Dear Dynare users,
I have a silly question about solution methods. As far I knew, we already have solution methods for DSGE models by Blanchard & Kahn (1980), Klein (2000), Sims (2002) or Uhlig (1999). But we also know that there are other techniques such as Pertubation and Projection methods. My question is: “when and where the specific solution methods should be used?”. Also, in the most Dynare models, we often log-linearize the equations manually or let Dynare do it automatically. So, which type of solvers that Dynare actually uses? Do we need to concern about Pertubation methods or we only need to know Sims and Klein?
Sorry for my stupid question. Hope to receive your answer!
Thanks in advance.
Sims/Klein/Blanchard-Kahn are all techniques to solve the stochastic linear difference equations occurring in a linear rational expectations model. Ultimately, they all give you the same result (apart from small numerical noise). Dynare essentially uses the Klein method, i.e. a QZ decomposition based approach.
The question is how to get to a stochastic linear difference equation. This is done be either manually log-linearizing or letting Dynare do it. This first order Taylor approximation is also known as first order perturbation techniques. Being based on a Taylor approximation, this type of solution method is only locally accurate around the approximation point and requires differentiability. Therefore it will deliver a wildly inaccurate solution if there are strong nonlinearities or non-differentiabilities (like an occasionally binding constraint like the zero lower bound).
In that case, you should go for a global solution technique like projection or value function/policy function iteration.
Thank you for your answer, Prof Johannes!
Acccording to your points, we (modellers) have to opt for log-linerization manually then declare in model(linear) or let DYNARE do its job. When we have a system of equations, Klein method will play its role.
So, why do we also need to concern non-linear numerical methods (pertubation, etc.) as you said that it could give us a noisy result? And, how is the strong nonlinearity? I mean how we can quantify the level of non-linearity?
If the non-linearity is just the subjective idea, can we forget it and stick to Sims/Klein/Blanchard-Kahn?
Many thanks!
Please have a look at Aruoba et al. (2006): “Comparing solution methods for dynamic equilibrium economies” (ideas.repec.org/a/eee/dyncon/v30y2006i12p2477-2508.html). That should answer most of your questions.