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Inequality Measurement: Methods and Data

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Abstract

In recent years there has been a surge of interest in the subject of inequality, fuelled by new facts and new thinking. The literature on inequality has expanded rapidly as official data on income, wealth, and other personal information have become richer and more easily accessible. Ideas about the meaning of inequality have expanded to encompass new concepts and different dimensions of economic inequality. The purpose of this chapter is to give a concise overview of the issues that are involved in translating ideas about inequality into practice using various types of data.

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References

  • Abul Naga RH, Stapenhurst C, Yalonetzky G (2020) Asymptotic versus bootstrap inference for inequality indices of the cumulative distribution function. Econometrics 8:1–15

    Google Scholar 

  • Alfons A, Templ M, Filzmoser P (2013) Robust estimation of economic indicators from survey samples based on Pareto tail modelling. Journal of the Royal Statistical Society: Series C (Applied Statistics) 62:271–286

    Google Scholar 

  • Alvaredo F (2011) A note on the relationship between top income shares and the Gini coefficient. Econ Lett 110:274–277

    Article  Google Scholar 

  • Alvaredo F, Atkinson AB, Chancel L, Piketty T, Saez E, Zucman, G (2016) Distributional national accounts (DINA) guidelines: Concepts and methods used in WID.world. WID.world working paper series 2016/2

    Google Scholar 

  • Anand S, Segal P (2015) The global distribution of income. In: Atkinson AB, Bourguignon F (eds) Handbook of income distribution, vol 2. Elsevier, New York

    Google Scholar 

  • Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244–263

    Article  Google Scholar 

  • Atkinson AB (2005) Top incomes in the UK over the twentieth century. J R Stat Soc Ser A 168:325–343

    Article  Google Scholar 

  • Atkinson AB (2007) Chapter 2: measuring top incomes: methodological issues. In: Atkinson AB, Piketty T (eds) Top incomes over the 20th century: a contrast between continental European and English-speaking countries. Oxford University Press, Oxford, pp 18–42

    Google Scholar 

  • Atkinson AB (2017) Pareto and the upper tail of the income distribution in the UK: 1799 to the present. Economica 84:129–156

    Article  Google Scholar 

  • Atkinson AB, Piketty T (eds) (2007) Top incomes over the 20th century: a contrast between continental European and English-speaking countries. Oxford University Press, Oxford

    Google Scholar 

  • Atkinson AB, Piketty T (2010) Top incomes: a global perspective. Oxford University Press, Oxford

    Google Scholar 

  • Atkinson AB, Piketty T, Saez E (2011) Top incomes in the long run of history. J Econ Lit 49(1):3–71

    Article  Google Scholar 

  • Bandourian R, McDonald JB, Turley RS (2003) A comparison of parametric models of income distribution across countries and over time. Estadística 55:135–152

    Google Scholar 

  • Bartels C, Metzing M (2019) An integrated approach for a top-corrected income distribution. J Econ Inequal 17:125–143

    Article  Google Scholar 

  • Bartels C, Waldenström D (2021) Inequality and top incomes. In: Handbook of labor, human resources and population economics. Springer

    Google Scholar 

  • Beirlant J, Goegebeur Y, Segers J, Teugels J (2004) Statistics of extremes: theory and applications. Wiley Series in Probability and Statistics

    Book  Google Scholar 

  • Benhabib J, Bisin A (2018) Skewed wealth distributions: theory and empirics. J Econ Lit 56:1261–1291

    Article  Google Scholar 

  • Biewen M (2002) Bootstrap inference for inequality, mobility and poverty measurement. J Econ 108:317–342

    Article  Google Scholar 

  • Blackorby C, Donaldson D, Auersperg M (1981) A new procedure for the measurement of inequality within and among population subgroups. Can J Econ 14:665–685

    Article  Google Scholar 

  • Blanchet T, Flores I, Morgan M (2018) The weight of the rich: Correcting surveys with tax data. WID.world working paper series 2018/12

    Google Scholar 

  • Blanchet T, Fournier J, Piketty T (2017) Generalized Pareto curves: Theory and applications. WID.world working paper series 2017/3

    Google Scholar 

  • Bollinger CR, Hirsch BT, Hokayem CM, Ziliak JP (2019) Trouble in the tails? What we know about earnings nonresponse 30 years after Lillard, smith, and Welch. J Polit Econ 127:2143–2185

    Article  Google Scholar 

  • Bourguignon F (2018) Simple adjustments of observed distributions for missing income and missing people. J Econ Inequal 16:171–188

