Fifth-Order Perturbation Solution to DSGE Models

31 Pages Posted: 9 Dec 2013 Last revised: 2 Mar 2017

See all articles by Oren Levintal

Oren Levintal

Interdisciplinary Center (IDC) Herzliyah

Date Written: February 24, 2017


This paper derives a fifth-order perturbation solution to DSGE models. The paper develops a new notation that reduces the notational complexity of high-order solutions and yields a faster code. The new notation consists of new matrix forms of high-order multivariate chain rules and a new representation of the model as a function of one vector variable. The algorithm that implements the new notation is between 3 to 55 times faster than Dynare , depending on model size and solution order.

Keywords: Perturbation, Fifth order, High order multivariate chain rules, Sylvester equation, DSGE, Symmetric tensors

JEL Classification: C63, C68, E0

Suggested Citation

Levintal, Oren, Fifth-Order Perturbation Solution to DSGE Models (February 24, 2017). Available at SSRN: or

Oren Levintal (Contact Author)

Interdisciplinary Center (IDC) Herzliyah ( email )

P.O. Box 167
Herzliya, 46150

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