Abstract
By mixing an idiosyncratic component with a common one, coupling schemes allow to model dependent credit-rating migrations. The distribution of the common component is modified according to macroeconomic conditions, favorable or adverse, that are encoded by the corresponding (unobserved) tendency variables as $1$ and $0$. Computational resources required for estimation of such mixtures depend upon the pattern of tendency variables. Unlike in the known coupling schemes, the credit-class-specific tendency variables considered here can evolve as a (hidden) time-homogeneous Markov chain. In order to identify unknown parameters of the corresponding mixtures of multinomial distributions, maximum likelihood estimators are suggested and tested on a Standard and Poor's dataset using MATLAB optimization software.