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Sample selection bias in non-traditional lending: A copula-based approach for imbalanced data

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  • Calabrese, Raffaella
  • Osmetti, Silvia Angela
  • Zanin, Luca

Abstract

Credit scoring models for non-traditional lending channels, such as peer-to-peer (P2P) lending platforms, are usually estimated only on the sample of accepted applicants. This may lead to biased estimates of the risk drivers. This issue can be addressed using a reject inference technique that includes the characteristics of rejected applicants in the model. Due to the low numbers of accepted applicants and default records, credit scoring models usually face a class imbalance problem. However, previous literature on sample selection models for credit scoring does not address the class imbalance issue. To fill this gap, we extend the Generalised Extreme Value (GEV) regression model for binary data to the sample selection framework. We consider the quantile function of the GEV distribution as a link function in both the selection and outcome equations. We use the copula function to model the dependence structure between the two equations for its flexibility. This proposal is called the Sample Selection Generalised Extreme Value (SSGEV) model and it is implemented in the R package BivGEV. We apply this model to a comprehensive dataset provided by Lending Club, and we show that parameter estimates obtained only on accepted P2P applicants are biased and coherently with the literature. The SSGEV model achieves a higher predictive accuracy than those obtained using univariate approaches or a sample selection probit model. Our proposal also provides more conservative estimates of the Value-at-Risk and the Expected Shortfall.

Suggested Citation

  • Calabrese, Raffaella & Osmetti, Silvia Angela & Zanin, Luca, 2024. "Sample selection bias in non-traditional lending: A copula-based approach for imbalanced data," Socio-Economic Planning Sciences, Elsevier, vol. 95(C).
    • Handle: RePEc:eee:soceps:v:95:y:2024:i:c:s0038012124002441
    DOI: 10.1016/j.seps.2024.102045
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    References listed on IDEAS

    as
    1. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    2. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    3. Andreeva, Galina & Calabrese, Raffaella & Osmetti, Silvia Angela, 2016. "A comparative analysis of the UK and Italian small businesses using Generalised Extreme Value models," European Journal of Operational Research, Elsevier, vol. 249(2), pages 506-516.
    4. Panagiotelis, Anastasios & Czado, Claudia & Joe, Harry & Stöber, Jakob, 2017. "Model selection for discrete regular vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 138-152.
    5. Chen, Xiao & Huang, Bihong & Ye, Dezhu, 2020. "Gender gap in peer-to-peer lending: Evidence from China," Journal of Banking & Finance, Elsevier, vol. 112(C).
    6. Marshall, Andrew & Tang, Leilei & Milne, Alistair, 2010. "Variable reduction, sample selection bias and bank retail credit scoring," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 501-512, June.
    7. G Verstraeten & D Van den Poel, 2005. "The impact of sample bias on consumer credit scoring performance and profitability," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 981-992, August.
    8. Raffaella Calabrese & Silvia Angela Osmetti, 2013. "Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(6), pages 1172-1188, June.
    9. Patrick Puhani, 2000. "The Heckman Correction for Sample Selection and Its Critique," Journal of Economic Surveys, Wiley Blackwell, vol. 14(1), pages 53-68, February.
    10. Xuchen Lin & Xiaolong Li & Zhong Zheng, 2017. "Evaluating borrower’s default risk in peer-to-peer lending: evidence from a lending platform in China," Applied Economics, Taylor & Francis Journals, vol. 49(35), pages 3538-3545, July.
    11. Clarke, Kevin A., 2007. "A Simple Distribution-Free Test for Nonnested Model Selection," Political Analysis, Cambridge University Press, vol. 15(3), pages 347-363, July.
    12. Raffaella Calabrese & Giampiero Marra & Silvia Angela Osmetti, 2016. "Bankruptcy prediction of small and medium enterprises using a flexible binary generalized extreme value model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(4), pages 604-615, April.
    13. Zhiyong Li & Xinyi Hu & Ke Li & Fanyin Zhou & Feng Shen, 2020. "Inferring the outcomes of rejected loans: an application of semisupervised clustering," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 631-654, February.
    14. Seth Freedman & Ginger Zhe Jin, 2008. "Do Social Networks Solve Information Problems for Peer-to-Peer Lending? Evidence from Prosper.com," Working Papers 08-43, NET Institute.
    15. Doriana Cucinelli & Lorenzo Gai & Federica Ielasi & Arturo Patarnello, 2021. "Preventing the deterioration of bank loan portfolio quality: a focus on unlikely-to-pay loans," The European Journal of Finance, Taylor & Francis Journals, vol. 27(7), pages 613-634, May.
    16. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    17. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.
    18. Banasik, John & Crook, Jonathan, 2007. "Reject inference, augmentation, and sample selection," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1582-1594, December.
    19. Raffaella Calabrese & Paolo Giudici, 2015. "Estimating bank default with generalised extreme value regression models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1783-1792, November.
    20. J Banasik & J Crook & L Thomas, 2003. "Sample selection bias in credit scoring models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 822-832, August.
    21. Dorfleitner, Gregor & Priberny, Christopher & Schuster, Stephanie & Stoiber, Johannes & Weber, Martina & de Castro, Ivan & Kammler, Julia, 2016. "Description-text related soft information in peer-to-peer lending – Evidence from two leading European platforms," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 169-187.
    22. Monir El Annas & Badreddine Benyacoub & Mohamed Ouzineb, 2023. "Semi-supervised adapted HMMs for P2P credit scoring systems with reject inference," Computational Statistics, Springer, vol. 38(1), pages 149-169, March.
    23. Zanin, Luca, 2020. "Combining multiple probability predictions in the presence of class imbalance to discriminate between potential bad and good borrowers in the peer-to-peer lending market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 25(C).
    24. Marra, Giampiero & Radice, Rosalba, 2013. "Estimation of a regression spline sample selection model," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 158-173.
    25. Carlos Serrano-Cinca & Begoña Gutiérrez-Nieto & Luz López-Palacios, 2015. "Determinants of Default in P2P Lending," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-22, October.
    26. Raffaella Calabrese & Silvia Angela Osmetti & Luca Zanin, 2019. "A joint scoring model for peer‐to‐peer and traditional lending: a bivariate model with copula dependence," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1163-1188, October.
    27. Karol Wyszynski & Giampiero Marra, 2018. "Sample selection models for count data in R," Computational Statistics, Springer, vol. 33(3), pages 1385-1412, September.
    28. J Banasik & J Crook, 2010. "Reject inference in survival analysis by augmentation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 473-485, March.
    29. Marc Cowling & Weixi Liu & Raffaella Calabrese, 2022. "Has previous loan rejection scarred firms from applying for loans during Covid-19?," Small Business Economics, Springer, vol. 59(4), pages 1327-1350, December.
    30. Crook, Jonathan & Banasik, John, 2004. "Does reject inference really improve the performance of application scoring models?," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 857-874, April.
    31. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.
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