Dynare forums

Hi,

I am having trouble computing the steady state of a model. I can solve it for certain parameter values but not for others (for instance, the steady state can be computed as it is for the mod file posted below, but if I change a_t = 1 in line 59 the steady state can no longer be computed), even though the residuals at the starting values I provide seem to be small and restricted to only two out of 49 equations. I realize that the best way would have been to solve for the steady state by hand, but I am not able to do so, given the highly complex/non linear nature of some of the equations. In the initval block, I have been able to simply the steady state computation to the point where I need to provide guesses for only two endogenous variables, and the rest can be computed recursively.
I have tried other options like homotropy but they dont seem to work. Any suggestions would be welcome. In particular, I would like an opinion on whether the problem is one of computation (so that moving to a more powerful computation platform can be helpful) or something fundamentally related to the model.

Thanks in advance

The parameter change you are considering seems to be rather large. Are you sure that a steady state exists for the parameter computation? Given the size of the model, I would try to go for a steady state file that uses a solver for the last few equations as is done in the NK_baseline.mod in the Dynare examples folders.

I highly recommended this reply. Thanks..

I tried the steady state file approach using fsolve and while its a bit better, I continue to face the problem of computing the steady state for most parameter values.
As mentioned before however, I can boil down the steady state computation to a problem of solving two non linear equations in two unknowns. I wanted an opinion on the following procedure, given that I am not able to compute the exact steady state, even numerically.

1.Instead of using fsolve or something similar, I solve the problem by doing a grid search in 2 dimensions.
2. Step (1) gives me a steady state which is not exact, so lets call it an approximate steady state.
3. Since this is not be an exact steady state, dynare prevents me from running a stochastic simulation based on this. But what if I use a brute force approach here- so that I linearize the model around the approximate steady state and feed the linear model into dynare and run a stochastic simulation to get impulse responses?

I wanted to know if this is sounds even remotely reasonable or are there glaring technical pitfalls here that I am completely overlooking.

Thanks

Before you try dirty hacks: if you can simplify your problem to two equations in two unknowns, why does this not deliver an exact steady state?

Hi Johannes,

Thanks a lot for your response.

I think there are two main issues (perhaps related) that I am still left facing even though the problem is simplified to a 2 equation system.
(a)complex roots, which I frequently encounter
(b) multiple equilibria-its a model of banking with default so a higher interest rate and a higher default rate is also an equilibrium. I think some unreasonable steady states I am getting are due to this issue-the global minimum happens to be at an inefficient point and the algorithm picks it out, whereas the solution that I am looking for is perhaps just a local minimum.