Introduction to Extreme Inequalities: measuring income and wealth distributions  Louis Chauvel University of Luxembourg, PEARL Institute for Research on Socio-Economic Inequality (IRSEI) With the support of

From inequality to strenghtening power vertical Introduction: history, civilization and extreme inequalities 1- Extreme inequality: theory and math 2- Extreme inequality today: are they back? 3- Wealth is back: repatrimonialization 4- Extreme consequences in the world 5- Tools: Pareto, Champernowne, Isograph 6- Implementation 7- A new method

1- Introduction: history, civilization and extreme inequalities

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

Introduction: civilization and (in)equality Commonsense: civilization is a process of equalization (welfare state development, Golden age, Wirtschaftswunder, Trente Glorieuses, blurring social class borders, increasing social mobility, etc.) Archeology: civilization is intrinsically characterized by inequality (criteria of civilization are Cities, labor specialization, concentration of surplus production, class structure, state organization, along with monuments, trade, art, writing and math) Charles L Redman, The Rise of Civilization : From Early Farmers to Urban Society in the Ancient Near East, San Francisco, Freeman, 1978, p. 277. The new Walter Scheidel’s book (jan 2017): great civilizations show high (& increasing?) levels of inequality In period of peace or social rest, inequality remain high and stable See also “Towards an explanation of inequality in premodern societies: the role of colonies, urbanization, and high population density” Economic History Review Branko Milanovic https://onlinelibrary.wiley.com/doi/full/10.1111/ehr.12613

Introduction: civilization and (in)equality The new Walter Scheidel’s book: four horsemen of the reduction of inequality Wars, Epidemics, Revolutions, State collapse Inequality trends in Europe (Scheidel p 87) And now? Albrecht Dürer 1498. The Four Horsemen, in Johannes (Saint), Book of Revelation (6:1–8) time

Introduction: civilization and (in)equality The new Walter Scheidel’s book: four perspectives in the reduction of inequality Wars, Epidemics, Revolutions, State collapse Inequality trends in Europe (Scheidel p 87) And now? Albrecht Dürer 1498. The Four Horsemen, in Johannes (Saint), Book of Revelation (6:1–8) time

Inequality trends in the U.S. (Scheidel p 110) And now? time

1- Extreme inequality: theory and math

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) set obs 10000 egen d1 = rndraw() ,  gb2(5.13 1 1 0.5) 2 distributions, same mean, with the same Gini of .30 D1: GB2(5.13;1;1;0.5) Poverty = .041 D2: GB2(5.13;1;1;1.5) Poverty = .115 We can show that  A lower Gini can go with higher relative poverty rates CONCLUSION: remaining unexplained gender wage gap is substantial  pointing towards other explanations

The theory: A “new” class structure: forget Quételet, learn Pareto Farewell to the theory of average (hu)man (Quetelet, Halbwachs) Welcome(back) to extreme society (Pareto, Nielsen) 1896 Nielsen, François. 2007. “Economic Inequality, Pareto, and Sociology: The Route Not Taken.”. American Behavioral Scientist 50 (5): 619–638. 𝑁= 𝐴 𝑥 α Vilfredo Pareto 1848-1922 Adolphe Quételet 1796-1874

1. The Zipf’s pyramidal model of extreme inequality $/person 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1 N Order 1 10 2 100 3 1,000 4 10,000 5 100,000 6 1,000,000 7 10,000,000 8 Gini index = 0.847 Share top 10% = 87.5% Share top 1% = 75.0% Share top 0.1% = 62.5%

𝑁= 𝐴 𝑥 α As for Pareto with a >1, the higher a the higher equality Zipf curve if a = 1, an extreme case of inequality (extreme in the sense that the integral diverges)  The speed limit of inequality? log($) Slope -1

Applications => in economic geography (size of cities) Vilfredo Pareto now: power tailed distributions Gabaix, X., "Power Laws in Economics and Finance," Annual Review of Economics, 1, 255–94, 2009. Power-tailed distributions (Pareto-Levy distributions) Zipf distributions => Krugman 1996 etc. Gabaix 1999 etc. Applications => in economic geography (size of cities) in finance (stock market statics and dynamics) log(city rank) α≈1 log(city size)

