Task Difficulty,Performance Measure Characteristicsand the Trade-Off betweenInsurance and Well-Allocated Effort

When designing incentives for a manager, the trade-off between insuranceand a “good” allocation of effort across various tasks is oftenidentified with a trade-off between the responsiveness (sensitivity, precision,signal-noise ratio) of the performance measure and its similarity(congruity, congruence) to the benefit of the manager’s employer. Anecessary condition for the trade-off between responsiveness and similarityto be meaningful is that a perfectly congruent measure createsa higher benefit than an equally responsive non-congruent measure.We show that this condition is met if and only if all tasks are exactlyequally difficult and there are no spill-overs or synergies across tasks.This means that for most practical purposes, notions of responsivenessand similarity are not informative about the tradeoff betweeninsurance and allocation. In order to understand this trade-off, taskdifficulty has also to be taken into account.....