On the uniqueness of solutions to rational expectations models

Klein (2000) advocates the use of the Schur decomposition of a matrix pencil to solve linear rational expectations models. Meanwhile his algorithm has become a center piece in several computer codes that provide approximate solutions to (non-linear) dynamic stochastic general equilibrium models. A subtlety not resolved by Klein is whether or not a certain Schur decomposition could fail to solve the model while a second one would provide a solution. We show that this cannot happen.