I am struggling with a Ramsey problem for my model. I solved the Ramsey problem with one instrument and it worked fine, but, when I add a second instrument, I cannot run the model as I get the following error:

Ramsey: The solution to the static first order conditions for optimal policy could not be found. Either the model doesn’t have a steady state, there are an infinity of steady states, or the guess values are too far from the solution

After “model diagnostic”, I get that my problem seems to be related to the steady state, but this puzzles me since I just changed few equations with respect to the one instrument case.

I’m aware that I am missing something about well understanding the Ramsey routine, can you please help me?

Dear Prof. Pfeifer, thank you very much for your reply.

I am not sure I understand correctly your comment. Before simulating the model, I created a conditional SS file and I check that every equation is properly closed . In this file, I tried different values for the two instruments controlled by the planner, and the SS seems to be correctly computed.

Can you please explain me further the meaning of your comment? What do you think can be done in addition?

Thanks again for your help and patience, have a nice afternoon.

Dear Professor, a quick follow up question. I managed to run my code for some specific values of the SS (that, however, is not in line what the expected calibration), and I got something else puzzling: the IRFs show a change in the variable omega, which however was meant to be constant (akin to a parameter).
As a check, I tried a version where omega actually is defined as a parameter, and I obtained the same dynamics of the other variables, yet of course without showing omega (now a parameter).

Can you please help me to understand why I observe this movement in omega?

NB if you increase the size of the shock, also the value of omega rises, then it does not seem to be a computational error.

For normal shock values, omega shows small changes of the type (10^-11) you would expect with numerical solution techniques.

The steady state problem is not with the conditional steady state, which refers to the private sector economy given the instruments. The problem is finding the steady state of the Ramsey model including the instruments.

I think I got your point; now I wonder, according to you, what is the best procedure to solve this problem? Am I supposed to write a file to find the steady state of the Ramsey model including the instruments?

That is a tricky question. Conditional upon the private sector steady state, the Ramsey steady state problem involves solving a linear equation. Usually that is straightforward. The fact that it triggers a problem in your case may suggest a more fundamental issue. Did you try varying your initial values for the instruments in initval?

Dear Professor, thank you for the kind answer.
Yes, I tried to vary the different initial values of the instruments and it did not work. Yet, I actually found some parametrization of the SS that let the routine work. Do you think there is something else that could be done to better understand the issue?

? You parameterize the model, not the steady state. If it’s a matter of parameters, you should try to understand what characterizes the parameterization for which the Ramsey problem can be solved.

Dear Professor, thank you for your reply. Yes, you are totally right, I meant particular steady state values, but I think I got your point. I will give a further look to my parametrization.