Background

Recent research suggests that the degree of income inequality in society may be related to the health status of a population. Greater income inequality has been linked to lower life expectancy in cross-national comparisons (Wilkinson, 1996); higher mortality rates (Kaplan et al. 1996; Kennedy et al. 1996) and worse self-rated health (Kennedy et al. 1998) at the U.S. state level; higher mortality at the U.S. metropolitan level (Lynch et al. 1998); as well as higher rates of obesity at the U.S. state level (Kahn et al. 1998). The mechanisms linking income inequality to health are still debated (Kawachi et al., 1999), but the association appears robust with respect to age, race, sex, and adjustment for individual socioeconomic characteristics (Kennedy et al, 1998; Soobader and LeClere, 1999).

Measurement Approaches

Several approaches exist for the measurement of income inequality across a geographic area (Atkinson 1970; Sen 1973; Cowell 1977). Some of the most commonly used measures include the Gini coefficient; the decile ratio; the proportions of total income earned by the bottom 50%, 60%, and 70% of households; the Robin Hood Index; the Atkinson index; and Theil's entropy measure. Each is described briefly:

Gini coefficient

The Gini coefficient is one of the most commonly used indicators of income inequality. The Gini is derived from the Lorenz curve, which plots the cumulative share of total income earned by households ranked from bottom to top. For example, in Figure 1 (example from Massachusetts), the curve shows the shares of income earned by successive deciles of households, arrayed in order from the bottom 10% upwards. If incomes were equally distributed, the Lorenz curve would follow the 45° diagonal. As the degree of inequality increases, so does the curvature of the Lorenz curve, and thus the area between the curve and the 45° line becomes larger. The Gini is calculated as the ratio of the area between the Lorenz curve and the 45° line, to the whole area below the 45° line.

Figure 1. Lorenz curve, Gini coefficient  and the Robin Hood index derivation.

Robin Hood Index

The Robin Hood Index, is equivalent to the maximum vertical distance between the Lorenz curve and the line of equal incomes. The value of the index approximates the share of total income that has to be transferred from households above the mean to those below the mean to achieve equality in the distribution of incomes (See Figure 1.).

Atkinson's Index

The Atkinson Index is one of the few inequality measures that explicitly incorporates normative judgments about social welfare (Atkinson 1970). The index is derived by calculating the so-called equity-sensitive average income (y_e), which is defined as that level of per capita income which if enjoyed by everybody would make total welfare exactly equal to the total welfare generated by the actual income distribution. The equity-sensitive average income is given by:

where y_i is the proportion of total income earned by the ith group, and e is the so-called inequality aversion parameter. The parameter e reflects the strength of society's preference for equality, and can take values ranging from zero to infinity. When e > 0, there is a social preference for equality (or an aversion to inequality). As e rises, society attaches more weight to income transfers at the lower end of the distribution and less weight to transfers at the top. Typically used values of e include 0.5 and 2.

The Atkinson Index (I) is then given by:

where µ is the actual mean income. The more equal the income distribution, the closer y_e will be to µ, and the lower the value of the Atkinson Index. For any income distribution, the value of I lies between 0 and 1.

Theil's entropy measure

A measure of inequality proposed by Theil (1967) derives from the notion of entropy in information theory. The entropy measure, T, is given by:

where s_i is the share of the ith group in total income, and n is the total number of income groups. The index has a potential range from zero to infinity, with higher values (greater entropy) indicating more equal distribution of income.

Comment

Obviously, there is no single "best" measure of income inequality. Some measures (e.g., the Atkinson Index) are more "bottom-sensitive" than others, i.e., more strongly correlated with the extent of poverty. The measures perform differently under various types of income transfers. For instance, the Gini is much less sensitive to income transfers between households if they lie near the middle of the income distribution compared to the tails. The Robin Hood Index is insensitive with respect to income transfers between households on the same side of the mean income, and so on. Investigators should select the measures based on the hypothesis to be addressed.

Measures of income inequality are usually calculated from Census data. As such, they tend to be based upon gross income, and are not adjusted for Federal and state taxes, or near-cash subsidies (such as food stamps, school lunches). Nor are they adjusted for household size and composition. Manipulation of Census micro-data are required to adjust income inequality measures for taxes, transfers, and household size. When these steps have been carried out, the relationship of inequality to mortality was found to persist (Kawachi and Kennedy, 1997). Similarly, the choice of measure does not appear to affect the relationship to mortality. Measures are typically highly correlated with each other (r > 0.8) (Kawachi and Kennedy, 1997).

References

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Cowell FA. Measuring Inequality. Oxford: Philip Allan, 1977.

Kahn HS, Tatham LM, Pamuk ER, Heath CW Jr. Are geographic regions with high income inequality associated with risk of abdominal weight gain? Social Science & Medicine 1998; 47: 1-6.

Kaplan GA, Pamuk ER, Lynch JW, Cohen RD, Balfour JL. Inequality in income and mortality in the United States: analysis of mortality and potential pathways. British Medical Journal 1996;312: 999-1003.

Kawachi I, Kennedy BP. The relationship of income inequality to mortality - Does the choice of indicator matter? Soc Sci Med 1997; 45: 1121-1127.

Kawachi I, Kennedy BP, Wilkinson RG. Income Inequality and Health. The Society and Population Health Reader. New York: The New Press, 1999.

Kennedy BP, Kawachi I, Prothrow-Stith D. Income distribution and mortality: cross-sectional ecological study of the Robin Hood Index in the United States. British Medical Journal 312: 1004-1007. See also erratum: British Medical Journal 1996; 312: 1253.

Kennedy BP, Kawachi I, Glass R, Prothrow-Stith. Income distribution, socioeconomic status, and self-rated health: A US multi-level analysis. Br Med J 1996; 317:917-21.

Lynch JW, Kaplan GA, Pamuk ER, Cohen RD, Balfour JL, Yen IH. Income inequality and mortality in metropolitan areas of the United States. American Journal of Public Health 1998;88: 1074-80.

Sen A. On Economic Inequality. Oxford: Oxford University Press, 1973.

Soobader M-J, LeClere FB. Aggregation and the measurement of income inequality: effects on morbidity. Social Science & Medicine 1999;48:733-44.

Theil H. Economic and Information Theory. Amsterdam: North Holland, 1967.