linking variables to data

[senaj]

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.

[reubenpjacob]

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

[senaj]

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.

[reubenpjacob]

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