Interpretation of Ramsey Steady State

Dear Professors,
I have a question about the interpretation of the Ramsey Steady State Values I obtained exploiting the Ramsey command in Dynare. Specifically, I calculated, with Matlab, my Steady State with some for values that I know having some economic sense. However, when I provide these values in the Ramsey mod file, the Steady State value of the instrument variable takes some puzzling value (e.g. I have a negative subsidy).

In other words, I found consistent values in the SS file when I set the instrument equal to zero, but, in the Ramsey simulation, even if I set the initval of the instrument equal to zero, I found a negative value for the instrument I am using (a subsidy).

So, I am sorry to bother, but I do not undertstand if it is a matter of interpretation or I am making some mistake in the file. If the latter is the case, what would you suggest to do?

Thank you very much, have a nice day

rams3.mod (10.8 KB)

There may be multiple steady states, some of them associated with minima of the problem. You should try different starting values. That being said, it is often not obvious what the steady state value of the instrument should be. Are you sure that a negative subsidy is not optimal?

Thank you for the answer, Professor. The model works and I concluded that also a negative subside can actually be optimal, as you suggested

One last doubt: why does the steady state of the instrument change? We set its initval equal to zero, but then the model returned back a different value. May it be due to the fact that the new steady state values are the result of the new optimization problem involved by the Ramsey problem?

Thanks again and have a nice day!

What you provided is the steady state of the private sector equilibrium conditions, conditional on the value of the instrument. But that is not yet the steady state of the Ramsey problem. Typically, a steady state of that problem requires finding a value of the instrument that induces a steady state of both the private sector FOCs and the equilibrium conditions of the Ramsey planner. Take the labor subsidy in the New Keynesian model with monopolistic competition. Any value of the subsidy is consistent with the private sector equilibrium. But we know that the optimal choice of the subsidy is to exactly counteract the monopolistic distortion to have an effective markup of 0. If you start with a an initval of 0, you will end up with a different value that is compatible with a steady state.

Dear Prof. Pfeifer,
once again thank you very much for your helpful comment and for the commitment!

Have a nice day