I am working on Bayesian estimation of open economy DSGE model. I made several experiments regarding different choices of observables and priors. Sometimes I get the following message in the command window:
Log data density [Laplace approximation] is -1111.810165.
MH: Multiple chains mode.
MH: Old _mh files succesfully erased!
MH: Searching for initial values…
MH: I couldn’t get a valid initial value in 100 trials.
MH: You should Reduce mh_init_scale…
MH: Parameter mh_init_scale is equal to 0.400000.
MH: Enter a new value…
I wonder whether it means that the dataset I used (I have only 40 quarterly observations of each variable) is somehow uninformative etc.
In order to assess the convergency of Metropolis iterations, we run different chains. We want the different chains to start at very different points in the parameter space.
In order to achieve that we draw initial parameters value in a multinormal distribution centered around the posterior mode and with variance matrix computed from the hessian of the log of the posterior at the mode.
This variance is then scaled by 2*mh_jscale.
However, for Metropolis to go somewhere, we don’t accept initial parameter values with too low a density, therefore the error message that you are getting some time.
It is true that if you have a flat prior on an unidentified parameter, this could generate such an error, but I don’t think that it is the only possible reason. You should start to look at the posterior mode and at the standard error of the parameters at the mode.
If putting priors tighter and with more shape suppress the problem, then you may be right and you have a problem of identification on some parameters.