1. 1
Economic Inequality: concept and measurement
• The analysis of the distribution of income, or
wealth, among different groups in society. Why?
• Motivation: (i) philosophical and ethical for aversion
to inequality per se; (ii) inequality in income and
wealth affects the possibility of growth; (iii) DCs are
prone to huge disparities in living standards
Outline
• Nature of economic inequality
• Measuring inequality
• Complete measures
2. 2
Economic inequality is the fundamental disparity that
permits one individual certain material choices, while
denying another individual those very same choices
• Disparities in wealth or income
Aspects of the distribution of income and wealth:
• Over which time period we study them? Current or
lifetime inequality hide considerations of social mobility
• The distribution of income can also be observed with
respect to the class of recipient (i.e. population grouped
by gender, ethnicity, age, marital status and
geographical area)
Perspectives on economic inequality
3. 3
Perspectives on economic inequality 2
• The distribution of income can be observed among the
population, called size (or personal) distribution of income,
and can be expressed between some demographic unit:
households, individual earners, or all individuals with
respect to the command over some definition of income
(gross or net) or expenditure.
• Functional distribution of income relates to disparities in
factors of production rewards: income inequality depends
on how labour, (physical and financial) capital and land are
rewarded with wage, profit, interest and rent (the last two
are property income), respectively.
• The distribution of wealth measures the value of a person’s
assets at some point in time. It is related to inheritance,
different propensities to save, investment talent/luck, and
income inequality. Empirically, it is very hard to measure it
because a stock of assets is measurable only when sold.
4. 4
Perspectives on economic inequality 3
Household2
Household3
Household4
WagesofDifferent
Skills
Profits
Rents
Production
Household1
FunctionalDistribution PersonalDistribution
Ownershipof Factors
Functional and personal distribution of income
6. 6
Measuring inequality: notation
• Goal: we have to develop indices that permit the ranking
of (lifetime) income or wealth distributions in two different
situations
• Suppose society is composed of i=1,2,…, n individuals;
income distribution is a description of how much yi is
received by each i: (y1, y2,… yn); we want to compare two
distributions
• Inequality measure, I, is a rule that assigns a degree of
inequality to each possible distribution of the national cake
• I=I(y1, y2,… yn), defined over all conceivable distributions
(y1, y2,… yn)
7. 7
Inequality measures: Lorenz curve 1
A diagrammatic way to depict distribution
• X-axis: cumulative percentages of the population
arranged in increasing of income
• Y-axis: % of national income accruing to any fraction of
the population thus arranged
• The graph connecting these points is the Lorenz curve
• If everybody earned the same income, this curve would
coincide with the 45o
line
• The overall distance between the 45o
line and the Lorenz
curve is indicative of the amount of inequality present in
the society
8. 8
Inequality measures: Lorenz curve 2
Cumulative Population 100%
100%
CumulativeIncome
20%
10%
A
80%
70%
B
45 0
LorenzCurve
The Lorenz curve of a distribution of income
9. 9
Inequality measures: Lorenz curve 3
0
L(1)
L(2)
45
0
CumulativePopulation
100%
CumulativeIncome
100%
Using Lorenz curve to make judgements
• L(1) lies above L(2)
• Interpretation: if we choose
a poorest x% of the
population, then L(1)
always has this poorest x%
earning at least as much as
they do under L(2)
• It stands to reason that L(1)
should be judged more
equal than L(2)
• This criterion for inequality comparison is known as Lorenz
criterion
10. 10
Lorenz curves for selected countries 1
Lorenz curves for different countries (Deininger and Squire, 1996)
Brazil
2
7
17
35
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
Mexico
3
10
22
41
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
Egypt
9
21
37
59
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
India
9
21
38
59
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome(%)
Kenya
3
10
21
38
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
Uganda
7
17
31
52
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
11. 11
Lorenz curves for selected countries 2
Korea
7
20
36
58
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome(%)
Taiwan
7
20
38
61
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
United Kingdom
8
20
36
59
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome(%)
United States
5
15
32
56
0
20
40
60
80
100
0 20 40 60 80 100
Cumulative Shares of Population (%)
CumulativeSharesofIncome
(%)
12. 12
References
Core readings:
• Ray D., (1998), Development Economics, Princeton University Press, Chapter: 6
• McKay A., (2002), “Defining and Measuring Inequality”, ODI Inequality briefing paper No
Recommended readings:
• Champernowne D.G. and Cowell F.A., (1998), Economic Inequality and Income Distribution,
Cambridge University Press, Chapters: 3 – 4. This is a valid alternative to the core readings,
but it is more detailed and technical.
