I’ve got such an impression that “a day before” implies an exact time point in the past (a day before that time) but “the day before” can be anytime before that day (not an exact time point). ——Am I right?
btw: If “since several years ago” is incorrect, how could “since several years before” be correct? e.g. The U.S. economy had been in a state of what is called stagflation [color=red]since several years before, with prices increasing amid a depression, and confidence in the dollar falling.
‘A day before’ suggests not necessarily the exact day ( as ‘the’ day before would) but the period of time that has elapsed - in other words 24 hours.
‘Ago’ suggests back from the present as in: Two days ago, where we are going back two days from now. ‘Before’ can be used from now and from then as in: Before today we were able to buy tickets at the office but as from today you have to buy tickets online. Before the war prices were much cheaper.
In your sentence: The U.S. economy had been in a state of what is called stagflation since several years before, we are using ‘before’ to describe that time in the past (had been) and ‘since’ suggests from that time. In that case ‘ago’ wouldn’t work because, as I said, it has to be a period back from now.