I have a question regarding your dynareOBC toolkit. It said ‘Impossible problem encountered. Try increasing TimeToEscapeBounds,or reducing the magnitude of shocks.’ But the variance is estimated from the data, so I cannot reduce that.
So I go to the other route. However I notice it also displays the following: The M matrix with T (TimeToEscapeBounds) equal to 9 is a P-matrix.
I am curious about the origins of the problem here. I wonder if you could possibly help me point out? Does it mean my model doesn’t return to deterministic steady state?
Meanwhile, In this case, do you have any suggestions how I should proceed?
That message means there’s no solution returning to the steady state within the horizon you set in TimeToEscapeBounds. It is possible that there may be a solution for a large enough value of TimeToEscapeBounds.
But, if I’m right in guessing that you’re working with an NK model with a Taylor type monetary rule and a ZLB then it’s almost certain that at least in some states there is no path returning to the steady state (whatever the value of TimeToEscapeBounds). This is the main point of the corresponding theory paper. https://www.econstor.eu/handle/10419/204472
The solution is to use a different monetary rule, e.g. one with a response to the price level, or to use Ramsey optimal monetary policy.
Thanks for your prompt reply. TimeToEscapeBounds is 32, as default, but why is it showing The M matrix with T (TimeToEscapeBounds) equal to 9 is a P-matrix (at most)? I think it meant only with TimeToEscapeBounds<9 can it return a solution, rather than your statement ’ there may be a solution for a large enough value of TimeToEscapeBounds.’ Am I right?
Thanks for the suggestion of changing the monetary rule. I will try it out. But as a general solution (i.e in cases not in NK model), does it mean we will need to do global solutions? such as value function iteration? It seems to me that VFI doesn’t require a returning to original steady state condition?
The corresponding case would be RBC models with borrowing constraints, the original S.S is at binding area. if the shock is large enough, firms would become unconstrained, then with no further shocks, they would differ with original S.S for sure.
If the M matrix with T=9 is a P matrix, then there is a unique solution conditional on the solution being permanently away from the bound by period 10. Again, see my theory paper to understand more.
There may be solutions which spend much longer at the bound in some states. And there may be other states with no solution at all.
You should only be using DynareOBC, OccBin or Extended Path to simulate if your agents believe that they will always eventually return to the original steady state. If your agents don’t believe this, then you need another tool. Global methods are one possibility.
With DynareOBC, if you do not want to constrain agents to always believe that inflation will be eventually positive, then you could generate simulation paths by simulating up until a problem it can’t solve, then using that state as an initial condition to simulate the path of an economy with interest rates pegged at zero and an extra sunspot equation. I can’t further help you with this though. It is not something DynareOBC does “out of the box”. Perhaps it should!
RBC models are not a relevant comparison, as they usually always have a unique solution, even with borrowing constraints or irreversible investment.