• Jenkins S., (1991), “The measurement of income inequality”, chapter 1 in Osberg L. (ed),
Economic inequality and poverty, M.E. Sharpe. It is a comprehensive exposition, with a
focus also on operational issues, on the measurement of inequality.
• Hale T., (2003), “The theoretical basis of popular inequality measures”, University of Texas
Inequality Project (UTIP), www.utip.gov.texas.edu
• Litchfield J.A., (1999), “Inequality: Methods and Tools”, Text for the World Bank PovertyNet
website: http://www.worldbank.org/poverty, March 1999
Other useful references for developing economies are on land and education inequality:
• Ray D., (1998), Development Economics, Princeton University Press, Chapter: 12
• Frankema E.H.P., (2006), “The Colonial Origins of Inequality: Exploring the Causes and
Consequences of Land Distribution”, Groningen Growth and Development Centre, Research
Memorandum GD-81, University of Groningen
• Frankema E.H.P. and Bolt J., (2006), “Measuring and Analysing Educational Inequality: The
Distribution of Grade Enrolment Rates in Latin America and Sub-Saharan Africa”, Groningen
Growth and Development Centre, Research Memorandum GD-86
Editor's Notes
Unequal access to lifetime economic resources begins from parental wealth and access to resources, so inequality and deprivation cannot be blamed on individuals’ bad decisions Growth spreading its benefits equitably or inequitably among the population People derive their satisfaction/happiness not from the absolute level of their consumption but from how their consumption compares with that of the people around them
Some ground clearing… inequality is multidimensional: encompasses both inequality in opportunities and inequality in outcomes Fundamental disparities are ultimately linked to differences in personal capabilities and political freedoms, but… by studying the analysis of differences across the population in access to and control over economic resources, we hope to capture the essence of inequality multidimensionality disparities in personal income and wealth stand for an important component of all differences
In the functional distribution view, Income inequality is determined by the market conditions in each of the factor markets as well as by the pre-existing distribution of wealth (financial and physical capital, and land or real estate property). This view is particularly relevant if we want to emphasise the analysis of the existent class structure of the society (workers, capitalists, landlords) and the degree of market power each has in the demand and supply of production factors. In relation to history and political economy causes, we have Market and Structural Inequality : the former arises from the very functioning of a market economy, i.e. rewards to risk-taking, entrepreneurship, skill acquisition and saving all affect income and wealth accumulation; the latter can be traced in discrimination due to political connections and social status due to historical factors (colonial legacy, gentry) that are at the origin of wealth disparities.
The 1 st set of arrows describes how income is generated from the production process The 2 nd set of arrows tells us different categories of income are funnelled to households; and the direction and magnitude of these flows depend on who owns which and how much factors of production Functional distribution is useful to understand how inequalities are created, and in turn how they are connected to growth
What are the desirable properties that an inequality index should satisfy? 4 principles: (i) Anonymity; (ii) Population; (iii) Relative income; (iv) Dalton principle it is difficult to reach unanimity on what a desirable index should satisfy There is inevitably a trade off: if you lay down weak criteria, then many indices can be suggested but probably giving contrasting results; if you impose strong criteria, you will reduce the number of admissible indices, but the criteria loses wide approval
The poorest 20% population earns 10% of overall income The slope of the curve at each point is simply the contribution of the person at that point to the cumulative share of national income 45-degree line: any cumulative fraction of the population would share exactly that very same fraction of national income The poor makes a small marginal contribution to national income – shallow Lorenz curve at low cumulative income values The rich makes a high marginal contribution to national income – steep Lorenz curve at high cumulative income values
It can be shown that an inequality measure is consistent with Lorenz criterion iff it is simultaneously consistent with the previous 4 criteria
