Forecasting variance decomposition vs historical decomposition

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?

I am looking forward to your answer soon

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.

Dear Prof. Pfeifer

Thank you so much for your interesting explanations

So I can say that the finding from forecasting and historical decomposition might be either identical or different. My understanding is correct?

Best wishes

As I said above: in finite samples that is true.

Dear Prof. Pfeifer, in the above mentioned case, which of the above methods should the researcher adopt if their results deviate from each other?

I am not sure what you mean. Please elaborate.

What I mean is if the results of the two methods are not the same, which one should we adopt for the analysis?

That depends if you want to say something about the sample at hand or the population properties.

Thanks! Could you please advise some literature that addresses this issue.

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.