## “The Tenuous Tradeoff Between Risk and Incentives,” C. Prendergast (2002)

The traditional tradeoff in mechanism design is between incentivizing agents to take the right action when only output is observable (hence paying them based on stochastic output) and offloading risk that risk-averse agents don’t like (hence paying a fixed salary). This theory suggests that, all else equal, firms should be more likely to offer fixed salaries for jobs where output has greater variance. Empirically, however, the opposite seems to be true. The bank manager in Canada gets a salary, while the Wall Street investor gets a variable bonus. The restaurant manager in Chicago gets a salary, while the woman bringing McDonald’s to Cameroon gets bonus incentives. What can explain this?

Prendergast claims the difference lies in how easy it is for a manager to know what should be done. That is, let output of a given project be a function of effort and randomness, with only the distribution of the randomness known to the manager, but the exact parameter value known to the agent. Let there be a series of possible projects the agent could work on, and give her an arbitrary small personal preference, B(i), for working on one of them, all things equal. At cost I, the manager can measure agent’s effort. At cost Y, he can measure the agent’s output (where this “cost”, for instance, implicitly includes all distortionary effects of output-based contracts such as multitasking concerns).

If B(i)=0, then the principal can just measure the agent’s costs, pay C(e*) where e* is the efficient level of effort, and the agent with pick the project with the highest realized random parameter since he is indifferent among all of them. If B(i)>0 for some i, though, this will no longer work. In that case, the contract with the highest ex-ante expected utility for the principal is restrict the projects where the agent gets paid to those with the highest mean value of their random parameter.

What of output-based contracts? If output is monitored, since B(i) is arbitrarily small, the optimal piece-rate contract just pays the agent to work on the project with the highest first-order statistic of its random variable. So the relevant comparison when deciding whether to pay input-based contracts (roughly, salaries), or output-based contracts (roughly, piece rates) is to compare the expected first order statistic (the highest realization across the projects’ random components) minus the cost of output monitoring to the highest mean across the projects’ random components minus the cost of input monitoring. Since more “risky” projects have higher variance, the value of the output based contract is increasing in the variance of the projects. That is, you will see more bonus pay in risky environments than in non-risky ones.

A couple caveats. First, there is no risk in the model from the perspective of the agent, so all risk-sharing motives in contracts have been assumed away. The relevant “riskiness” is the riskiness observable by the econometrician. The basic point of the model goes through even if there is an idiosyncratic random component to project output that the agent does not know. Second, if you think that multitask concerns are particularly worrisome in environments like McDonald’s in Cameroon, where headquarters isn’t even sure which task the agent could work on, you might want to link the cost of monitoring output to the variance of the projects in an environment. Third, if you’re a pure theorist, the “proofs” in this paper will surprise you: there really aren’t any. What stands for proofs are a few worked out examples with specific statistical distributions. Basically, any mathematical complexity aside from project choice has been assumed away into parameters. This actually means that the ways that risk-sharing, or multitasking, or other normal contract worries can affect the problem have been assumed to have a very specific form, and as that specific form is not obvious at first glance, generalizing the model as you read is no trivial matter. That said, Prendergast’s paper is one of the most cited papers on contracting in the last decade, so perhaps this style isn’t so crazy after all.

http://faculty.fuqua.duke.edu/~qc2/BA532/2002%20JPE%20Prendergast.pdf (Final JPE version)