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

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

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)

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]

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 0471457167, 9780471457169 www.louischauvel.org/kk.pdf 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

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

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.

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.

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

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(http://www.vankerm.net/stata) replace *net install _grndraw , from(http://www.vankerm.net/stata) replace clear set obs 10000 egen d1 = rndraw(), gb2( 5.14 1 1 0.5 ) egen d2 = rndraw(), gb2( 2.8 1 1 1.5 ) 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

My problem with Gini 2 completely different distributions can give the same Gini Index D2 D1 D1 D2 *net install _grndraw , from(http://www.vankerm.net/stata) replace clear set obs 10000 egen d1 = rndraw(), gb2( 5.14 1 1 0.5 ) egen d2 = rndraw(), gb2( 2.8 1 1 1.5 ) 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 = 1.968 ; D1/Med = .606  D1 more inequality at the top, less at the bottom D2: D9/Med = 1.916 ; D1/Med = .477  D2 less inequality at the top, more at the bottom

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. www.louischauvel.org/abghmethodov31.pdf

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

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. 

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

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

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

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

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

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

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

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

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: 10.1111/Roiw.12161 Sweden Germany (W) France U.K. U.S. Israel 6 Strobiloids Change

Data Variables Survey of Consumer Finances (SCF) (+ HFCS wave II) 1992 – 2013 (3 years intervals) 4500-6500 respondents each wave Stratified sample  large sub-sample of wealthy households (=> complicated weights => confidence intervals = bootstrapping) Age 25 - 74 Variables Income – “disposable income” (after some taxes) per Consumption Unit Wealth – current value of total marketable wealth and assets, net of debt

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

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

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

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%

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%

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.

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)

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

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.