# Equations converges to zero by hand however not by Dynare

Hi professor, I was running a ramsey model. In the steady state file, I calculate the steady state of values conditional on instrument “RTR(policy rate)”. The case is that there were two equations that were always failing to converge to zero. The two equations are as follows:

% (16) Auxiliary price-setting x1

exp(x1)=exp(pm)exp(Y)+phipexp(Lam(+1))(exp(Pi(+1))/exp(Pigammap))^epsi*exp(x1(+1));

% (17) Auxiliary price-setting x2

exp(x2)=exp(Y)+phipexp(Lam(+1))(exp(Pi(+1))/exp(Pi*gammap))^(epsi-1)*exp(x2);

However, when I was trying to calculate each equations by using the steady state I assign to the model, there are zeros. I put screen shot here for your reference.

I was struggling a lot since I literally cannot debug this error. Could you please give any hint? Thank you so much for you help.

In addition, I want to know that whether I correctly set a conditional steady state where there exists parameters dependent on instruments. To make it clearer, I set a param_ss first to calculate calibrated parameters and steady state of variables conditional on instruments and added it to steady state file, then I write the steady state values in the steady state based on the values in param_ss. I am uploading my .mod file. Thank you so much for your help.
test.zip (59.9 KB)

Hi professor, the problem solved. However, I came across another problem. The result said that there is no stable equilibrium. But the model works when I use the Taylor rule instead of the ramsey rule. I cannot figure out why this happens.In addition, when I change to another instrument, the result still said that there is no stable equilibrium. In this case, would that be probably resulted from the wrong conditional steady state? Could please give me any hint? Is this because that I didn’t correctly set the conditional steady state? Thank you so much for your help.

test.zip (60.8 KB)

See

Thank you so much Professor. I tried many initial values as you suggested, but unfortunately, I haven’t find the proper initials. My question is, in this case, should I just give up calculating the ramsey policy? Is it possible that there is no such stable equilibrium or proper initials? Thank you so much for your help. I am really looking forward to your reply.

That depends on your goal. It is rather unusual that Ramsey does not work. In principle, you could have Ramsey returning an explosive and therefore unbounded solution.

Thank you so much for your reply. How can I have Ramsey return an explosive solution? Is there any example that I can refer to? I have a follow up question, does the explosive solution has any economic meaning? How should I explain the explosive solution.

Professor, I also tried OSR, the result still said no stable equilibrium. Considering that the model works with Taylor rule, it seemed that there is little thing that I can resort to other than changing the initials. Am I right? Since you said it’s unusual Ramsey does not work, I was confused a lot about the reason behind the failure. Thank you so much again.

1. Dynare does not allow you to simulate explosive paths. Typically, the interpretation would be that unconditional welfare should be infinite. That’s why this is rather strange.
2. The fact that OSR is also unstable is strange. Shouldn’t that nest the Taylor rule?

Thank you so much for your reply and suggestion. There should be something wrong with my model set. But my question is that when I use the Taylor rule, the model works and can run the irf. So the problem must be on the conditional steady state, am I right?

As I wrote, the Taylor rule is a special case of an simple rule, so it’s strange that does not work, but the Taylor rule does. I don’t think there is a problem with the steady state file. After all, a proper steady state is found.