In many credit risk and pricing applications, credit transition matrix is modeled by a constant transition probability or generator matrix for Markov processes. Based on empirical evidence, we model rating transition processes as piecewise homogeneous Markov chains with unobserved structural breaks. The proposed model provides explicit formulas for the posterior distribution of the time-varying rating transition generator matrices, the probability of structural break at each period and prediction of transition matrices in the presence of possible structural breaks. Estimating the model by credit rating history, we show that the structural break in rating transitions can be captured by the proposed model. We also show that structural breaks in rating dynamics are different for different industries. We then compare the prediction performance of the proposed and time-homogeneous Markov chain models.

This paper aims to provide a theoretical underpinning of the dynamic efficiency model pioneered by [Ahn, S.C., Good, D.H., Sickles, R.C., 2000. Estimation of long-run inefficiency levels: A dynamic frontier approach. Econometric Reviews 19, 461–492]. In the context of a quadratic loss function this paper formulates a multi-period forward-looking rational expectations model on the evolution of the technical inefficiency level, which correctly produces a dynamic panel data model. The model is illustrated using panel data of 112 French banks. Encouraging evidence of superiority in favor of the model is reached. Substantial cost inefficiency prevails in this industry, where the constituent banks are characterized as having volatile adjustment speeds toward their long-run steady states. The sample banks exhibit increasing returns to scale and product-mix economies.