1 / 22

The Gini Index

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

teva
Download Presentation

The Gini Index

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Gini Index Paige Stillwell and Tanya Picinich

  2. 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

  3. 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

  4. 20% of the population makes 20% of the income and so on Lorenz curve has the equation y=x Perfect Income Equality: Utopia

  5. Complete Inequality • One person makes all the money. Everyone else makes nothing

  6. 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

  7. The Gini Index for perfect equality is 0 • The Gini Index for total inequality is 1

  8. Example: L(t) = t2 • What’s the Gini Index for a country that has a Lorenz curve of L(t) = t2 ?

  9. Example: L(t) = t3 • Will the Gini Index increase or decrease from the previous example if the equation changes to L(t) = t3?

  10. 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

  11. 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

  12. 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

  13. Riemann Sum • The definition of an integral of f from a to b is: • Using right end points: • Using left end points:

  14. Riemann Sum • Using right end points: • Using left end points:

  15. 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:

  16. Trapezoidal Rule Actual Gini Index = .463

  17. 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

  18. 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:

  19. 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

  20. 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

  21. United States Over Time

  22. Questions?

More Related