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Regression Model for Proportions with Probability Masses at Zero and One

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  • Raffaella Calabrese

    (Geary Dynamics Lab, Geary Institute, University College Dublin)

Abstract

In many settings, the variable of interest is a proportion with high concentration of data at the boundaries. This paper proposes a regression model for a fractional variable with nontrivial probability masses at the extremes. In particular, the dependent variable is assumed to be a mixed random variable, obtained as the mixture of a Bernoulli and a beta random variables. The extreme values of zero and one are modelled by a logistic regression model. The values belonging to the interval (0,1) are assumed beta distributed and their mean and dispersion are jointly modelled by using two link functions. The regression model here proposed accommodates skewness and heteroscedastic errors. Finally, an application to loan recovery process of Italian banks is also provided.

Suggested Citation

  • Raffaella Calabrese, 2012. "Regression Model for Proportions with Probability Masses at Zero and One," Working Papers 201209, Geary Institute, University College Dublin.
    • Handle: RePEc:ucd:wpaper:201209
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    References listed on IDEAS

    as
    1. Bastos, João A., 2010. "Forecasting bank loans loss-given-default," Journal of Banking & Finance, Elsevier, vol. 34(10), pages 2510-2517, October.
    2. Calabrese, Raffaella & Zenga, Michele, 2010. "Bank loan recovery rates: Measuring and nonparametric density estimation," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 903-911, May.
    3. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
    4. Julie Agnew & Pierluigi Balduzzi & Annika Sundén, 2003. "Portfolio Choice and Trading in a Large 401(k) Plan," American Economic Review, American Economic Association, vol. 93(1), pages 193-215, March.
    5. Dermine, J. & de Carvalho, C. Neto, 2006. "Bank loan losses-given-default: A case study," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1219-1243, April.
    6. Grunert, Jens & Weber, Martin, 2009. "Recovery rates of commercial lending: Empirical evidence for German companies," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 505-513, March.
    7. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
    8. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
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    Cited by:

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    2. Dionne, Georges & Desjardins, Denise, 2017. "Reinsurance Demand and Liquidity Creation," Working Papers 17-3, HEC Montreal, Canada Research Chair in Risk Management.
    3. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.

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    More about this item

    Keywords

    proportions; mixed random variable; beta regression; skewness; heteroscedasticity;
    All these keywords.

    JEL classification:

    • B14 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Socialist; Marxist

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