A0499
Title: Backward error and condition number analysis of linear DSGE solutions
Authors: Alexander Meyer-Gohde - Goethe-University Frankfurt (Germany) [presenting]
Abstract: The aim is to develop and implement a backward and forward error analysis of the numerical reliability of the solutions of linear dynamic stochastic general equilibrium (DSGE) models. Comparing seven different solution methods from the literature, we demonstrate an economically significant loss of accuracy in the 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 two production-based asset pricing models, a simple model of external habits with a readily available symbolic solution and a model 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 backwards-error metrics and condition numbers are shown to warn of such potential inaccuracies successfully. The analysis is then performed for a database of roughly 100 DSGE models from the literature and a large set of draws from a given model. While economically relevant errors do not appear pervasive from these latter applications, accuracies that differ by several orders of magnitude persist.
