1990s on health inequality or equity, it is the latter idea that has been more popular.

There is now a growing body of literature which deals with the measurement of the socioeconomic inequality of health. The question that underlies this line of inquiry is: To what extent are there inequalities in health that are systematically related to socioeconomic status? Different indicators have been proposed for the measurement of this type of inequality. Among health economists the index that is widely perceived as the best available one to measure socio-economic inequality of health is the ‘concentration index’, which was first proposed by Wagstaff et al. (1991). The idea is very close to that of the well-known Gini coefficient, yet the two differ. The concentration index is based on the ‘concentration curve’, exactly in the same way as the Gini coefficient is related to the Lorenz curve. An impressive number of studies are now available, which suggest that the health concentration index provides useful insights into important aspects of the socioeconomic inequality of health.

For the concentration curve, the X axis represents the cumulative proportion of the population belonging to different socio-economic groups arranged in a hierarchical manner, beginning with those who belong to the lowest socio-economic level. The Y axis represents the cumulative share of total health outcome for these groups. If the concentration curve coincides with the diagonal, it indicates that people across all socio-economic groups enjoy the same level of health.

Literature on the measurement of inequality in other dimensions of human functioning can hardly match the fast growing literature on measurement of health inequality. Egalitarianism in educational attainments has been justified on several grounds, highlighting both intrinsic and instrumental roles of education. While education is instrumental in bringing about other kinds of real freedom that people have reason to value, it also constitutes human development, as ‘being knowledgeable’ is considered to be one of the most valued human functionings. However, there have been very limited attempts so far to capture quantitatively inequality in educational achievements. The few studies that have so far focused on inequalities in education have used either standard deviation or some version of the Gini coefficient. In other words, they all attempted to measure ‘pure’ inequality rather than socio-economic inequality. Birdsall and London (1997) used standard deviation of schooling to show that there was a negative correlation between education dispersion and income growth. Thomas et al (2001) apply what they call education Gini index to measure inequality in school attainment for a large number of countries.

We take a departure from this line of evaluative exercise. To our knowledge, no study has so far made any attempt to apply a comprehensive measure similar to health concentration index to assess socio-economic inequality in educational attainment. No matter how we choose to measure it, we argue that there are several reasons why inequality in education should rather be measured with respect to different socio-economic groups. First, the moral significance of ‘pure’ inequality in educational attainment as measured by the education Gini index of Thomas et al is not clear. As education Gini measures inequality in educational attainment across all individuals, its value will be zero when everyone has the same level of attainment. Does it mean that societies should strive for this kind of equality? Strict equality of outcome of this kind is not an attractive view. Almost always inequalities in health or education refer to inequality in outcomes. Yet, equalizing outcome can hardly be a practical goal of any egalitarian policy. An objective to attain equal educational attainment across individuals would have to completely ignore the role of personal choice and effort. It would be more meaningful to focus on the socio-economic determinants of outcome inequality which are beyond individual’s control. If the average attainment of a certain group systematically lags behind others we have reason to be morally concerned. Equality would then mean that an individual’s ability to receive the minimum normative length of schooling should depend neither on her ability or willingness to pay nor on the social group which she belongs to. In other words, although it is possible to measure ‘interpersonal distribution of years of schooling’ along the lines of interpersonal distribution of income, it would be more meaningful to conceptualise inequality in this case across social and economic groups.

There is an important policy implication that can be drawn from a focus on inter-group inequality in educational achievement. If we consider equality of opportunity as a desirable goal, we should equalize the educational achievements of all socio-economic types, but not equalize the achievements of individuals within types, which differ according to effort expended (Roemer, 1998). To tie the description of inequality or variation in achievements to a recognized socio-economic structure will make the description more pertinent to the political discussion. Besides disparity across economic classes, rural-urban disparity, gender disparity, or disparity between scheduled castes, scheduled tribes and others are examples of meaningful groupings from analytical point of view.

