Can we set up the following more direct observation equation?
What exactly is the question? If you take the logarithm of the above equation, you have a standard observation equation used in many papers.
I’m looking at the Dynare manual regarding the specification of observation equations, and it seems to strongly emphasize the issue of removing the mean from the estimation data. However, my observation equations directly use seasonally adjusted data for estimation, so I’m worried about this issue. My understanding of why the estimation data needs to have the mean removed is not very thorough, so I’m concerned that my nonlinear observation equation might be incorrectly specified.
The guide just stresses that data and model need to be consistent. You can easily handle non-demeaned data but of course need to take care when matching that to growth rates of model variables, which are necessarily mean 0.