Dear Johannes Pfeifer,
Thank you very much. That response helped me rethink the issue in a new light. The transformed variables, i.e. y_t=Y_t/X_t, where X_t is the nonstationary (labor-augmenting) productivity process is a deviation from the stochastic trend and can therefore be compared to the deviation from the deterministic trend in Smets and Wouters (2007).
Smets and Wouters (2007) also consider stationary technology shocks. To make the comparison more complete, one can have both a stochastic trend and also shocks to the level of technology z_t. That way, deviations from the stochastic trend can respond on impact to technology even though, by construction, they net out much of an effect of a shock to the growth rate of technology.
So, for an analysis along the lines as SW, one can have a stochastic trend alongside shocks to the level of neutral productivity and focus on the deviation of stochastic trend. In this case, a conditional forecast error variance decomposition is very informative as the contribution of the shock matters greatly with the horizon.
And, of course, one can also examine the forecast error variance of growth rates, which have a different information content.
I note that the model in in your paper “Fiscal news and macroeconomic volatility” featured both stationary and nonstationary technology shocks. You choose to conduct the FEVD in terms of growth rates in Table 3. Though I now generally regard this issue as closed, I ask in closing if this choice mostly driven by comparability to the literature or also because of substantive features of the research question/model?