# Problems with Ramsey Problem

Hi everyone,

I am working on a model that embedds a public sector with its budget constraint. I simulated the Ramsey optimal policy and I have three questions about it:

1. Growing upon the results of Schimtt-Grohe Uribe 2004 (paper attached), I expected to observe a random walk property for the public debt and taxes (they both reach a different SS). The shock I am performing is quite different, but the fundamental setup is pretty similar. That said, my first doubt is whether it is possible to reach a new steady state exploting the Ramsey routine in Dynare. Since I am new to this approach, I would like to know what I am missing.

2. My second doubt is that even though I provided an instrumental steady state for Ramsey, the routine seems to work only for initial values of my instruments equal to zero. I am aware that the SS I obtained in Matlab for my model is mildly different for the one obtained by Ramsey, but I am struggling to get the reason of this constrained behaviour.

3. I tried also to add another instrument controlled by the planner (for a total of 3 instruments) in the government budget constraint, but as far as I tried I always get an indeterminacy problem.

Thank you very much for your help,
Have a nice afternoon!

doubt.mod (5.1 KB)

1. I am not sure I understand the question. There often are infinitely many steady states for the debt level, but you seem to select a particular one in your `steady_state_model`-block with `B = 0;`
2. Steady state finding for the Ramsey model still involves solving an equation system. All numerical solvers tend to depend on the starting values. That being said, some of your steady state values look hardcoded. Are you sure the `steady_state_model` can accommodate arbitrary instrument values? When I use
``````initval;
v=0.2;
t=0.2;
end;
``````

I get

Error using print_info (line 32)
Ramsey: The steady state file does not solve the static first order conditions conditional on the instruments.

which suggests a problem with the steady state file.

Dear Prof. Pfeifer, thank you for the answer.

I am sorry, you are right, I uploaded a wrong file (now the correct one is attached). As you will see, it semms to work only for initial values of the instruments equal to zero. I also tried, through my SS matlab file, to set the SS value of B in order to obtain the corresponding SS for the instrument t. Then,I provided this value (i.e the one of t) to the Dynare ramsey file, as initial value of this instrument. However, in this way the model does not work any longer…

What is wrong with my procedure? I expected to find the corresponding steady state… Probably there is something I am missing about the Ramsey SS.

In addition, as you can see, the IRF for B returns back to the SS, and this is the opposite behavior with respect to SGU 2004, since in their model the debt changes SS.

Thanks again and have a nice evening
I am very grateful

doubt2.mod (5.1 KB)

1. I am not sure I get the point, but for different initial values of your instrument, I get different steady state with different values of debt and of the instrument.
2. SGU describe near-unit root behavior, not a unit root. Their IRFs will ultimately return. Moreover, the persistence depends on the model features.

Dear Professor, as usual, thank you very much for your help. Now I see what I was mistaking.

Sorry to bother again.

I will try to be more clear: my goal would be to simulate my model assuming a specific value for the debt B, but due to the conditional SS, I am forced to pin down the SS value of B from one of my instruments. In order to do this, I tried the approach I mentioned above (i.e. calculating a value of one of the instruments from the SS and than setting it as initial value for the instrument itself).

Would it be possible to work around the problem? Does it exist an alternative solution?
As far as I understood, the SS value for Ramsey is a bit different, but some level of control on the level of some variables could be useful to me.

Really thank you again,
Have a nice day!

I am not sure I understand the problem. It seems your instrument in steady state is not really a degree of freedom for the planner. If debt is a function of the instrument, how would you independently pick it?