On the Equivalence of General and Specific Control in Organizations

Abstract

Most principal-agent relationships in firms are multidimensional. In the presence of multiple tasks and multiple performance signals, the contract between principal and agent not only has to motivate the agent, but also has to direct the agent to allocate effort among different tasks. The value of efforts for a specific task accrues not only through the principal's expected returns, but also through its contribution to overall risk, and therefore to the risk diversification of the task portfolio. Hence, if the agent is risk-averse, multitask relationships can be considered as a portfolio problem coupled with incentive constraints. We examine the relationship between specific control (SC) and general control (GC) for multitask principal-agent problems. Under SC, the principal observes the outcome of each individual task and uses this set of information for compensation. Under GC, contracts are based only on the aggregate signal, such as cumulative profits of all tasks. We describe two sets of multitask problems for which GC and SC are equivalent. That is, contracts based only on aggregate performance signals impose the same incentives for the agent as a contract that is based on the outcome of each task. The first multitask problem is characterized by homogeneous tasks. In the second multitask problem, all activities are perfect substitutes in the cost function of the agent. The equivalence of SC and GC arises since GC provides insurance to the agent and yields the same overall risk premium as specific control. Moreover, GC allows the principal to set the same incentives as SC, since the marginal returns from GC are equal to the sum of the marginal returns for each task under SC. The results described in this paper can serve as benchmarks where GC and SC are equivalent. We show how the equivalence can be relevant for a variety of business situations, such as the compensation of sales persons or managers at all hierarchy levels. We also discuss the reasons when GC and SC differ. Suppose, for instance, that tasks are technologically separable and the precision of the performance of one task is low. Then, the principal is forced under GC to adopt an incentive scheme that implements only a low effort across all tasks since the average precision matters. Under SC, however, the principal can tailor the optimal efforts to each task.