There is no shred of research showing that bonuses improve performance, nor do firms paying them customarily do better. The incentives thesis saw its nadir in 2002 when Bristol City Academy tried paying students to get higher GCSE and A-level passes. The scheme was abandoned when teachers found that students did not do any better, tending to do well because they liked doing well.Much as I am critical of the use of bonuses I think this is a bit wide of the mark. There is evidence that performance-related pay can improve performance, for certain types of tasks. And in response to the 'paying for grades' claim as I've blogged before, much more recent work by Roland Fryer has found that actually paying kids for certain outputs can improve their knowledge, vocabulary etc.
(Actually the Fryer stuff is very interesting as he got better results from paying kids to turn up to class and read a set number of books than by actually paying for grades. He classes this as paying for inputs rather than outputs, and speculates that this effect may occurs because don't know how to deliver good grades (it's not a simple task), whereas they know how to turn up and read a book. In addition Fryer was trying to improve poor performance. So maybe we shouldn't expect to see motivation crowding because arguably there's no intrinsic motivation there currently.)
The most common critique financial rewards is that they don't work, or backfire, where people are already motivated (this what motivation crowding and overjustification theories claim). Financial incentives also don't seem to work where the task involved is not straightforward, algorithmic or easily measurable. They also may not work, or can have a negative effect, if the recipient perceives them as controlling. And even behaviourists say that you may need to keep tweaking the rewards/reinforcers for them to work properly. So there are plenty of grounds on which to challenge them.
However, if the job is dull, simple and easily measurable, and the employee/student is not motivated to do it well, then rewards/bonuses may indeed have a positive effect on performance, even if fleeting. How relevant that is is to FTSE100 directors, bankers etc is another question.