1. Income and wealth distribution
Income and wealth distribution Extreme Inequality in Joint Income and Wealth Distributions in the United States, 1995 to 2016 (LWS data)
Louis Chauvel, University of Luxembourg, IRSEI
Eyal Bar-Haim, University of Luxembourg, IRSEI
Anne Hartung, University of Luxembourg, IRSEI
Philippe Van Kerm, University of Luxembourg, IRSEI and LISER

2. www.louischauvel.org Extreme inequalities & wealth distributions
Middle class dynamics & class structures
Models of comparative socio historical change
Generational/Cohort change
Pareto Levy distributions
Simmel – Geiger Th.
Mannheim theory of social change
Lotka Voltera prey-predator models

3. Outline Introduction Background Method Results
Extreme problem of extreme inequality measurement
My problem with Gini
From intensity of inequality to shape of inequality
The Isograph
Background
Focus on income AND wealth (I and W diagnoses can differ)  Piketty, 2014; Wolff, 2016
Wealth to Income (W/I) ratio  skyrocketed in many countries (Piketty as usual)
Expect changing roles of merit and inheritance  Killewald, Pfeffer, & Schachner, 2017
Expect massive changes between the 1990’s and the 2010’s  All & al. 20xx
Method
ISOgraph  a new way to detect level-specific inequalities and observe change
New method for joint distributions
US Data SCF series in LWS
Results
Wealth inequality increased substantially and significantly
Income inequality … the same
The upper-middle class benefitted more (in I and W) relatively to the top elite or the median
Increasing importance of wealth over income in inequality (higher W/I ratio)

4. Initial Results LWS– U.K./U.S. Wealth Comparison
clear all
local fifi " uk11"
foreach toto in `fifi' {
local pers "$`toto'p"
local house "$`toto'h"
use `house' , clear
keep hid iso2 year dnw dhi hwgt nhhmem
sort hid
*keep if hid!=hid[_n-1]
*noi su *
save "$mydata/prosoc/`toto'w" , replace }
clear
matrix B=J(1 , 4, .)
append using "$mydata/prosoc/`toto'w"
gen INTwgt=int(hwgt*1000)+1
gen networth=dnw
gen lw=ln(dnw)
gen INCUC=dhi/sqrt(nhhm)
gen li=ln(INC)
su INCUC [fw=INTwgt] , d
replace INCUC=INCUC/r(p50)
replace networth=networth/r(p50)
su networth [fw=INTwgt] , d
isograph networth [pw=INTwgt]
isograph INCUC [pw=INTwgt]

5. Introduction Extremely skewed distributions of wealth and income
The bible : K&K
Statistical Size Distributions in Economics and Actuarial Sciences
Christian Kleiber, Samuel Kotz / Wiley-IEEE, 2003
ISBN ,
Introduction
Extremely skewed distributions of wealth and income
Small fraction of the pop. can control a considerable share of the resource
“Easy” to compare Income versus wealth inequality
Difficult to compare US and Chile distributions
Zipf (Pharaoh) distribution

6. Lorenz curve & the Gini index
Gini = 0 in case of “perfect” equality, & 1 in case of “perfect inequality” => one single individual possesses everything
Income in Luxembourg
(hfcs 2010)
Gini = 0.34
 % of cumulated income
Wealth in Luxembourg
(hfcs 2010)
Gini = 0.64
The 60 % less affluent pop cumulate 36 % of the tot income
Gini of income = 0.20  the world lowest
Gini of income = 0.35  European nations
Gini of income = 0.45  the U.S.
Gini of income = 0.60  Brazil
Gini of wealth = 0.65  European nations
Gini of wealth = 0.80  the U.S.
Zipf distribution (Pharaoh)
Gini = 0.85
 % of pop ranked by income

7. Frank Cowell, Brian Nolan, Javier Olivera and Philippe Van Kerm 2017 “Wealth, Top Incomes and Inequality”, K. Hamilton and C.Hepburn (Eds.). Wealth: Economics and Policy, Oxford University Press.

8. Frank Cowell, Brian Nolan, Javier Olivera and Philippe Van Kerm 2017 “Wealth, Top Incomes and Inequality”, K. Hamilton and C.Hepburn (Eds.). Wealth: Economics and Policy, Oxford University Press.

9. Frank Cowell, Brian Nolan, Javier Olivera and Philippe Van Kerm 2017 “Wealth, Top Incomes and Inequality”, K. Hamilton and C.Hepburn (Eds.). Wealth: Economics and Policy, Oxford University Press.
Saturation of inequality

10. My problem with Gini
2 completely different distributions can give the same Gini Index
GB2 generator coming from Philippe Van Kerm STATA tool
net install _grndraw , from( replace
*net install _grndraw , from( replace
clear
set obs 10000
egen d1 = rndraw(), gb2( )
egen d2 = rndraw(), gb2( )
fastgini d1
fastgini d2
*ssc install glcurve
glcurve d1, gl(gl1) p(p1) lorenz nograph
glcurve d2, gl(gl2) p(p2) lorenz nograph
sort p1
twoway (line gl1 p1, c(L)) (sca gl2 p2) , scale(.1)
*ssc install ineqdeco
ineqdeco d1
ineqdeco d2
2 distributions, same mean, with the same Gini of .30
D1: GB2(5.14;1;1;0.5) Relat. poverty rate 50% = .041
D2: GB2(2.8;1;1;1.5) Relat. poverty rate 50% = .115
CONCLUSION: remaining unexplained gender wage gap is substantial
 pointing towards other explanations
We can show that
 A lower Gini can go with higher relative poverty rates

