I am wondering if there are any studies that examine the efficacy of software projects in CMMI-oriented organizations. For example, are CMMI organizations more likely to finish projects on time and/or on budget than non-CMMI organizations?

Edit for clarification:

CMMI stands for "Capability Maturity Model Integration". It's developed by the Software Engineering Institute at Carnegie-Mellon University (SEI-CMU).

It's not a certification, but there are various companies that will "appraise" your organization to various levels of CMMI, such as level 2 and level 3. (I believe CMMI level 1 is an animalistic, Hobbesian free-for-all that nobody aspires to. In other words, everybody is at least CMMI level 1, even if you've never heard of CMMI before.)

I'm definitely not an expert, but I believe that an organization can be appraised for CMMI levels within different scopes of work: i.e. service delivery, software development, foobaring, etc. My question is focused on the software development appraisal: is an organization that has been appraised to CMMI Level X for software projects more likely to finish a software project on time and on budget than another organization that has not been appraised to CMMI Level X?

However, in the absence of hard data about software-oriented CMMI, I'd be interested in the effect that CMMI appraisals have on other activities as well.

I originally asked the question because I've seen various studies conducted on software (e.g. the essays in The Mythical Man Month refer to numerous empirical studies, as does McConnell's Code Complete), so I know that there are organizations performing empirical studies of software development.