The Zero Root Problem: A Note on the Dynamic Determination of the Stationary Equilibrium in Linear Models - Giavazzi, Francesco; Wyplosz, Charles (Review of Economic Studies, 1985)
Singularity of the transition matrix in differential equation systems implies indeterminacy of the stationary equilibrium: we show that this indeterminacy is only apparent, and we provide the unique solution. There are many examples of, and good theoretical reasons for, singular transition matrices. The main result is that, when stability conditions arc satisfied, the resulting stationary equilibrium will depend upon the intial conditions and the parameters describing the speed of adjustment.