the gini index l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
The Gini Index PowerPoint Presentation
Download Presentation
The Gini Index

Loading in 2 Seconds...

play fullscreen
1 / 22

The Gini Index - PowerPoint PPT Presentation


  • 372 Views
  • Uploaded on

The Gini Index. Paige Stillwell and Tanya Picinich. Overview . Lorenz Curve Perfect Income Equality / Complete Income Inequality Gini Index Calculation Examples United States Gini Index Riemann Sum and Trapezoidal Rule Potential Issues with the Gini Index

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'The Gini Index' - teva


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
the gini index

The Gini Index

Paige Stillwell

and

Tanya Picinich

overview
Overview
  • Lorenz Curve
    • Perfect Income Equality / Complete Income Inequality
  • Gini Index
    • Calculation Examples
  • United States Gini Index
  • Riemann Sum and Trapezoidal Rule
  • Potential Issues with the Gini Index
  • Why is the Gini Index Important?
  • Gini Index Comparison Across Countries
  • United States Gini Index Over Time
the lorenz curve
The Lorenz Curve
  • Shows the share of total income of the population from 0 to t where t is the rank of a household’s income as a percentage of the total population
complete inequality
Complete Inequality
  • One person makes all the money. Everyone else makes nothing
gini index
Gini Index
  • Gives information about the income inequality of a country in one number
  • Ranges from 0 to 1
  • Calculated as the area between perfect equality (y=x) and the Lorenz curve
slide7
The Gini Index for perfect equality is 0
  • The Gini Index for total inequality is 1
example l t t 2
Example: L(t) = t2
  • What’s the Gini Index for a country that has a Lorenz curve of L(t) = t2 ?
example l t t 3
Example: L(t) = t3
  • Will the Gini Index increase or decrease from the previous example if the equation changes to L(t) = t3?
reality how the gini index is calculated
Reality: How the Gini Index is Calculated
  • In real life we are not given functions
  • We must use data points to find the Gini Index
  • We use income quintiles which are made available by the U.S. Census Bureau
the united states gini index 2007
The United States Gini Index 2007
  • The United States Gini Index for 2007 is quoted by the U.S. Census Bureau as G(t)=.463
  • This value may vary depending on what is considered as income and whether individuals or households are examined
riemann sum and trapezoidal rule
Riemann Sum and Trapezoidal Rule
  • Approximates an integral when the equation of the function is unknown
  • Using the 2007 data we can approximate the Gini Index
  • Riemann sums use either right or left endpoints to form rectangles
  • The trapezoidal rule is the average of the right and left endpoint approximations
riemann sum
Riemann Sum
  • The definition of an integral of f from a to b is:
  • Using right end points:
  • Using left end points:
riemann sum14
Riemann Sum
  • Using right end points:
  • Using left end points:
trapezoidal rule
Trapezoidal Rule
  • Basically an average of the right and left endpoints from the Riemann Sum
  • Using the 2007 Income Quintiles as data points we get:
trapezoidal rule16
Trapezoidal Rule

Actual Gini Index = .463

potential issues
Potential Issues
  • The Gini Index glosses over many details
  • Gives a more accurate picture of the relationship between the upper class and middle class than the relationship between the upper class and lower class
  • Does not reflect unreported income and money received through welfare systems
ways to calculate a more accurate gini index
Jackknife

Calculate the Gini Index many times, but remove one data point each time

Produces a mean distribution and a standard deviation for the Gini Index

Bootstrap

Calculate the Gini Index from a random sample of the income data many times

Produces a mean distribution and a standard deviation for the Gini Index

Ways to calculate a more accurate Gini Index:
why is the gini index so important
Why is the Gini Index so important?
  • Compiles information about income inequality into 1 number
  • Allows for comparisons with other countries
  • Shows how income inequality changes over time
  • This information has great social, political, and economic implications
comparisons across countries
Comparisons Across Countries
  • The Gini index for the entire world = 56 - 66
  • Tolerance for inequality of income varies between countries
    • US = higher tolerance for income inequality
    • European countries = lower tolerance for income inequality
    • Underdeveloped countries have a higher income inequality