What is inequality and how we measure it. Milanovic, “Global inequality and its implications” Lectures 1 & 2. Absolute vs. relative. Absolute vs. relative. Is conception of inequality based on absolute or relative income distances?
Milanovic, “Global inequality and its implications”
Lectures 1 & 2
The tide rises all boats by the same proportion of their initial income; no Δ in relative inequality
But absolute income differences increase
Source: Ravallion (2003)
People at the bottom (up to 30th percentile) dissave; people at the top (richest 30 percent) save
South African 1998 expenditure and income per capita (in logs)
Blue line: the story as before. Red line: high C households dissave.
Gini for YPC = 28.4; Gini for XPC = 26.7
Data Poland Heide; see XYratios.xls file
Overall C/Y ratio = 1.09
Blue line: the same story as before; Red line: C-rich people underreport their income
Source: Serbia LSMS 2002; file poorAZ.xls
Graph shows where in YPC distribution are people from the 20th (highest) C ventile whose reported C/Y is greater than 2. They are across all income distribution even among those who are income poor.
Source: Serbia LSMS 2002;
Expressed in terms of either mean per capita or mean per HH income.
Source: South Africa 1994-95
Source: Hungary 1993
The methods of Italian writers…are not…comparable to his [Dalton’s] own, inasmuch as their purpose is to estimate, not the inequality of economic welfare, but the inequality of incomes and wealth, independently of all hypotheses as to the functional relations between these quantities and economic welfare or as to the additive character of the economic welfare of individuals.
Corrado Gini, Measurement of Inequality of Incomes, Economic Journal, March 1921.
Where π=share (of recipients) in total income, p=share in total population, s=share (of income source) in total income, μ=mean, L=overlap term and Ri=cov(xi,r(y))/cov(xi,r(xi) source correlation coefficient with total income
Where fi=frequency of i-th group, qi=cumulative share of income received by the bottom i groups
Often, the “true” Gini is approximated by the following heuristic formula:
True Gini = 1/3 Gini (min) + 2/3 Gini (max)
The very lowest and the very top interval (both in italics) are assumed.
The results are as follows (using Kakwani’s formulas). Gini minimum is 26.09, Gini maximum is 27.51 (a difference of 5.4 percent). The heuristic Gini would then be 27.04.
A very simple formula (approximation; when N, it is exact; practically, good as soon as N>10 or 12):
Source: thepast.xls (lorenz2)