# Estimation - my lack of understanding

Hi,

I would appreciate some help on understanding the basics of estimation.

Say I start with the Basic RBC Model with Monopolistic Competion by Jesus Fernandez-Villaverde but that I do not know tau and I want to estimate it. I know all of the other params. The only data I have is actual GDP data.

Since the steady state depends on tau, and I am modelling deviations from the steady state, I can not simply HP filter GDP data and use this detrended data for estimation, can I? The reason is that the simple detrended data is no where near the steady state thus estimation using this data is nonsensical.

On the other hand, I can construct a data series that is consistent with some initial steady state, but since I do not know tau, I do not know the steady state and thus can not construct data that is consistent with the unknown steady state.

So, the bottom line question is: if I want to estimate the model using actual data, what transformations of the data do I need to make to the data before using it in estimation?

I do appreicate any help on this question that demonstrated my lack of understanding.

Thank you.

Any help out there?

If you HP-filter your logged data and take the cyclical component, this component has the interpretation as percentage deviations from the empirical steady state (as you assume that the trend is your steady state).
For estimation purposes, you have to find the corresponding variable in your model, which would also be log-deviations of output from its steady state. By using this variable as the observed one, the estimation tries to fit the model to the data as good as possible. This obviously includes the steady state (that enters the log-deviation from steady state as the denominator) as well as any other moments of the data that are influenced by the parameter tau that you are trying to estimate.

Obviously, you can use other filters to transform your data and make it consisten with your model specification. For example you could specify a stochastic trend in your model and estimate the model with first differences of the data by using an observation equation.