Review of Quantitative Finance and Accounting

, Volume 40, Issue 3, pp 467–483 | Cite as

Corporate credit default models: a mixed logit approach

  • Martin Kukuk
  • Michael Rönnberg
Original Research


The popular logit model is extended to allow for varying stochastic parameters (mixed logit) and non-linearities of regressor variables while analysing a cross-sectional sample of German corporate credit defaults. With respect to economic interpretability and goodness of probability forecasts according to disriminatory power and calibration, empirical results favor the extended specifications. The mixed logit model is particularly useful with respect to interpretability. However, probability forecasts based on the mixed logit model are not distinctively preferred to extended logit models allowing for non-linearities in variables. Further potential improvements with the help of the mixed logit approach for panel data are shown in a Monte Carlo study.


Credit default models Binary response models Model specification Estimation of probabilities of default Mixed logit 

JEL Classification

C52 G24 


  1. Altman EI (1968) Financial ratios, discriminant analysis, and the prediction of corporate bankruptcy. J Finance 23(4):589–609. doi: 10.2307/2978933 CrossRefGoogle Scholar
  2. Altman EI, Sabato G (2005) Modeling credit risk for SMEs: Evidence from the US market. Working Paper URL∼ealtman/ModelingCreditRiskforSMEs
  3. Amemiya T (1981) Qualitative response models: a survey. J Econ Lit 19(4):1483–1536Google Scholar
  4. Atiya AF (2001) Bankruptcy prediction for credit risk using neural networks: a survey and new results. IEEE Trans Neural Netw 12(4):929–35CrossRefGoogle Scholar
  5. Aziz MA, Dar HA (2006) Predicting corporate bankruptcy: where we stand. Corp Gov 6(1):18–33. doi: 10.1108/14720700610649436 CrossRefGoogle Scholar
  6. Basel Committee on Banking Supervision (2005) Studies on the validation of internal rating systems. URL
  7. Beaver WH (1966) Financial ratios as predictors of failure. J Acc Res 4:71–102. doi: 10.2307/2490171 CrossRefGoogle Scholar
  8. Dakovic R, Czado C, Berg D (2010) Bankruptcy prediction in Norway: a comparison study. Appl Econ Lett 17(17):1739–46CrossRefGoogle Scholar
  9. Engelmann B, Hayden E, Tasche D (2003) Testing rating accuracy. Risk 1:82–86Google Scholar
  10. Grunert J, Norden L, Weber M (2005) The role of non-financial factors in internal credit ratings. J Bank Finance 29(2):509–31. doi: 10.1016/j.jbankfin.2004.05.017 CrossRefGoogle Scholar
  11. Hamerle A, Rösch D (2006) Parameterizing credit risk models. J Credit Risk 2(4):101–122Google Scholar
  12. Hastie TJ, Tibshirani RJ (1995) Generalized additive models. 1st edn. Chapman & Hall, LondonGoogle Scholar
  13. Hensher DA, Greene WH (2003) The mixed logit model: the state of practice. Transportation 30(2):133–176. doi: 10.1023/A:1022558715350 CrossRefGoogle Scholar
  14. Hensher DA, Jones S (2007) Forecasting corporate bankruptcy: optimizing the performance of the mixed logit model. Abacus 43(3):241–64. doi: 10.1111/j.1467-6281.2007.00228.x CrossRefGoogle Scholar
  15. Hensher DA, Jones S, Greene WH (2007) An error component logit analysis of corporate bankruptcy and insolvency risk in Australia. Econ Rec 83(260):86–103. doi: 10.1111/j.1475-4932.2007.00378.x CrossRefGoogle Scholar
  16. Jones S, Hensher DA (2004) Predicting firm financial distress: a mixed logit model. Acc Rev 79(3):1011–1038. doi: 10.2308/accr.2004.79.4.1011 CrossRefGoogle Scholar
  17. Kalotay E (2007) Discussion of Hensher and Jones. Abacus 43(3):265–70. doi: 10.1111/j.1467-6281.2007.00229.x CrossRefGoogle Scholar
  18. Lennox C (1999) Identifying failing companies: a reevaluation of the logit, probit and DA approaches. J Econ Bus 51(4):347–64. doi: 10.1016/S0148-6195(99)00009-0 CrossRefGoogle Scholar
  19. Murphy AH, Winkler RL (1992) Diagnostic verification of probability forecasts. Int J Forecast 7(4):435–55. doi: 10.1016/0169-2070(92)90028-8 CrossRefGoogle Scholar
  20. Niemann M, Schmidt JH, Neukirchen M (2008) Improving performance of corporate rating prediction models by reducing financial ratio heterogeneity. J Bank Finance 32(3):434–46. doi: 10.1016/j.jbankfin.2007.05.015 CrossRefGoogle Scholar
  21. Ohlson JA (1980) Financial ratios and the probabilistic prediction of bankruptcy. J Acc Res 18(1):109–131. doi: 10.2307/2490395 CrossRefGoogle Scholar
  22. Porath D (2004) Estimating probabilities of default for German savings banks and credit cooperatives. Discussion Pap Ser 2: Bank Financial Superv No 6Google Scholar
  23. Redelmeier DA, Bloch DA, Hickam DH (1991) Assessing predictive accuracy: how to compare brier scores. J Clin Epidemiol 41(11):1141–1146. doi: 10.1016/0895-4356(91)90146-Z CrossRefGoogle Scholar
  24. Revelt D, Train K (2000) Customer-specific taste parameters and mixed logit. Working paper URL
  25. Rönnberg M (2010) Bedeutung der Spezifikation für Ratingmodelle. PhD thesis, Universität Würzburg, URL
  26. Spiegelhalter DJ (1986) Probabilistic prediction in patient management and clinical trials. Stat Med 5(5):421–33. doi: 10.1002/sim.4780050506 CrossRefGoogle Scholar
  27. Sun L (2007) A re-evaluation of auditors’ opinions versus statistical models in bankruptcy prediction. Rev Quant Finance Acc 28:55–78. doi: 10.1007/s11156-006-0003-x CrossRefGoogle Scholar
  28. Train K (2009) Discrete choice methods with simulation, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  29. Trustorff J, Konrad PM, Leker J (2011) Credit risk prediction using support vector machines. Rev Quant Finance Acc 36:565–81. doi: 10.1007/s11156-010-0190-3 CrossRefGoogle Scholar
  30. Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2):307–33. doi: 10.2307/1912557 CrossRefGoogle Scholar
  31. White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50(1):1–25. doi: 10.2307/1912526 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Faculty of EconomicsUniversity of WürzburgWuerzburgGermany

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