A comparative study on the estimation of factor migration models

In this paper, we study the statistical estimation of some factor migration models. This class of models is based on the assumption that rating migrations are driven by a set of common factors representing the business cycle evolution. In particular, we compare the estimation of the ordered Probit model as described for instance in Gagliardini and Gourieroux (2005) and of the multi-state latent factor intensity model used in Koopman et al. (2008). For these two approaches, we also distinguish the case where the underlying factors are observable and the case where they are assumed to be unobservable. The paper is supplied with an empirical study where the estimation is made on historical Standard & Poor's rating data on the period [01/2006 − 01/2014]. We find that the intensity model with observable factors is the one that best fits empirical transition probabilities. In line with Kavvathas (2001), this study shows that short migrations of investment grade firms are significantly correlated to the business cycle whereas, because of lack of observations, it is not possible to state any relation between long migrations (more than two grades) and the business cycle. Concerning non investment grade firms, downgrade migrations are negatively related to business cycle whatever the amplitude of the migration.