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I used your zip-file with the mod-file nonlinearomega.txt

My apologies, but what do you mean by saying that the mode-file does not describe a mode.
Can you try, please, with this new version and see if the problem persist?

There are two mat-file. The _mode.mat and the mh_mode.mat. The likelihood value stored in both is massively different, showing that you did not start the MCMC at the point of highest likelihood.

Thank you for your last observation. I also confirmed what you said in the version below. What could be the model' s misspecification behind mode.mat and mh_mode.mat different mode outputs. Could it be related with the fact that I am working with a small identity matrix in order to obtain
a positive definite Hessian? This may also explain why after 1000000 draws I didn't reach convergence? What shall I do?

Run an intensive mode-finding first, e.g. mode_compute=9. When doing this, use the current _mh_mode.mat as the mode-file you load.

I already did what you suggested before. Still, the mode from the mode.mat and the mh_mode.mat are significantly different.
What I understand is that the mode in mode_mat corresponds to the point that maximises the likelihood for the parameter set without compute the posterior with the metropolis hastings algorithm. On the contrary, the mode in the mh_mode.mat is computed with the metropolis hastings algorithm. Nevertheless I didn't understand yet why the mode from both files should be almost the same.

The check mode plots, priors, posteriors, mode.mat and mh_mode.mat files are annexed below. Overall shock decompositions are Ok, but the posteriors are not very good and with the same model I didn't reach convergence after 1000000 draws. I tried the command use_tarb weeks ago but it didn't work either. Can the problem with the mode explain these non satisfactory results?

You mode_check plots still show that you did not start at the mode. Forcing the MCMC by not using the Hessian just overrides this issue. But then convergence will be hard to obtain as the MCMC will move to regions of higher likelihood. When you start at the mode, the MCMC wanders around this same mode and the two mode-files from mode-finding and from the MCMC will be pretty much the same. But this is not the case here. You need to put more effort and time into finding the mode.

Thank you! Just to confirm what you said. Are you suggesting to not use a small identity matrix instead of the hessian? This is what I am trying to do at moment but it seems almost impossible to estimate by bayesian methods the parameter set of the present model.

I also estimate the same model for the Japanese economy (please, see the annex below ). Here it seems that the mode from the mh_mode.mat and mode.mat are pretty similar. Am I right?

Looking at the mode_check plots you are still having the same problem. You did not find the mode. Theory tells you that your MCMC will asymptotically converge to the ergodic distribution with any positive definite covariance matrix for the proposal distribution. But this might take a long time. The Hessian in principle is more efficient, but only if you are at the mode. What you are currently doing with starting the MCMC far away from the mode is running a very inefficient version of mode_compute=6. Unless you solve the mode-finding/convergence issue, your estimation results will be poor.
What still puzzles me, though, is the small range of feasible points for some of the parameters in the first mode_check plot. You should try to understand what is going on there. Maybe this indicates a mistake or that your prior allows for too wide a parameter range.

The small range of feasible points for some of the parameters in the first mode_check plot and in the sixth mode_check corresponds to growth balance path parameters of oil and technology at the steady state. Perhaps I should not estimate this four parameters but only calibrate them.

There is another thing I do not understand well. I thought that the purpose of the MCMC algorithm was only to compute the integral of the posterior density function. Why should it start at the mode? Is something wrong with my reasoning?

I would try that.

jpfeifer wrote:There are two mat-file. The _mode.mat and the mh_mode.mat. The likelihood value stored in both is massively different, showing that you did not start the MCMC at the point of highest likelihood.

dear professor,
does this mean that i can load the mh_mode.mat as the initial value to run MCMC,until the likelihood does not change too much?

Yes, that is possible. The risk you run is that it will take long and you may get stuck near your local maximum instead of searching for a global one.