Applications => in finance (stock market statics and dynamics) Vilfredo Pareto now: power tailed distributions Applications => in finance (stock market statics and dynamics) "Why Has CEO Pay Increased So Much?", Xavier Gabaix & Augustin Landier, Quarterly Journal of Economics, vol. 123(1), 2008, p. 49-100 α=1/ζ≈1

Applications => linguistics, terrorism, wars, astrophysics Upper tail power distributions everywhere Applications => linguistics, terrorism, wars, astrophysics Power-Law Distributions in Empirical Data , SIAM Rev., 51(4), 661–703. Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman 2009 Pareto is pervasive and almost everywhere …

Applications => linguistics, terrorism, wars, astrophysics Upper tail power distributions everywhere Applications => linguistics, terrorism, wars, astrophysics Power-Law Distributions in Empirical Data , SIAM Rev., 51(4), 661–703. Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman 2009 Pareto is pervasive and almost everywhere …

The Zipf law as it looks

2- Extreme inequality today: are they back?

Income Inequality: Economic Disparities and the Middle Class in Affluent Countries edited by: Janet C. Gornick and Markus Jäntti (Stanford University Press) 2013  http://www.sup.org/book.cgi?id=21329 Louis Chauvel, 2016, La Spirale du déclassement Essai sur la société des illusions [the Spiral of downward mobility, an essay on the society of illusions], Seuil, Paris.

The bad news (Piketty) *Capital expansion and wage stagnation *Structural Matthew effect(1): R(real interest rates) > G(real eco growth) => the new era *The richer will save, not the poorer *Auto-generated spiral of accumulation of wealth and inequalities *Farewell to meritocracy (1): “For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken even that which he hath”. Matthew 25:29, King James Version.

Even worse news (Alderson, Beckfield, etc. etc.) End of the 1960-70 Western social dream Demography-connected changes: baby-boom overcrowding effects, homogamy, role of education Market transformations: deindustrialization, global competition (new-developed countries and destabilization of the western upper working class), technological bias, winner take all Economic & Social policies: Tax reforms at the top, declining minimum wages and decay of social regulations at the bottom Godechot, Olivier 2012 Is finance responsible for the rise in wage inequality in France? Socio-Economic Review 10(3), 447-470 Robert H. Frank and Philip J. Cook 1995 The Winner-Take-All Society (New York: The Free Press,).

height Median = Mean M=177 cm sd=10.1 1- Normal law world max height = 227 cm (in a 1.000.00 sample) Max/Median = 1.280 (in a 1.000.00 sample) Gini index = .12 In the US: Robert Wadlow, the tallest person 272 cm = 1.53 the median Median = Mean M=177 cm sd=10.1 Louis

US Income Mean=1.4 * Median M=177 cm sd=10.1 Median 2- Typical Income Pareto-Champernowne-Fisk law with a gini index = .45 Max/Median Income = 700 (in a 1.000.000 sample) In the US 2013 LNG Charif Souki $141 Millions =3154 times the median US FT yearly earning lvl Mean=1.4 * Median M=177 cm sd=10.1 Median Louis Fits based on SCF 2011

No wealth based middle class 3- Typical Wealth Pareto-Champernowne-Fisk law with a gini index = .72 Max/Median Income = 71 000 (in a 1.000.00 sample) In the US 6 Walton family members own $152 Billions =250 000 times the median wealth =500 000 times the median US FT yearly earning US Wealth Mean=4.3 * Median M=177 cm sd=10.1 Median Louis Fits based on SCF 2011 No wealth based middle class

Changes in the general shapes of income distribution Globalization of the income distribution: The rich are indexed on global firms size The others on the BRICs working and wage earner classes Even more massive changes in the distributions still to come ?… Upper middle class The strobiloid representation of income distribution

The strobiloid = graph changing shapes

3- Wealth is back: repatrimonialization

Income Strobiloïd EU-SILC 2010 and Wealth (LWS) in euro 100 = median income 100 = median wealth Luxembourg Gini= 27.5% Gini= 70% Median wealth : 380K€ Median income : 36K€/UC/year

Piketty

Piketty In 1980 = wealth is 3 years of income In 2010 = wealth is 6 years of income

US 1980 Income Gini=.35 Wealth Gini=.75 Mean wealth=3.7 med income Median Income

US 2010 Income Gini=.45 Wealth Gini=.79 Mean wealth=8.5 med income Median Income

US 2040 Central Scenario Income Gini=.55 Wealth Gini=.82 Mean wealth=15.5 med income Median Income