11. My problem with Gini
2 completely different distributions can give the same Gini Index D2 D1 D1 D2
*net install _grndraw , from( replace
clear
set obs 10000
egen d1 = rndraw(), gb2( )
egen d2 = rndraw(), gb2( )
fastgini d1
fastgini d2
*ssc install glcurve
glcurve d1, gl(gl1) p(p1) lorenz nograph
glcurve d2, gl(gl2) p(p2) lorenz nograph
sort p1
twoway (line gl1 p1, c(L)) (sca gl2 p2) , scale(.1)
*ssc install ineqdeco
ineqdeco d1
ineqdeco d2
CONCLUSION: remaining unexplained gender wage gap is substantial
 pointing towards other explanations
D1: D9/Med = ; D1/Med = .606
 D1 more inequality at the top, less at the bottom
D2: D9/Med = ; D1/Med = .477
 D2 less inequality at the top, more at the bottom

12. From intensity of income/wealth inequality to shape of inequality
Gini provides an overall diagnosis
But reliability across the distribution is limited
Possibility to compare all the percentile ratios (D9/med, etc.)
Or all the cdf, density, etc.
But difficult to be systematic…
Chauvel, L. (2016). The intensity and shape of inequality: the ABG method of distributional analysis. Review of Income and Wealth, 62(1), 52–68.

13. Frank Cowell, Brian Nolan, Javier Olivera and Philippe Van Kerm 2017 “Wealth, Top Incomes and Inequality”, K. Hamilton and C.Hepburn (Eds.). Wealth: Economics and Policy, Oxford University Press.
Saturation of inequality

14. The old Pen’s Parade graph
Swedish median SE
Pros’ arguments:
Visualization of hierarchy Easy to handle Very usual graph
(A’Hearn, B., & Vecchi, G. (2015). Cowell, F. A., & Van Kerm, P. (2015))
Cons’ arguments:
All these graphs look the same Poorest countries spuriously look more equal Unhelpful for tail comparison Border problems near to x=0 and x=1 DE
German median
Source: Silc microdata 2011
Pen's (1973) “Parade of Dwarfs”
See: Hao, L., & Daniel Q. Naiman. (2010). Assessing Inequality. Thousand Oaks, CA: SAGE Publications, Inc. 

15. Income Distributions US
Jan Pen’s Parade
Medianized income
Pen’s Parade
Saturation of inequality
2013
Median income= 1
1992
Percentile rank

16. Wealth Distributions Jan Pen’s Parade Medianized wealth
Saturation of inequality
2013
Median wealth = 1
1992
Percentile rank

17. ISOGRAPH
X = logit of the fractional rank r (=logitrank) of resource (income, wealth, etc.) [r between 0 and 1]
Y = log medianized resource (resource divided by its median)
ISO=Y/X is a measure of Level-specific inequalities
If ISO=a (constant)  Champernowne-Fisk (double Pareto) distribution with a = Gini (Dagum, 1977)
X=𝑙𝑜𝑔𝑖𝑡( 𝑟 𝑖
Y=ln⁡( 𝑖𝑛𝑐𝑜𝑚𝑒 𝑖 𝑚𝑒𝑑𝑖𝑎𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 )
𝐼𝑆 𝑂 i = ln⁡( 𝑖𝑛𝑐𝑜𝑚𝑒 𝑖 𝑚𝑒𝑑𝑖𝑎𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 ) 𝑙𝑜𝑔𝑖𝑡( 𝑟 𝑖 17

18. Wealth Distributions 2013 Ln Medianized wealth
Log-logit transformation of Jan Pen’s Parade
1992
Median ln(wealth) = 0
Logit percentile rank

19. ISOGRAPH
X = logit of the fractional rank r (=logitrank) of resource (income, wealth, etc.) [r between 0 and 1]
Y = log medianized resource (resource divided by its median)
ISO=Y/X is a measure of Level-specific inequalities
If ISO=a (constant)  Champernowne-Fisk (double Pareto) distribution with a = Gini (Dagum, 1977)
X=𝑙𝑜𝑔𝑖𝑡( 𝑟 𝑖
Y=ln⁡( 𝑖𝑛𝑐𝑜𝑚𝑒 𝑖 𝑚𝑒𝑑𝑖𝑎𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 )
𝐼𝑆 𝑂 i = ln⁡( 𝑖𝑛𝑐𝑜𝑚𝑒 𝑖 𝑚𝑒𝑑𝑖𝑎𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 ) 𝑙𝑜𝑔𝑖𝑡( 𝑟 𝑖 19

