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 1 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 2 1- Introduction: history, civilization and extreme inequalities 3 % of cumulated income Wealth in Luxembourg (hfcs 2010) Gini = 0.64 Zipf distribution (Pharaoh) Gini = 0.85 .2 .4 The 60 % less affluent pop

cumulate 36 % of the tot income 0 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. Income in Luxembourg (hfcs 2010) Gini = 0.34 .8 1 Lorenz curve & the Gini index .6 Gini = 0 in case of perfect equality,

& 1 in case of perfect inequality => one single individual possesses everything 0 .2 .4 .6 Cumulative population proportion .8 1 % of pop ranked by income 4 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 Scheidels 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 5 Introduction: civilization and (in)equality The new Walter Scheidels book: four horsemen of the reduction of inequality Wars, Epidemics, Revolutions, State collapse Inequality trends in Europe (Scheidel p 87) And now?

time 6 Albrecht Drer 1498. The Four Horsemen, in Johannes (Saint), Book of Revelation (6:18) Introduction: civilization and (in)equality The new Walter Scheidels book: four perspectives in the reduction of inequality Wars, Epidemics, Revolutions, State collapse Inequality trends in Europe (Scheidel p 87) And now? time 7 Albrecht Drer 1498. The Four Horsemen, in Johannes (Saint), Book of Revelation (6:18)

Inequality trends in the U.S. (Scheidel p 110) And now? time 8 1- Extreme inequality: theory and math 9 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) 1.5 2 distributions, same mean, with the same Gini of .30 D1: GB2(5.13;1;1;0.5) Poverty = .041 We can show that A lower Gini can go with higher

relative poverty rates 0 .5 Density 1 D2: GB2(5.13;1;1;1.5) Poverty = .115 0 1 2 3 The theory: A new class structure: forget Qutelet, learn Pareto Farewell to the theory of average (hu)man (Quetelet, Halbwachs) Welcome(back) to extreme society (Pareto, Nielsen) 1896

Nielsen, Franois. 2007. Economic Inequality, Pareto, and Sociology: The Route Not Taken.. American Behavioral Scientist 50 (5): 619 638. = Vilfredo Pareto 1848-1922 11 Adolphe Qutelet 1796-1874 1. The Zipfs pyramidal model of extreme inequality $/person N Order 1 1 10,000,000 10

2 1,000,000 100 3 100,000 1,000 4 10,000 10,000 5 1,000 100,000 6 100 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% 10 1 12 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? 20 log($) 15 f(x) = x + 16.12 R = 1 10

Slope -1 5 0 0 5 10 15 20 13 Vilfredo Pareto now: power tailed distributions Gabaix, X., "Power Laws in Economics and Finance," Annual Review of Economics, 1, 25594, 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) 1 14 log(city size)

Vilfredo Pareto now: power tailed distributions Applications => in finance (stock market statics and "Why Has CEO Pay Increased So Much?", dynamics) Xavier Gabaix & Augustin Landier, Quarterly Journal of Economics, vol. 123(1), 2008, p. 49-100 =1 / 1 15 Pareto is pervasive and almost everywhere Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman 2009 Power-Law Distributions in Empirical Data , SIAM Rev., 51(4), 661703. Applications => linguistics, terrorism, wars, astroph per tail power distributions everywhere 16 Pareto is pervasive and almost everywhere Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman 2009 Power-Law Distributions in Empirical Data , SIAM Rev., 51(4), 661703. Applications => linguistics, terrorism, wars, astroph per tail power distributions everywhere

17 0 Simulated GB2(a=1;b=1;p=1;q=1) 10 20 30 The Zipf law as it looks 0 .2 .4 Density .6 .8 18 0 .2 .4 Density .6 .8 19

0 Simulated GB2(a=1;b=1;p=1;q=1) 10 20 30 2- Extreme inequality today: are they back? 20 Income Inequality: Economic Disparities and the Middle Class in Affluent Countries edited by: Janet C. Gornick and Markus Jntti (Stanford University Press) 2013 http://www.sup.org/book.cgi?id=21329 Louis Chauvel, 2016, La Spirale du dclassement Essai sur la socit 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

Alderson, A. S., J. Beckfield and F. Nielsen, "Exactly How Has Income Inequality Changed? Patterns of Distributional Change in Core Societies." International Journal of Comparative Sociology, 46, 405-423, 2005. Robert H. Frank and Philip J. Cook 1995 The Winner-Take-All Society (New York: The Free Press,). Godechot, Olivier 2012 Is finance responsible for the rise in wage inequality in France? Socio-Economic Review 10(3), 447-470 23 220 200 180 heightcm Max/Median = 1.280 (in a 1.000.00 sample) height Median = Mean M=177 cm sd=10.1 Gini index = .12 140 160 In the US: Robert Wadlow, the tallest person 272 cm = 1.53 the median

24 120 1- Normal law world max height = 227 cm (in a 1.000.00 sample) 0 .01 Density .02 .03 .04 5 US Income 2- Typical Income Pareto-Champernowne-Fisk law with a gini index = .45 M=177 cm sd=10.1 In the US 2013 LNG Charif Souki $141 Millions

