Run the simulation again with the estimated structural parameters

[jpfeifer]

That is up to you and very much depends on what you are trying to achieve. The following post may be relevant:

Model validation of Bayesian estimation

This is a rather philosophical matter. Historically, models were calibrated to long-run growth facts and then cross-validated by looking at the implies short- to medium-run implications for the business cycle, which is in a sense a different dataset. When estimating a model, the parameters are chosen by looking at the same dataset for which you try to match second moments. You could argue that this is not a rigid “out of sample” test. People nevertheless do this, because when estimating, you t…