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A New Model of Personal Income Distribution: Specification and Estimation

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Modeling Income Distributions and Lorenz Curves

Part of the book series: Economic Studies in Equality, Social Exclusion and Well-Being ((EIAP,volume 5))

Abstract

The research deduces a new model of income distribution by size from a set of elementary assumptions. Its main properties are analyzed and five methods of parameter estimation are proposed. The mathematical form of the Lorenz curve and the Gini concentration ratio associated with the specified model are also deduced. The model is fitted to the observed income distributions of four very dissimilar countries: Argentina, Canada, Sri Lanka and the USA. The fits obtained for the USA in 1960 and in 1969 are compared with those obtained using the lognormal, the gamma and the Singh-Maddala models, working with the sum of squares of deviations and the bounds for the Gini concentration ratio proposed by Gastwirth. In conclusion, the specified model fared better than the others for almost all of the fourteen properties introduced in this paper.

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References

  • Aitchison, J. and J. A. C. Brown (1957) The Lognormal Distribution with Special Reference to its Uses in Enonomics, Cambridge University Press, Cambridge.

    Google Scholar 

  • Ammon, O. (1895) Die Gesellschaftsordnung und ihre Natrlichen Grundlagen, Jena.

    Google Scholar 

  • Amoroso, L. (1924) Ricerche Intorno alla Curva dei Redditi, Annali di Mathematica Pura ed Applicata, Serie 4-21, II, 123-157.

    Google Scholar 

  • Bartels, C. P. A. and H. van Metelen (1975) Alternative Probability Density Func-tions of Income, Vrije University Amsterdam: Research Memorandum No. 29, 30 pages.

    Google Scholar 

  • Birta, L. G. (1976) OPTPAK a Program Package for Unconstrained Function Mini-mization, Technical Report TR 76-02, University Ottawa, 22 pages.

    Google Scholar 

  • Budd, E. C. (1970) Distribution Issues: Trends and Policies. Postwar Changes in the Size Distribution of Income in the U.S., A. E. R., 60(2), 247-260.

    Google Scholar 

  • Central Bank of Ceylon (1974) Survey of Sri Lanka’s Consumer Finances 1973, Colombo, Department of Economic Research, Central Bank of Ceylon.

    Google Scholar 

  • Champernowne, D. G. (1952) The Graduation of Income Distributions, Economet-rica, 20(4), 591-615.

    Article  Google Scholar 

  • Champernowne, D. G. (1953) A Model of Income Distribution, Economic Journal, 63(2), 318-351.

    Article  Google Scholar 

  • Conade-Cepal (1965) Distribucion del Ingreso y Cuentas Nacionales en la Argentina, tomos I-V, Buenos Aires, Presidencia de la Nacion Argentina.

    Google Scholar 

  • Cram ér, H. (1946) Mathematical Methods of Statistics, Princeton University Press, Princeton.

    Google Scholar 

  • D’Addario, R. (1949) Ricerche sulla Curva dei Redditi, Giornale degli Economisti e Annali di Economia, 8, 91-114.

    Google Scholar 

  • Dagum, C. (1973) Un Mod èle non Lin éaire de R épartition Fonctionnelle du Revenu, Economie appliqu ée, XXVI(2-3-4), 843-876.

    Google Scholar 

  • Dagum, C. (1975) A Model of Income Distribution and the Conditions of Existence of Moments of Finite Order, Proceedings of the 40th session of the International Statistical Institute, vol. XLVI, Book 3, Warsaw, pp. 196-202.

    Google Scholar 

  • Dagum, C. (1977a) A New Model of Income Distribution, the Lorenz Curve and the Gini Concentration Ratio, forthcomming paper.

    Google Scholar 

  • Dagum, C. (1977b) Analyse R égionale de la r épartition du Revenu au Canada, Economie appliqu ée, XXX(2).

    Google Scholar 

  • Dagum, C. (1977c) El Modelo Log-Logistico Y La Distribucion Del Ingreso En Argentina, El Trimestre Economico, XLIV (4)(176), 837-864.

    Google Scholar 

  • Figueroa, A. (ed.) (1974) Estructura del Consumo y Distribution de Ingresos en Lima Metropolitana, 1968-1969, Serie Estudios Economicos No. 1, Lima, Pontificia Universidad Catolica del Peru.

    Google Scholar 

  • Fisk, P. R. (1961) The Graduation of Income Distributions, Econometrica, 29(2), 171-185.

