# Observation equation and first differences

Dear all,
Dear Mr. Pfeifer,

I already read the paper “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” but I still stuck with a problem there. First of all, my estimation in Dynare is running and the results seem to be good. I used data for Spain and my detrending method is first differences. My model is entered nonlinearly in Dynare, so everything is in exp() as described in chapter 4.4 page 40. So I took the log first differences from e.g. per capita real GDP and demeaned the data afterwards. Now to my question: I wrote the corresponing observations equations in the following way: y_obs = y-steady_state(y)+eps_yobs. So I used the observation equation in chapter 4.5 and the observation error in chapter 6.1. In the beginning of chapter 4.5 there is a note, that the one-sided HP filter is used for this example. I know that the HP filter already demeans the data. But can I use the above mentioned equation when I use first differences and then demean the data? It then should be the same, shoudn’t it? The chapter 4.6 tells that first differences is explained in the next chapter. There, the observation equation for first differences with demeaned data is: y_obs=y_tilde−y_t i lde (−1) ; //matched to demeaned growth r a t e. The problem is: The estimation also runs with this equation, but the results are worse than in the former case.
Is it ok to use the first equation also in case of first differences when the data is demeaned afer taking log first-differences? Or do I have to use the second observation equation?

Thank you very much!

``````is a percentage deviation from steady state. You cannot match this to a first difference, which is defined as
[code]y_obs=y_tilde−y_tilde (−1) [/code]``````

is a percentage deviation from steady state. You cannot match this to a first difference, which is defined as