Should we use posterior mean or posterior mode

Dear Pfeifer,
I am very thankful for your previous advice. I already increased the chain to 50000 draws, however, I didn’t reach convergence . The convergence diagnostics plots are posted below.
Unfortunately, I clumsy overwrite the trace plots. Nevertheless, it also showed that only very few parameters had converged.
Should the chain must be longer or there is probably some misspecification issue with my model?

In matter of fact I must inform you that, initially, it was very hard to find the posterior mode . With only very few parameters to estimate I simple got the error: Error using chol - The matrix must be positive definite.

Therefore following your previous advice (Saving the estimated shocks) **although you didn’t always recommended it I replaced the line chol(hh) in the try-catch-statement of dynare_estimation_1.m by hh=1e-4*eye(size(hh)). **

Today, I have tried to remake the calculation with the original code of dynare_estimation_1.m. I found that it is not out of question that some kind of model misspecification is related to the match between my model and observable variables namely, gov_share_jp_obs, oilprod_jp_deltalog_obs, oilprod_for_deltalog_obs, oilprod_jp_deltalog_obs_quarterly.

**Futhermore, with the original code of dynare_estimation_1.m, the output from compute_mode = 9 is the following
POSTERIOR KERNEL OPTIMIZATION PROBLEM!
(minus) the hessian matrix at the “mode” is not positive definite!
=> posterior variance of the estimated parameters are not positive.
You should try to change the initial values of the parameters using
the estimated_params_init block, or use another optimization routine.
**
If you have some time to give me a better insight on this matter I shall be extremely obliged to you.
nonlinear_JP_31 August Bodeinstein 1 copy.0059 long chain copy 5.zip (641 KB)