A study by economists from Tel Aviv University and the Centre for Economic Policy Research (CEPR) entitled "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."
"Projects written for the Linux operating system have lower output per contributor than projects written for other operating systems..."They also observed that the median # of contributors in "restrictive" projects (13) to be much less than for "non-restrictrive" projects (35).
"Output per contributor in projects oriented towards end users (DESKTOP) is significantly lower than that in projects for developers."
They chose the 71 most active projects on SourceForge in January 2000 and studied them over an 18 month period starting in January 2002. They measure these projects every 2 months over this period resulting in 9 samples. The metrics they used include: Source lines of code (SLOC), #contributors, the "restrictiveness" of the license (ranging from GPL = very; LGPL, Mozilla, NPL, MPL = moderate; or BSD = non), operating system, age of project, if it is a desktop or system application, language (C++ or C = 1; all others = 0), and others. They took in to account the difference between the LOC of language by separately also looking at just the C++ or C projects.
I do not understand the lag in choosing the projects (January 2000) and the start of the data sampling (January 2002). This in itself could have skewed the results, i.e. the 71 most active projects in 2000 would almost definitely NOT be the most active 2 years later. I think this may be a major flaw in this study.
I also don't think that the sampling size is large enough & that the sampling method should have been a random selection of projects that met some reasonable criteria, like:
- had at least C contributors
- had at least L lines of code contributed over the last M months
- had at least D downloads over the last M months (penalized very new & very unpopular projects??)
I haven't taken too much time to go over all of their experimental design, model & stats....
This study builds on an earlier study titled "The Scope of Open Source Licensing" 2005, (pre-print), which is where the authors get their view of "restrictiveness" for licenses. This study found:
"Projects geared toward end-users tend to have restrictive licenses, while those oriented toward developers are less likely to do so. Projects that are designed to run on commercial operating systems and whose primary language is English are less likely to have restrictive licenses. Projects that are likely to be attractive to consumers—such as games—and software developed in a corporate setting are more likely to have restrictive licenses. Projects with unrestricted licenses attract more contributors."This study used all 40k SourceForge projects available (2002).
 Fershtman, C. & N. Gandal. 2007. Open source software: Motivation and restrictive licensing. International Economics and Economic Policy. http://dx.doi.org/10.1007/s10368-007-0086-4
 Lerner J, Tirole J (2005) The scope of open source licensing. Journal of Law, Economics and Organization 21:20–56