TY  - UNPD
A1  - Huber, Johannes
A1  - Meyer-Gohde, Alexander
A1  - Saecker, Johanna
T1  - Solving linear DSGE models withstructure-preserving doubling methods
N2  - This paper applies structure preserving doubling methods to solve the matrix quadratic underlying the recursive solution of linear DSGE models. We present and compare two Structure-Preserving Doubling Algorithms ( SDAs) to other competing methods – the QZ method, a Newton algorithm, and an iterative Bernoulli approach – as well as the related cyclic and logarithmic reduction algorithms. Our comparison is completed 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 both SDAs perform very favorably relative to QZ, with generally more accurate solutions computed in less time. While we collect theoretical convergence results that promise quadratic convergence rates to a unique stable solution, the algorithms may fail to converge when there is a breakdown due to singularity of the coefficient matrices in the recursion. One of the proposed algorithms can overcome this problem by an appropriate (re)initialization. This SDA also performs particular well in refining solutions of different methods or from nearby parameterizations.
T3  - Working paper series / Institute for Monetary and Financial Stability - 195 
KW  - Numerical accuracy
KW  - DSGE
KW  - Solution methods
Y1  - 2023
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/71224
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-712247
UR  - https://www.imfs-frankfurt.de/forschung/imfs-working-papers/details.html?tx_mmpublications_publicationsdetail%5Bcontroller%5D=Publication&tx_mmpublications_publicationsdetail%5Bpublication%5D=461&cHash=f53244e0345a27419a9d40a3af98c02f
N1  - This research was supported by the DFG through grant nr. 465469938 "Numerical diagnostics and improvements for the solution of linear dynamic macroeconomic models” and grant nr. 465135565 “Models of Imperfect Rationality and Redistribution in the context of Retirement".
PB  - Johann Wolfgang Goethe-Univ., Inst. for Monetary and Financial Stability
CY  - Frankfurt am Main
ER  -