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We demonstrate improvements in predictive power when introducing spline functions to take account of highly nonlinear relationships between firm failure and leverage, earnings, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive nonlinearities yields substantially improved bankruptcy predictions, on the order of 70%–90%, compared with a standard logistic model. The spline model provides several important and surprising insights into nonmonotonic bankruptcy relationships. We find that low-leveraged as well as highly profitable firms are riskier than those given by a standard model, possibly a manifestation of credit rationing and excess cash-flow volatility.
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