    Article  Google Scholar 

  • Gastwirth, J. L. (1972) The Estimation of the Lorenz Curve and Gini Index, Review of Economics and Statistics, 54, 306-316.

    Article  Google Scholar 

  • Gibrat, R. (1931) Les In égalits économiques, Sirey, Paris.

    Google Scholar 

  • Kakwani, N. C. and N. Podder (1976) Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations, Econometrica, 44 (1), 137-149.

    Article  Google Scholar 

  • Kloek, T. and H. K. van Dijk (1976) Efficient Estimation of Income Distribution Pa-rameters, Report 7616/E, Econometric Institute, Erasmus University, Rotterdam, 15 pages.

    Google Scholar 

  • L évy, P. (1925) Calculs des Probabilits, Gauthier-Villars, Paris.

    Google Scholar 

  • Mandelbrot, B. (1960) The Pareto-L évy Law and the Distribution of Income, International Economic Review, 1, 79-106.

    Article  Google Scholar 

  • Mandelbrot, B. (1963) The Pareto-L évy Law and the Distribution of Income, International Economic Review, IV, 111-115.

    Google Scholar 

  • March, L. (1898) Quelques Exemples de Distribution de Salaries, Journal de la Soci ét é statistique de Paris, pp. 193-206.

    Google Scholar 

  • McAlister, D. (1879) The Law of the Geometric Mean, Proceedings of the Royal Society, vol. 29, pp. 367.

    Article  Google Scholar 

  • Metcalf, E. C. (1972) An Econometric Model of the Income Distribution, Markham Publishing Company, Chicago.

    Google Scholar 

  • Morgenstern, O. (1963) On the Accuracy of Economic Observations, 2nd ed., Princeton University Press, Princeton.

    Google Scholar 

  • Pareto, V. (1895) La Legge della Domanda, Giornale degli Economisti, pp. 59-68, Gennaio.

    Google Scholar 

  • Pareto, V. (1896) Ecrits sur la Courbe de la R épartition de la Richesse, Euvres compl étes de Vilfredo Pareto publi ées sous la direction de Giovanni Busino, Gen éve, Librairie Droz, 1965.

    Google Scholar 

  • Pareto, V. (1897) Cours d’Economie Politique, Lausanne, Rouge, New edition by Bousquet G. H. et G. Busino (1964). Gen éve, Librairie Droz.

    Google Scholar 

  • Pearson, K. (1934) Tables of the Incomplete Beta-Function, Cambridge University Press, Cambridge.

    Google Scholar 

  • Rao, C. R. (1973) Linear Statistical Inference and its Applications, 2nd ed., John Wiley, New York.

    Book  Google Scholar 

  • Rutherford, R. S. G. (1955) Income Distibutions: A New Model, Econometrica, 23(3), 277-294.

    Article  Google Scholar 

  • Salem, A. B. Z. and T. D. Mount (1974) A Convenient Descriptive Model of Income Distribution: the Gamma Density, Econometrica, 42(6), 1115-1127.

    Article  Google Scholar 

  • Singh, S. K. and G. S. Maddala (1976) A Function for Size Distribution of Incomes, Econometrica, 44(5), 963-970.

    Article  Google Scholar 

  • Statistics Canada (1975) Income Distributions by Size in Canada, 1973, Catalogue 13-207, Ottawa.

    Google Scholar 

  • Thurow, L. C. (1970) Analyzing the American Income Distribution, American Economic Review, 48, 261-269.

    Google Scholar 

  • US Bureau of the Census (1961-1971) Income of Families and Persons in the United States, Current Population Reports, Series P-60, US Government Printing Office, Washington.

    Google Scholar 

  • Vinci, F. (1921) Nuovi Contributi allo Studio della Distribuzione dei Redditi, Giornale degli Economisti e Rivista di Statistica, 61, 365-369.

    Google Scholar 

  • Wold, H. (1961) Unbiased Predictors, Proceedings of the Fourth Berkeley Sympo-sium of Mathematical Statistics and Probability, vol. 1, pp. 719-761.

    Google Scholar 

  • Wold, H. (1963) On the Consistency of the Least Squares Regression, Sankya, A, 25 (2), 211-215.

    Google Scholar 

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Dagum, C. (2008). A New Model of Personal Income Distribution: Specification and Estimation. In: Chotikapanich, D. (eds) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72796-7_1

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