Hallo every one
I have a question concerning the Bayesian estimation of DSGE and VAR models.
In the VAR model, we do not need to find the maximum a posterior density. Indeed, we just do the sampling procedure, in particular, the Gibbs sampling algorithm, based on the conditional marginal posterior distribution of each underlying parameter. So, the initial value for this sampling algorithm is typically arbitrary.
however, in the estimation of DSGE mode, before doing the sampling algorithm, especially the MH algorithm, we have to find a ‘local’ maximum level of the conditional joint probability distribution of all underlying parameters. Indeed, this procedure is well-known as maximum a posteriori estimation (MAE).
So my question is that doing the MAE is to find the initial values for the sampling algorithm such as the MH algorithm? Why in the estimation of the DSGE model, we have to do that? But in the estimation of the BVAR, we never do it?
Thank you so much and please correct my understanding