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National Science Foundation (NSF) in US enforces a limit on salary compensation over all grants, often referred to as the two-ninths-rule:

Summer salary for faculty members on academic-year appointments is limited to no more than two-ninths of their regular academic-year salary. This limit includes summer salary received from all NSF-funded grants.

So, for a 9-mo faculty who can fill up to 3 months of their own summer salary, NSF as the sole source of salary compensation doesn't work no matter how many grants one has.

Compared to the NIH model where there is no such limit, in fact 100% of salary can be recovered in theory via NIH grants, this is a rather strong limit.

What is the motivation of the NSF two-ninths-rule? Why not three-ninths to cover the whole summer salary?

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I don't know for sure if this is historically accurate, but the story I've always heard is that the two-ninths rule was an attempt to avoid the vacation issue. If you take three months of summer salary, then that leaves no time at all for any vacation, since you can't accept summer salary for any time not spent on research. The fear was that if three months of summer salary were allowed, lots of people would request it (since a 9% salary increase would be tough to resist), but the public would be concerned that many of them were probably cheating and going on holiday with their families for part of that time anyway. The two-ninths rule minimizes the extent to which the NSF has to deal with this issue, since there's one month reserved for vacation or other activities.

Incidentally, this fits consistently with Bill Barth's answer: solving the vacation problem this way is probably more attractive for an agency that has less money in the first place.

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The motivation is to reduce the scarceness of money the NSF has available. It's there to encourage everyone to apply to other agencies and sources of summer salary. NSF grants are very competitive, and if everyone went for 3 months salary, NSF'd run out of funds sooner, or program officers would spend more time cutting budgets to try to fund everything that reviewed well.

It's also not a hard and fast rule. with PO permission, you can get around it if necessary. Plenty of large instruments have full-time staff funded by NSF grants alone.

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One way to look at this is actually look at your question slightly differently - what assumptions do NSF vs. NIH funding make about who you are, and why they're funding you.

The NIH model is clearly meant to support dedicated, purely-NIH funded research positions run on 100% soft money, or something very, very near to it (a floating hard money fund for like, 5% effort to cover proposal development time, for example, is somewhat common). This implicitly implies that the NIH is funding the usual employment-related absences - sick days, vacation, etc. And that anything they don't pay for might as well not exist, in the case of a 100% soft money position.

In contrast, the NSF model is clearly paying for directed research time, under the assumption that someone else (presumably state/university funding) is picking up the rest of the tab. There's no reason then, for them to pay for things like vacation time or the other things. They only want to pay for the time one might reasonably be expected to be working directly on NSF-funded projects, and between other summer responsibilities and travel, that's probably not your entire summer. As some other's have said, that they're also cash constrained probably helps inform that position.

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Bill Barth already outlines one part of the reason: to alleviate the scarcity of resources. Another one is that NSF's mission includes education, and allowing faculty to only do research instead of paying their salaries exclusively from external funding would undermine their ability to integrate research and education.

This might call for a 3-months rule instead of the current 2-months rule; the difference may be explained using arguments such as Bill's.

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