Perfect foresight implementation NK model (Bilbiie & Melitz, 2023)

Perfect foresight simulations
1

Hello everyone,

I am trying to implement forward guidance into the Entry-Exit NK model by Bilbiie & Melitz (2023).

While I managed to replicate the model on Dynare using their Loglinearized equations, I am struggling to find a way to add forward guidance (and to add it in a way that allows me to find perfect foresight solutions).

Here is the .mod that I currently have.

Thanks for your help

Project.mod (1.1 KB)

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Where exactly is the problem? Perfect foresight naturally lends itself to anticipated shocks.

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The idea is to compare outcomes following a negative demand shock, with and without forward guidance. Ideally, we’d want to hit the ZLB, and have that clearly visible in the graphs.

We’re facing two main issues:

  • The model equations seem fine overall, but we’re not quite sure how to implement a shock with persistence. We tried something using the log(B) equation, but it’s either unsatisfactory or leads to no solution under perfect foresight.

  • For our Taylor rule, we’re unsure what value of i to target to actually reach the ZLB. Since we’re working in log-linear terms, “i = 0” just means no deviation from the steady state, so it’s not clear what numerical value of “i” would correspond to hitting the ZLB. We’ve been aiming for “-r”, assuming r = 0.01 in steady state—but we’re not sure if that’s appropriate. We also do not know if it is possible —and how it would be implemented — to plot the level of the nominal interest rate (to clearly see the ZLB) while still being in a log linearized model.

Thanks for your help.

Here is the latest code
Entry_FG.mod (2.1 KB)

4
  1. You should test bringing the model gradually to the ZLB.
  2. Have a look at the various ZLB implementations in OccBin, e.g. Occbin simulation does not converge in certain cases - #4 by jpfeifer
    They show what the lower bound must be.