Iterative refinement of the QZ decomposition for solving linear DSGE models

The standard approach to solving linear DSGE models is to apply the QZ method. It is a one-shot algorithm that leaves the researcher with little alternative than to seek a different algorithm should the result be numerically unsatisfactory. We develop an iterative implementation of QZ that delivers the standard result as its first iteration and further refinements at each subsequent iteration. We demonstrate that our algorithm successful corrects for accuracy losses identified in particular cases of a macro finance model and does not erroneously attempt to refine sufficiently accurate solutions.