Partial Equilibrium Analysis in Dynare

Dear all,

Let’s suppose that I have a model with several shocks and a standard Taylor rule, and I would like to simulate the model (or get IRFs) in a setting where the nominal interest rate does not react to one particular shock in my model. This way, I can analyze the effects of this particular shock under fixed interest rates while ensuring that the Taylor principle is satisfied (because monetary policy reacts to the rest of shocks).

An example of this is Nakamura and Steinsson 2014. They are interested on studying the government spending multiplier under a Taylor rule, fixed real rates, and fixed nominal rates.

I wonder if one can do this in Dynare without the need of log-linearizing the model by hand, i.e. just working in levels as usual, and with small changes to the code that one would use with a standard Taylor rule.

What the authors of that paper do (Appendix A) is to log-linearize, by hand, impose this restrictions, find the policy functions and get the interest rate rule that satisfies this (where the particular shock would enter on the taylor rule in a linear way, undoing the effect). I wonder if this could directly be done in Dynare, either:

  • By somehow imposing this restriction on the policy function in such a way that Dynare takes this restriction into account when implementing the method of undetermined coefficients.
  • Using macros.
  • Or taking advantage of the zero lower bound literature, perhaps with the use of news shocks?

I have a different model from this paper, which is simpler and national, but the same principle applies.

Thanks indeed.

nakamura-steinsson-2014-fiscal-stimulus-in-a-monetary-union-evidence-from-us-regions.pdf (841.1 KB)
fiscalAppendix.pdf (322.5 KB)

It seems like you should add a Taylor rule like their equation (11) in the paper and then use a solver to find the feedback coefficient that makes the interest rate not react to the shock.

Thank you very much, Professor Pfeifer, this is a very simple and effective way to analyze the effect of a shock under different monetary policy regimes or under fixed nominal interest rates.

I wonder, can this solver be implemented within Dynare? the feedback coefficient is going to be a function of the parameters of the model, but I would just need to find it numerically every time that I simulate the model for a given set of parameters. Can Dynare directly solve for it numerically given our set of parameters? Which functions would you recommend me to explore?

Thanks indeed, this is extremely helpful and I really appreciate it.
Jose

One can do this in Dynare along the lines of the optimizer in DSGE_mod/RBC_IRF_matching at master · JohannesPfeifer/DSGE_mod · GitHub

I can assist.

Thanks indeed, professor. I really appreciate this.