MEASURES OF INEQUALITY AND EMPIRICAL RESULTS · 2019-04-15 · Advantages and disadvantages...
Transcript of MEASURES OF INEQUALITY AND EMPIRICAL RESULTS · 2019-04-15 · Advantages and disadvantages...
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/