# Fifth-order perturbation solution to DSGE models

*Oren Levintal*

*Journal of Economic Dynamics and Control*, 2017, vol. 80, issue C, 1-16

**Abstract:**
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 and 55 times faster than Dynare++, depending on model size and solution order.

**Keywords:** Perturbation; Fifth order; Rare disasters; High-order multivariate chain rules; DSGE (search for similar items in EconPapers)

**JEL-codes:** C63 C68 E0 (search for similar items in EconPapers)

**Date:** 2017

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:dyncon:v:80:y:2017:i:c:p:1-16

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