Solving Linear DSGE Models with Newton Methods (Replication)

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.