    Article  Google Scholar 

  • Burkhauser RV, Feng S, Jenkins SP, Larrimore J (2011) Estimating trends in US income inequality using the current population survey: the importance of controlling for censoring. Journal of Economic Inequality Paper 9:393–415

    Article  Google Scholar 

  • Burkhauser RV, Feng S, Jenkins SP, Larrimore J (2012) Recent trends in top income shares in the United States: reconciling estimates from march CPS and IRS tax return data. Rev Econ Stat 94(2):371–388

    Article  Google Scholar 

  • Chakravarty SR (1990) Ethical social index numbers. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Chancel L, Piketty T (2019) Indian income inequality, 1922–2015: from British raj to billionaire raj? Rev Income Wealth 65:S33–S62

    Article  Google Scholar 

  • Chantreuil F, Courtin S, Fourrey K, Lebon I (2019) A note on the decomposability of inequality measures. Soc Choice Welf 53:283–298

    Article  Google Scholar 

  • Chantreuil F, Trannoy A (1999) Inequality decomposition values: the trade-off between marginality and consistency. Working papers 99–24, Université de Cergy-Pontoise

    Google Scholar 

  • Charpentier A, Flachaire E (2022) Pareto models for top incomes and wealth. Journal of Economic Inequality (forthcoming)

    Google Scholar 

  • Coder J (1991) Exploring nonsampling errors in the wage and salary income data from the march current population survey. Housing and Household Economic Statistics Division, U.S. Bureau of the Census

    Google Scholar 

  • Cowell FA (1980) Generalized entropy and the measurement of distributional change. Eur Econ Rev 13:147–159

    Article  Google Scholar 

  • Cowell FA (2011) Measuring inequality, 3rd edn. Oxford University Press, Oxford

    Book  Google Scholar 

  • Cowell FA, Ebert U (2004) Complaints and inequality. Soc Choice Welf 23:71–89

    Article  Google Scholar 

  • Cowell FA, Fiorio C (2011) Inequality decompositions – a reconciliation. J Econ Inequal 9:509–528

    Article  Google Scholar 

  • Cowell FA, Flachaire E (2007) Income distribution and inequality measurement: the problem of extreme values. J Econ 141:1044–1072

    Article  Google Scholar 

  • Cowell FA, Flachaire E (2015) Statistical methods for distributional analysis. In: Atkinson AB, Bourguignon F (eds) Handbook of income distribution, vol 2. Elsevier, New York

    Google Scholar 

  • Cowell FA, Flachaire E (2017) Inequality with ordinal data. Economica 84:290–321

    Article  Google Scholar 

  • Cowell FA, Flachaire E (2018) Inequality measures and the median: why inequality increased more than we thought. PEP discussion paper, STICERD, LSE

    Google Scholar 

  • Cowell FA, Flachaire E (2021) Maximum inequality: the case of categorical data. Res Econ Inequal 29:95–103

    Google Scholar 

  • Cowell FA, Flachaire E, Bandyopadhyay S (2013) Reference distributions and inequality measurement. J Econ Inequal 11:421–437

    Article  Google Scholar 

  • Cowell FA, Van Kerm P (2015) Wealth inequality: a survey. J Econ Surv 29:671–710

    Article  Google Scholar 

  • Cowell FA, Victoria-Feser M-P (1996) Robustness properties of inequality measures. Econometrica 64:77–101

    Article  Google Scholar 

  • Cowell FA, Victoria-Feser M-P (2003) Distribution-free inference for welfare indices under complete and incomplete information. J Econ Inequal 1:191–219

    Article  Google Scholar 

  • Cowell FA, Victoria-Feser M-P (2007) Robust stochastic dominance: a semi-parametric approach. J Econ Inequal 5:21–37

    Article  Google Scholar 

  • Dalton H (1920) Measurement of the inequality of incomes. Econ J 30:348–361

    Article  Google Scholar 

  • Davidson R, Flachaire E (2007) Asymptotic and bootstrap inference for inequality and poverty measures. J Econ 141:141–166

    Article  Google Scholar 

  • de Barros RP, Ferreira F, Chanduvi J, Vega J (2008) Measuring inequality of opportunities in Latin America and the Caribbean. Palgrave Macmillan

    Google Scholar 

  • Deaton AS (1997) The analysis of household surveys. Johns Hopkins Press for the World Bank, Baltimore

    Book  Google Scholar 

  • Deutsch J, Silber J (2008) On the Shapley value and the decomposition of inquality by population subgroups with special emphasis on the Gini index. In: Betti G, Lemmi A (eds) Advances on income inequality and concentration measures. Routledge

