Measuring Income Inequality. Measuring Income Inequality. Income Inequality The extent of income concentration within a country or group.
(1) Anonymity Principle: permutations of incomes amongst ‘n’ people should not matter for inequality measures, so that
(2) Population Principle: the size of a country’s population is unimportant but what is important is the proportions of the population that earn different levels of income.
(3) Relative Income Principle: it is not the absolute level of income that is important to inequality but the relative size of incomes.
E.G. If Thabo has $1 and Tshepo has $2, then Tshepo has twice as much as Thabo or has 2/3rds of all the income. If Thabo has $1500 and Tshepo has $2000 then Tshepo has 4/7th of total income and income inequality between the two has declined.
The Dalton Principle: If Distribution ‘A’ can be achieved from Distribution ‘B’ by constructing a sequence of regressive (from poor to rich) transfers then A is more unequal than B.
The issue of whether income inequality changes with growth and development or whether initial income inequality is important to sustainable growth is discussed in the Pro-Poor growth lecture.
The Gini Coefficient:
This average is simply the total income of all individuals divided by the number of individuals. Hence,
= income difference
Example of calculating a Gini Coefficient.
South Africa is assumed to have 6 people earning respectively,
R1000, R100, R15000, R150, R50, R100
The Gini Coefficient here is?
Firstly we must calculate the income differences for each j and k..
The Lorenz Curve
Example from Ray (1998, pp. 183).
Other Income Inequality Indices
E.g. Theil Index
The entropy measures have the desirable property of being decomposable so that inequality within a group (intra-group inequality) and between groups (inter-group inequality) can be estimated. This can have important implications for policy makers.
Other Income Inequality Measures
Theil Index – Entropy Measure.
Entropy means ‘disorder’ – deviations from perfect income equality.
The basic form of the Thiel Index is
Theil Index cont…
Where is income of individual ‘i’, and is the average income of the population, ‘n’.
Can calculate the Theil Index from given income per capita data.
Theil Index cont…
Theil Index cont…
Can decompose the Theil index into between group inequality and within group inequality.
E.g. Look at income inequality within racial groups and then between racial groups.
Practically this entails estimating Theil index for each of the racial groups and then summing them according to some weight (e.g. population weight) to give total within-race inequality, Tw.
Then calculate the Theil using the ratio of average income for each racial group/average income of entire population to give between race income inequality, Tb.
Add the two together for overall Theil index = Tw+Tb
See “Describing Income Inequality Theil Index and Entropy Class Indexes”by Lorenzo Giovanni Bellù, and Paolo Liberati, Food and Agriculture Organization of the United Nations, FAO.
Bellu, L., and Liberati, P., (2006), “Describing Income Inequality Theil Index and Entropy Class Indexes”, Food and Agriculture Organization of the United Nations, FAO.
Ray, D., (1998), Development Economics, Princeton University Press.
Foster, Greer and Thorbecke (1984), “A class of decomposable poverty measures”, Econometrica, Vol 52(3), pp. 761-6.
Foster and Shorrocks (1988), “Poverty Orderings”, Econometrica, Vol 56, pp. 173-7.
Atkinson (1987), “On the Measurement of Poverty”, Econometrica, Vol 55(4), pp. 749-64.