Given the availability of data different indicators can be used to capture inequality. They include enrollment ratios, years of schooling, grade attainment, quality of infrastructure and resource inputs, test scores, and so on. In what follows we apply the idea of the concentration curve and concentration index in the context of distribution of the average years of education across economic classes as well as social groups in India.

3. Concentration index and concentration curve for education
The concentration curve for the distribution of years of education across economic classes can be obtained by taking along the X axis the cumulative proportions of population across different classes arranged in decreasing order of disadvantage that the classes face, and along the Y axis the cumulative share of the total years of education of the corresponding classes.

If we have information on the economic status of individuals we can classify them into, say, N groups and rank them in increasing order of economic status (eg. per capita expenditure classes as reported in the National Sample Survey reports of the Government of India). We then estimate the average years of education for the whole group as well as for each expenditure class separately. It would then be just a matter of few steps to obtain a concentration curve as in Figure 1.
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The concentration curve L(P) for education years shows the cumulative proportion of education years by individuals against the cumulative proportion of population ranked by economic status beginning with the poorest. Unlike Lorenz curve, we are not ranking the variable whose distribution we are examining. We rather look at the distribution of education years across the population grouped by economic status. If L(p) coincides with the diagonal, all groups irrespective of their economic status show the same level (years) of education. If L(p) lies above the diagonal, inequalities in educational achievement favour the poor and in such a case it may be called ‘pro-poor inequality’. If L(p) lies below the diagonal, the distribution of education is pro-rich. The further the L(p) lies from the diagonal, the greater the degree of inequality in educational attainment across economic classes. Suppose the concentration curves of two states A and B lie below the diagonal. If the concentration curve of state A, for example, lies everywhere above the concentration curve of state B, then we can say that state A's concentration curve dominates that of state B, which means we can unambiguously conclude that economic inequality in educational attainment in state A is less than that in state B.

The dominance relation does not hold when two concentration curves intersect each other, and in that case it is not possible to compare inequalities in the two states. We then need a Gini-like index to turn the two distributions into two scalar numbers. Concentration index (CI) is used for that purpose. It is defined as twice the area between L(p) and the diagonal. CI is zero when L(p) coincides with the diagonal, negative when L(p) lies above the diagonal and positive when L(p) lies below the diagonal. The value of CI thus ranges between -1 and +1. If all the years of education are obtained exclusively by the highest economic class, CI will have a value of +1. In general, with N economic groups, CI can be expressed as

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Where h = average years of education for the whole population, pn = proportion of the nth group in total population; hn = average years of education in the nth group; Rn = relative rank of the nth group; n = 1,…, N.

One particular problem that the health concentration index (HCI) confronts, may not arise in the context of education. The major problem with HCI arises due to the fact that the measurement of health is fundamentally different from the measurement of income. Most of the applications of HCI have been on self-reported morbidity data. As a matter of fact, there is no natural unit for the measurement of health status of this kind, and any particular unit seems to be as good as any other. Should health be measured on a scale between 0 and 1 or 0 and 100? Does it make sense to say that your health has doubled when your health status changes from, say, x to 2x? The health status indicator is an essentially qualitative variable which might be used to order people according to their health situation, but no conclusion can be drawn about the intensity corresponding to a specific value of the health indicator. In other words, the most appropriate scale for health status measurement is perhaps an ordinal variable, not a cardinal one. As no clear meaning can be given to the average of an ordinal variable, the value of HCI, which assumes cardinal comparability, should also be interpreted with caution. Fortunately, however, our education CI is free from this problem as the indicator that we are going to use for educational attainment, viz. years of schooling, is measured in cardinal (ratio) scale.

