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How can "institutional support (i.e., administrative) - salaries and benefits" be placed in different IPEDS Finance categories by different schools. The IPEDS Finance instructions seem pretty clear to me. I just don't think there is much ambiguity. I don't think it could be as big a problem as you say.
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The problem is the denominator. The IPEDs data is very inconsistent in picking up each colleges spending. I pointed out earlier that Amherst and Swarthmore spend exactly the same amount per student ($70,000+). Yet IPEDS only picks up $60,000 for Swarthmore and $40,000 for Amherst.
They also spend exactly the same for Institutional Support salaries: $7.71 for Swarthmore, $7.97 for Amherst. Your tables are showing distinctions without a difference.