Appendix

• Author: Dobkowitz, Sonja; Evrard, Johanne; Carmassi, Jacopo; Silva, André; Parisi, Laura; Wedow, Michael
• Pages: 54-54

ECB Occasional Paper Series No 208 / April 2018

54

Appendix

PD estimation and in-sample test

Starting from the specification A of the model implemented to estimate the default

probability of banks, an in-sample test has been performed to compare the predicted

results with the real, observed ones. According to the estimated regressors (see

Table 1), the default probability has been calculated for the entire sample of banks,

and for the period ranging from 2000 to 2013 (same period used to estimate the

model). Given that the outcome of the model is a probability (continuous variable,

between 0 and 1) while the observed defaults are classified as a dummy variable (0

in case of non-default, 1 in case of default), two different thresholds have been used

to transform the estimated PDs into dichotomic values:

(i) When the estimated PD is higher than the PD corresponding to the

97th percentile of the distribution, the bank is classified as in default.

This choice is consistent with the 3% riskiest banks failing scenario;

(ii) When the estimated PD is higher than the PD corresponding to the

90th percentile of the distribution, the bank is classified as in default.

This choice is consistent with the 10% riskiest banks failing scenario.

Table A1 summarises the performance of the model specification A under options (i)

and (ii).

Table A1

Performance of the model used to estimate default probabilities

Diagnostic

(i) (ii)

97th percentile as threshold 90th percentile as threshold

TP 99 155

TN 46 496 45 384

FP 767 1 879

FN 413 357

Accuracy 98% 95%

Sensitivity 19% 30%

Specificity 98% 96%

Source: ECB staff calculations based on Bankscope, ECB Statistical Data Warehouse and European Commission dataset on state aid

measures, 1999:Q1 – 2013:Q4.

Note: TP abbreviates True Positive (default events correctly estimated as defaults); TN abbreviates True Negative (non-default events

correctly estimated as non-defaults); FP abbreviates False Positive (or false alarms, non-default events estimated as defaults); FN

abbreviates False Negative (or II type errors, default events estimated as non-defaults). Accuracy is calculated as the ratio between

TP+TN and the overall population; Sensitivity is calculated as the ratio between TP and TP+FN; Specificity is calculated as the ratio

between FP and FP+TN.

On the one hand, the overall accuracy of the model is extremely high under both

options (i) and (ii); on the other hand, the discrimination between failing and non-

failing banks based on the 90th percentile (option (ii)) seems to substantially

increase the sensitivity of the model.