Transforming per capita variables back to total variables for forecasting

Hi all,

I have a question about data treatment. Let’s say I have a (log-linearized) model in which I have per capita variables. I thus have treated the data for estimation in order to match that feature, among others.
Now, after estimation I do forecast a subset of these variables but many people in the literature show overall variables in their forecasts. How do I convert them back?

As an example, you can think about output growth. Where the SPF for instance shows overall output growth and not per capita.

Del Negro and Schorfheide (2013) for instance talk about this issue but not how to resolve it:

Finally, the various DSGE models only produce forecasts for per-capita output, while Blue Chip and Greenbook forecasts are in terms of total GDP. When comparing RMSEs between the DSGE models and Blue Chip/Greenbook we therefore transform per-capita into aggregate output forecasts using (the final estimate of) realized population growth.

I am sorry if this is trivial or has been answered previously.

Thank you :slight_smile:

Obviously, you need an estimate of population growth for that.

Thank you for your answer. I may have some follow-up questions though, hopefully you can further clarify them.
I think my issue was more that the population data that I used is quite fuzzy since it includes aftercounts etc. After smoothing it out or using a different metric is is easily done and I get my wished results.

Nonetheless, thank you for very much your time :slight_smile: