Extended Kalman Filter2

[ecrgap]

Hi Tom,

Further to our previous discussion about the threhold interest rate rules and the extended Kalman filter, I am attaching another paper that is much closer to what I want to do.

The last time I confused you a bit, since I was not clear.

So, I am trying to code the attached paper. Do you have any suggestions?

Best regards

[TomDoan]

Unfortunately, that's just number crunching; repeatedly computing numerical integrals with interpolated functions. Although RATS has the %ITRAPEZOID function to help with the numerical integrals, the high-end instructions like DSGE can't do anything.

[ecrgap]

Ok, thank you very much.

So, do we have in RATS any code available for the solution of nonlinear state space models (dsge) as that of Uhlig ("A toolkit for analyzing nonlinear economic dynamic models easily") for example?

I was thinking that if there are thresholds in the dsge model, we could just solve for the different sub-models depending on which threshold we are at by applying the Sims method for linear systems in each sub-model of the initial model. How do you find this approach? However, I m not sure that this is correct. I know also that there is not any standard technique for the solution of nonlinear dynamic systems as in standard linear ones.

What is your suggestion?

[TomDoan]

The Uhlig paper is a set of tricks for quickly log-linearizing a model which has things like a non-linear production function, non-linear utility function, etc. Those are useful if you have to do the model expansion by hand, but aren't necessary if you're using the DSGE instruction in RATS, since it has a symbolic differentiator.

Davig and Leeper is completely different since it has an equation which not only isn't differentiable, it isn't even continuous. Their solution procedure, while it certainly would be applicable to larger models, probably becomes computationally infeasible in a much larger setting.

I'm not sure how broadly one could apply the technique of switching between state-space representations. The point in Davig and Leeper is that the agents have to take into account the probability that the monetary authority will be applying the tight vs loose branch, which will vary depend upon the current value of inflation.