# Observation Equations in nonlinear model

Hello everyone,

I read Professor Pfeifer’s guide “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” but I would like to check if I correctly specify my observable equation in a nonlinear model when the exp substitution is not used.

My model completely abstracts from economic growth. As Professor Pfeifer usually recommends, I plan to create auxiliary variables to define the logarithm of the variables of interest and thus avoid making the exp substitution to the entire model (there are more than 50 equations) therefore, imagine that in my model block I define output as Y_t, and generate an auxiliary variable of the form logY_t = log(Y_t).

For estimation, I have the GDP time series to which I applied logarithms and subsequently applied the one side HP filter, thus my observable equation would be:

Y^{obs}_t= logY_t - logY_{ss}

Is this correct?

And just to make sure I´ve done things right, if I have the gross inflation rate defined in the model block as \Pi_t, and if I take the series of the Consumer Price Index (CPI) and apply CPI_t/CPI_{t-1}, therefore, Should my observable equation be like this?

dS^{obs}_t = dS_t

Cheers

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1. Yes, you correctly define percentage deviations from trend.
2. For the second one, you did not define your notation.
1. Sorry for my typo in the equations. I meant that I have the Inflation time series constructed as \Pi^{obs}_t = CPI_t/CPI_{t-1}, while in the non-linear model I have gross inflation (\Pi_t), therefore, Should my observable equation be like this?

\Pi^{obs}_t = \Pi_t

Thanks for your help

Yes, that is correct as well.

Professor @jpfeifer, just a small question, in Dynare coding the equation {Y_t^{obs}=\log{Y_t}-\log{Y_{ss}}} should be {Yobs=log(Y)-steady\_state(log(Y))} or {Yobs=log(Y)-log(steady\_state(Y))}?

Strictly speaking, the latter. But those two operations are interchangeable.

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