So, paying students to put more time in, to complete assignments, etc. works; but paying them based on final grade doesn't. Furthermore, they find no evidence that the incentives (once discontinued) will decrease student's intrinsic motivation to perform well.
Our results suggest that student incentives increase achievement when the rewards are given for inputs to the educational production function, but incentives tied to output are not effective. Relative to popular education reforms of the past few decades, student incentives based on inputs produce similar gains in achievement at lower costs.
Read the paper here.