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№1 слайд![Measuring Inequality An](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img0.jpg)
Содержание слайда: Measuring Inequality
An examination of the purpose and techniques of inequality measurement
№2 слайд![in equal i ty Function noun](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img1.jpg)
Содержание слайда: in·equal·i·ty
Function: noun
1 : the quality of being unequal or uneven: as a : lack of evenness b : social disparity c : disparity of distribution or opportunity d : the condition of being variable : changeableness
in·equal·i·ty
Function: noun
1 : the quality of being unequal or uneven: as a : lack of evenness b : social disparity c : disparity of distribution or opportunity d : the condition of being variable : changeableness
2 : an instance of being unequal
№3 слайд![](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img2.jpg)
№4 слайд![If a single person holds all](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img3.jpg)
Содержание слайда: If a single person holds all of a given resource, inequality is at a maximum. If all persons hold the same percentage of a resource, inequality is at a minimum.
Inequality studies explore the levels of resource disparity and their practical and political implications.
№5 слайд![Physical attributes](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img4.jpg)
Содержание слайда: Physical attributes – distribution of natural ability is not equal
Physical attributes – distribution of natural ability is not equal
Personal Preferences – Relative valuation of leisure and work effort differs
Social Process – Pressure to work or not to work varies across particular fields or disciplines
Public Policy – tax, labor, education, and other policies affect the distribution of resources
№6 слайд![Why measure Inequality?](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img5.jpg)
Содержание слайда: Why measure Inequality?
Measuring changes in inequality helps determine the effectiveness of policies aimed at affecting inequality and generates the data necessary to use inequality as an explanatory variable in policy analysis.
№7 слайд![How do we measure Inequality?](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img6.jpg)
Содержание слайда: How do we measure Inequality?
Before choosing an inequality measure, the researcher must ask two additional questions:
Does the research question require the inequality metric to have particular properties (inflation resistance, comparability across groups, etc)?
What metric best leverages the available data?
№8 слайд![Choosing the best metric](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img7.jpg)
Содержание слайда: Choosing the best metric
Range
Range Ratio
The McLoone Index
The Coefficient of Variation
The Gini Coefficient
Theil’s T Statistic
№9 слайд![Range](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img8.jpg)
№10 слайд![Range Pros Easy to Understand](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img9.jpg)
Содержание слайда: Range
Pros
Easy to Understand
Easy to Compute
№11 слайд![Range Ratio](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img10.jpg)
Содержание слайда: Range Ratio
№12 слайд![Range Ratio Pros Easy to](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img11.jpg)
Содержание слайда: Range Ratio
Pros
Easy to understand
Easy to calculate
Not skewed by severe outliers
Not affected by inflation
№13 слайд![The McLoone Index](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img12.jpg)
Содержание слайда: The McLoone Index
№14 слайд![The McLoone Index Pros Easy](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img13.jpg)
Содержание слайда: The McLoone Index
Pros
Easy to understand
Conveys comprehensive information about the bottom half
№15 слайд![The Coefficient of Variation](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img14.jpg)
Содержание слайда: The Coefficient of Variation
№16 слайд![The Coefficient of Variation](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img15.jpg)
Содержание слайда: The Coefficient of Variation
Pros
Fairly easy to understand
If data is weighted, it is immune to outliers
Incorporates all data
Not skewed by inflation
№17 слайд![The Gini Coefficient The Gini](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img16.jpg)
Содержание слайда: The Gini Coefficient
The Gini Coefficient has an intuitive, but possibly unfamiliar construction.
To understand the Gini Coefficient, one must first understand the Lorenz Curve, which orders all observations and then plots the cumulative percentage of the population against the cumulative percentage of the resource.
№18 слайд![A Equality Diagonal](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img17.jpg)
Содержание слайда: A – Equality Diagonal Population = Income
A – Equality Diagonal Population = Income
B – Lorenz Curve
C – Difference Between Equality and Reality
№19 слайд![The Gini Coefficient](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img18.jpg)
Содержание слайда: The Gini Coefficient
Mathematically, the Gini Coefficient is equal to twice the area enclosed between the Lorenz curve and the equality diagonal.
When there is perfect equality, the Lorenz curve is the equality diagonal, and the value of the Gini Coefficient is zero.
