An identification problem

Dear all,

I encountered the following identification problem. Does anybody have similar experiences?

When I triggered the identification command, there is no problem when testing the prior mean. But problem arised when doing monte carlo analysis, the error message is

Monte Carlo Testing

Testing MC sample

All parameters are identified in the model (rank of H).

The rank of J (moments) is deficient for 1 out of 250 MC runs!

eps_MP is collinear w.r.t. all other params 36.4% of MC runs!
rho_MP is collinear w.r.t. all other params 37.2% of MC runs!
phi1_MP_star is collinear w.r.t. all other params 19.2% of MC runs!
phi2_MP is collinear w.r.t. all other params 6% of MC runs!
phi3_MP is collinear w.r.t. all other params 20.4% of MC runs!

The code and log file are attached. I have tried other prior settings and sometimes the problem does not pop up. So it seems to me that this problem may have something to do with the prior I set. Am I right? What should I do in this case? Can I simply ignore this identification warning?

Thanks a lot in advance!!!
iden_problem.rar (3.85 KB)

It’s generally hard to tell. The way identification is tested is “local identifiability”, i.e. in the neighbourhood to some value. There may be regions in the parameter space where local identifiability does not hold and a parameter is not globally identified (Sidenote: there is almost always some region where this is the case, e.g. because the parameter completely drops from the model for some parameter combinations).
The big question is how problematic this is. You are testing a wide prior hypercube here. It could be that the identification problem appears in an area of the parameter space the posterior considers extremely unlikely, i.e. the MCMC will not spend much time there and the problem will thus be limited.
If you can restrict your prior to a more narrrow range where this does not happen (and the prior is still defensible), I would do this.

Dear Johannes,

Thanks so much for your answer. I got your point.

Dear jpfeifer.How to make a parameter space that satisfies BK condition visualization. For example, household and firm model parameters are calibrated. Then the three reaction coefficients of Taylor’s rule, including inflation, output gap and interest rate, are made into visual parameter Spaces that meet BK conditions.