However, a different shortcoming of HCI remains present in our application of education CI on the data on monthly per capita expenditure as reported by the NSS. A well-known limitation of HCI is due to the following. Although HCI apparently captures the relationship that exists between income and health, as far as income is concerned the index takes into account only the ranks and not the levels of income. A given ranking of incomes may hide very different levels of income. Both a relatively equal and a relatively unequal distribution of income are compatible with any given ranking. Therefore, if changes occur in the distribution of income which do not affect the income ranks (e.g. a series of transfers which make the distribution more equal), there will be no effect on CI.
4. Application of education concentration index to Indian data

We have calculated education CI values for seventeen major states of India for both rural and urban areas of the states using data from the NSS 55th Round (1999-2000) with respect to economic classes first, and then social groups. The educational attainment data are given for the sample of population aged seven years and above, separately for males and females in rural and urban areas of all the Indian states. The data are given in cross-tabulated form by per capita income classes, by different social groups, viz, Scheduled Tribes (ST), Scheduled Castes (SC), Other Backward Classes (OBC), and ‘others’. Educational attainment of the population is classified into seven levels, viz illiterate, literate but below primary, primary, middle, secondary, higher secondary, and graduation and above.

We first converted the categories of attainment into numerical years of schooling according to the following rule: i) Illiterate = 0 ii) Literate (below primary) = 2 iii) Primary = 4 iv) Middle = 7 v) Secondary = 10 vi) High Secondary = 12 vii) Graduation and above =16

Table 1 gives the average years of education separately for males and females in rural and urban areas. Even though the average attainment is generally low in India, there are large rural-urban and gender gaps in the years of education. In some states the average educational levels attained by rural females are even less than one-fourth of that by urban males, as the last column in Table 1 reveals. Such gaps are the lowest in Kerala.

Table 1: Average years of education
|State |Rural |Urban |Urban Male/Rural |
| | | |Female |
| |Male |Female |Person |Male |Female |Person | |
|Andhra Pradesh |3.0 |1.6 |2.3 |6.8 |4.6 |5.7 |4.3 |
|Assam |4.2 |3.0 |3.7 |7.4 |6.0 |6.8 |2.5 |
|Bihar |3.2 |1.2 |2.2 |6.3 |4.2 |5.3 |5.3 |
|Gujarat |4.2 |2.4 |3.3 |7.0 |5.5 |6.3 |2.9 |
|Haryana |4.5 |2.5 |3.6 |6.4 |5.1 |5.8 |2.6 |
|Himachal Pradesh |5.3 |3.7 |4.5 |8.4 |7.5 |8.0 |2.3 |
|Jammu & Kashmir |4.7 |2.7 |3.7 |7.1 |4.9 |6.1 |2.6 |
|Karnataka |4.1 |2.3 |3.2 |7.5 |5.9 |6.7 |3.3 |
|Kerala |6.1 |5.5 |5.8 |7.1 |6.7 |6.9 |1.3 |
|Madhya Pradesh |3.1 |1.3 |2.2 |6.6 |4.6 |5.7 |5.1 |
|Maharashtra |4.8 |2.9 |3.9 |7.3 |5.9 |6.6 |2.5 |
|Orissa |3.5 |2.0 |2.7 |6.0 |4.4 |5.3 |3.0 |
|Punjab |4.1 |3.1 |3.7 |6.3 |5.7 |6.0 |2.0 |
|Rajasthan |3.4 |1.0 |2.3 |6.8 |4.3 |5.6 |6.8 |
|Tamil Nadu |4.2 |2.8 |3.5 |7.0 |5.6 |6.3 |2.5 |
|Uttar Pradesh |3.8 |1.7 |2.8 |6.0 |4.5 |5.3 |3.5 |
|West Bengal |3.7 |2.8 |3.0 |6.9 |5.5 |6.3 |2.5 |

Source: Calculated from NSS Report No 473, 2001

Table 2 presents the concentration indices for economic status related inequality in different states of India. The first point to be noted is that in most of the states economic status related inequality is more among the females than among the males, and inequality is generally higher in urban areas than in rural areas. While the economic status related inequality is the least among the rural males, it is the highest among the urban females. In other words, the economic status of the household matters more in the case of a female’s educational attainment than for a male; and it maters even more if the female happens to live in the urban area.

One well-known pattern found by most of the studies on health inequality or education inequality is that there is a negative relationship between the average level and the inequality in its distribution.

