Unable to find perfect foresight solution of simple NK model with ZLB

Perfect foresight simulations
1

Hi everyone,

I’ve adapted the example available at https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_5_commitment_ZLB.mod to find a perfect foresight solution of a simple model consisting of the usual Phillips and IS curves, plus a “strict inflation targeting” rule of the form [mcp=‘i>0’] pi = 0. However, I’m surprised that Dynare is struggling to find a solution. In particular, I get the following:

Simulation of the perfect foresight model failed!
Switching to a homotopy method…

Iter. | Lambda | status | Max. residual
++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 | 0.50000 | succeeded | 1.776357e-15
2 | 1.00000 | failed | 5.557033e+00
3 | 0.75000 | failed | 2.778516e+00
4 | 0.62500 | failed | 1.389258e+00
5 | 0.56250 | failed | 6.946291e-01
6 | 0.53125 | failed | 3.473146e-01
7 | 0.51563 | failed | 1.736573e-01
8 | 0.50781 | failed | 8.682864e-02
9 | 0.50391 | failed | 4.341432e-02
10 | 0.50195 | failed | 2.170716e-02
11 | 0.50098 | failed | 1.085358e-02
12 | 0.50049 | failed | 5.426790e-03
13 | 0.50024 | failed | 2.713395e-03
14 | 0.50012 | failed | 1.356697e-03
15 | 0.50006 | failed | 6.783487e-04
16 | 0.50003 | failed | 3.391744e-04
17 | 0.50002 | failed | 1.695872e-04
++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Failed to solve perfect foresight model

Is anyone able to suggest strategies for dealing with this problem?

A copy of my code is attached. Note that I’ve used “%%%” to comment out equations and variables that were specific to the example I mentioned above, and if you uncomment those parts you’ll see that the code runs fine.

Thanks very much!

Best,
N2K2

Gali_chap5__v1c.mod (1.6 KB)

2

Are you sure that model has a solution? If I use

pi(+1) = 0;

as the strict inflation targeting policy rule, a solution is immediately found. Maybe there is an economic reason it does not work in Dynare.

3

Thank you very much for your reply, Professor Pfeifer. I would think that with the rule pi = 0 the model would correspond to the “no response” case reported in section seven of Gali’s recent JME (https://www.sciencedirect.com/science/article/pii/S0304393219301357).

4

Did you check whether that rule works in your model without the ZLB? That is, conduct the same experiment without the ZLB.