Gini in a Bottle: The Mathematics of Income Inequality

Transcription

1 Gini in a Bottle: The Mathematics of Income Inequality Rich Beveridge Clatsop Community College rbeveridge@clatsopcc.edu

2 Statistics and Social Justice In 1999, I took my high school math class to the library and asked them each to find a data set that they thought was interesting and to make a graph of it. They were then to write a paragraph explaining why they chose the data set and what their graph showed.

3 Statistics and Social Justice I was looking through the Statistical Abstract of the United States and came across the budget summary. There are some interesting things you can do with the information in the budget summary.

4 Statistics and Social Justice I decided to look at how much the federal government collects from the corporate income tax. The 1999 budget contains revenue information from Corporate income taxes collected were $182,293,000,000 and the total revenues were $1,579,292,000,000.

5 Statistics and Social Justice This comes out to about 11.5% of total federal revenue. I wondered what this percentage looked like over time. I collected the data going back to about 1920 and produced a graph very much like the next slide.

6

7

8 Statistics and Social Justice About five years ago, my interest was piqued again by the next graph. Share of income for the top 10% ( ) Piketty/Saez

9

10

11

12 Statistics and Social Justice There are many factors that affect this income distribution. One of them is tax policy, so I decided to look at the top tax rates during the 20 th century. These are the marginal rates charged just on income over a certain (very high) threshold.

13 % 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% Highest Marginal Tax Rate

14 US Top Marginal Tax Rate (Federal Individual Income Tax) 100% 90% Top MTR (Federal Individual Income Tax) 80% 70% 60% 50% 40% 30% 20% 10% 0% Source: statistics computed by the author

15 50% 45% 40% 35% 30% 25% Share of total income going to Top 10% FIGURE 1A The Top Decile Income Share in the United States, Source: Piketty and Saez (2003), series updated to Income is defined as market income including realized capital gains (excludes government transfers).

16 Statistics and Social Justice Inequality is rising we ll examine the Gini Index in detail later. Corporate profits have skyrocketed in the last years, but this hasn t translated into increased income for all Americans.

17 Statistics and Social Justice The next graph shows corporate profits as a percentage of Gross Domestic Product. GDP is defined as the market value of all officially recognized final goods and services produced in the United States.

18

19 Statistics and Social Justice As corporate profits have increased, CEO compensation has also increased. Calculated as multiple of the median wage for each corporation.

20

21 Statistics and Social Justice CEO multiple web page

22 Statistics and Social Justice While corporate profits and CEO compensation have increased dramatically, the income growth for other groups has been stagnant.

23

24

25

26 Statistics and Social Justice As the median income has stagnated, Americans have increased their credit card debt.

27

28 Statistics and Social Justice There has also been a disconnect between worker productivity and worker compensation in the last 30 years.

29 Figure A Growth of real hourly compens ation forr production/nonsupervisory workers and productivity, Note: Hourly compensation is of production/nonsupervisory workers in the private sector and productivity is for the total economy. Source: Author's analysis of unpublished total economy data from Bureauu of Labor Statistics, Labor Productivity and Costs program and Bureauu of Economic Analysis, National Income and Product Accounts public data series

30 Unemployment High unemployment is also a problem. The next graph examines the Beveridge Curve for the last 10 years. The Beveridge Curve compares the unemployment rate with the job openings rate.

31 Unemployment The Beveridge Curve was developed in 1958 by British economists J.C.R. Dow and L.A. Dicks-Mireaux and named for British economist William Beveridge.

32 Unemployment As the job openings increase, the unemployment decreases. In the graph of the Beveridge Curve we see a disconnect in the way businesses are hiring now as compared with the period before 2008.

