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Second, an alternative approach to assess the default prediction
accuracy is an examination of the type I and type II error. Type I error
refers to cases where firms are predicted as non-defaulters but
they default, while type II error refers to cases where firms are predicted
as defaulters but they do not default. These errors are based
on a binary classification for default and non-default. Given the
estimated probability of default from the probit regression models,
the binary classification can be derived by applying a cut-off value.
If the firm’s estimated probability of default lies above the cut-off
value, we predict that the firm will default and vice versa. To derive
the optimal cut-off value we apply a cost function weighting the
number of false-negative and false-positive with different costs.
The related literature has emphasized that false-negatives lead to
substantially higher costs than false-positives (e.g., Grunert et al.,
2005). Therefore, we assign higher error costs to type I errors than
to type II errors by setting the cost ratio of false-negatives over
false-positives to 20:1. Assuming an interest rate of 5%, a non-predicted
default would lead to a loss of the face value of €100 (falsenegative)
and a denying of a non-default credit (false-positive)
would lead to a loss of the potential interest payment of €5. Based
on this cost ratio we derive the optimal cut-off points for the full
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