I am an student who does some research on sustainability of public debt.
Which papers are essential to understand what determines the sustainable debt threshold, and the sustainable level of public debt?
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A big debate started after a flaw had been found in the conference paper "Growth in a Time of Debt" by Reinhart and Rogoff. There are several replications and many articles in the media and blog posts. Reinhart and Rogoff have the book "This Time is Different" on the topic and several well published articles, cf. here. Research on the topic continues to be published in top journals, e.g. "Is There a Debt-Threshold Effect on Output Growth?", Review of Economics and Statistics 99:1, March 2017. You should look at the references and also at which papers have cited the ones you find important.
These books might be of help:
Also, this chapter from the Handbook of Macroeconomics, Volume 2 (2016) might be of help: