Abstract
Probabilistic bankruptcy prediction models based on accounting numbers and other financial information are commonly estimated from non-random samples of firms, where the proportion of bankrupt firms is much larger than in most real world situations. This "choice based sample bias" leads to estimated bankruptcy probabilities that are biased. Given that unbiased probabilities are required in risk assessments or discounted cash flow valuation modelling, such probabilities can be severely misleading. The purpose of the paper is to analyze this bias in probabilistic bankruptcy prediction models (typically probit/logit analysis), and to investigate whether it can be mitigated without having to resort to cumbersome model re-estimations. The authors show that there is a clear-cut linkage between sample based probabilities and the corresponding unbiased probabilities. Also, the authors show that sample based probabilities can be calibrated for the choice based sample bias, provided that randomly selected firms from the sub-populations of bankrupt and survival firms are used in the estimation of a prediction model. Non-calibrated bankruptcy probabilities are commonplace in previous empirical research, implying that reported misclassification errors and/or misclassification costs can be more or less misleading. Observed regularities in previous studies are in line with the presented analyses, demonstrating a need for a more insightful treatment of this bias in future research.