Sensitivity, Precision, and Linear Aggregation of Signals for Performance Evaluation
研究如何将多个会计及其他信号线性加总为经理人绩效评价指标，并找出该线性加总方式最优的条件，帮助理解最优线性指标中各信号的权重如何由信号的敏感性和精确性决定。
Several accounting and other signals are generally available for the construction of a managerial performance evaluation measure on which an optimal compensation contract is based. The demand for aggregation in evaluating managerial performance arises because reporting all the basic transactions and other nonfinancial information about performance is costly and impracticable (see Ashton [1982], Casey [1978], and Holmstrom and Milgrom [1987]). We identify necessary and sufficient conditions on the joint density function of the signals under which linear aggregation, a simple and commonly employed way to construct a performance evaluation measure, is optimal. This characterization suggests that the linear form of aggregation is optimal for a large class of situations. Focusing on performance measures that are linear aggregates enables us to determine the relative weights on the individual signals in the optimal linear aggregate, since these weights are invariant for all realizations of the signals. We interpret these weights in terms of statistical characteristics (sensitivity and precision) of the joint distribution of the signals.