On the Prudence of Rewarding A While Hoping for B

In multiple-task hidden-action models, the (mis-)allocation of effort may play an important role for benefit creation. Signals which capture this benefit and which are used in incentive schemes should thus not only be judged by the noise and the associated costs but also by the mis-allocation which they induce. How can mis-allocation be measured? This article presents two requirements for such a measure (invariance and monotonicity) and analyses whether they are met by proposed measures of mis-allocation. All examined measures assert that an unbiased signal for benefit leads to the lowest mis-allocation. Here, the signal leading to the lowest mis-allocation is computed and shown to be unbiased for the benefit only under restrictive assumptions on the cost function (equal marginal costs for different tasks). Generally, using an unbiased signal does not imply the lowest mis-allocation.