TY  - JOUR
A1  - Meyer-Gohde, Alexander
A1  - Saecker, Johanna
T1  - Solving linear DSGE models with Newton methods
T2  - Economic modelling
N2  - 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.
KW  - Numerical accuracy
KW  - DSGE
KW  - Solution methods
Y1  - 2024
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/82887
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-828870
SN  - 0264-9993
VL  - 133
IS  - 106670
PB  - Elsevier
CY  - Amsterdam
ER  -