Model with trend AND one sided HP filtered data

Dear Johannes,

As your said in your book, generally, models with explicitly specified trend use data in first differences.

But if I use one sided hp filtered data , how should I specify the measurement equation for the model with trend?

Here, y_obs is the filtered log (GDP per capita), y is the log-linearized model output after detrend

Would the measurement equation be like this? (h not detrended)

y_obs=y; c_obs=c; I_obs=i; h_obs=h;

Many thanks,

As both the data and the model variables are percentage deviations from trend, this looks correct. But I find it unusual to not use the model-implied trend for the data as well.

Dear Johannes,
i also wonder that if it is correct to use hp filtered data to estimate a model with deterministic trend.
because if i estimate the model with first difference filtered data, the second moment from the model are huge different from the data moment. and when i use hp filtered data it works well.

or is it means that my model with deterministic trend can not fit the data, and i should build a model without deterministic trend ?


I am not sure I am following. If your model estimated on first differences provides different moments for the first differences than in the data, there must be mistake in the observation equations, potentially an issue with the mean growth rate (as the HP-filter demeans the data)