I need some advice regarding typing observable variables into the data

When looking at employment in the US from 1947 to 2004 there is an upward trend and I normalized that variable to one and entered it in Dynare like this.

n=n_obs*n_ss;

n is employment in the model and n_ss is steady state employment in the model which means that when n_obs is normalized to one, n=n_obs*n_ss holds. However, since n_obs has an upward trend I am instead considering to redefine a new observed variable like dn_obs=n_obs/n_obs(-1) and enter

dn_obs=gamma_n*n/n(-1)

gamma_n is the average upward trend you see in the data. On average gamma_n=1.0005 for quarterly data.

The answer depends on what you are trying to achieve. It seems to me that you are considering employment and not employment per population. You somehow need to consider the increase in population. If you detrended your other variables, you need to detrend employment as well. But note that you should only subtract the population trend, not the trend of output and TFP.

The varaible n_obs is defined as (Nonfarm Business Sector: Employment)/(Civilian Noninstitutional Population) between 1947 and 2004. So it actually is employment per population. The upward trend seems to start somewhere at 1970.

You donâ€™t see the similar pattern when looking at US data?