For most of its history, the United States had an unwritten term limit on Presidents of two four-year terms. This sufficed until World War II, where President Franklin Delino Roosevelt ignored the rule and served four terms, prompting a constitutional amendment. Other countries, such as Honduras and Venezuela, have seen efforts (failed and successful) to amend the constitution to allow incumbent president's to serve beyond previously established term limitations.
It is these evasions of term limitations -- presidential "over-stayers" -- that interest Tom Ginsburg in his latest work in progress (with Zachary Elkins and James Melton), "On the Evasion of Executive Term Limits". In systems with fixed term limits, we can divide executives into three categories: (1) understayers (those who serve for less than the constitutional maximum, for example, those who lose a re-election campaign, retire due to illness, or are removed in a coup), (2) those who serve the maximum term and then exit punctually (George W. Bush or Bill Clinton), and (3) overstayers, those who take action to stay in power beyond the constitutionally-governed rules in place when they entered office.
A plurality of executives are actually understayers, and most of those leave for "normal" reasons (election defeat or retirement). Professor Ginsburg, however, is most interested in the interplay between categories two and three. Amongst executives with an opportunity to overstay, a not-inconsequential number (nearly 20%) stay longer then they would otherwise be allowed. They do this via constitutional amendment, declaration of emergency, or by simply rewriting the constitution wholesale. And these figures might understate the problem: they don't include, for example, an executive who installs a crony or relative to take his or her place upon retirement, or one who simply diverts power to a new office and assumes that upon retirement (in both cases, think Vladimir Putin).
Measuring all reported instances of executive overstay, the authors found (among other things) that older leaders were more likely to overstay than younger ones, leaders with military backgrounds were more likely to overstay compared to executives with other backgrounds (generally lawyers), and that a history of overstays actually decreased the likelihood of repetition (each time an executive overstayed, it decreased the probability that next executive would do the same). Moreover, they found that overstay via "extra-constitutional" means was becoming increasingly rare, and that overstay rarely seems to provoke a constitutional crisis.
The paper also examines way that countries can guard against executive overstay. It's worth noting here that this presumes that overstay is a problem and, as a corollary, that term limits are a good thing -- something that is not necessarily clear. Most obviously, term limits prevent the polity from re-electing a leader that they otherwise would support -- it is an interference with pure majoritarianism, possibly deprives a country of experienced leaders, raises the problem of what to do with retired, former presidents, and forces voters to select a devil they don't know over one that they do. There are, of course, solid arguments for term limits -- overcoming voter apathy, guarding against tyrannical instincts, preventing executives from entrenching themselves indefinitely via corruption and fraud -- the point is that the debate over how to check against overstay necessarily presumes certain conclusions about the usefulness of term limits.
Professor Ginsburg forwards several institutional models for reducing overstay. Countries could offer rewards to executives who step down on time. These rewards could be monetary (such as Mo Ibrahim's $5 million award, plus $200,000 a year for life, to African leaders who step down from power) or governmental -- France makes all ex-presidents ex officio members of the country's constitutional court. For many leaders, international opportunities with the United Nations or other international organizations might help cushion the blow of being out of power. Alternatively, countries could modify the electoral system to account for incumbency advantages -- the authors consider a version of Bruce Ackerman's "supermajoritarian escalator" in suggesting that incumbents should have to gain ever-higher shares of the voters each time they run for re-election (plurality in the first run, majority in the second, 55% in the third, and so on).
The broader point is that, regardless of whether one generally thinks fixed executive term limits are advisable or not, the debate would benefit from an infusion of empirical data. How often overstay threatens the political fabric of a country, which policies are effective in checking overstay and which policies are not, and what factors make overstay more or less likely are all of use to policymakers seeking to construct governmental systems with an eye towards writing the rules of the executive branch.