Table 2: Concentration index showing economic status related inequality in educational attainment

|State |Rural |Urban |
| |Male |Female |Person |Male |Female |Person |
|Andhra Pradesh |0.19 |0.23 |0.21 |0.24 |0.28 |0.26 |
|Assam |0.18 |0.19 |0.19 |0.18 |0.23 |0.20 |
|Bihar |0.20 |0.30 |0.23 |0.26 |0.35 |0.30 |
|Gujarat |0.16 |0.23 |0.19 |0.19 |0.25 |0.21 |
|Haryana |0.15 |0.20 |0.17 |0.18 |0.23 |0.22 |
|Himachal Pradesh |0.15 |0.13 |0.15 |0.12 |0.14 |0.17 |
|Jammu & Kashmir |0.07 |0.08 |0.09 |0.15 |0.23 |0.19 |
|Karnataka |0.18 |0.29 |0.22 |0.18 |0.22 |0.20 |
|Kerala |0.10 |0.10 |0.11 |0.13 |0.12 |0.12 |
|Madhya Pradesh |0.19 |0.20 |0.18 |0.20 |0.28 |0.24 |
|Maharashtra |0.26 |0.17 |0.17 |0.16 |0.22 |0.18 |
|Orissa |0.26 |0.32 |0.29 |0.23 |0.28 |0.25 |
|Punjab |0.14 |0.17 |0.16 |0.19 |0.24 |0.21 |
|Rajasthan |0.13 |0.23 |0.16 |0.19 |0.29 |0.24 |
|Tamil Nadu |0.15 |0.17 |0.17 |0.18 |0.21 |0.20 |
|Uttar Pradesh |0.16 |0.24 |0.19 |0.23 |0.29 |0.26 |
|West Bengal |0.20 |0.25 |0.22 |0.24 |0.29 |0.26 |

We present in Figures 1 through 6 the scatter plots of the average years of education and their distribution across economic classes for different states, separately for males, females and persons in rural and urban areas. They all show negative relationships between the concentration index and the average years of education. Table 3 gives the correlation coefficients.

Table 3 Correlation coefficients between average years of schooling and concentration index
| |Rural |Urban |
|Male |-0.44 |-0.69 |
|Female |-0.65 |-0.87 |
|Person |-0.61 |-0.78 |
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We now apply the education concentration index again to examine the pattern of inequality across social groups. Among the social groups the Scheduled Tribes (ST) are generally considered to be the most disadvantaged, followed by the Scheduled Castes (SC) and Other Backward castes (OBC). There have been a good number of studies in India that focus on inter-group disparities in various indicators. To our knowledge, there has been no attempt to express the degree of inequality among the four groups in terms of a single scalar index. Inequalities among culturally determined groups, groups that have salience for their members and/or others in society, for example, among races, ethnic groups, religions, religious sects, regions and so on, are referred to as horizontal inequalities (Stewart, 2002). Political scientists have noted the connection between the rise of modern democracy and the conceptualisation of the social world based on individual selves as the fundamental units for the calculation of social welfare. The collective identity in the modern democracy is supposed to form around common interests, and therefore condensation of individuals into groups is never permanent in a modern democracy. In India, however, perception of disadvantage often tends to be more collective than individual, and collectivity is seen as solidarities that are not interest based. As Kabiraj (1996) notes Disadvantage is seen more as unjust treatment of whole communities, like lower castes, minority religious groups and tribal communities, which are thus seen as potential political actors for social equality….Certainly, people who are part of democratic mobilizations are predominantly poor, but the principle of their self-identifying action is not poverty but discrimination.

We find strong negative correlations between the average years of education and social group related inequality in both rural and urban areas (Figures 7 and 8), yet again. In other words, all our findings on the connection between average educational attainments and socio-economic inequalities are in conformity with that of the earlier studies on inequalities in non-income dimensions, such as health and education. This is not surprising as we discussed at the beginning that because of the existence of natural upper limits it is always true that as the average value of an indicator for the whole population increases inequality decreases.