    Google Scholar 

  • Dufour J-M, Flachaire E, Khalaf L (2019) Permutation tests for comparing inequality measures. J Bus Econ Stat 37(3):457–470

    Article  Google Scholar 

  • Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling extremal events. Applications of mathematics: stochastic modelling and applied probability. Springer-Verlag, Berlin, Heidelberg

    Book  Google Scholar 

  • Fedotenkov I (2018) A review of more than one hundred pareto-tail index estimators. MPRA paper 90072

    Google Scholar 

  • Ferreira FHG, Lustig N, Teles D (2015) Appraising cross-national income inequality databases: an introduction. J Econ Inequal 13:497–526

    Article  Google Scholar 

  • Foster JE, Shneyerov AA (1999) A general class of additively decomposable inequality measures. Economic Theory 14:89–111

    Article  Google Scholar 

  • Foster JE, Shneyerov AA (2000) Path independent inequality measures. J Econ Theory 91:199–222

    Article  Google Scholar 

  • Gabaix X (2009) Power laws in economics and finance. Annual Review of Economics 1:255–293

    Article  Google Scholar 

  • Garbinti B, Goupille-Lebret J, Piketty T (2018) Income inequality in France, 1900–2014: evidence from distributional National Accounts (DINA). J Public Econ 162:63–77

    Article  Google Scholar 

  • Gastwirth JL (2014) Median-based measures of inequality: reassessing the increase in income inequality in the U.S. and Sweden. Stat J IAOS 30:311–320

    Google Scholar 

  • Gini C (1912) Variabilità e mutabilità. Studi Economico-Giuridici dell’Università di Cagliari 3:1–158

    Google Scholar 

  • Gradín C (2020) Quantifying the contribution of a subpopulation to inequality: an application to Mozambique. J Econ Inequal 18:391–419

    Article  Google Scholar 

  • Groves RE, Couper MP (1998) Nonresponse in household interview surveys. Wiley, New-York

    Book  Google Scholar 

  • Higgins S, Lustig N, Vigorito A (2018) The rich underreport their income: assessing bias in inequality estimates and correction methods using linked survey and tax data. Ecineq WP:475

    Google Scholar 

  • Hlasny V (2020) Nonresponse bias in inequality measurement: Crosscountry analysis using Luxembourg income study surveys. Social Science Quaterly 101:712–731

    Article  Google Scholar 

  • Hlasny V, Verme P (2016) Top incomes and the measurement of inequality in Egypt. World Bank Econ Rev 32(2):428–455

    Google Scholar 

  • Hlasny V, Verme P (2018) Top incomes and inequality measurement: a comparative analysis of correction methods using the EU SILC data. Econometrics 6:30

    Article  Google Scholar 

  • Jenkins SP (2017) Pareto models, top incomes and recent trends in UK income inequality. Economica 84:261–289

    Article  Google Scholar 

  • Jenkins SP (2021) Inequality comparisons with ordinal data. Rev Income Wealth 67(3):547–563

    Google Scholar 

  • Jones CI (2015) Pareto and Piketty: the macroeconomics of top income and wealth inequality. J Econ Perspect 29:29–46

    Article  Google Scholar 

  • Kolm S-C (1969) The optimal production of social justice. In: Margolis J, Guitton H (eds) Public economics. Macmillan, London, pp 145–200

    Chapter  Google Scholar 

  • König J, Schröder C, Wolff EN (2021) Wealth inequalities. In: Handbook of labor, human resources and population economics. Springer

    Google Scholar 

  • Korinek A, Mistiaen JA, Ravallion M (2006) Survey nonresponse and the distribution of income. J Econ Inequal 4:33–55

    Article  Google Scholar 

  • Korinek A, Mistiaen JA, Ravallion M (2007) An econometric method of correcting for unit nonresponse bias in surveys. J Econ 136:213–235

    Article  Google Scholar 

  • La Haye R, Zizler P (2019) The Gini mean difference and variance. Metro 77:43–52

    Article  Google Scholar 

  • Lakner C, Milanovic B (2016) Global income distribution: From the fall of the Berlin wall to the great recession. World Bank Econ Rev 30(2):203–232

    Google Scholar 

  • Lorenz MO (1905) Methods for measuring concentration of wealth. J Am Stat Assoc 9:209–219

    Google Scholar 

  • Lustig N (2019) The missing rich in household surveys: causes and correction approaches. CEQ working paper 75

    Google Scholar 

  • Morelli S, Smeeding T, Thompson J (2015) Post-1970 trends in within-country inequality and poverty: rich and middle-income countries. In: Atkinson AB, Bourguignon F (eds) Handbook of income distribution, vol 2. Elsevier, New York

