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A model of personal income distribution with application to Italian data

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Abstract

This article proposes the κ-generalized distribution as a descriptive model for the distribution and dispersion of income within a population based on the deformed exponential and logarithm functions recently introduced by Kaniadakis (Phys A 296:405–425, 2001; Phys Rev E 66:056125, 2002; Phys Rev E 72:036108, 2005). Expressions are reported which facilitate the analysis of the associated moments and various tools for the measurement of inequality. An empirical application, including a comparison of alternative distributions, is made to household income data in Italy for the years 1989 to 2006.

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References

  • Aitchison J, Brown JAC (1954) On criteria for descriptions of income distribution. Metroeconomica 6: 81–144

    Article  Google Scholar 

  • Aitchison J, Brown JAC (1957) The lognormal distribution with special reference to its use in economics. Cambridge University Press, New York

    Google Scholar 

  • Akaike H (1973) Information theory and an extension of the likelihood ratio principle. In: Petrov BN, Csaki F (eds) Proceedings of the second international symposium of information theory. Akademiai Kiado, Budapest, pp 257–281

  • Amiel Y, Cowell FA, Polovin A (1996) Inequality among the kibbutzim. Economica 63: S63–S85

    Article  Google Scholar 

  • Arnold BC (1983) Pareto distributions. International Co-operative Publishing House, Fairland

    Google Scholar 

  • Arnold BC (1987) Majorization and the Lorenz order: a brief introduction. Springer-Verlag, Berlin

    Google Scholar 

  • 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 

  • Atoda N, Suruga T, Tachibanaki T (1988) Statistical inference of functional forms for income distribution. Econ Stud Q 39: 14–40

    Google Scholar 

  • Bartels CPA (1977) Economic aspects of regional welfare: income distribution and unemployment. Martinus Nijhoff, Leiden

    Google Scholar 

  • Bordley RF, McDonald JB, Mantrala A (1996) Something new, something old: parametric models for the size distribution of income. J Income Distrib 6: 91–103

    Google Scholar 

  • Brachmann K, Stich A, Trede M (1996) Evaluating parametric income distribution models. Alleg Stat Arch 80: 285–298

    Google Scholar 

  • Brandolini A (1999) The distribution of personal income in post-war Italy: source description, data quality, and the time pattern of income inequality. Giorn Econ 58: 183–239

    Google Scholar 

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

    Article  Google Scholar 

  • Chandra M, Singpurwalla ND (1981) Relationships between some notions which are common to reliability theory and economics. Math Oper Res 6: 113–121

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Cowell FA (1980b) 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 (1981a) Additivity and the entropy concept: an axiomatic approach to inequality measurement. J Econ Theory 25: 131–143

    Article  Google Scholar 

  • Cowell FA, Kuga K (1981b) 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 

  • Espinguet P, Terraza M (1983) Essai d’extrapolation des distributions de salaires français. Econ Appl 36: 535–561

    Google Scholar 

  • Esteban JM (1986) Income-share elasticity and the size distribution of income. Int Econ Rev 27: 439–444

    Article  Google Scholar 

  • Gastwirth JL (1971) A general definition of the Lorenz curve. Econometrica 39: 1037–1039

    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 (trans: On the measurement of concentration and variability of characters. Metron 63:3–38, 2005)

    Google Scholar 

  • Hardy GH, Littlewood JE, Pólya G (1929) Some simple inequalities satisfied by convex functions. Messenger Math 58: 145–152

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jaynes ET (1978) Where do we stand on maximum entropy?. In: Levine RD, Tribus M (eds) The maximum entropy formalism. MIT Press, Cambridge, pp 18–115

    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 

  • Kaniadakis G (2009) Maximum entropy principle and power-law tailed distributions. Eur Phys J B 70: 3–13

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  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

    Google Scholar 

  • Majumder A, Chakravarty SR (1990) Distribution of personal income: development of a new model and its application to U.S. income data. J Appl Econ 5: 189–196

    Article  Google Scholar 

  • Mandelbrot B (1960) The Pareto-Lévy law and the distribution of income. Int Econ Rev 1: 79–106

    Article  Google Scholar 

  • Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New York

    Google Scholar 

  • McDonald JB (1984) Some generalized functions for the size distribution of income. Econometrica 52: 647–665

    Article  Google Scholar 

  • McDonald JB, Ransom MR (1979) Functional forms, estimation techniques and the distribution of income. Econometrica 47: 1513–1525

    Article  Google Scholar 

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

    Google Scholar 

  • Metcalf CE (1972) An econometric model of the income distribution. Markham Publishing Company, Chicago

    Google Scholar 

  • 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 (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org

  • Rajaonarison D (2008) Deterministic heterogeneity in tastes and product differentiation in the K-logit model. Econ Lett 100: 396–398

    Article  Google Scholar 

  • Rajaonarison D, Bolduc D, Jayet H (2005) The K-deformed multinomial logit model. Econ Lett 86: 13–20

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6: 461–464

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tachibanaki T, Suruga T, Atoda N (1997) Estimations of income distribution parameters for individual observations by maximum likelihood method. J Jpn Stat Soc 27: 191–203

    Google Scholar 

  • Taillie C (1981) Lorenz ordering within the generalized gamma family of income distributions. In: Taillie C, Patil GP, Baldessari BA (eds) Statistical distributions in scientific work, vol 6. D Reidel Publishing Company, Dordrecht, pp 181–192

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Wilfling B (1996a) Lorenz ordering of generalized beta-II income distributions. J Econ 71: 381–388

    Google Scholar 

  • Wilfling B (1996b) A sufficient condition for Lorenz ordering. Sankhya Ser B 58: 62–69

    Google Scholar 

  • Wilfling B, Krämer W (1993) The Lorenz ordering of Singh-Maddala income distributions. Econ Lett 43: 53–57

    Article  Google Scholar 

Download references

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Correspondence to Fabio Clementi.

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Clementi, F., Gallegati, M. & Kaniadakis, G. A model of personal income distribution with application to Italian data. Empir Econ 39, 559–591 (2010). https://doi.org/10.1007/s00181-009-0318-2

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