After I do Bayesian Estimation on Dynare, it shows up 2 tables of results.
So I wonder which one i should use for the estimated parameter?
The values in “post.mean” column of Table 1 or the one in “mode” column of table 2?
prior mean post. mean 90% HPD interval prior pstdev
rho 0.900 0.9921 0.9860 0.9985 beta 0.0500
Stde 0.500 0.0635 0.0579 0.0698 invg Inf
RESULTS FROM POSTERIOR ESTIMATION
prior mean mode s.d. prior pstdev
rho 0.900 0.9948 0.0030 beta 0.0500
Stde 0.500 0.0632 0.0036 invg Inf
In your case, the posterior mean and the posterior mode are not very different. That said, the choice between posterior mean or mode is rather ad hoc. There is a rational behind this choice: you need to choose (here is the ad hoc part) a loss function that given a value for the parameter returns your loss if this parameter value is wrong. But you do not know the true value of the parameter, so the rational is to report the value of the parameter that minimizes the expected (with respect to the posterior distribution) loss. If your loss function is quadratic it is easy to show that the optimal value for the parameter is the posterior mean. If your loss is a 0-1 function (1 iff the value is wrong), then the optimal value is the posterior mode. Obviously you can imagine a lot of loss functions, and for each loss function you will end up with a different point estimate. An easy to read detailed explanation of this is given in the first chapter of Zellner’s textbook (An Introduction to Bayesian Inference in Econometrics).
Usually in the literature the posterior mean is reported (after the MCMC), and you can also plot the marginal posterior densities.