33 Source: Bureau of Labor Statistics, Current Population Survey and Job Openings and Labor Turnover Survey, February 12, This graph plots the job openings rate against the unemployment rate. This graphical representation is known as the Beveridge Curve, named after the British economist William Henry Beveridge ( ). The economy s position on the downward sloping Beveridge Curve reflects the state of the business cycle. During an expansion, the unemployment rate is low and the job openings rate is high. Conversely, during a contraction, the unemployment rate is high and the job openings rate is low. The position of the curve is determined by the efficiency of the labor market. For example, a greater mismatch between available jobs and the unemployed in terms of skills or location would cause the curve to shift outward, up and toward the right. From the start of the most recent recession in December 2007 through the end of 2009, each month s point on the curve moved lower and further to the right as the job openings rate declined and the unemployment rate rose. From 2010 to the present, the point moved up and to the left as the job openings rate increased and the unemployment rate decreased. In December 2012, the job openings rate was 2.6 percent and the unemployment rate was 7.8 percent. 4

34 Wealth Inequality In 2005 behavioral economists Dan Ariely and Michael Norton conducted a survey that asked 5,000 Americans what they thought the distribution of wealth was in America, and what they thought it should be.

35 out of balance A Harvard business prof and a behavioral economist recently asked more than 5,000 Americans how they thought wealth is distributed in the United States. Most thought that it s more balanced top 20% n second 20% n third 20% n fourth 20% n bottom 20% n than it actually is. Asked to choose their ideal distribution of wealth, 92% picked one that was even more equitable. actual distribution of wealth what americans think it is what they would like it to be Source: Michael I. Norton, Harvard Business School; Dan Ariely, Duke University

36 50% 45% 40% 35% 30% 25% Share of total income going to Top 10% FIGURE 1A The Top Decile Income Share in the United States, Source: Piketty and Saez (2003), series updated to Income is defined as market income including realized capital gains (excludes government transfers).

37

38 Income Inequality The problem of income inequality has been in the news more in the last few years than it has previously. One way to measure the distribution of income in a population is through the use of the Gini Index of an income distribution.

39 Income Inequality The Gini Index was developed by the Italian statistician Corrado Gini in Gini s index was based on the work of Max O. Lorenz, an American statistician of the same era.

40 Max O. Lorenz Max Lorenz was born in Iowa in 1876 and received his Ph.D. in Economics from University of Wisconsin at Madison in Lorenz published a paper in 1905 while he was still a student called Methods of Measuring the Concentration of Wealth.

41 Measuring Income Inequality Prior to the work of Lorenz and Gini, measures of income inequality had relied on the work of the Italian economist Vilfredo Pareto. Both Lorenz and Gini were unsatisfied with Pareto s method because they felt it was ill-suited to detailed analysis of income distributions.

42 The Lorenz Curve In Lorenz s 1905 paper, he outlined the development of what is known as the Lorenz Curve. In Lorenz s original curve, he graphed the percentages of income along the horizontal axis and the percentiles of the population along the vertical axis.

43

44 The Lorenz Curve In a modern Lorenz Curve of income distribution, the percentiles of the population are graphed on the horizontal axis and the percentage of the income they receive is graphed on the vertical axis.

45

46 The Lorenz Curve The straight diagonal line in the graph is the graph of perfect equality. This is an idealized graph which represents 20% of the population earning 20% of the income, 40% of the population earning 40% of the income and so on up to 100%.

47 The Lorenz Curve Although this is not a realistic expectation for income distribution it does provide a convenient and stable comparison for all of the actual income distributions.

48 Lorenz Curve The Lorenz Curve measures the dispersion/concentration within a data set and can be used for data other than income. Here is a Lorenz Curve for the share of business done by auctioneers in 1820s New York.

49

50 Lorenz Curve The Lorenz Curve is a convenient way to look the dispersion within a statiscal data set. While an improvement over previous methods, it still is somewhat complicated. Corrado Gini s contribution was to simplify this graph and express it as a single number the Gini Index or Gini Coefficient.

51 Corrado Gini Corrado Gini was born in 1884 near Treviso in northeast Italy. Gini was from a wealthy family and studied law, biology, mathematics and statistics.

52 Corrado Gini He began to teach statistics in 1909 and ended up at the University of Rome where he remained until Gini founded the international journal of statistics Metron in 1920 and was president of the Italian Central Institute of Statistics from

53 Corrado Gini In 1932 Gini and Mussolini had a disagreement about the Central Institute of Statistics and Gini resigned, but remained in his position at the University of Rome.

