Linking variables to data

Dear all,
I’d like to estimate parameters of the NK model (46 endogenous nonlinear equations) using the Bayesian approach. The model includes 8 observable variables.

The time series used here are detrended by HP filter. On the other hand the model variables are stationary around the steady state. I tried to link the data to model by adding the following equations:
x_obs-x_obs(-1)=x-log(xs)-(x(-1)-log(xs))
after the simplification:
x_obs-x_obs(-1)=x-x(-1);

The problem is that the posterior modes are exactly the same as the means of the prior.
Should I use another transformation?
Thanks,
m.

i am not sure if i have understood you correctly.

suppose you have log output= log(Y) in the data.
if you detrend log(Y), then you get something equivalent to Y-hat in your model.
otherwise, if you compute log (Yt) - log(yt-1) ie. the growth rates in the data, this is equal to y-hat (t) - y-hat(t-1) in your model. if you have no growth in your model, then better demean the growth rates in the data.

reuben

Thank you Rauben,
there is no trend in my model and data is detrended. So, probably the best way how to link variables to data is :
Y_obs=Y-log(Y_SteadyState)
But here I’m not sure how to define Y_SteadyState. Should I use intital values?

Matus.

you dont need to specify log y bar
your detrended(log(realGDP)) is the same as Y-hat in your model.