2 Median i 3 Max/Median Income = 700 (in a 1.000.000 sample) 4 Mean=1.4 * Median 1 =3154 times the median US FT yearly earning lvl 0 Fits based on SCF 2011 25 0 .2 Density .4 .6

.8 5 3- Typical Wealth Pareto-Champernowne-Fisk law with a gini index = .72 US Wealth Max/Median Income = 71 000 (in a 1.000.00 sample) M=177 cm sd=10.1 =250 000 times the median wealth =500 000 times the median US FT yearly earning 26 0 .2 .4 Density .6 .8

1 Fits based on SCF 2011 No wealth based middle class 0 1 2 Median w 3 In the US 6 Walton family members own $152 Billions 4 Mean=4.3 * Median 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 Upper middle class The strobiloid representation of income distribution Even more massive changes in the distributions still to come ? 4 de2010 1 0 1 1 il1979 il2010 1 0

1 0 1 2 us2010 2 us1979 0 1 0 -1 0 3 3 3 lu2010 2 lu1985

-1 4 -1 4 1 fr2010 0 1 0 1 0 0 4 -1 fr1978 2 de1978 2 dk2010

2 dk1987 3 4 3 3 4 The strobiloid = graph changing shapes -1 0 1 -1 0 128 3- Wealth is back: repatrimonialization 29 Strobilod EU-SILC 2010 and Wealth (LWS) in euro Luxembourg Income

100 = median income 100 = median wealth 400 Income (per capita) 10 % are above 3,95 times the median wealth Gini= 27.5% 300 200 100 25 % are above 2,32 times the median wealth 10 % are above 1,92 times the median income Average wealth 25 % are above 1,39 times the median income Median income Yearly median per: 36K/UC/year Average income capita

disposable income : 65 KF 25 % are below 0,72 times the median income 0 Gini= 70% C 5 % are above 2,33 times the median income Wealth (by household) 10 % are below 0,55 times the median income C I I E O E O Median wealth :

Median household gross wealth : 380K 500 KF 25 % are below 0,15 times the median wealth Piketty 31 Piketty In 1980 = wealth is 3 years of income In 2010 = wealth is 6 years of income 32 4 US 1980 Wealth Gini=.75 3 Income Gini=.35 Mean wealth=3.7 med income

0 1 2 Median Income -1 -.5 0 .5 1 33 44 US 2010 Wealth Gini=.79 2 3 3

Income Gini=.45 Mean wealth=8.5 med income 0 1 1 2 Median Income -.5 0 .5 1 0 -1 -1 -.5

0 .5 1 34 444 US 2040 Central Scenario Wealth Gini=.82 2 2 3 33 Income Gini=.55 Mean wealth=15.5 med income 0 0 1

1 1 2 Median Income -.5 -.5 00 .5 .5 11 0 -1 -1 -1 -.5 0 .5 1

35 4- Extreme consequences in the world 36 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) 37 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) 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 39 Power tailed distributions Gabaix, X., "Power Laws in Economics and Finance, Annual Review of Economics, 1, 25594, 2009. Power-tailed distributions (Pareto-Levy distributions) Zipf distributions => Krugman 1996 etc. Gabaix 1999 etc. Applications => cities) in economic geography (size of Main messages: in finance (stock market statics and dynamics) *Lognormal hypothesis not acceptable *difficult to identify the real process log(city rank) 1 40 log(city size)

Pareto 1896: Log N = Log A - a Log x a>1 ln (x) Ln(Npoptot) Ln(N >R) A N a x Slope - a Pareto a > 1, if not => mean income diverges aA R a-1 (a - 1) R0 41 Pareto distribution x () 150 200 300 400 500 600

700 800 900 1000 2000 3000 4000 5000 10000 50000 N 320162 190061 101616 61720 45219 33902 27008 22954 19359 17963 7611 4480 3050 2292 853 68 ln(x) 5,01 5,30 5,70 5,99

6,21 6,40 6,55 6,68 6,80 6,91 7,60 8,01 8,29 8,52 9,21 10,82 ln(N) 12,68 12,16 11,53 11,03 10,72 10,43 10,20 10,04 9,87 9,80 8,94 8,41 8,02 7,74 6,75 4,22 42

Pareto of England 1880 16,00 a = 1.39 12,00 8,00 y = -1,395x + 19,473 R2 = 0,997 4,00 0,00 4,00 6,00 8,00 10,00 43 12,00 Pareto in the first Pikettys book France incomes 1905-1995 Data : http://www.jourdan.ens.fr/piketty/_mpublic/ipublic.php Tableau 2-1 : Level of living of percentiles Revenu moyen 1900-1910 1900-1910

versus 1990-1998 Fractiles P0-100 P90-100 P95-100 P99-100 P99,5-100 P99,9-100 P99,99-100 (en francs de 1998) 28847,7455 50 129814,855 95 196164,669 97,5 548107,164 99,5 865432,364 99,75 2307819,64 99,95 8654323,64 99,995 Fractiles P0-100 P90-100 P95-100 P99-100 P99,5-100

