Open Access

Alexander Meyer-Gohde, Johanna Saecker

• Highlights • Six Newton methods for solving matrix quadratic equations in linear DSGE models. • Compared to QZ using 99 different DSGE models including Smets and Wouters (2007). • Newton methods more accurate than QZ with comparable computation burden. • Apt for refining solutions from alternative methods or nearby parameterizations. Abstract This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. We find that Newton-based methods compare favorably in solving DSGE models, providing higher accuracy as measured by the forward error of the solution at a comparable computation burden. The methods, however, suffer from their inability to guarantee convergence to a particular, e.g. unique stable, solution, but their iterative procedures lend themselves to refining solutions either from different methods or parameterizations.