Sunspot Shock In Gali, Lopez-Salido, Valles (2004)


Can anyone suggest how to simulate a sunspot shock in a linear model as in Figure 4 of the above-mentioned paper, available here:

Thank you!

You should be able to use Bianchi/Nicolo’s method. See e.g.

Thank you very much for pointing me to Bianchi and Nicolo’s recent paper.

I am unable to match the IRFs exactly as in Figure 4 here:

Just wanted to check if I am implementing it correctly. To simulate a sunspot shock to output, I have added the following auxiliary equation to the code of Gali et al (2004):

omeg = (1/alph)*omeg(-1) + sunspot - (y - expectation(-1)(y));

I’ve changed lambda = 0.85 (which is otherwise not feasible in the standard model) and alph=0.5 to ensure this is explosive.

I would really appreciate it if you could please advise if this is the correct way to implement this. Thank you!

Unfortunately, the original paper is not very explicit in how they did this. So I cannot really answer your question.

I understand, thank you so much!

I have a naive question: Could something be done to simulate a sort of counterfactual (stable model) in case of instability in the model? I understand that in the case of indeterminacy, we can choose one of the multiple paths as in Bianchi and Nicolo’s paper, but is something possible for unstable models also?

In principle, that is feasible, but not easily doable in Dynare. If you know the initial condition, you could simply iterate the explosive system forward.

Hello Professor @jpfeifer ,

I just wanted to understand how do you determine which variable should get the expectations error, as in this post:

In the case of Gali et al. (2004), would this be be on output?

Many thanks!

Have a look at A generalized approach to indeterminacy in linear rational expectations models | Bianchi | Quantitative Economics
They state

choice of which expectational errors to include in (6) does not affect the solution.

This is very helpful, thank you very much!