    Google Scholar 

  • Novokmet F, Piketty T, Zucman G (2018) From soviets to oligarchs: inequality and property in Russia 1905–2016. J Econ Inequal 16:189–223

    Article  Google Scholar 

  • Okamoto M (2011) Source decomposition of changes in income inequality: the integral-based approach and its approximation by the chained Shapley-value approach. J Econ Inequal 9(2):145–181

    Article  Google Scholar 

  • Paul S (2004) Income sources effects on inequality. J Dev Econ 73:435–451

    Article  Google Scholar 

  • Pigou AC (1912) Wealth and welfare. Macmillan, London

    Google Scholar 

  • Piketty T (2001) Les hauts revenus en France au 20eme siècle – Inégalités et redistributions,1901–1998. Editions Grasset, Paris

    Google Scholar 

  • Piketty T (2003) Income inequality in France, 1901–1998. J Polit Econ 111:1004–1042

    Article  Google Scholar 

  • Piketty T, Saez E (2003) Income inequality in the United States, 1913–1998. Q J Econ 118:1–39

    Article  Google Scholar 

  • Piketty T, Saez, E (2006) Response by Thomas Piketty and Emmanuel Saez to: the top 1% … of what? By Alan Reynolds. http://www.econ.berkeley.edu/saez/answer-WSJreynolds.pdf

    Google Scholar 

  • Piketty T, Saez E (2014) Inequality in the long run. Science 344(6186):838–843

    Article  Google Scholar 

  • Piketty T, Saez E, Zucman G (2018) Distributional national accounts: methods and estimates for the United States. Q J Econ 133:553–609

    Article  Google Scholar 

  • Piketty T, Yang L, Zucman G (2019) Capital accumulation, private property, and rising inequality in China, 1978–2015. Am Econ Rev 109:2469–2496

    Article  Google Scholar 

  • Ruiz N, Woloszko N (2016) What do household surveys suggest about the top 1% incomes and inequality in OECD countries? OECD economics department working paper no. 1265

    Google Scholar 

  • Sastre M, Trannoy A (2002) Shapley inequality decomposition by factor components: some methodological issues. Journal of Economics Supplement 9:51–90

    Article  Google Scholar 

  • Schluter C (2018) Top incomes, heavy tails, and rank-size regressions. Econometrics 6(10):1–16

    Google Scholar 

  • Schluter C, Trede M (2002) Statistical inference for inequality and poverty measurement with dependent data. Int Econ Rev 43:493–508

    Article  Google Scholar 

  • Sen AK (1973) On economic inequality. Clarendon Press, Oxford

    Book  Google Scholar 

  • Shorrocks AF (1980) The class of additively decomposable inequality measures. Econometrica 48:613–625

    Article  Google Scholar 

  • Shorrocks AF (1982) Inequality decomposition by factor components. Econometrica 50(1):193–211

    Article  Google Scholar 

  • Shorrocks AF (1983) The impact of income components on the distribution of family income. Q J Econ 98:311–326

    Article  Google Scholar 

  • Shorrocks AF (2013) Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. J Econ Inequal 11:99–126

    Article  Google Scholar 

  • Silber J, Yalonetzky G (2021) Ordinal variables and the measurement of inequality, poverty and welfare. In: Handbook of labor, human resources and population economics. Springer

    Google Scholar 

  • Theil H (1979) The measurement of inequality by components of income. Econ Lett 2:197–199

    Article  Google Scholar 

  • Yaari ME (1988) A controversial proposal concerning inequality measurement. J Econ Theory 44(4):381–397

    Article  Google Scholar 

  • Yitzhaki S (1979) Relative deprivation and the Gini coefficient. Q J Econ 93:321–324

    Article  Google Scholar 

  • Yitzhaki S (1982) Stochastic dominance, mean variance and Gini’s mean difference. Am Econ Rev 72:178–185

    Google Scholar 

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Acknowledgments

Responsible Section Editor: Eva Sierminska.

The chapter has benefitted from comments of the editors. The work was supported financially by ESRC project ES/L016273/1, and by projects ANR- 17-EURE-0020, ANR-17-CE41-0007-02, and ANR-19-FRAL-0006 managed by the French National Research Agency (ANR). There is no conflict of interest. We are grateful to Visheshika Baheti for help in producing the final version of the chapter.

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Cowell, F.A., Flachaire, E. (2021). Inequality Measurement: Methods and Data. In: Zimmermann, K.F. (eds) Handbook of Labor, Human Resources and Population Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-57365-6_148-1

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