Solving linear DSGE models with structure-preserving doubling methods

Abstract This paper applies Structure-Preserving Doubling Algorithms (SDAs) to solve the matrix quadratic that underlies linear DSGE models. We present and compare two SDAs to other competing methods—the QZ method, a Newton algorithm, and an iterative Bernoulli approach—as well as linking them to the cyclic and logarithmic reduction algorithms included in Dynare. Our evaluation, conducted across 142 models from the Macroeconomic Model Data Base and multiple parameterizations of the Smets and Wouters (2007) model, demonstrates that SDAs generally provide more accurate solutions in less time than QZ. We also establish their theoretical convergence properties and robustness to initialization issues. The SDAs perform particularly well in refining solutions provided by other methods and for large models.