Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

A new model of income distribution: the κ-generalized distribution

  • Published:
Journal of Economics Aims and scope Submit manuscript

Abstract

This paper proposes a three-parameter statistical model of income distribution by exploiting recent developments on the use of deformed exponential and logarithm functions as suggested by Kaniadakis (Phys A 296:405–425, 2001; Phys Rev E 66:056125, 2002; Phys Rev E 72:036108, 2005). Formulas for the shape, moments and standard tools for inequality measurement are given. The model is shown to fit remarkably well the personal income data for Great Britain, Germany and the United States in different years, and its empirical performance appears to be competitive with that of other existing distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Arnold BC, Laguna L (1977) On generalized Pareto distributions with applications to income data. Iowa State University Press, Ames

    Google Scholar 

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

    Article  Google Scholar 

  • Bach S, Corneo G, Steiner V (2009) From bottom to top: the entire income distribution in Germany, 1992–2003. Rev Income Wealth 55: 303–330

    Article  Google Scholar 

  • Bandyopadhyay S, Cowell FA, Flachaire E (2009) Goodness-of-Fit: an Economic Approach. STICERD–Distributional Analysis Research Programme Papers 101, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. http://sticerd.lse.ac.uk/dps/darp/darp101.pdf

  • Burkhauser RV, Butrica BA, Daly MC, Lillard DR (2001) The cross-national equivalent file: a product of cross-national research. In: Becker I, Ott N, Rolf G (eds) Soziale sicherung in einer dynamischen gesellschaft. Festschrift für Richard Hauser zum 65 (Social insurance in a dynamic society. Papers in honor of the 65th birthday of Richard Hauser). Geburtstag Campus, Frankfurt, New York, pp 354–376

  • Champernowne DG (1953) A model of income distribution. Econ J 63: 318–351

    Article  Google Scholar 

  • Chernobai A, Rachev S, Fabozzi F (2005) Composite goodness-of-fit tests for left-truncated loss samples. Technical report, Department of Statistics and Applied Probability, University of California Santa Barbara. http://www.pstat.ucsb.edu/research/papers/KSmissing20050604-JFE.pdf

  • Clementi F, Gallegati M, Kaniadakis G (2010) A model of personal income distribution with application to Italian data. Empir Econ 39: 559–591

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Cowell FA (1980) On the structure of additive inequality measures. Rev Econ Stud 47: 521–531

    Article  Google Scholar 

  • Cowell FA (1995) Measuring inequality. Prentice Hall/Harvester Wheatsheaf, Hemel Hempstead

    Google Scholar 

  • Cowell FA, Kuga K (1981) Additivity and the entropy concept: an axiomatic approach to inequality measurement. J Econ Theory 25: 131–143

    Article  Google Scholar 

  • Cowell FA, Kuga K (1981) Inequality measurement: An axiomatic approach. Eur Econ Rev 15: 287–305

    Article  Google Scholar 

  • Dagum C (1977) A new model of personal income distribution: specification and estimation. Econ Appl 30: 413–436

    Google Scholar 

  • Drăgulescu AA, Yakovenko VM (2001) Evidence for the exponential distribution of income in the USA. Eur Phys J B 20: 585–589

    Article  Google Scholar 

  • Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York

    Google Scholar 

  • Feenberg D, Coutts E (1993) An introduction to the TAXSIM model. J Policy Anal Manag 12: 189–194

    Article  Google Scholar 

  • Gibrat R (1931) Les inégalités économiques. Applications: Aux inégalités des richesses, à la concentration des entreprises, aux population des villes, aux statistiques des familles, etc., d’une loi nouvelle: La loi de l’effet proportionnel. Librairie du Recueil Sirey, Paris

  • Gini C (1914) Sulla misura della concentrazione e della variabilità dei caratteri. Atti del Reale Istituto veneto di scienze, lettere ed arti 73:1201–1248 (English translation: On the measurement of concentration and variability of characters. Metron 63:3–38, 2005)

  • Hagenaars AJM, De Vos K, Zaidi MA (1994) Poverty statistics in the late 1980s: research based on micro-data. Office for Official Publications of the European Communities, Luxembourg

