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Bivariate Income Distributions for AssessingInequality and Poverty Under Dependent Samples

Author

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  • Andrea Vinh
  • William E. Griffiths
  • Duangkamon Chotikapanich

Abstract

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh-Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh-Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.

Suggested Citation

  • Andrea Vinh & William E. Griffiths & Duangkamon Chotikapanich, 2010. "Bivariate Income Distributions for AssessingInequality and Poverty Under Dependent Samples," Department of Economics - Working Papers Series 1093, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:1093
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    References listed on IDEAS

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    1. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    4. José Sarabia & Enrique Castillo & Marta Pascual & María Sarabia, 2007. "Bivariate income distributions with lognormal conditionals," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 371-383, December.
    5. McDonald, James B & Ransom, Michael R, 1979. "Functional Forms, Estimation Techniques and the Distribution of Income," Econometrica, Econometric Society, vol. 47(6), pages 1513-1525, November.
    6. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    7. Kmietowicz, Z W, 1984. "The Bivariate Lognormal Model for the Distribution of Household Size and Income," The Manchester School of Economic & Social Studies, University of Manchester, vol. 52(2), pages 196-210, June.
    8. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
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    Cited by:

    1. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    2. Lee, Chien-Chiang & Chang, Chi-Hung & Chen, Mei-Ping, 2015. "Industry co-movements of American depository receipts: Evidences from the copula approaches," Economic Modelling, Elsevier, vol. 46(C), pages 301-314.

    More about this item

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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