1,014
Views
8
CrossRef citations to date
0
Altmetric
GENERAL

A Simple and Effective Inequality Measure

&
Pages 328-343 | Received 01 Mar 2016, Published online: 04 Jun 2018

References

  • ABS (2011), Household Data and Income Distribution, Australian Bureau of Statistics Report 6523.0, Canberra, ACT, Australia. Available at www.ausstats.abs.gov.au.
  • Alvaredo, F., Atkinson, A. B., Piketty, T., and Saez, E. (2013), “The Top 1 Percent in International and Historical Perspective,” Journal of Economic Perspectives, 27, 3–20.
  • Atkinson, A. B. (2015), Inequality: What can be Done? Boston, MA: Harvard University Press.
  • Beach, C. M., and Davidson, R. (1983), “Distribution-Free Statistical Inference with Lorenz Curves and Income Shares,” Review of Economic Studies, L, 723–735.
  • Bee, M. (2015), “Estimation of the lognormal-Pareto Distribution using Probability Weighted Moments and Maximum Likelihood,” Communications in Statistics: Simulation and Computation, 44, 2040–2060.
  • Bourguignon, F. (1979), “Decomposable Income Inequality Measures,” Econometrica, 47, 901–920.
  • ——— (2015), The Globalization of Inequality, Princeton, NJ: Princeton University Press.
  • Burkhauser, R. V., Feng, S., and Jenkins, P. (2009), “Using the p90/p10 Index to Measure U.S. Inequality Trends with Current Population Survey Data: A View from Inside the Census Bureau Vaults,” The Review of Income and Wealth, 55, 166–195.
  • Chen, C., Tsaur, T., and Rhai, T. (1982), “The Gini Coefficient and Negative Income,” Oxford Economic Papers, 34, 473–478.
  • Chotikapanich, D. (ed) (2008), “Modeling Income Distributions and Lorenz Curves,” Economic Studies in Inequality, Social Exclusion and Well-Being, New York: Springer.
  • Clementi, F., and Gallegati, M. (2005), “Power Law Tails in the Italian Personal Income Distribution,” Physica A: Statistical Mechanics and its Applications, 350, 427–438.
  • Cobham, A., Schlögl, L., and Sumner, A. (2016), “Inequality and the Tails: The Palma Proposition and Ratio Revisited,” Global Policy, 7, 25–36.
  • Cowell, F. A. (2011), Measuring Inequality, (3rd ed.), Oxford: Oxford University Press.
  • Cowell, F. A., and Flachaire, E. (2007), “Income Distribution and Inequality Measurement: The Problem of Extreme Values,” Econometrics, 141, 1044–1072.
  • Cowell, F. A., and Victoria-Feser, M. P. (1996), “Robustness Properties of Inequality Measures” Econometrica, 64, 77–101.
  • Cowell, F. A., and Victoria-Feser, M. P. (2002), “Welfare Rankings in the Presence of Contaminated Data,” Econometrica, 70, 1221–1233.
  • Cowell, F. A., and Victoria-Feser, M. P. (2003), “Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information,” The Journal of Economic Inequality, 1, 191–219.
  • Dagum, C. (1977), “A New Model of Personal Income Distribution: Specification and Estimation,” Economie Appliquée, 30, 413–437.
  • Dalton, H. (1920), “The Measurement of the Inequality of Incomes,” Economic Journal, 30, 348–361.
  • DasGupta, A. (2006), Asymptotic Theory of Statistics and Probability, New York: Springer.
  • DasGupta, P., Sen, A., and Starrett, D. (1973), “Note on the Measurement of Inequality,” Journal of Economic Theory, 6, 180–187.
  • Davidson, R. (2009), “Reliable Inference for the Gini Index,” Journal of Econometrics, 150, 30–40.
  • Davison, A. C. (2003), “Statistical Models,” Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge, UK: Cambridge University Press.
  • ——— (2013), SMPracticals: Practicals for use with Davison (2003) Statistical Models, R package version 1.4-2.
  • De Maio, F. G. (2007), “Income Inequality Measures,” Journal of Epidemeology and Community Health, 61, 849–852.
  • Development Core Team (2008), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Dorfman, R. (1979), “A Formula for the Gini Coefficient,” The Review of Economics and Statistics, 61, 146–149.
  • Dutang, C., Goulet, V., and Pigeon, M. (2008), “actuar: An R package for actuarial science,” Journal of Statistical Software, 25, 38.
  • Gastwirth, J. L. (1971), “A General Definition of the Lorenz Curve,” Econometrika, 39, 1037–1039.
  • ——— (2014), “Median-based Measures of Inequality: Reassessing the Increase in Income Inequality in the U.S. and Sweden,” Statistical Journal of the International Association for Official Statistics, 30, 311–320.
  • Ghosh, A., Gangopadhyay, K., and Basu, B. (2011), “Consumer Expenditure Distribution in India, 1983-2007: Evidence of a Long Pareto Tail,” Physica A, 390, 83–97.
  • Gini, C. (1914), “Sulla Misura Della Concentrazione e Della Variabilit‘a dei Caratteri,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 73, 1203–1248. English translation (2005) in Metron Vol. 63, pp. 3–38.
  • Greselin, C. (2014), “More Equal and Poorer, or Richer but more Unequal?” Economic Quality Control, 29, 99–117.
  • Grigio, G. (1999), “Income Inequality Measurement; the Statistical Approach,” Economic Thought, vol. 71, The Netherlands: Springer, pp. 245–267.
  • Hajek, J., and Sidak, Z. (1967), Theory of Rank Tests, New York: Academic Press.
  • Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986), Robust Statistics: The Approach Based on Influence Functions, New York: Wiley.
  • Hoeffding, W. (1948), “A Class of Statistics with Asymptotically Normal Distribution,” The Annals of Mathematical Statistics, 19, 293–325.
  • Hyndman, R. J., and Fan, Y. (1996), “Sample Quantiles in Statistical Packages,” The American Statistician, 50, 361–365.
  • Jantzen, R. T., and Volpert, K. (2012), “On the Mathematics of Income Inequality: Splitting the Gini in Two,” Mathematical Monthly, 119, 824–837.
  • Jedrzejczak, A. (2012), “Estimation of Concentration Measures and their Standard Errors for Income Distributions in Poland,” International Advances in Economics Research, 18, 287–297.
  • Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994), Continuous Univariate Distributions, Vol. 1, New York: Wiley.
  • ——— (1995), Continuous Univariate Distributions, Vol. 2, New York: Wiley.
  • Kleiber, C. (2008), “A Guide to the Dagum Distributions,” in Chotikapanich, pp. 97–117.
  • Langel, M., and Tillé, Y. (2013), “Variance Estimation of the Gini Index: Revisting a Result Several Times Published,” Journal of the Royal Statistical Society, Series A 7, 521–540.
  • Lorenz, M. O. (1905), “Methods of Measuring the Concentration of Wealth,” Publications of the American Statistical Association, 9, 209–219.
  • Lyon, M., Cheung, L. C., and Gastwirth, J. L. (2016), “The Advantages of using Group Means in Estimating the Lorenz Curve and Gini Index from Grouped Data,” The American Statistician, 70, 25–32.
  • McNeil, A. J. (1997), “Estimating the Tails of Loss Severity Distributions using Extreme Value Theory,” ASTIN Bulletin: The Journal of the International Actuarial Association, 27, 117–137.
  • Mosteller, F. (1946), “On Some Useful ”Inefficient” Statistics,” Annals of Mathematical Statistics, 17, 377–408.
  • Nadarajah, S. (2013). Complognormal: Functions for Actuarial Scientists, R Package Version 3.0.
  • Nadarajah, S., and Bakar, S. (2013), “CompLognormal: An R package for Composite Lognormal Distributions,” R Journal, 5, 98–104.
  • Palma, J. G. (2011), “Homogeneous Middles vs. Heterogeneous Tails, and the End of the Inverted-U': The Share of the Rich is what it's All About,” Development and Change, 42, 87–153.
  • Parzen, E. (1979), “Nonparametric Statistical Data Modeling,” Journal of the American Statistical Association, 7, 105–131.
  • Pigou, A. C. (1912), Wealth and Welfare, London: Macmillan and Company, ltd.
  • Piketty, T. (2015), The Economics of Inequality, Cambridge, MA: The Belknap Press of Harvard University Press. Translated from the French by Goldhammer, A.
  • Prendergast, L. A., and Staudte, R. G. (2016a), “Exploiting the Quantile Optimality Ratio in Finding Confidence Intervals for Quantiles,” Stat, 5, 70–81.
  • ——— (2016b), “Quantile Versions of the Lorenz Curve,” Electronic Journal of Statistics, 10, 1896–1926.
  • ——— (2017), “When Large n is not Enough—Distribution-free Interval Estimators for Ratios of Quantiles,” Journal of Economic Inequality, 15, 277–293.
  • Resnick, S. I. (1997), “Discussion of the Danish Data on Large Fire Insurance Losses,” ASTIN Bulletin: The Journal of the International Actuarial Association, 27, 139–151.
  • Sen, A. (1995), Inequality Reexamined, New York: Harvard University Press.
  • Silber, J. (ed). (2012), “Handbook of Income Inequality Measurement,” in Business & Economics (2nd ed.) New York: Springer Science & Business Media.
  • Stephenson, A. G. (2002), “evd: Extreme Value Distributions,” R News, 2, 0.
  • Stiglitz, J. (2012), The Price of Inequality, New York: W. W. Norton & Company.
  • Stock, J. H., and Watson, M. W. (2003), Introduction to Econometrics, Addison-Wesley.
  • Thompson, W. A., Jr. (1976), “Fisherman’s Luck,” Biometrics, 32, 265–271.
  • Tillé, Y., and Langel, M. (2012), “Histogram-based Interpolation of the Lorenz Curve and Gini Index for Grouped Data,” The American Statistician, 66, 225–231.
  • Tukey, J. W. (1965), “Which Part of the Sample Contains the Information?” in Proceedings of the Mathemetical Academy of Science USA, 53, 127–134.
  • Zenga, M. (2007), “Inequality Curve and Inequality Index Based on the Ratios Between Lower and Upper Arithmetic Means,” Statistica & Applicazioni, 1, 3–27.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.