Yes! Over 13 nation, peer-reviewed studies have been conducted on OER use in higher education over the past five years. None of these studies showed results in which students who utilized OER performed worse than their peers who used traditional textbooks or course materials. In fact, all studies showed that students who had unlimited access to their course materials and were engaged in open pedagogy assignments performed better or the same as their peers with traditional course materials and more limited access.
For a complete list on every major study conducted on OER efficacy and/or teacher/student perceptions of such resources in actual practice, please see the Open Educational Group's list of reviewed studies: