On the Accuracy of Linear DSGE Solution Methods and the Consequences for Log-Normal Asset Pricing

Abstract

"This paper demonstrates an economically significant loss of accuracy in standard,

generalized Schur (or QZ) decomposition based solutions methods for linear dynamic

stochastic general equilibrium (DSGE) models. This is illustrated in a simple productionbased

asset pricing model with external habit formation, calibrated to match post-war

US consumption growth and the equity premium. When there is insufficient eigenvalue

separation about the unit circle, QZ-based numerical solutions miss the equity premium by

up to several annualized percentage points. While none of the numerical solution methods

gave any indication of this error, easily implementable backward-error metrics are shown

to successfully warn of such potential inaccuracies."