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

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  • Filippo Domma
  • Sabrina Giordano

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    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

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    File URL: http://hdl.handle.net/10.1007/s10260-012-0192-5
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    Bibliographic Info

    Article provided by Springer in its journal Statistical Methods & Applications.

    Volume (Year): 21 (2012)
    Issue (Month): 3 (August)
    Pages: 375-389

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    Handle: RePEc:spr:stmapp:v:21:y:2012:i:3:p:375-389

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    Related research

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

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Tullio Jappelli & Luigi Pistaferri, 2009. "The Consumption Response to Income Changes," CSEF Working Papers 237, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Tullio Jappelli & Marco Pagano & Marco di Maggio, 2008. "Households’ Indebtedness and Financial Fragility," CSEF Working Papers 208, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Sep 2010.
    3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    4. 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.
    5. Christian Kleiber, 2007. "A Guide to the Dagum Distributions," Working papers 2007/23, Faculty of Business and Economics - University of Basel.
    6. 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.
    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. 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.
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    Cited by:
    1. 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.

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