    Google Scholar 

  • Haisken-DeNew JP, Frick JR (2005) Desktop Companion to the German Socio-Economic Panel (SOEP). German Institute for Economic Research (DIW). http://www.diw.de/documents/dokumentenarchiv/17/diw_01.c.38951.de/dtc.409713.pdf

  • Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106: 620–630

    Article  Google Scholar 

  • Jaynes ET (1957) Information theory and statistical mechanics. II. Phys Rev 108: 171–190

    Article  Google Scholar 

  • Jenkins SP (2009) Distributionally-sensitive inequality indices and the GB2 income distribution. Rev Income Wealth 55: 392–398

    Article  Google Scholar 

  • Kakwani N (1980) Income inequality and poverty: methods of estimation and policy applications. Oxford University Press, New York

    Google Scholar 

  • Kaniadakis G (2001) Non-linear kinetics underlying generalized statistics. Phys A 296: 405–425

    Article  Google Scholar 

  • Kaniadakis G (2002) Statistical mechanics in the context of special relativity. Phys Rev E 66: 056125

    Article  Google Scholar 

  • Kaniadakis G (2005) Statistical mechanics in the context of special relativity.II. Phys Rev E 72: 036108

    Article  Google Scholar 

  • Kapur JN (1989) Maximum entropy models in science and engineering. Wiley Eastern, New Delhi

    Google Scholar 

  • Kleiber C (1996) Dagum vs. Singh–Maddala income distributions. Econ Lett 53: 265–268

    Article  Google Scholar 

  • Kleiber C (1997) The existence of population inequality measures. Econ Lett 57: 39–44

    Article  Google Scholar 

  • Kleiber C (2008) A guide to the Dagum distributions. In: Chotikapanich D (eds) Modeling income distributions and Lorenz curves. Springer Science+Business Media, LLC, pp 97–117

    Chapter  Google Scholar 

  • Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley, New York

    Book  Google Scholar 

  • Leipnik RB (1990) A maximum relative entropy principle for distribution of personal income with derivations of several known income distributions. Commun Stat Theory 19: 1003–1036

    Article  Google Scholar 

  • Lorenz MO (1905) Methods of measuring the concentration of wealth. Pub Am Stat Assn 9: 209–219

    Article  Google Scholar 

  • McDonald JB, Xu YJ (1995) A generalization of the beta distribution with applications. J Econ 66: 133–152 (Errata. J Econometrics 69:427–428)

    Google Scholar 

  • Nadarajah S, Kotz S (2006) \({{\texttt R}}\) programs for computing truncated distributions. J Stat Softw 16 (Code Snippet 2). http://www.jstatsoft.org/v16/c02/paper

  • Ord JK, Patil GP, Taillie C (1981) The choice of a distribution to describe personal incomes. In: Taillie C, Patil GP, Baldessari BA (eds) Statistical distributions in scientific work, vol 6, D. Reidel Publishing Company, Dordrecht, pp 193–201

    Google Scholar 

  • R Development Core Team (2011) \({{\texttt R}}\): a Language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org

  • Salem ABZ, Mount TD (1974) A convenient descriptive model of income distribution: The gamma density. Econometrica 42: 1115–1127

    Article  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Sys Tech J 27:379–423; 623–657

    Google Scholar 

  • Singh SK, Maddala GS (1976) A function for size distribution of incomes. Econometrica 44: 963–970

    Article  Google Scholar 

  • Stephens MA (1986) Tests based on EDF statistics. In: D’ Agostino RB, Stephens MA (eds) Goodness-of-fit techniques. Marcel Dekker, New York, pp 97–193

    Google Scholar 

  • Takayasu H (1990) Fractals in the physical sciences. Manchester University Press, Manchester

    Google Scholar 

  • Theil H (1967) Economics and information theory. North-Holland, Amsterdam

    Google Scholar 

  • Thode HC Jr (2002) Testing for normality. Marcel Dekker, New York

    Book  Google Scholar 

  • Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57: 307–333

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fabio Clementi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clementi, F., Gallegati, M. & Kaniadakis, G. A new model of income distribution: the κ-generalized distribution. J Econ 105, 63–91 (2012). https://doi.org/10.1007/s00712-011-0221-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00712-011-0221-0

Keywords

JEL Classification