Difference between Dynare 3rd pertrubation and Fernandez-Villaverde et al. (2006)

#1

Hello Pfeifer and Stéphane,

When I look it at the dynare reference manual, “The main algorithm for solving stochastic models relies on a Taylor approximation, up to third order, of the expectation functions (see Judd (1996), Collard and Juillard (2001a), Collard and Juillard (2001b), and Schmitt-Grohé and Uríbe (2004))”. I am trying to understand how the method used by Dynare for 3rd order is different than the method introduced in Fernandez-Villaverde et al. (2006) in their article “Comparing solution methods for dynamic equilibrium economies”

Thanks in Advance

#2

What do you mean? That article by Aruoba et al. did not introduce this method, but just compared it to other methods.

#3

Hi Professor Johannes,

Seoane(2015) [Near Unit Root Small Open Economies ∗
published in Journal of Economic Dynamics and Control , 2015, vol. 53, issue C, 37-46]. has mentioned that for 3rd order Perturbation methods closely follows Fernandez-Villaverde et al. (2006). Then, only paper I could see his references is “Fernandez-Villaverde, J., Arouba, S., Rubio-Ram´ırez, J., 2006. Comparing solution methods for dynamic equilibrium economies. Journal of Economic Dynamics and Control 30, 2477– 2508”

This may be a naïve question as I just stared learning 3rd order Perturbation. My Question was Is the method of perturbation used by Dynare is typically same or different than used by Seoane(2015).? Do I need to go through Judd (1996), Collard and Juillard (2001a), Collard and Juillard (2001b), and Schmitt-Grohé and Uríbe (2004))”to understand 3rd perturbation algorithm used Dynare. Do you have any specific reference for me.?

I would appreciate your guidance.

#4

Third order perturbation is simply a generalisation of first order perturbation. The reference Seoane cites here is not appropriate, because it did neither invent nor summarize this technique. Moreover, the reference only refers to first order perturbation. So that paper is not helpful at all. But the algorithm in Dynare is the same as the one by Seoane (although I have not read the paper and does not know how it deals with pruning).

#5

Thank you so much. I got what I was looking for.