When one member of the population holds all of the resource, the value of the Gini Coefficient is one.
№20 слайд![The Gini Coefficient Pros](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img19.jpg)
Содержание слайда: The Gini Coefficient
Pros
Generally regarded as gold standard in economic work
Incorporates all data
Allows direct comparison between units with different size populations
Attractive intuitive interpretation
№21 слайд![Theil s T Statistic Theil s T](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img20.jpg)
Содержание слайда: Theil’s T Statistic
Theil’s T Statistic lacks an intuitive picture and involves more than a simple difference or ratio.
Nonetheless, it has several properties that make it a superior inequality measure.
Theil’s T Statistic can incorporate group-level data and is particularly effective at parsing effects in hierarchical data sets.
№22 слайд![Theil s T Statistic Theil s T](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img21.jpg)
Содержание слайда: Theil’s T Statistic
Theil’s T Statistic generates an element, or a contribution, for each individual or group in the analysis which weights the data point’s size (in terms of population share) and weirdness (in terms of proportional distance from the mean).
When individual data is available, each individual has an identical population share (1/N), so each individual’s Theil element is determined by his or her proportional distance from the mean.
№23 слайд![Theil s T Statistic](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img22.jpg)
Содержание слайда: Theil’s T Statistic
Mathematically, with individual level data Theil’s T statistic of income inequality is given by:
where n is the number of individuals in the population, yp is the income of the person indexed by p, and µy is the population’s average income.
№24 слайд![Theil s T Statistic The](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img23.jpg)
Содержание слайда: Theil’s T Statistic
The formula on the previous slide emphasizes several points:
The summation sign reinforces the idea that each person will contribute a Theil element.
yp/µy is the proportion of the individual’s income to average income.
The natural logarithm of yp /µy determines whether the element will be positive (yp /µy > 1); negative (yp /µy < 1); or zero (yp /µy = 0).
№25 слайд![Theil s T Statistic Example](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img24.jpg)
Содержание слайда: Theil’s T Statistic – Example 1
№26 слайд![Theil s T Statistic Often,](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img25.jpg)
Содержание слайда: Theil’s T Statistic
Often, individual data is not available. Theil’s T Statistic has a flexible way to deal with such instances.
If members of a population can be classified into mutually exclusive and completely exhaustive groups, then Theil’s T Statistic for the population (T ) is made up of two components, the between group component (T’g) and the within group component (Twg).
№27 слайд![Theil s T Statistic](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img26.jpg)
Содержание слайда: Theil’s T Statistic
Algebraically, we have:
T = T’g + Twg
When aggregated data is available instead of individual data, T’g can be used as a lower bound for Theil’s T Statistic in the population.
№28 слайд![Theil s T Statistic The](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img27.jpg)
Содержание слайда: Theil’s T Statistic
The between group element of the Theil index has a familiar form:
where i indexes the groups, pi is the population of group i, P is the total population, yi is the average income in group i, and µ is the average income across the entire population.
№29 слайд![Theil s T Statistic Example](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img28.jpg)
Содержание слайда: Theil’s T Statistic – Example 2
№30 слайд![Group analysis with Theil s T](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img29.jpg)
Содержание слайда: Group analysis with Theil’s T Statistic:
As Example 2 hints, Theil’s T Statistic is a powerful tool for analyzing inequality within and between various groupings, because:
The between group elements capture each group’s contribution to overall inequality
The sum of the between group elements is a reasonable lower bound for Theil’s T statistic in the population
Sub-groups can be broken down within the context of larger groups
№31 слайд![Theil s T Statistic Pros Can](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img30.jpg)
Содержание слайда: Theil’s T Statistic
Pros
Can effectively use group data
Allows the researcher to parse inequality into within group and between group components
№32 слайд![Next Steps Those interested](/documents_6/78d86ddcdfb73259677e6719bc3bb63c/img31.jpg)
Содержание слайда: Next Steps
Those interested in a more rigorous examination of inequality metrics with several numerical examples should proceed to The Theoretical Basics of Popular Inequality Measures.
Otherwise, proceed to A Nearly Painless Guide to Computing Theil’s T Statistic which emphasizes constructing research questions and using a spreadsheet to conduct analysis.