Mode jumping MCMC

I am struggling in getting estimated parameters with mode jumping MCMC. As a proposal density I tried either an identity matrix and the prior variance but there seems to be a scaling problem (see priors&posteriors). I am attaching log files under both proposal densities. The model is baseline Smets & Wouters and the estimation works regularly using the default Hessian at a posterior mode.
According to my little understanding, it looks like the MCMC sampler is having hard time to cross regions where the density is very low but the reason why one may use jumping MCMC is to address bimodality (e.g. the cases discussed here: [Bimodal Posteriors)). Is that correct?
Can you help me to get the jumping MCMC working?
Do you have any advice in how to uncover genuine multimodality in the model?
Thank you very much (14 KB)
priors_and_posteriors.pdf (10.1 KB)
identity_matrix.txt (57.1 KB)
prior_variance.txt (56 KB)

Hi, could it be that you are confusing something? The

option is for specifying a the covariance for the standard Random-Walk Metropolis-Hastings sampler. The reason I used that command was that it allowed me to scale the proposal density to a size that allowed jumping to a differerent mode. Also I knew where the second mode was so that I had a feeling how large the scaling needed to be. While this wide proposal density allowed crossing regions, the sampler became hugely inefficient. For higher-dimensional problems, this is completely impractical.

As should be clear, this procedure is not a mode-jumping MCMC. While we would like to have something like that in Dynare, it is not yet there.

Regarding finding multimodality: my only advice would be to start mode-finding from different starting points and see where it converges to. Slices through the likelihood then provide an indication whether that is actually a mode.