I have an estimation that lead to an acceptance rate of 0.04 (which is bad according to the dynare userguide).
Is tuning the mh_jscale will change:
- the log data density ?
- the estimation results ?
For instance, I have 2 similar models which I want to compare.
- Can I always compare these two models even if in their mod files they do not have the same mh_jscale ? - of course I have the same dataset across models.
A low acceptance rate is not “bad”, it just will be very inefficient, i.e. you need many draws to correctly sample from the posterior because the posterior draws will be highly correlated. As long as you chain has converged, this should not affect any of the results (apart from differences due to the usual numerical standard errors).
In particular, both the log data density will in principle not be affected by acceptance rates (again as long as there is convergence of the chain). Nevertheless, assuring convergence is already hard with a decent acceptance rate. Thus, you should adjust mh_jscale.
The marginal data density (and the asymptotic properties of the MCMC sampler and thus of all results) are independent of the proposal covariance matrix including its scaling. Again, you are only affecting efficiency.