Markovian Credit Risk Transition Probabilities under Non-Negativity Constraints for the US Portfolio 1984-2004

Credit risk transition probabilities between aggregate portfolio classes constitute a very useful tool when individual transition data are not available. Jones (2005) estimates Markovian Credit Transition Matrices using an adjusted least squares method. Given the arguments of Judge and Takayama (1966) a least squares estimator under inequality constraints is consistent but has unknown distribution, thus parameter testing is essentially not immediately available. In this paper we view transition probabilities as parameters from a Bayesian perspective, which allows us to impose the non-negativity constraints to transition probabilities using prior densities and then estimate the model via Monte Carlo Integration. This approach reveals the empirical distribution of transition probabilities and makes statistical inference readily available. Our empirical results on the US portfolio of non-performing loan proportions, are in some cases close to the estimates of Jones (2005), but also exhibit some statistically significant differences regarding the estimated transition probabilities. Furthermore, in-sample forecast evaluation statistics indicate that our estimator tends to slightly over-predict (under-predict) non-performing (performing) loan proportions consistent with asymmetric preferences and is substantially more accurate in all cases.