Thank you David, this is a very helpful post.
One question: in either the setup of the DSGE model or in postestimation, is there a way to generate an estimate of an unobserved **control** variable (in this example, the output gap term [x] )? Obviously, in this instance, seeing the model-consistent estimate of the output gap would be of great interest to a macroeconometrician!
If not, how might one modify the Woodward (2003) model to make the output gap estimatable?