I think the approach suggested by Akram Shavkatovich Hasanov is acceptable for this particular dataset. It's the easiest approach here.
So you can just predict 2001 based on 2018,2017,...,2002. Then the same for 1999.
I also recommend plotting the series as spaghetti plots, see this poster:
Poster A Visual Framework for Longitudinal and Panel Studies (with ...
One potential issue here is that Imputing the series values with backcasting will affect the applicability of tests such as those mentioned on the ePoster. So, if you want to use panel data tests and methods for unbalanced datasets, perhaps, it's better to keep only 2002-2018 period.