Montclair State University; Research Methods: Spring 2015 ON INEQUALITY: MEASUREMENT AND OTHER ISSUES
WHAT IS INEQUALITY? If there were in the world today any large number of people who desired their own happiness more than they desired the unhappiness of others, we could have a paradise in a few years Bertrand Russell
WHAT IS INEQUALITY? Intellectual and Emotional Rationalization the justification for inequality Scarcity: Real or Imposed Mathematically: Naming and collecting groups that number greater than apportioned resources. The pigeonhole principle
WHAT IS INEQUALITY? Sociologically: The separation and classification of people into categories. Inter-racial, Intra-racial, Familial Economically via pricing (Education, Health Care) Socially (Labor and Housing Markets (covenants), Salaries and Wages)
MEASURING INEQUALITY Normative Inequality: Social Welfare Objective Inequality: Measure of difference in distribution
MEASURING INEQUALITY Normative Inequality: Social Welfare Objective Inequality: Measure of difference in distribution Numeric quantification of the distributional apportionment of a resource or good.
MEASURING INEQUALITY The Empirical Cumulative Distribution Function: ECDF The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
ECDF OF 2008 INCOME Empirical Distribution (Function) on CPI-U-RS Money Income, 2008 0.0 0.2 0.4 0.6 0.8 1.0 All White Black Equal 0 50000 100000 150000
MEASURING INEQUALITY: THE LORENZ CURVE The Lorenz Curve: Np L(p) (N x) 1 x (i) i 1 (N x) 1 Np 1 F N i 1 (i N)
MEASURING INEQUALITY: THE LORENZ CURVE Lorenz Curves on CPI U RS Money Income, 2008 0.0 0.2 0.4 0.6 0.8 1.0 All, 0.37 White, 0.36 Black, 0.42 Equal, 0 0.0 0.2 0.4 0.6 0.8 1.0
MEASURING INEQUALITY: THE GINI COEFFICIENT The scaled concentration of a distribution Defined as the ratio of observed distance from equality to the maximum distance from equality. This distance is just the area between the 45 degree line Lorenz curve for a uniform distribution and the observed Lorenz curve divided by 1/2
MEASURING INEQUALITY: THE GINI COEFFICIENT 1 N 1 N N 1 N p 1 N 2 p 1 N L(p) G 1 2 1 2 L(p) 1 2 1 N N p 1 N -1 Np 1 F N i 1 (N x) 1 (i N)
MEASURING INEQUALITY For a uniformly distributed population, where all persons have equivalent income: the ECDF is a 45 degree line from the origin. the Lorenz curve is a 45 degree line from the origin to the right-hand corner of the unit square. the Gini coefficient is zero.
MEASURING INEQUALITY For a singularly distributed population, where one person holds all the income: the ECDF is a step function: zero everywhere but at the total income where it reaches 1. the Lorenz curve is the lower and right sides of the unit square. the Gini coefficient is 1.
INEQUALITY WORLDWIDE
INEQUALITY WORLDWIDE
INEQUALITY WORLDWIDE
INEQUALITY WITHIN COUNTRIES To some degree charity is a racket in a capitalist system, a way of making our obligations to one another feel optional and of keeping poor people feeling a sense of indebtedness to the rich.
INEQUALITY WITHIN COUNTRIES To some degree charity is a racket in a capitalist system, a way of making our obligations to one another feel optional and of keeping poor people feeling a sense of indebtedness to the rich. -Shawn Carter
INEQUALITY WITHIN COUNTRIES
INEQUALITY WITHIN COUNTRIES Gini 25 30 35 40 45 50 55 Honduras Chile Paraguay Philippines United States Nigeria Uzbekistan Portugal Israel Egypt Czech Republic Gini 25 30 35 40 45 50 55 Colombia Panama Costa Rica Nigeria Tunisia Belarus Czech Republic Georgia United States Gini 25 30 35 40 45 50 55 United States Uzbekistan Japan Brazil Malaysia Mexico Bolivia Egypt Nigeria Sweden Sweden Sweden 0.5 0.6 0.7 0.8 0.9 1.0 HDI2010 0 200 400 600 800 # Incarcerated / 100k 10 20 30 40 50 60 70 % Share of Economy `Unofficial' (a) HDI (b) Rate of Jailing (c) Uno cial Economy
US INEQUALITY The problem facing...people here in America is bigger than all other personal or organizational differences...we must stop worrying about the threat that we seem to think we pose to each other...and concentrate our united efforts toward solving the unending hurt.
US INEQUALITY The problem facing...people here in America is bigger than all other personal or organizational differences...we must stop worrying about the threat that we seem to think we pose to each other...and concentrate our united efforts toward solving the unending hurt. -Malcolm X
US INEQUALITY
US INEQUALITY Gini vs. GDP per capita Gini vs. Violent Crime Rate Gini vs. 8th Grade Math Prof. Pct. Gini vs. Infant Mortality GDP per capita 40 60 80 100 120 140 160 AK UT DE CT WY MA WA WV ID TX MS NY LA DC Violent Crime Rate 2007 0 10 20 30 40 AK UT NH NV MD KS IN OR ME SC TN LA AR TX PA NY KY MS DC Pct. 8th Grade Math Prof. 10 20 30 40 50 NH AK UT MA MN NJ PA ME IL KY NV RI OK CA WV TX NY TN LA AL MS DC Infant Mortality 5 6 7 8 9 10 11 AK UT MD OH KS WA MA MS LA AL AR GA TX NM NY CA DC 0.38 0.40 0.42 0.44 0.46 0.48 0.38 0.40 0.42 0.44 0.46 0.48 0.38 0.40 0.42 0.44 0.46 0.48 0.38 0.40 0.42 0.44 0.46 0.48 Gini Gini Gini Gini (a) GDP (b) Violent Crime (c) Math Scores (d) Infant Mortality
US INEQUALITY
FINAL WORDS [One cannot derive ought from is.]...since vice and virtue are not discoverable merely by reason, or the comparison of ideas, it must be by means of some impression or sentiment they occasion, that we are able to mark the difference betwixt them. -David Hume