Model uncertainty and aggregated default probabilities: new evidence from Austria

Abstract

Understanding the determinants of aggregated corporate default probabilities (PDs) has attracted substantial research interest over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: model uncertainty and multicollinearity among the regressors. We present Bayesian model averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian data set. Our findings suggest that factor prices like short-term interest rates (STIs) and energy prices constitute major drivers of default rates, while firms’ profits reduce the expected number of failures. Finally, we show that the results of our model are fairly robust with respect to the choice of the BMA parameters.

Keywords:

• model uncertainty
• Bayesian model averaging
• firm failure
• ridge regression

JEL Classification:

• E44
• C52
• E37

Funding

The first author’s research is supported by the Oesterreichische Nationalbank Jubiläumsfond (OeNB) under the grant 14663.

Notes

¹ Any inverted gamma prior for and would maintain conjugacy within the Gibbs sampling framework. Here, we approximate the limiting improper priors which are proportional to and , respectively, using for the shape and rate parameters of the inverse gamma priors.

² For convenience, we omit subscripts to PIP throughout this article.

³ Note that as described in section ‘Model size’, a prior model size of 7 does not mean each model includes exactly 7 variables, but that each candidate regressor has a probability of inclusion, which yields on average a model size of 7.

⁴ For the sake of completeness, we provide here posteriors related to the shrinkage parameter (see section ‘Ridge regression and Bayesian ridge regression’). We find for the shrinkage parameter a posterior mean of 0.72, whereby flat (uninformative) hyperpriors on and were assumed. The posterior means of the variances and are 0.12 and 0.17, respectively.

⁵ For further details on the results, see Hofmarcher et al. (2011).

⁶ These variables are ranked 52, respectively, 35 in the baseline model and appear therefore not in Table 3.