Variance Decomposition Analysis for Nonlinear Economic Models1

Abstract

In this paper, we propose a new method called the total variance method and algorithms to compute and analyse variance decomposition for nonlinear economic models. We provide theoretical and empirical examples to compare our method with the only existing method called generalized forecast error variance decomposition (GFEVD). We find that the results from the two methods are different when shocks are multiplicative or interacted in nonlinear models. We recommend that when working with nonlinear models researchers should use the total variance method in order to see the importance of indirect variance contributions and to quantify correctly the relative variance contribution of each structural shock. JEL Classification numbers: C15, C32, C53, E37. *We would like to thank Francesco Zanetti (Editor) and three anonymous referees for their excellent comments/suggestions. We also thank participants at the 2018 North American Summer Meeting of the Econometric Society and the 2019 SNDE Meeting at the Dallas Fed for their comments. We acknowledge the financial support from the Faculty Scholarship Initiative (FSI) Program of the Cleveland State University. We are also grateful for the support from the Ohio Supercomputer Center. This paper was previously circulated under the title 'Variance Decomposition Analysis for Nonlinear DSGE Models: An Application with ZLB'. 1 An incomplete list of papers using nonlinear models with a ZLB constraint includes Fernandez-Villaverde et al.

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