Is there any reason not to crowdsource a subset of exam questions? We're considering incentivising students to submit questions for the final exam in a large grad class (> 200 students) as we feel like the process of designing a problem and a grading rubric encourages students to study the material to more depth.

Is this commonly done? What are the pros/cons in the literature, or that you can think of with implementing an exam where a few questions are generated by the class? What precautions should we be taking? What should we incentivise?
Is this commonly done?


I have no sources to answer this, but in my experience, no, it's not commonly done.


  What are the pros/cons [...] that you can think of with implementing an exam where a few questions are generated by the class?


I can see two main issues:


It's not clear to me how you want to handle the communication of the questions and how you plan to use them, but some or, possibly, many students will know the questions in advance before the final exam. 
As pointed out by @trikeprof in a comment, students might perceive this as a lazy strategy. Furthermore, they might not like the idea of being assessed on the basis of questions formulated by their peers.


I think that the idea of having students designing questions is good, but those questions shouldn't be directly used in the final exam.

An alternative proposal could be that of assigning the design of a question as homework, with the additional agreement that good questions will be collected in a booklet of questions/exercises, with recognition of the authors.