Rotemberg pricing model_Calibration issue

General DSGE Modeling
1

Greetings everyone,
I have a question concerning the Rotemberg pricing model. My issue lies in calibrating the “gamma” parameter, which represents the Rotemberg adjustment cost. I followed Professor Pfeifer’s guidance from a previous post (How to do a calbiration?) for calibrating gamma. After equalizing the slope of the PC, the resulting value for gamma is 49. However, the model fails to run when gamma exceeds a value of 1.2.
To provide some context, I will explain the steps I followed. I replaced the Calvo equations with the Rotemberg equation, as shown below:

Calvo equations:    
    %Y     = Z/Delta*L^(1-alpha)*(K(-1)*Omega(-1))^alpha;
    %1     = theta*(1+pi)^(epsilon-1) + (1-theta)*pstar^(1-epsilon);
    %pstar = Xi1/Xi2;
    %Xi1   = epsilon/(epsilon-1)*mu*Y   + theta*SDF*(1+pi(+1))^epsilon    *Xi1(+1);
    %Xi2   = Y   + theta*SDF*(1+pi(+1))^(epsilon-1)*Xi2(+1);
    %Delta = (1-theta)*pstar^(-epsilon) + theta*(1+pi)^epsilon*Delta(-1);

Rotemberg equation:
    1-epsilon+epsilon*mu=gamma*(pi-1)*pi-gamma*SDF*(pi(+1)-1)*pi(+1)*(Y(+1)/Y);

The initial values for the other parameters are as follows:
epsilon = 4.167;
theta = 0.779; % Calvo
beta = 0.995;

Any insight into the potential causes of this problem would be greatly appreciated!
Thank you.

2

What is the error message you are getting? But my impression is you got the signs wrong in your NKPC.

3

Thank you for your reply.

I reviewed the signs carefully, and they seem correct.
I can run the model with gamma <= 1.2.

Here is the error message:

Largest absolute residual at iteration 71: 525.633

WARNING: NaN or Inf detected in the residuals or endogenous variables.
.
.
.

Largest absolute residual at iteration 99: 0.000

Largest absolute residual at iteration 100: 0.000

25 | 0.67854 | failed | 2.214748e-05
++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Failed to solve perfect foresight model

Total computing time : 0h00m27s
Note: warning(s) encountered in MATLAB/Octave code

4

But that’s just a problem with finding a perfect foresight solution if the NKPC becomes very nonlinear. Have you tried a smaller shock size?

5

Now it works.
Thank you so much, Professor Pfeifer.