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 seventy 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.
http://www.ipc-undp.org/pub/IPCPolicyResearchBrief7.pdf
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This is pretty funny. Just yesterday I was thinking about how obnoxious GDP was when used as an indicator of a recovery, when I sure as hell haven't been recovering of late.
I immediately thought of chopping off the top 2-3 percent in income and taking the median instead of the mean as a further correction. Then I thought even that was probably not good enough. There had to be a function somewhere that could be fit into either the slope intercept or some form of differential where you could take the derivative and find the trend...
This was a very cool paper and explained what I was looking for. The paper was an enjoyable way to pass the time between SS checks and the continuous rise in fees, insurance, and credit card rates...oh, yeah and food, gas, pharma and everything I can't live without.
Check out Figure 1, The Lorenz Curve and note C. C is a ray that intersects the L-curve where 80 percent of the population lays on the curve. The text uses the change in the slope of C to measure the change toward or away from greater equality (inequality).
``we can also work backwards by first summing the cumulative income proportion of the first four quintiles (0.05 + 0.10 + 0.15 + 0.20 = 0.50) and dividing them by the corresponding cumulative population proportion (0.80) to get 0.625, which is also the ratio of the vast majority per capita income to the average. This is useful because the cumulative income proportion is the y-axis of the Lorenz curve and the cumulative population proportion its x-axis. Therefore, the vast majority income ratio (VMIR) is simply the slope of the ray through the origin to the point on the curve which represents 80 per cent of the population, which is the slope of the line C in Figure 1.''
It would make a really good LBO Newsletter to crank the appropriate data over time using VMIR to show how fast as we going down the toilet. .
CG CG