Deal with forecast uncertainty due to measurement error

Currently, Bayesian forecasts completely neglect the presence of measurement error. Theoretically, is is not clear whether we should display

1. the true value of the underlying variable
2. the observed value of the variable including measurement error While the mean forecast should be unaffected, the presence of measurement error should widen the uncertainty associated with forecasts. But this is in no way reflected in our forecasts. Additionally, neglecting the effect of measurement error on forecasts breaks the equivalence of specifying measurement error as a "structural" shock vs. specifying it using the Dynare command.

At a minimum, we should document the treatment.