Should these two observable data be divided by GDP deflator and population

Dear Johannes,
I plan to incorporate such as U.S. sentiment data and U.S. stock market index data as observable variables in my DSGE model, all other observable variables such as output, consumption and investment are detrended by GDP deflator and divided by population, I am wondering that for sentiment and stock market index data, should I also divide them by both GDP deflator and population?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

That depends. Sentiment is not a growing variable that depends on the number of people or price increases. So no, you should not scale it. It’s different for the stock market index. If it’s a performance index, it will grow with the price level over time. Thus, you need to make it real. But you should usually not scale it by the number of people.

Dear Johannes,
Thank you very much. But I feel a little confused about your comment ‘So no, you should scale it.’, so should I scale consumer sentiment index or not? If I scale consumer sentiment index, should I divide it by population or by GDP deflator, or by both population and GDP deflator?
Thank you very much!
Best regards,
Jesse

It was a typo. I fixed it. No scaling.