4- Extreme consequences in the world

Even worse news: World level inequality Overall world income inequality is massive It declines (Branko Milanovic) in terms of Gini (China, the Empire of the median, is richer) But world relative poverty increase (China is farther and farther above Africa) Gini (line) and relative poverty rate (bars) (below 50% the world median)

Even worse news: World level inequality Overall world income inequality is massive; world wealth is pharaonic Lorenz curve of income (bold) and of wealth 2015 (thin)

5- More on Pareto 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 5- More on Pareto

Power tailed distributions Gabaix, X., "Power Laws in Economics and Finance,“ Annual Review of Economics, 1, 255–94, 2009. Power-tailed distributions (Pareto-Levy distributions) Zipf distributions => Krugman 1996 etc. Gabaix 1999 etc. Applications => in economic geography (size of cities) in finance (stock market statics and dynamics) Main messages: *Lognormal hypothesis not acceptable *difficult to identify the real process log(city rank) α≈1 log(city size)

Slope - a Pareto Pareto 1896: Log N = Log A - a Log x ln (x) Ln(Npoptot) Ln(N >R) Slope - a Pareto a > 1, if not => mean income diverges

Pareto distribution

Pareto of England 1880 a = 1.39

Pareto in the first Piketty’s book France incomes 1905-1995 Data : http://www.jourdan.ens.fr/piketty/_mpublic/ipublic.php Tableau 2-1 : Level of living of percentiles 1900-1910 versus 1990-1998

Champernowne I La proportion d'individus dont la richesse est comprise entre R et R+dR est :

Champernowne I

6- Implementation Florence Catasto of 1427 : www.louischauvel.org/catasto.do http://cds.library.brown.edu/projects/catasto/overview.html http://chnm.gmu.edu/worldhistorysources/d/89/whm.html

7- A new methodology 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

Many proposals in the Bible: Vilfredo Pareto now: PROBLEMS OK for the upper tail Good enough for simulations (Piketty 1999 etc. Milanovic 2013 etc. Van Kerm 2014 etc. ) So what for the rest of the distribution? We notice plenty of significant curvatures // Pareto & others (GB2) Many proposals in the Bible: Kleiber, C. and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley, Hoboken, NJ, 2003. Plus even newer ones: Jenkins, S. P., "Distributionally-Sensitive Inequality Indices and the GB2 Income Distribution," Review of Income and Wealth, 55, 392–98, 2009.

Why? How? Parker, S.C., "The generalized beta as a model for the distribution of earnings", Economics Letters, 62, 197–200, 1999. => “A neoclassical model of optimising firm behaviour, which predicts the earnings distribution to follow the flexible and well-known generalised beta distribution of the second kind.”

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) set obs 10000 egen d1 = rndraw() ,  gb2(5.13 1 1 0.5) 2 distributions, same mean, with the same Gini of .30 D1: GB2(5.13;1;1;0.5) Poverty = .041 D2: GB2(5.13;1;1;1.5) Poverty = .115 We can show that  A lower Gini can go with higher relative poverty rates CONCLUSION: remaining unexplained gender wage gap is substantial  pointing towards other explanations

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

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. 

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

Jan Pen’s Parade Wealth Distributions 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 58

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

NOTE We express the rank of an individual as a proportion p € [0,1] of the cumulative population below her/him on the scale of resource (earning, income, wealth <randomization of ex-eaquo> Logitrank = ln( p / (1-p) ) It is not totally new ex : John Copas, The Effectiveness of Risk Scores: The Logit Rank Plot Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 48, No. 2 (1999), pp. 165-183 Generalization of log Tam’s “Positional Status Index (PSI)” (Rotman, Shavit, Shalev 2014; rank measure of social origins) inflation neutral, inequality shape neutral, A convenient way to consider quantiles Allows bottom and top quantile details Can be applied to any ordinal variable A way to standardize variables in comparative inequality contexts When computed by (country/year), it provides a baseline for national comparisons (any country has its own bottom 5% or top 1%) implemented in Stata: abg.ado (Chauvel 2014)

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 61

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 Each point represent ISO at the X (specific-level inequality) 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 ] 63

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