Variance Decomposition Analysis for Nonlinear Economic Models1
| Date | 01 December 2021 |
| Published date | 01 December 2021 |
| Author | Phuong V. Ngo,Maksim Isakin |
| DOI | http://doi.org/10.1111/obes.12369 |
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©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 82, 6 (2020) 0305–9049
doi: 10.1111/obes.12369
Variance Decomposition Analysis for Nonlinear
Economic Models*
Maksim Isakin,†Phuong V. Ngo†
†Department of Economics, Cleveland State University, 2121 Euclid Avenue, Cleveland, OH
44115, USA (e-mail: p.ngo@csuohio.edu)
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 differentwhen 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.
I. Introduction
Nonlinear or global solution methods for nonlinear models such as stochastic dynamic
general equilibrium (DSGE) models have become increasingly popular recently due to
an occasionally binding zero lower bound on nominal interest rates (ZLB), and due to
other reasons such as occasionally binding debt constraints and monetary/fiscal policy
switching.1When policy functions are nonlinear, computing and analysing forecast error
variance decomposition (FEVD) become more complicated because impulse responses
and variance decomposition are not only state dependent but also shock and composition
dependent (Koop, Pesaran and Potter, 1996).
Although the generalized impulse response function (GIRF) proposed by Koop et al.
(1996) has been used more frequently to analyse dynamic responses for nonlinear DSGE
models, variance decomposition analyses are very limited. Nevertheless, such analyses
often provide important economic insights. One important reason for the lack of variance
JEL Classification numbers: C15, C32, C53, E37.
*We would like to thank Francesco Zanetti (Editor) and three anonymous referees for their excellent com-
ments/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’.
1An incomplete list of papers using nonlinear models with a ZLB constraint includes Fernandez-Villaverdeet al.
(2015), Wolman(2005), Nakata (2016), Ngo (2014), and Richter, Throckmorton and Walker (2014).
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