When you have an index of hours worked (for example: FRED - HOANBS) and each variable in your model is divided by the population aged 16 years and over. What is the correct treatment of the variable that represents the hours worked?

HOANBS / POP_16

Creating a population index taking the same base year as HOANBS and using the quotient as in (1).
or

Take the first differences of the index and specify that L_obs = L - L (-1)?

For me option two looks feasible.
But you should take into account the artificial dynamics in the civilian noninstitutional population series ( CNP16OV) that arise from irregular updating (see Edge et al., 2013 and the guide of Prof. Pfeifer on page 20 and 21).
You need to smooth the spikes in the growth rates of this series.

You need to map aggregate hours into a per capita or per worker variable. See

The second issue is the scaling. The time endowment in most models is arbitrary. So typically percentage deviations from the mean or growth rates are used, which both do not rely on the exact level. Here, I don’t see how having the same base year for indices would help.

All the variables in my model are divided by the population over 16 years of age. But here, another question arises: should the hours worked index be divided by the population over 16 years index or by the working population index?