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The value of academic libraries is often strongly tied to the value of colleges and universities themselves. There are many reports on the impact of universities and colleges and higher education on the economics of a community.
2005 Colorado Academic Library Impact Study (Feb. 2006)
Libraries Designed for Learning by Scott Bennett
OCLC Report: Research Libraries, Risk and Systemic Change (pdf: 579K/20 pp.)
ACRL and ARL
ACRL has a list if 8 studies here:
The ARL Statistics and Assessment resources are here:
The ARL site covers some of the StatQual, ServQual, ClimtaeQual, DigiQual, and LibQual resources which are other metrics used in academic libraries to judge effectiveness, impact, and value.
In addition it is worthwhile reviewing some of the work in the following: