I have a DSGE model with more than 30 parameters to estimate, including the persistence and standard deviations of seven shocks. I am taking Bayesian estimation strategy to estimate the model. At the first stage to find the mode, I take “mode_compute = 4” in Dynare 4.4.3, which is essentially to use the Chris Sim’s optimization function “csminwel” to search for the mode. Yet, something strange comes out. There is one estimated parameter (not shock process), which is specified with relatively loose prior. It turns out that, under this loose prior, the estimated mode value of this parameter is highly depends on the choice of its initial value in the “estimated_params” block. If I start with a low initial value (around 2 or 3), the estimated mode is around 10; If I start with a high initial value (around 30), the estimated mode rises up to more than 50. The discrepancy is very much significant. Moreover, for both cases, the “model_check” plots indicate this parameter is well identified, evidenced by the facts that each of the mode standing at the peak of the associated posterior likelihood function (a parabola going downwards).
I have several puzzling issues
1, Does that mean there are something wrong with my model setup?
2, Can we say this parameter have two modes?
3, Is this parameter poorly identified, maybe not locally but globally?
4, In general, what would be the reason for this situation to happen?
5, Could you give some suggestions on how to deal with this issue?
Many thanks in advance!