I employed a plain vanilla RBC to recover the TFP implied by a partially calibrated model.
The only parameter estimated is the standard deviation of the technology shock. My observable is a first-differenced series of y=c+i (in log terms). I asked Dynare to compute the loglinear solution.
My questions is: if my observable is in first differences the smoothed variable Z (TFP) will already be first differenced? (I don’t use the prefilter option in estimation) or is it enough to get the first differences of the smoothed TFP estimated?
The smoothed variables will always correspond to the concepts used in the model. Just because you have one observable in first differences does not mean other level variables are suddenly in first differences as well.