I recently found a very puzzling outcome from running estimation. For example, u is the unemployment rate and is observable. When we get the smoothed variable of u, the smoothed one is exactly like the original u, except for a constant!
I expect the smoothed one to be the same as the observation, if it is observable (by definition). But where is the constant from? Did dynare subtract the mean of the smoothed variable somewhere in producing the smoothed variable in the oo_.? I guess the mean is the constant.
Thanks a lot,
I found out the answer by myself through looking at the dynare m files. The Kalman Filter implemented in Dynare is Diffuse Kalman Filter, instead of usual one we learned in class. We have to add the steady state value back, which is stored in the oo_.Smoother.Steady_State.
Hope it helps those who have similar questions. Also, looking at the dynare m files is quite fun.
Indeed you have to add back the steady state to the smoothed variable. But that has nothing to do with the type of Kalman filter. Actually Dynare uses a Diffuse Kalman Filter for models with a unit root only.