The NY Times has published an excellent piece on the unintended consequences of pay for performance incentives introduced at Chinese universities. This type of "Freakonomics" highlights several issues in modern economics. Back in 2000, Ed Lazear wrote a clean AER paper where he studies how productivity changes at a windshield replacement firm when it switches over to "pay for performance". He finds that workers work harder when their compensation is tied to "output" rather than to how many hours have passed (i.e a fixed wage per hour).
In the case of research, what is "output"? As the NY Times article highlights, China's universities have introduced a $ pay bonus system such that publications in top tier journals (think of Nature or Science) yield huge % increases in pay. This bonus system leads young scientists to devote more effort but the Times article focuses on a second dimension of effort. The Times argues that this incentive system contributes to cheating through faking data.
The Times article goes on to say that another problem in the Chinese system is that the universities do not have Deans who can judge excellent work. In this case, the journal editors are the judges and the journal editors can be tricked by forged data. This issue arises in academic economics. The senior faculty determine who is promoted in a department. If the senior faculty can "read the papers", then the journal names where the papers are published matters less because the senior faculty has the confidence to make up their own minds about the quality of the work. In contrast, if the senior faculty are insecure and don't know a field of scholarship then they will simply "count papers" weighted by the prestige of the journals where they are published.
Everyone knows that it is easier to count output than to judge its quality. In the case of Lazear's windshields, the variation in quality is small because a machine makes the windshields and then duded glue them in to the car. In the case of academia, the variance of output quality is huge.
Competition across universities in terms of seeking to rise in the national rankings will reward those schools who show "good judgment".
In standard Principal/agent models, the agent chooses her "effort" level and effort is costly but you can imagine models that distinguish between productive effort (learning new math techniques) versus socially unproductive effort (i.e cheating). How does the principal design a contract to encourage the former and to discourage the latter?
The Holmstrom and Milgrom (1991) model is relevant here.