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Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind

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  • Monique Graf
  • Desislava Nedyalkova

Abstract

type="main"> There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU-SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo-likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU-SILC survey. An ad-hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non-linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo-likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.

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  • Monique Graf & Desislava Nedyalkova, 2014. "Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 821-842, December.
    • Handle: RePEc:bla:revinw:v:60:y:2014:i:4:p:821-842
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    3. Ann-Kristin Kreutzmann, 2018. "Estimation of sample quantiles: challenges and issues in the context of income and wealth distributions [Die Schätzung von Quantilen: Herausforderungen und Probleme im Kontext von Einkommens- und V," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(3), pages 245-270, December.
    4. Mathias Silva, 2023. "Parametric estimation of income distributions using grouped data: an Approximate Bayesian Computation approach [Working Papers / Documents de travail]," Working Papers hal-04066544, HAL.
    5. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    6. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    7. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    8. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2020. "A functional approach to small area estimation of the relative median poverty gap," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1273-1291, June.
    9. Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D. S. Prasada Rao, 2018. "Using the GB2 Income Distribution," Econometrics, MDPI, vol. 6(2), pages 1-24, April.
    10. Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D.S. Prasada Rao, 2018. "Using the GB2 Income Distribution: A Review," Department of Economics - Working Papers Series 2036, The University of Melbourne.
    11. Louis Chauvel, 2014. "The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis," LIS Working papers 609, LIS Cross-National Data Center in Luxembourg.
    12. 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.
    13. Nartikoev, Alan & Peresetsky, Anatoly, 2019. "Modeling the dynamics of income distribution in Russia," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 54, pages 105-125.
    14. Mathias Silva, 2023. "Parametric models of income distributions integrating misreporting and non-response mechanisms," Working Papers hal-04093646, HAL.
    15. Louis Chauvel, 2016. "The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(1), pages 52-68, March.

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