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Bivariate income distributions for assessing inequality and poverty under dependent samples

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  • Vinh, Andrea
  • Griffiths, William E.
  • Chotikapanich, Duangkamon

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

  • Vinh, Andrea & Griffiths, William E. & Chotikapanich, Duangkamon, 2010. "Bivariate income distributions for assessing inequality and poverty under dependent samples," Economic Modelling, Elsevier, vol. 27(6), pages 1473-1483, November.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:6:p:1473-1483
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    References listed on IDEAS

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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
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    3. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    4. 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.
    5. David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2021. "Posterior Probabilities for Lorenz and Stochastic Dominance of Australian Income Distributions," The Economic Record, The Economic Society of Australia, vol. 97(319), pages 504-524, December.
    6. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.

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    More about this item

    Keywords

    C23 C46 Copulas Income distributions Inequality Panel data Dependent sample;

    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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