Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/279899 
Year of Publication: 
2023
Series/Report no.: 
IMFS Working Paper Series No. 193
Publisher: 
Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS), Frankfurt a. M.
Abstract: 
This paper develops and implements a backward and forward error analysis of and condition numbers for the numerical stability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods from the literature, I demonstrate an economically significant loss of accuracy specifically in standard, generalized Schur (or QZ) decomposition based solutions methods resulting from large backward errors in solving the associated matrix quadratic problem. This is illustrated in the monetary macro model of Smets and Wouters (2007) and two productionbased asset pricing models, a simple model of external habits with a readily available symbolic solution and the model of Jermann (1998) that lacks such a symbolic solution - QZ-based numerical solutions miss the equity premium by up to several annualized percentage points for parameterizations that either match the chosen calibration targets or are nearby to the parameterization in the literature. While the numerical solution methods from the literature failed to give any indication of these potential errors, easily implementable backward-error metrics and condition numbers are shown to successfully warn of such potential inaccuracies. The analysis is then performed for a database of roughly 100 DSGE models from the literature and a large set of draws from the model of Smets and Wouters (2007). While economically relevant errors do not appear pervasive from these latter applications, accuracies that differ by several orders of magnitude persist.
Subjects: 
Numerical accuracy
DSGE
Solution methods
Condition number
Backward error
Forward error
JEL: 
C61
C63
E17
Document Type: 
Working Paper

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