  Measuring interdependence between probabilities of default (PDs) in different
industry sectors of an economy plays a crucial role in financial stress
testing. Thereby, regression approaches may be employed to model the impact of
stressed industry sectors as covariates on other response sectors. We identify
vine copula based quantile regression as an eligible tool for conducting such
stress tests as this method has good robustness properties, takes into account
potential nonlinearities of conditional quantile functions and ensures that no
quantile crossing effects occur. We illustrate its performance by a data set of
sector specific PDs for the German economy. Empirical results are provided for
a rough and a fine-grained industry sector classification scheme. Amongst
others, we confirm that a stressed automobile industry has a severe impact on
the German economy as a whole at different quantile levels whereas e.g., for a
stressed financial sector the impact is rather moderate. Moreover, the vine
copula based quantile regression approach is benchmarked against both classical
linear quantile regression and expectile regression in order to illustrate its
methodological effectiveness in the scenarios evaluated.
