Policy May/2008 no. 7 research brief The International Poverty Centre is jointly supported by the Brazilian Institute for Applied Economic Research (IPEA) and the Bureau for Development Policy, United Nations Development Programme, New York. International Poverty Centre By Anwar Shaikh and Amr Ragab The Vast Majority Income (VMI): A New Measure of Global Inequality Introduction GDP per capita is by far the most popular measure of international levels of development. It is fairly well understood and widely available across countries and time. But it is also recognized that GDP per capita is an imperfect proxy for important factors such as health, education and well-being. An alternative approach has been to work directly with the variables of concern, as in the UNDP Human Development Index (HDI). The HDI combines GDP per capita with life expectancy and schooling into a single composite index. But, the HDI is difficult to compile. Moreover, because it is an index, it cannot tell us about the absolute standard of living of the underlying population: it can only provide rankings of nations at any moment in time and changes in these rankings over time. It turns out that the rankings produced by the GDP per capita and the HDI are quite highly correlated. Given that GDP per capita also provides an absolute measure of income; it is understandable that it remains so popular. Both the GDP per capita and the HDI measures suffer from that fact that “they are averages that conceal wide disparities in the overall population” (Kelley, 1991). As a result, it becomes necessary to either supplement these measures with information on distributional inequality as in the Gini coefficient, or to directly adjust GDP per capita and other variables for distributional variations. Sen (1976) derives (1-Gini) as the appropriate adjustment factor for real income. Since a higher inequality implies a lower (1-Gini), this penalizes regions or countries with higher inequalities. The 1993 HDI used this procedure to adjust GDP per capita in various countries. Subsequently, it was extended to encompass the variables in the HDI using discount factors based on the degrees of inequality in their specific distributions. Later, the index incorporated gender-based adjustments by discounting a country’s overall HDI according to the degree of gender-inequality (Hicks, 2004). The above measures of welfare will be re-examined in light of our own finding that inequality-discounted GDP per capita can be interpreted as a measure of the relative per capita income of the first eighty per cent of a nation’s population. This Policy Research Brief introduces a new measure of worldwide income and inequality, which we call the Vast Majority Income (VMI). The Vast Majority Income: a Combination of Income and Inequality Information As indicated above, GDP per capita has the great virtue of being an absolute measure of average national income. But, because the distribution of income and consumption can be highly skewed within countries, we cannot use average income as representative of the income of the vast majority of the population. This is particularly true in the developing world, where there can be a large discrepancy between the two incomes. Indeed, a rise in GDP per capita can be attended by a worsening in the distribution of income, so that the standard of living of the vast majority of the population may actually decline even as GDP per capita rises. Consider an example in which there are five people with dollar incomes of $5, $10, $15, $20, and $50, respectively. The per capita income of the vast majority that is the first 80 per cent of the population is the average of the first four incomes, which is $12.5 per person. By comparison, the overall average is $20. Their ratio is 0.625 (= $12.5/$20), which tells us that GDP per capita is a poor proxy for the vast majority income or VMI. Moreover, if this ratio varies over time, then the trend of GDP per capita would also be an unreliable guide to the progress of the VMI. What we need, therefore, is a direct measure of the standard of living of the vast majority. As noted above, this can be derived directly from income distribution data, and has a simple representation on the Lorenz curve. The Lorenz curve is a plot of the cumulative population proportion (x) on the horizontal axis and the cumulative income proportion (z) on the vertical axis based on an ordered ranking of individual or group incomes. In our previous example, when individuals are ranked by income from the lowest to the highest, the first 20 per cent of the population (the first person) will have five per cent of total income; the 40 per cent (the first two people) of the population will have 15 per cent of total income, and so on. The resulting Lorenz curve will be therefore “bowed-inward” as in curve B below (Lampert, 2001, pp. 23-26). If instead all individuals had the same income, the resulting curve would be the 45-degree line A (the line of equality) in Figure 1 (next page). One way to summarize the underlying degree of inequality is to divide the area between the 45-degree line of equality (line A) and the actual inequality curve (curve B), by the area under the line A. This is the Gini coefficient G (Lampert, 2001, pp. 26-27). Under complete equality the Lorenz curve would be on the 45-degree line, so that G = 0 per cent. At the other extreme, under complete inequality the first four people would have zero incomes and the last would have $100, so that the Lorenz curve would run along the x-axis until it jumped to 100 per cent of cumulative income at 100 per cent of the population. In this case the area below the curve would be the same as that under line A, so that G = 100 per cent. In general the Gini Coefficient lies somewhere between 0 and 100, with higher Gini’s representing higher degrees of inequality. 1 It should be obvious that we could work equally well with (1-G) instead, which is a measure of equality. This is given by the area under curve B divided by the area below line A, so that a higher (1-G) represents a higher degree of equality.