How to fix "! Dimension too large." when using pgfplotsx?

To me it looks a bit similar to something like

and is a limitation of pdf-plots – or to be more precise: Imaging you spent a cm per 10 units, then your 1966 is nearly 2 meters out.
You can restrict your y-domain first (though then you do not see all your data probably) – or scale down your data before.