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To begin, perhaps your understanding of institutional endowment funds may have missed an important concept or two:1a. Endowments (unlike annual donations) are designed to provide institutional support for CENTURIES. Generally, the endowment’s principal – and much of its accrued earnings – are never used, which is why endowments solvently endure for many generations. Normally, only about 5 percent of the fund’s value (usually, somewhat less than its annual earnings) are withdrawn from the financial corpus yearly and employed for the specific purpose(s) the endowment was established to support.
1b. In addition, most endowments are “restricted,” which means they can ONLY be utilized for the purpose delineated in the contract between the donor(s) and the university. “Unrestricted” endowments, of course, exist; however, they are far less common.
1c. It is a frequent misconception that university endowments can be employed for whatever purposes the institutional leaders deem necessary (e.g., “Wow, we have a $7.5B total endowment, let’s provide every student with a ‘full ride’ scholarship for the next fifty years”). This is plainly untrue, for the reasons cited in 1a and 1b. To illustrate, if a donor establishes an endowment to provide undergraduate scholarships to female cheerleader graduates of X high school, then the annually releasable funds – only about 5 percent of that endowment’s (principal plus earnings) value – can be utilized for that purpose alone (however, universities always will suggest to donors that the agreement be broadly, rather than narrowly, drafted).
To summarize. endowments are NOT a huge, unconstrained “checkbook” that can be applied to address any challenge(s) the university wishes. Turning to "elite," I agree with the factors you've cited (although, possibly others could be added). Obviously however, the key, insoluble problem is there are no precise (or quantitative) definitions of elite stature. For example, my brother (a PhD from Ohio State) loves OSU and ardently believes it's an "elite" research university (and he'll cite facts including its size, the scope of its programs and majors, the research it conducts, its *U S News* ranking, its extensive service to Ohio's citizens, etc. to bolster his assertion). Others will find his claim ludicrous *(Gee, it's not even in U S News' top 50)*. This sort of disagreement simply can never be resolved.