20. Wealth Distributions Log-logit transformation of Jan Pen’s Parade Y
Ln Medianized wealth
2013
For X=2
ISO 2013= Slope Y/X in 2013
1992
Median ln(wealth) = 0
Substantial increase in wealth inequality
For X=2 ISO 1992 = Slope Y/X in 1992
X=2 X
Logit percentile rank

21. ISOGRAPH Reading the ISOGRAPH
Each point represent ISO at the X (specific-level inequality)
Differences in inequality between levels indicate variation in inequality levels
The higher ISO, the higher the inequality at this specific level (=stronger stretch of the distribution)
Chauvel, L. (2016). The intensity and shape of inequality: the ABG method of distributional analysis. Review of Income and Wealth, 62(1), 52–68.
L Chauvel, E Bar-Haim (2017) ISOGRAPH: Stata module to compute inequality over logit ranks of social hierarchy - Statistical Software Components, 2017
[ = STATA : ssc install isograph ] 21

22. LIS examples of ISO on equivalized disposable income = “level of living”
Old date
New date
new
old
new
new
new
old
old
old
Source: LIS data, various years and countries

23. Sweden Germany (W) France U.K. U.S. Israel 6 Strobiloids Change
Chauvel, L., 2016, “The Intensity And Shape Of Inequality: The Abg Method Of Distributional Analysis”, Review Of Income And Wealth. Doi: /Roiw.12161
Sweden
Germany (W)
France
U.K.
U.S.
Israel
6 Strobiloids Change

24. Data Variables Survey of Consumer Finances (SCF) (+ HFCS wave II)
1992 – 2013 (3 years intervals)
respondents each wave
Stratified sample  large sub-sample of wealthy households (=> complicated weights => confidence intervals = bootstrapping)
Age
Variables
Income – “disposable income” (after some taxes) per Consumption Unit
Wealth – current value of total marketable wealth and assets, net of debt

25. Initial Results– U. S. wealth exceptionalism (or the E. U
Initial Results– U.S. wealth exceptionalism (or the E.U. a bunch of outliers…)
W isograph
I isograph
W isograph
I isograph x x x
Source: US SCF 2013 and EU-HFCS II

26. Initial Result– U. K. /U. S. comparison – Net W (or the E. U
Initial Result– U.K./U.S. comparison – Net W (or the E.U. a bunch of outliers…)
U.K U.S.
This is almost a Zipf!!!
W isograph
W isograph
I isograph
I isograph x x
Source: LWS 2013 and U.K. LWS 2011

27. Initial Results– U. K. /U. S. comparison – Net W (or the E. U
Initial Results– U.K./U.S. comparison – Net W (or the E.U. a bunch of outliers…)
U.S.
W isograph
Top 5%!!!
U.K.
I isograph x
Source: LWS 2013 and U.K. LWS 2011

28. Result 1 – Income inequality increases U.S.
Significant increase in income inequality for incomes with logit rank of 2 (top 11%) and above. No significant change for the highest 2% and around the median income.
2016
1995
ISO
Significant increase in income inequality
Logitrank(Income)
X=2  Top 11%
X=5.5  Top 2%

29. Result 2 – Wealth inequality increases
Significant increase in wealth inequality for wealth above the median (logit rank 0). No significant change above the top 0.5% and around the median income.
2016
1995
ISO
Significant increase in W inequality
Logitrank(Wealth)
X=0.5  Top 38%
X=5.5  Top 0.5%

30. Joint Distribution of Income and Wealth by Logitranks
Using logitranks instead of percentiles, The association is much clearer. Especially in the upper part of the distribution.

31. Result 3: stronger Income-Wealth Association (1992-2013)
The income/wealth association became stronger over the years. Most of the increase is during the first decade of the 21st century.
Significant increase in the I x W association
R2 of Log(Income) x Log(wealth)
R2 of LR(Income) x LR(wealth)

32. Result 4: increasing Wealth to Income ratios
(W/I) (in Years …)
Near to the top 2%, in 2016, Wealth=10 years of income
2016
1995
Above to the Median,
On both years, Wealth= 2 years of income
Significant increase in the W/I ratio
Near to the top 2%, in 1995, Wealth=6 years of income

33. The 15 Proposals from Tony Atkinson’s ‘Inequality – What can be done?’
Conclusions
Only bad news for equality:
Income and wealth inequality increased over the period (R1 & R2)
Wealth inequality increased almost everywhere above the median (R2)
The very top fractiles (above top 1%) are less significantly affected (data or reality?)
The wealth-income association increased: even more consistent relation income rich and wealth rich are more and more the same ones (R3)
The W/I ratio increased (R4) mostly near to the top decile from 7 to 11 years
… Plus initial result (R0): Wealth inequality in the U.S. is really exceptional (compared to Europe)
 R0, R1, R2, R3, R4: 5 synergetic aspects of increasing inequalities in the U.S.
The 15 Proposals from Tony Atkinson’s ‘Inequality – What can be done?’
Proposal 7: A public Investment Authority should be created, operating a sovereign wealth fund with the aim of building up the net worth of the state by holding investments in companies and in property.
Idea to pursue: a re-examination of the case for an annual wealth tax and the prerequisites for its successful introduction.
Idea to pursue: a global tax regime for personal taxpayers, based on total wealth.