Hallo everyone
I have one question related to forecasting variance and historical decompositions in DSGE model
One of the different points btw these two methods is that forecasting variance decomposition is a out-of-sample based technique, whereas historical decomposition is a in-sample technique. So my question is that are the finding from this two different approaches exactly identical to each other? For example, in terms of forecasting variance decomposition, I find that technology is main driver of output fluctuation, then this finding would be identical to that by using historical decomposition?

The variance decomposition is a theoretical and importantly asymptotic concept. It relies on shocks being orthogonal, i.e. uncorrelated. In contrast, in finite samples even theoretically uncorrelated shocks can show a correlation. For that reason, the historical shock decomposition can yield a different picture.

No, there isn’t because researchers usually don’t point to these conflicts. And you as the researcher on your paper need to decide what you are interested in.