Dynamic Stochastic General Equilibrium (DSGE) Models. Errors of Numerical Methods

The most computations with DSGE models are use linear approximation with perturbation method. It is rare when higher order approximations are used, but linear approximation is necessary step for computation of higher order approximations. However, conventional approximation techniques can be inaccurate. It is related to properties of QZ-decomposition code, which is used for finding linear approximation. This problem was discovered recently with small-scale DSGE model example. This paper investigate how large numerical errors for different DSGE models. Simple measure is suggested for estimation of corresponding inaccuracy. One version of measure is likelihood based. Alternative versions are moments based. Various DSGE models are analyzed. They are small scale and medium-large scale models; conventional DSGE models and models with unconventional structure; models that are focused on nonlinear properties and models that do not pay attention to nonlinear properties. This problem is important only for minority of the models. However, the errors are large for few models (small-scale). Known approach against numerical inaccuracy (that is based on special matrix balancing) decreases errors, but such decreases are not large enough for problem solving. Thus, it is important to recognize whether numerical errors of DSGE models linear approximation are large or no what can be done with suggested measure.