Models with Expectations of More Distant Future Values

[sp1589]

Hi All,

I know that Dynare is programmed to use the Blanchard-Khan regularity conditions. However, there is a class of models with expectations of more distant future values. For instance, in the fiscal theory of the price level, the price level depends on the present value of all future fiscal surpluses. Hence, there is an infinite sum that enters the equilibrium conditions. I know Blanchard-Khan's method can't solve this class of models. There is a generalized framework developed by Sims (2002) that can deal with this problem.

However, since I am not completely familiar with Dynare, is there any possibility that models (that use the fiscal theory of the price level) can be solved (somehow) in Dynare?

Thank you

[jpfeifer]

Which exact reference do you have in mind? Having expectations into the far future is not a problem in Dynare. E.g.

Code: Select all

c(+2)

is the conditional expectations of consumption at time t+2 given the information set at time t. More problematic is the infinite sum, which needs to be either written recursively so that it has a finite representation or you need to truncate the sum at some point.

[sp1589]

Hi Jpfeiffer,

Yes, I am referring to the infinite sum. If I understand you correctly, if I were to truncate the sum, I can solve the model, but that would be at the expense of the quantitative results, since they would be an approximation to the actual solution?

[jpfeifer]

Yes, typically the more distant terms of the sum get geometrically declining weight, so leaving them out will be associated with a hopefully small approximation error. As you are using a perturbation approximation in any case, that small additional error can often be tolerated. But as I said, trying to find a finite recursive representation often works better (a case in point is the recursive representation of the Calvo pricing problem FOC arising in New Keynesian models when deriving the New Keynesian Phillips Curve)

[sp1589]

I am not quite sure how I would do it, since I haven't written the model in dynare yet, since I am working out some details. Can you send me a link to a code that`s incorporating Calvo pricing, so that I can see how they code that exactly?

Thank you

[jpfeifer]

Have a look at Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez (2006): "A Baseline DSGE Model", available at http://economics.sas.upenn.edu/~jesusfv/benchmark_DSGE.pdf. There they define f1/f2 and g1/g2 to get rid of the infinite sums.

[sp1589]

Thank you. I really appreciate your help in this forum!

[sp1589]

Hi Johannes,

I have another question. I have to introduce Epstein-Zin preferences since I want to generate term premia within the same framework I originally made this post about. Can you tell me if there are issues one can encounter in Dynare with solving a model with Epstein-Zin preferences. I searched for this in the forum and I saw that you had a few posts related to Epstein-Zin preferences, but I would appreciate it if you can briefly summarize any issues that one may typically encounter with solving a model with these preferences in Dynare?

A separate questions is related to Dynare`s ability to perform third order approximation. I know Dynare provides accurate 1st and 2nd order approximations, but what about a 3rd order?

Thanks in advance!

[jpfeifer]

1. You need at least second order
2. You need to correctly specify the auxiliary variables arising in EZ (see https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Caldara_et_al_2012/Caldara_et_al_2012.mod)
3. To avoid numerical issues, you should introduce a normalizing constant, see http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=11877&p=33070

How do you define "accurate"? We verify that the third-order approximation of Dynare is correct by cross-checking it with the Mathematica results of Fernandez-Villaverde et al (2012) "Risk matters". If you have Euler errors in mind, then the answer depends on the respective model and you need to check. A general guide on accuracy is the Caldara et al (2012)-paper.