A study by economists from Tel Aviv University and the Centre for Economic Policy Research (CEPR) titled "Open source software: Motivation and restrictive licensing" (pre-print) looks at the productivity of developers on Open Source projects and concludes:
"...that the output per contributor in open source projects is much higher when licenses are less restrictive and more commercially oriented."and observe:
"Projects written for the Linux operating system have lower output per contributor than projects written for other operating systems..."
Not the results I would have expected.
More info & critical examination of the study at my blog Zzzoot. [Sorry, as a new member I can't as yet syndicate my external blog to this blog].