In Section Sample Clauses

In Section describes a very general model class allowing for a variety of specifica- tions for the means and variances of the normal distributions of the latent PD scores and rating errors. We use parametric models which group obligors based on the available co-variates (for the data set at hand, industry affil- iation, legal form and exposure). For the error distributions, bank effects as well as group/bank interaction terms are considered. We also investi- gate models allowing for general correlation patterns between rating errors. For each fitted model, we compute the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC, also known as Schwarz’s Bayesian criterion). The best model is then selected based on these criteria. The parameters of the mixed-effects models are estimated via maximum like- lihood (e.g., ▇▇▇▇▇▇▇▇ and ▇▇▇▇▇, 2000) The best model found by the model selection procedure uses industry affiliation as the sole grouping variable and a single variance parameter PD score, and is given by Sij = Si + µg(i),j + σg(i),▇ ▇▇▇ , Si ∼ N (νg(i), τ 2), (3.1) where µg,j is the rating bias to the mean PD score of bank j for obligors in industry g, σg,j is the standard deviation of the rating error of bank j for obligors in industry g, and νg is the mean PD score in industry g. This model forms the basis for further analysis. Note that the µ and σ parameters are unestimable for industry/bank combinations with no observations. We begin our analysis of the estimation results by showing the parameters describing the distribution of the true latent scores. These are the industry specific means νg and the standard deviation τ . For ease of interpretation we additionally show the images under the inverse link function of the mean PD scores for each industry and the respective one standard deviation intervals (see Table 3.3). Industry νg Φ(νg) Φ(νg − τ ) Φ(νg + τ ) Manufac −2.542 55.1 17.7 151.1 Energy −2.993 13.8 3.8 44.2 Constr −2.448 71.8 23.8 190.9 Trading −2.375 87.7 29.8 227.5 Finance −3.256 5.6 1.5 19.2 RealEst −2.474 66.8 22.6 174.7 Public −3.330 4.3 1.1 15.1 Service −2.517 59.2 19.8 157.0 Private −2.296 108.4 40.0 267.4 Table 3.3: Industry specific means νg and PD intervals measured in basis points (10−4). Intervals are obtained by applying the standard normal dis- tribution to νg ± τ . We infer from Table 3.3 that on an aggregate level the portfolio of our sample banks might exhibit important differences in average credit quality across indu...