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A stress–strength model with dependent variables to measure household financial fragility

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  • Filippo Domma
  • Sabrina Giordano

Abstract

The paper is inspired by the stress–strength models in the reliability literature, in which given the strength (Y) and the stress (X) of a component, its reliability is measured by P(X > Y). In this literature, X and Y are typically modeled as independent. Since in many applications such an assumption might not be realistic, we propose a copula approach in order to take into account the dependence between X and Y. We then apply a copula-based approach to the measurement of household financial fragility. Specifically, we define as financially fragile those households whose yearly consumption (X) is higher than income (Y), so that P(X > Y) is the measure of interest and X and Y are clearly not independent. Modeling income and consumption as non-identically Dagum distributed variables and their dependence by a Frank copula, we show that the proposed method improves the estimation of household financial fragility. Using data from the 2008 wave of the Bank of Italy’s Survey on Household Income and Wealth we point out that neglecting the existing dependence in fact overestimates the actual household fragility. Copyright Springer-Verlag 2012

Suggested Citation

  • Filippo Domma & Sabrina Giordano, 2012. "A stress–strength model with dependent variables to measure household financial fragility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 375-389, August.
  • Handle: RePEc:spr:stmapp:v:21:y:2012:i:3:p:375-389
    DOI: 10.1007/s10260-012-0192-5
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    References listed on IDEAS

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    1. Annamaria Lusardi & Daniel Schneider & Peter Tufano, 2011. "Financially Fragile Households: Evidence and Implications," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 42(1 (Spring), pages 83-150.
    2. Tullio Jappelli & Marco Pagano & Marco Di Maggio, 2013. "Households' indebtedness and financial fragility," Journal of Financial Management, Markets and Institutions, Società editrice il Mulino, issue 1, pages 23-46, January.
    3. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    4. Tullio Jappelli & Luigi Pistaferri, 2010. "The Consumption Response to Income Changes," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 479-506, September.
    5. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    6. Ando,Albert & Guiso,Luigi & Visco,Ignazio (ed.), 1994. "Saving and the Accumulation of Wealth," Cambridge Books, Cambridge University Press, number 9780521452083.
    7. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    8. Sarah Brown & Karl Taylor, 2008. "Household debt and financial assets: evidence from Germany, Great Britain and the USA," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(3), pages 615-643, June.
    9. Adimari, Gianfranco & Chiogna, Monica, 2006. "Partially parametric interval estimation of Pr{Y>X}," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1875-1891, December.
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    Cited by:

    1. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    2. Filippo Domma & Sabrina Giordano, 2013. "A copula-based approach to account for dependence in stress-strength models," Statistical Papers, Springer, vol. 54(3), pages 807-826, August.
    3. Hejazi, Taha-Hossein & Badri, Hossein & Yang, Kai, 2019. "A Reliability-based Approach for Performance Optimization of Service Industries: An Application to Healthcare Systems," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1016-1025.
    4. Gijbels, Irène & Herrmann, Klaus, 2014. "On the distribution of sums of random variables with copula-induced dependence," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 27-44.
    5. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 196-215, March.

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    Keywords

    Reliability; Dagum distribution; Copula; IFM; SHIW data; 60E05; 62H20; 91B82;
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