Ram (1990) had earlier used the standard deviations of schooling to illustrate the existence of an education Kuznets curve. He observed that as the average level of schooling rose, educational inequality would first increase, and after reaching a peak, would start declining. The turning point, according to Ram, is about seven years of education. It is interesting that in our case only the negative part of the curve is apparent, and the negative relationship shows up even though the average attainment levels are much below the seven-year threshold in all the states.

One might be curious to know if there was any connection between the two types of inequalities – economic status related inequality and social group related inequality. They are indeed positively related. The values of the correlation coefficients between the two types of concentration indices are 0.56 for rural India and 0.67 for urban India.

Figure 7 Association between social group related education inequality and average years of education (rural)
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Figure 8 Association between social group related education inequality and average years of education (urban)
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5. Conclusion

There are two basic approaches to measuring inequality in non-income dimensions. One views inequality as variation of an outcome indicator across individuals and the other views inequality as essentially disparities across socioeconomic groups. While the latter view now dominates the inequality measurement in health, measurement of education inequalities has so far taken the first view. In this paper, we have argued the importance of reckoning inequality in socio-economic group terms and advocated use of an ‘education concentration index’ exactly in the same way as the health concentration index measures socio-economic inequalities in health. The index has been applied to the Indian data to reckon two kinds of inequalities in educational attainment (years of education) – one across economic classes and the other across socially identified groups such as the Scheduled Tribes, Scheduled Castes and others. We find a strong correlation between the two types of inequalities across the states of India. We also find, as one would expect, that the inequality index values are negatively correlated with the average years of education. However, in actual policy context, analysis of the outliers might be more illuminating than studying the general pattern.

References
Birdsall, Nancy and Juan Luis Londono (1997) ‘Asset Inequality Matterss: An Assessment of the World Bank’s Approach to Poverty Reduction’, American Economic Review 87(2).

Chakraborty, Achin (2002) Issues in Social Indicators, Composite Indices and Inequality, Economic and Political Weekly, March 30.

Chakraborty, Achin and U.S. Mishra (2003) ‘Making Inter-Country Comparison of Life Expectancy Inequality Sensitive’, Social Indicators Research, Vol. 64.

Hicks, D.A. (1997) ‘The Inequality-Adjusted Human Development Index: A Constructive Proposal’, World Development, 25(8), 1283-1298.

Kaviraj, S. (1996) ‘India: Dilemmas of Democratic Development’, in A. Leftwich (ed.) Democracy and Development, Cambridge: Polity Press.

Le Grand (1987) Inequalities in Health: Some International Comparisons’, European Economic Review 31.

Ram, Rati (1990) ‘Educational Expansion and Schooling Inequality: International Evidence and Some Implications’ Review of Economics and Statistics, 72(2)

Roemer, John (1998) Equality of Opportunity, Cambridge, MA: Harvard University Press.

Sen, Amartya (1980) ‘Equality of What?’ in S. McMurrin (ed) Tanner Lectures on Human Values. Cambridge: Cambridge University Press.

Stewart, F. (2002) ‘Horizontal inequalities: A neglected dimension of development’ Queen Elizabeth House Working Paper Series 81.

Thomas, Vinod, Yan Wang and Xibo Fan (2001) ‘Measuring Education Inequality: Gini Coefficients of Education’ World Bank Policy Research Working Paper 2525.

Tobin, James (1970) ‘On Limiting the Domain of Inequality’, Journal of Law and Economics.

Wagstaff, Adam, P. Paci and E. van Doorslaer (1991) ‘On the Measurement of Inequalities in Health’, Social Science and Medicine, 33.

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[1] For a discussion of the problems in using Gini coefficient to adjust life expectancy at birth for equality see Chakraborty (2002), Chakraborty and Mishra (2003).

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Cumulative education years

0

100

L(p)

Cumulative population percentage

Figure 1: Education years Concentration Curve

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