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Vícerozměrný pravděpodobnostní model rozdělení příjmů českých domácností
[Multivariate Probability Model For Incomes of the Czech Households]

Author

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  • Ivana Malá

Abstract

The equivalised total net annual incomes of the Czech households (in CZK) in 2007-2010 are analysed in the text. The set of all households is very nonhomogeneous (with respect to incomes) and the aim of the analysis is to determine more homogeneous subsets (components) and to describe the distribution of incomes in these components. The components are supposed to be artificial, the membership of households in components is not known (or observable). A multivariate mixture of normal distributions (four dimensional component distributions) is used to describe a vector of logarithms of incomes, models with 2 to 9 components are fitted. Maximum likelihood estimates of unknown parameters were found with the use of EM algorithm. Akaike information criterion was used (accompanied by bootstraped test) and models with 3 or 4 components were selected to be acceptable for the description of distribution of incomes. Cluster analysis was performed in order to classify households into components and good performance of the model was found.

Suggested Citation

  • Ivana Malá, 2015. "Vícerozměrný pravděpodobnostní model rozdělení příjmů českých domácností [Multivariate Probability Model For Incomes of the Czech Households]," Politická ekonomie, Prague University of Economics and Business, vol. 2015(7), pages 895-908.
    • Handle: RePEc:prg:jnlpol:v:2015:y:2015:i:7:id:1040:p:895-908
    DOI: 10.18267/j.polek.1040
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    References listed on IDEAS

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    1. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    2. Roberto Zelli & Maria Grazia Pittau, 2006. "Empirical evidence of income dynamics across EU regions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 605-628.
    3. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    4. Jitka Bartošová & Nicholas T. Longford, 2014. "A Study of Income Stability in the Czech Republic by Finite Mixtures," Prague Economic Papers, Prague University of Economics and Business, vol. 2014(3), pages 330-348.
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    More about this item

    Keywords

    multivariate normal distribution; maximum likelihood estimate; finite mixture of distributions; EM algorithm; distribution of incomes; cluster analysis;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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