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On Unbalanced Sampling in Bankruptcy Prediction

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  • Marek Gruszczyński

    (Institute of Econometrics, SGH Warsaw School of Economics, 02-554 Warszawa, Poland)

Abstract

The paper discusses methodological topics of bankruptcy prediction modelling—unbalanced sampling, sample bias, and unbiased predictions of bankruptcy. Bankruptcy models are typically estimated with the use of non-random samples, which creates sample choice biases. We consider two types of unbalanced samples: (a) when bankrupt and non-bankrupt companies enter the sample in unequal numbers; and (b) when sample composition allows for different ratios of bankrupt and non-bankrupt companies than those in the population. An imbalance of type (b), being more general, is examined in several sections of the paper. We offer an extended view of the relationship between the biased and unbiased estimated probabilities of bankruptcy—probability of default (PD). A common error in applications is neglecting the possibility of calibrating the PD obtained from a bankruptcy model to the unbiased PD that is population adjusted. We show that Skogsviks’ formula of 2013 coincides with prior correction known for the logit model. This, together with solutions for other binomial models, serves as practical advice for obtaining the calibration of unbiased PDs from popular bankruptcy models. In the final section, we explore sample bias effects on classification.

Suggested Citation

  • Marek Gruszczyński, 2019. "On Unbalanced Sampling in Bankruptcy Prediction," IJFS, MDPI, vol. 7(2), pages 1-13, June.
    • Handle: RePEc:gam:jijfss:v:7:y:2019:i:2:p:28-:d:237438
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    References listed on IDEAS

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    1. Edward I. Altman, 1968. "The Prediction Of Corporate Bankruptcy: A Discriminant Analysis," Journal of Finance, American Finance Association, vol. 23(1), pages 193-194, March.
    2. Altman, Edward I. & Eisenbeis, Robert A., 1978. "Financial Applications of Discriminant Analysis: A Clarification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(1), pages 185-195, March.
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    5. Stewart Jones & David Johnstone & Roy Wilson, 2017. "Predicting Corporate Bankruptcy: An Evaluation of Alternative Statistical Frameworks," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 44(1-2), pages 3-34, January.
    6. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-1988, November.
    7. King, Gary & Zeng, Langche, 2001. "Logistic Regression in Rare Events Data," Political Analysis, Cambridge University Press, vol. 9(2), pages 137-163, January.
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    Cited by:

    1. Marek Gruszczyński, 2020. "Women on Boards and Firm Performance: A Microeconometric Search for a Connection," JRFM, MDPI, vol. 13(9), pages 1-13, September.

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