54 Corrado Gini During the period from , Gini worked on creating an effective measure of dispersion in a data set. He would apply this to income distributions as what became known as the Gini Index.

55 Gini Index Gini s idea was to take the Lorenz Curve for an income distribution and measure the area between idealized perfectly equal distribution and the actual distribution data.

56

57 Gini Index In Calculating the Gini index, we first look at the area under the idealized perfect equality portion of the graph. This corresponds to the sum of sections A and B. This is a triangle with base=1 and height=1 so the area is one half.

58

59 Gini Index Then after the Lorenz curve for an income distribution is plotted, the area under this curve is calculated. This is the section marked B.

60

61

62 Gini Index To find the area of the section marked A, we simply subtract the area under the Lorenz Curve from the area under the triangle this gives us the difference between the actual income distribution and the idealized distribution.

63

64 Gini Index This value for A is then turned into a percentage by dividing it by the area under the idealized distribution.

65 Gini Index As an example, let s calculate the Gini Index for the U.S. household income data from 1980 and Percentile Income Share Cumulative Share 20% 4.2% 4.2% 40% 10.2% 14.4% 60% 16.8% 31.2% 80% 24.7% 55.9% 100% 44.1% 100%

66 Gini Index The graph for this is below:

67 Gini Index Now, we calculate the area under each of the five regions. The first is a triangle and the rest are trapezoids A A A A A A A *.2* *.2*( ) *.2*( ).0456 *.2*( ) *.2*(.559 1) 2 A 3 A 4 A

68

69 Gini Index The area of the triangle was 0.5, so the area A between the idealized line and the Lorenz Curve is = Then, /0.5= for a Gini Index of about 38.

70 Gini Index 2011 Percentile Income Share Cumulative Share 20% 3.2% 3.2% 40% 8.4% 11.6% 60% 14.3% 25.9% 80% 23.0% 48.9% 100% 51.1% 100%

71 Gini Index The graph for this is below:

72 Gini Index Now, we calculate the area under each of the five regions. The first is a triangle and the rest are trapezoids A A A A A A A *.2* *.2*( ) *.2*( ) *.2*( ) *.2*(.489 1) 2 A 3 A 4 A

73

74 Gini Index The area of the triangle was 0.5, so the area A between the idealized line and the Lorenz Curve is = Then, /0.5= for a Gini Index of about 44.

75

76 Income Inequality Former Chairman of the Federal Reserve Bank Alan Greenspan on income inequality: As I ve often said, this is not the type of thing which a democratic society a capitalist democratic society can really accept without addressing. (2005)

77 Graph Sources Individual and corporate income taxes as a percent of all federal revenues Source data: Office of Management and Budget Graph source: Sources of federal revenue Source data: Federal Budget Graph source: Share of income for the top 10% Source data: Piketty/Saez Graph source: Paul Krugman Increasing income share top 1%/0.1% Source data: Piketty/Saez Graph Source: Slate/Catherine Mulbrandon

78 Top marginal tax rates Source data: Piketty/Saez Graph source: ach.pdf Corporate profits to GDP Source data: FRED (Federal Reserve Economic Data) Graph Source: CEO pay ratio Source data: Economic Policy Institute Graph source: Low, middle and high income growth Source: Economic Policy Institute Real mean household income by quintile Source data: Census Bureau Graph source:

79 Real median household income Source data: Census Bureau Graph Source: Growth in credit card debt vs growth in real wages Source data: innovestgroup.com Graph source: Productivity vs. hourly compensation Source data: Econommic Policy Institute Lawrence Mishel Graph source: Beveridge curve Source data: Bureau of Labor Statistics Graph source: Economic Populist Wealth distribution survey Source data: Dan Ariely Michael Norton Graph Source:

80 Top 1% share of income more than doubled Source data: Congressional Budget Office Graph source: Lorenz curve Source: #1 OC%29.pdf Source: #2 Inequality among auctioneers in New York City 1820s Source: Gini coefficient illustrations Source: Gini index income disparity since WWII Source: ns