P99,9-100 P99,99-100 Revenu moyen 1990-1998 (en francs de 1998) 129380,059 50 419015 95 543087,334 97,5 1006844,61 99,5 1334204,86 99,75 2587710,36 99,95 7154769,23 99,995 10,2697871 11,7738645 12,1867097 13,2142261 13,6709845 14,6518138 15,9735696 3,91202301 1,60943791 0,91629073 -0,69314718 -1,38629436

-2,99573227 -5,29831737 8 4 y = -2,4364x + 33,056 0 11,7705095 12,945662 13,2050254 13,8223318 14,1038461 14,766284 15,7832897 4 1,60943791 0,91629073 -0,69314718 -1,38629436 -2,99573227 -5,29831737 2 R = 0,9989 y = -1,6089x + 20,524 2 R = 0,9994 6

8 10 12 14 -4 -8 44 16 18 Champernowne I 1 p( r R ) a R 1 La proportion d'individus dont la richesse est comprise entre R et R+dR est : a- 1 aR dp a dR 2 ( R 1)

45 Champernowne I 1,8 Socit 1 % de "pauvres" 6,63 1,6 Socit 5 % de "pauvres" 1,4 4,25 1,2 France 1989 12,5 % de "pauvres" 2,81 1 0,8 Angleterre 1890 28 % de "pauvres" 1,35 0,6 0,4 0,2 0 0

0,5 1 1,5 2 2,5 46 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 47 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 48 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, 39298, 2009. 49 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 wellknown generalised beta distribution of the second kind. 50 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) 1.5 2 distributions, same mean, with the same Gini of .30 D1: GB2(5.13;1;1;0.5) Poverty = .041 We can show that A lower Gini can go with higher relative poverty rates 0 .5 Density 1 D2: GB2(5.13;1;1;1.5) Poverty = .115 0 1

2 3 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 40 50 The old Pens Parade graph SE eqincKeur 20 30 Swedish median Pros arguments:

DE Visualization of hierarchy Easy to handle Very usual graph (AHearn, B., & Vecchi, G. (2015). Cowell, F. A., & Van Kerm, P. (2015)) 0 10 German median 0 .2 .4 quantiles Source: Silc microdata 2011 .6 .8 Pen's (1973) Parade of Dwarfs See: Hao, L., & Daniel Q. Naiman. (2010). Assessing Inequality. Thousand Oaks, CA: SAGE Publications, Inc. 1

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 8 Income Distributions Medianized income Jan Pens Parade Pens Parade 4 6 Saturation of inequality 2013 Median income= 1 0 2 1992

0 .2 .4 INCU2013 56 .6 INCU1992 .8 1 Percentile rank Medianized wealth Jan Pens Parade Jan Pens Parade 100 150 200 Wealth Distributions

Saturation of inequality 50 2013 Median wealth = 1 0 1992 0 .2 .4 netw2013 57 .6 netw1992 .8 1 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) Y =ln ( ( ) ) ISO=Y/X is a measure of Level-specific inequalities If ISO=a (constant) Champernowne-Fisk (double Pareto) distribution with a = Gini (Dagum, 1977) 58 ln ( ) ( )

i= 58 4 Wealth Distributions Ln Medianized wealth Log-logit transformation of Jan Pens Parade 2013 2 1992 -2 0 Median ln(wealth) = 0 -1 0 1 lnetw2013

59 2 lnetw1992 3 4 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 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 Tams 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) 60 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) Y =ln (

( ) ) ISO=Y/X is a measure of Level-specific inequalities If ISO=a (constant) Champernowne-Fisk (double Pareto) distribution with a = Gini (Dagum, 1977) 61 ln ( ) ( ) i= 61 Wealth Distributions Log-logit transformation of Jan Pens Parade For X=2 ISO 2013=

Slope Y/X in 2013 2013 1992 2 4 Y Ln Medianized wealth Substantial increase in wealth inequality Median ln(wealth) = 0 0 For X=2 ISO 1992 = Slope Y/X in 1992 X=2 -2 X -1 0

1 lnetw2013 62 2 lnetw1992 3 4 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), 5268. L Chauvel, E Bar-Haim (2017) ISOGRAPH: Stata module to compute inequality over logit [ranks of social

- Statistical Software = STATA : ssc hierarchy install isograph ] 63 Components, 2017 63 .6 LIS examples of ISO on equivalized disposable income = level of living Old date New date de1978 de2010 fr1978 fr2010 .4 .5 dk1987 dk2010 .3 new

.6 .2 old us1979 us2010 .5 uk1979 uk2010 il1979 il2010 new new .4 new .3 old old .2 old

-4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 64 Graphs by col

64 Source: LIS data, various years and countries 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 4 de11 1 0 1 1 3 il07 1 2 il79 0 1 0 1

Israel us10 2 us79 0 1 2 uk10 0 -1 0 U.S. 3 3 U.K. uk79 -1

4 -1 4 1 fr11 0 1 0 1 0 0 4 -1 fr79 2 de83 2 se11 2

se81 France 3 4 Germany (W) 3 3 4 6 Strobiloids Change Sweden -1 0 1 -1 0 1