Thanks for your reply,
Yes, I did check with several toolboxes (including Dynare builtin ramsey_model which was what I asked about).
Other than Dynare’s built-in ramsey_planner I tried to write my own code (using the symbolic toolbox for the Ramsey FOCs) and tried using Bodenstein et al (2019) toolbox for “Macroeconomic Policy Games”.
(CAN SKIP THIS paragraph, it’s just context on the SS solution)
On the Citation and Method used for the SS conditional on an instrument:
The citation I mention for the SS just refers to the procedure followed in all these toolboxes for finding an instrument conditional SS ( https://faculty.wcas.northwestern.edu/~lchrist/d16/d1606/ramsey.pdf). The difference to the standard method is given by the fact that you ex-ante set a value for the instrument, then solve for the rest of variables (economic variables and policy lagrange mult).
This also seems to be what Dynare does and the reason of why when running with external files we cannot impose a given value in the steady-state file. In another post you helped me fix the code so that my SS file uses the instrument that Dynare is imposing in the current iteration (and not one I am providing as initial).
The added difficulty from setting the instrument value ex-ante is that you have some extra equations in the static system (as many more as instruments you are setting exante). Hence the solution to the static system is not the typical of finding N unknowns from N static variables. In the algorithms these toolboxes follow, find an approximate solution repeatedly for several values of the instrument and at the end, the Instrument Steady State is given the value that minimizes a norm of a vector of errors (very similar to how in an OLS the beta vector of size K minimizes the norm of the errors in N equations, with N > K)
(Answer continues here)
So Yes, I found the Ramsey SS and Dynare ramsey_planner didn’t
From there (the other Matlab codes and toolboxes) is where I can tell you that I have been able to find the Steady State for the Cooperative case (also for the non-cooperative ones but those cases are working). In the case of Cooperation I find 2 steady states, i.e., the mentioned algorithm converges to 2 solutions depending of my initial point.
When I solve the minimization leading me to the instrument steady state the solution looks like this:
(each row is a solution with a different initial point, allTools is the SS of the instrument, given symmetry the second one is the SS inst. value for two peripheral countries. Fval is just the value of the function being minimized):
As you can see there are two potential SS: (-0.863, -0.696) and (-0.017, 0.279).
This does not occur with the other cases (Nash, Semicooperation 1 and 2).
Unfortunately, even after having the SS for the RamseyCoop model the Blanchard-Kahn conditions won’t hold with any toolboxes or my code so my guess is that even if Dynare ramsey_model() would obtain the SS, probably the same would happen.
My questions are two-fold:
Why Dynare cannot find the SS and obtain a solution for the Cooperative case with 1 planner and 3 instruments? (it worked for 1 instrument).
What does it mean to find 2 Steady States (as I did in Cooperation)?. Is this a sign of a multiple equilibria case and gives any hints on why the Blanchard-Kahn condition won’t hold with the other toolboxes (or my code using the symbolic toolbox) leading to indeterminacy?