There's a widespread perception that presidents get afflicted by Second Term Blues, which led Lawrence Summers to propose in a recent op-ed that we abolish second terms and give chief executives a single, six-year term.
More specifically, he says the idea "requires much more study and debate."
The Confederate States of America operated under this plan, but didn't have much success with it. Mexico has also long limited its presidents to a single term. But James Alt, Ethan Bueno de Mesquita, and Shanna Rose have been able to exploit state-by-state variance in term limits rules to quantitatively study the impact of term limits on the performance of governors.
They find two things that both cut against Summers' proposal. Specifically, they "show that economic growth is higher and taxes, spending, and borrowing costs are lower under reelection-eligible incumbents than under term-limited incumbents (accountability), and under reelected incumbents than under first-term incumbents (competence), all else equal."
In other words, governors get better at governing when they've been in office longer. But at the same time, governors who are eligible to run for reelection do better than governors who are ineligible.
This suggests that if the second-term curse is real (Jonathan Bernstein offers some doubts), then the cure is more likely to be the opposite of Summers' prescription. It could be that by rendering second-term presidents ineligible for future terms in office, the 22nd Amendment is slightly undermining the quality of governance by eliminating the basic mechanism of electoral accountability.