# Question about varexo_det and linearization

I am trying to use dynare to compare the non-linear solution I have to a model (computed with other tools) to the behavior of a linear solution. The paper is about interactions between fiscal and monetary policy, and we are trying to determine when nonlinear methods are needed to capture such interactions.

The model has a standard New Keynesian monetary policy rule where the nominal interest rate responds to inflation. We want to quantify the impact of 1. a fiscal transfer and 2. the combination of a fiscal transfer and a temporary deterministic change in the monetary policy rule.

We currently are using varexo_det to temporarily change the coefficient in our monetary rule on inflation, and I am wondering whether such a parameter change is itself linearly approximated in a first-order stochastic simulation, or whether the parameter change itself is computed exactly (which would result in a different transition matrix for our linearized model before and after the parameter change). Is there a description somewhere of what numerical methods are used when varexo_det is called? Perhaps initval and endval would be another approach we could use instead, or histval?

This detail I think matters quite a bit for whether our linear solution would allow for interactions between monetary and fiscal policy that interest us (or whether they are assumed away a priori).

(The full paper is here, solved with nonlinear methods, but we are less familiar with dynare. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4283119 )

Adding to my coauthor message, here is a version of the dynare code. All files are required to run the full code. The main file is titled â€ścovid_code_v11.modâ€ť. Thanks!

covid_code_v11.mod (28.9 KB)
default_integrals.m (1.9 KB)
getDefaultFcts.m (953 Bytes)
getRefiRates.m (773 Bytes)
integEpsGL.m (462 Bytes)

You also need these two .mat files to run the code. Thanks again!

params_file.mat (4.2 KB)
SS_file.mat (1.4 KB)

Sorry for the delay, but I had to figure out the implementation myself. I donâ€™t think `varexo_det` will work in your case as it relies on a linearized system also with respect to the `varexo_det`. See varexo_det: Implementation Â· Wiki Â· Dynare / dynare Â· GitLab

That would be different in the context of `perfect_foresight` where you can solve a nonlinear model. But it would require a linearization of the equations you want to have linear as the `linear_approximation` would again yield a linear version of the model.

1 Like