System reduction and the accuracy of solutions of DSGE models: A note

Many algorithms that provide approximate solutions for dynamic stochastic general equilibrium (DSGE) models employ the generalized Schur factorization since it allows for a flexible formulation of the model and exempts the researcher from identifying equations that give raise to infinite eigenvalues. We show, by means of an example, that the policy functions obtained by this approach may differ from those obtained from the solution of a properly reduced system. As a consequence, simulation results may depend on the numeric values of parameters that are theoretically irrelevant. The source of this inaccuracy are ill-conditioned matrices as they emerge, e.g., in models with strong habits. Therefore, researchers should always cross-check their results and test the accuracy of the solution.