Abstract
The paper provides a survey of results related to the “κ-generalized distribution”, a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties, interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, such as the Gini index and the Lorenz curve. An extension of the basic model that is most able to accommodate the special features of wealth data is also reviewed. The survey of empirical applications given in this paper shows the κ-generalized models of income and wealth to be in excellent agreement with the observed data in many cases.
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References
A. Chatterjee, S. Yarlagadda, B.K. Chakrabarti, Econophysics of Wealth Distributions (Springer-Verlag Italia, Milan, 2005)
V.M. Yakovenko, in Encyclopedia of Complexity and System Science, edited by R.A. Meyers (Springer-Verlag, Berlin, 2009), p. 2800
V.M. Yakovenko, J. Barkley Rosser, Jr., Rev. Mod. Phys. 81, 1703 (2009)
B.K. Chakrabarti, A. Chakraborti, S.R. Chakravarty, A. Chatterjee, Econophysics of Income and Wealth Distributions (Cambridge University Press, New York, 2013)
J.E. Stiglitz, The Price of Inequality: How Today’s Divided Society Endangers Our Future (W. W. Norton & Company, New York, 2012)
T. Piketty, Capital in the Twenty-First Century (The Belknap Press of Harvard University Press, Cambridge MA, 2014)
A.B. Atkinson, Inequality: What Can Be Done? (Harvard University Press, Cambridge MA, 2015)
J.E. Stiglitz, The Great Divide: Unequal Societies and What We Can Do About Them (W. W. Norton & Company, New York, 2015)
V. Pareto, Giorn. Econ. 10, 59 (1895)
V. Pareto, 1896, reprinted in Œeuvres complètes de Vilfredo Pareto, Tome 3: Écrits sur la courbe de la répartition de la richesse, edited by G. Busino (Librairie Droz, Geneva, 1965), p. 1
V. Pareto, Cours d’économie politique (Macmillan, London, 1897)
V. Pareto, Giorn. Econ. 14, 15 (1897)
C. Kleiber, S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences (John Wiley & Sons, New York, 2003)
F. Clementi, M. Gallegati, G. Kaniadakis, Eur. Phys. J. B 57, 187 (2007)
F. Clementi, T. Di Matteo, M. Gallegati, G. Kaniadakis, Physica A 387, 3201 (2008)
F. Clementi, M. Gallegati, G. Kaniadakis, J. Stat. Mech. 2009, P02037 (2009)
F. Clementi, M. Gallegati, G. Kaniadakis, Empir. Econ. 39, 559 (2010)
F. Clementi, M. Gallegati, G. Kaniadakis, J. Econ. 105, 63 (2012)
F. Clementi, M. Gallegati, G. Kaniadakis, J. Stat. Mech. 2012, P12006 (2012)
F. Clementi, M. Gallegati, The Distribution of Income and Wealth: Parametric Modeling with the κ-Generalized Family (Springer International Publishing, Switzerland, 2016)
G. Kaniadakis, Physica A 296, 405 (2001)
G. Kaniadakis, Phys. Rev. E 66, 056125 (2002)
G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)
G. Kaniadakis, Eur. Phys. J. B 70, 3 (2009)
G. Kaniadakis, Eur. Phys. J. A 40, 275 (2009)
B. Trivellato, Math. Method. Oper. Res. 69, 1 (2009)
D. Imparato, B. Trivellato, in Algebraic and Geometric Methods in Statistics, edited by P. Gibilisco, E. Riccomagno, M.P. Rogantin, H.P. Wynn (Cambridge University Press, New York, 2010), p. 307
B. Trivellato, Int. J. Theor. App. Finance 15, 1250038 (2012)
G. Kaniadakis, Entropy 15, 3983 (2013)
M. Cravero, G. Iabichino, G. Kaniadakis, E. Miraldi, A.M. Scarfone, Physica A 340, 410 (2004)
B. Trivellato, Entropy 15, 3471 (2013)
E. Moretto, S. Pasquali, B. Trivellato, Physica A 446, 246 (2016)
D. Rajaoarison, D. Bolduc, H. Jayet, Econ. Lett. 86, 13 (2006)
D. Rajaoarison, Econ. Lett. 100, 396 (2008)
