MEASURES OF INEQUALITY AND EMPIRICAL RESULTS

Maria Wrzeszcz, Martina Slomski & Sascha Rybarczyk14th May 2010

Agenda

1. Introduction

2. Definition of inequality

3. How to measure?

4. Coefficient of variation

5. Theil index

6. Gini coefficient

7. Advantages and disadvantages

8. Critique

Introduction

F. Scott Fitzgerald: “The rich are different from us.”

Ernest Hemingway: “Yes, they have more money.”

Definition of inequality

What is inequality?

„State or condition of being unequal”

economic inequality: resources vs. population

Which persons/groups?

What kind of conditions?

Definition: reasons for inequality

labor market

inborn ability

wealth

condensation

culture

risk

preferences

race

education

work

preferences

gender

leisure

preferences

within one country

under-

development

(post-)

colonialism

exploitation

imperialism

corruption

between countries

tax

Definition: effects of inequality

Definition: importance of inequality

Policy making

Economic performance

Requirements on the measurement

data?

properties?

metric?

How to measure?

Range (ratios)

Variance

Relative mean deviation

Coefficient of variation

Hoover index

Atkinson index

Theil index

Gini coefficient

… etc.

How to measure?

Basic criteria

income distribution

n people with income xi (with i = 1,…,n)

x1 ≤ x2 ≤ … ≤ xn (ascending order)

Characteristics

scale invariance

principle of transfer

sensitivity to transfer

Coefficient of variation

Source: http://www.equalitytrust.org.uk/resources

Theil index

Decomposition:

with T‘g - between group element

and TWg - within group element

Theil index

Gini coefficient

Lorenz curve

Source: http://content.answers.com/main/content/img/oxford/Oxford_Geography/0198606737.lorenz-curve.1.jpg

Gini coefficient

Gini coefficient

Source: http://www.laits.utexas.edu/lawdem/unit03/reading2/Gini_definition.jpg

Gini index worldwide

Source via Internet: The World Fact Book, Central Intelligence Agency; U.S. Census Bureau 2009

Gini index worldwide

Advantages and disadvantages

Coefficient of variation Theil index Gini coefficient

Easy to understand

Immune to outliers (for weighted data)

Includes all data

Not affected by inflation (i.e. not skewed )

Use of group data

Splitting into within and between group components possible

Most commonly used measure in economic work (“gold standard”)

Includes all data

Direct comparison between units with different size populations feasible

Intuitive interpretation

Advantages and disadvantages

Coefficient of variation Theil index Gini coefficient

Exhaustive individual level data is needed

No standard for an reasonable level of inequality

No intuitive motivating picture

Not directly comparable across populations with different sizes or group structures

Mathematically complex

Sensitivity to transfer among the lower range

Exhaustive individual level data is needed

Complex, sophisticated computations

Sensitivity to transfer especially in the middle range

Critique

Social welfare function

Which measure is the best one?

Which one do you like?

Thank you for your attention!!!

References

Allison, Paul D.: Measure of Inequality, in: American Sociological Review, 1978, Vol. 43, pp. 865 – 880

Atkinson, Anthony B.: On the Measurement of Inequality, in: Journal of Economic Theory, 1970, Vol.2, pp. 244 – 263

Kaplow, Louis: Why Measure Inequality, in: Journal of Economic Inequality, Vol. 3 (1), pp. 65 – 79

Bureau of Economic Analysis, http://www.bea.gov/

Central Intelligence Agency: The World Factbook, https://www.cia.gov/library/publications/the-world-factbook/

The Equality Trust, http://www.equalitytrust.org.uk

U.S. Census Bureau, http://www.census.gov/