This paper shows that the scope for bond yields to fall below zero is strictly limited by market expectations about how far below zero central banks are willing to set their short-term policy rates. If a central bank communicates a credible commitment to keeping its policy rate above a given level under all circumstances, then bond yields must be higher than that level. This result holds true even in a model in which central banks are able to depress the term premium in bond yields below zero via large-scale purchases of long-term bonds, also known as quantitative easing (QE). QE becomes less effective as bond yields approach their lower bound.
The data underlying this analysis are available here.