S. Landini, in The Distribution of Income and Wealth: Parametric Modeling with the κ-Generalized Family, by F. Clementi, M. Gallegati (Springer International Publishing, Switzerland, 2016), p. 93
R. D’Addario, Giorn. Econ. Ann. Econ. 33, 205 (1974)
C.P.A. Bartels, H. van Metelen, Alternative probability density functions of income: A comparison of the lognormal-, Gamma- and Weibull-distribution with Dutch data. Research Memorandum No. 29 (1975)
C.P.A. Bartels, Economic aspects of regional welfare, income distribution and unemployment (Martinus Nijhoff, Leiden, 1977)
P. Espinguet, M. Terraza, Econ. Appl. 36, 535 (1983)
J.B. McDonald, Econometrica 52, 647 (1984)
N. Atoda, T. Suruga, T. Tachibanaki, Econ. Stud. Quart. 39, 14 (1988)
R.F. Bordley, J.B. McDonald, A. Mantrala, J. Income Distrib. 6, 91 (1996)
K. Brachmann, A. Stich, Trede, All. Stat. Arch. 80, 285 (1996)
T. Tachibanaki, T. Suruga, N. Atoda, J. Japan. Statist. Soc. 27, 191 (1997)
B. Mandelbrot, Int. Econ. Rev. 1, 79 (1960)
M.O. Lorenz, Publ. Am. Stat. Assoc. 9, 209 (1905)
C. Gini, Atti Reale Istit. Veneto Sci. Lett. Art. 73, 1203 (1914)
M. Okamoto, Extension of the κ-generalized distribution: New four-parameter models for the size distribution of income and consumption. LIS Working Paper No. 600 (2013), available at: http://www.lisdatacenter.org/wps/liswps/600.pdf
A.A. Drăgulescu, V.M. Yakovenko, Eur. Phys. J. B 20, 585 (2001)
P.D. Allison, Am. Sociol. Rev. 43, 865 (1978)
F.A. Cowell, Eur. Econ. Rev. 13, 147 (1980a)
F.A. Cowell, Rev. Econ. Stud. 47, 521 (1980b)
A.F. Shorrocks, Econometrica 48, 613 (1980)
F.A. Cowell, K. Kuga, J. Econ. Theory 25, 131 (1981a)
F.A. Cowell, K. Kuga, Eur. Econ. Rev. 15, 287 (1981b)
H. Theil, Economics and Information Theory (North-Holland, Amsterdam, 1967)
C. Kleiber, Econ. Lett. 57, 39 (1997)
C. Rao, Linear Statistical Inference and its Applications (John Wiley & Sons, New York, 1973)
J.K. Ghosh, Higher Order Asymptotics (Institute of Mathematical Statistics and American Statistical Association, Hayward CA, 1994)
R.J. Schoenberg, Comput. Econ. 10, 251 (1997)
C. Dagum, in Encyclopedia of Statistical Sciences, Second Edition, Volume 5, edited by N. Balakrishnan, C.B. Read, B. Vidakovic (John Wiley & Sons, New York, 2006), p. 3363
C. Dagum, Statistica 66, 235 (2006)
J.B. Hagerbaumer, Rev. Econ. Stat. 59, 377 (1977)
G. Pyatt, C.-N. Chen, J. Fei, Q. J. Econ. 95, 451 (1980)
Y. Amiel, F.A. Cowell, A. Polovin, Economica 63, S63 (1996)
S.P. Jenkins, M. Jäntti. Methods for Summarizing and Comparing Wealth Distributions. ISER Working Paper No. 2005-05 (2005), available at: https://www.iser.essex.ac.uk/publications/working-papers/iser/2005-05.pdf
F.A. Cowell, Measuring Inequality (Oxford University Press, New York, 2011)
G. Kaniadakis, M. Lissia, A.M. Scarfone, Physica A 340, 41 (2004)
G. Kaniadakis, M. Lissia, A.M. Scarfone, Phys. Rev. E 71, 046128 (2005)
E. Parzen, J. Am. Stat. Assoc. 74, 105 (1979)
W.J. Reed, Physica A 319, 469 (2003)
W.J. Reed, J. Income Distrib. 13, 7 (2004)
D.G. Champernowne, Econ. J. 63, 318 (1953)
S.K. Singh, G.S. Maddala, Econometrica 44, 963 (1976)
C. Dagum, Econ. Appl. 30, 413 (1977)
M. Okamoto, Econ. Bull. 32, 2969 (2012)
W.J. Reed, M. Jorgensen, Commun. Stat.-Theor. M. 33, 1733 (2004)
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Clementi, F., Gallegati, M., Kaniadakis, G. et al. κ-generalized models of income and wealth distributions: A survey. Eur. Phys. J. Spec. Top. 225, 1959–1984 (2016). https://doi.org/10.1140/epjst/e2016-60014-2
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DOI: https://doi.org/10.1140/epjst/e2016-60014-2