Sensitivity, Precision, and Linear Aggregation of Signals for Performance Evaluation

TLDR

Managerial performance evaluation relies on multiple accounting and other signals, but aggregating them is necessary because reporting all basic transactions and nonfinancial information is costly and impracticable. The study seeks to determine the conditions on the joint density of signals that make linear aggregation optimal for performance evaluation. By focusing on linear aggregates, the authors derive invariant weights for each signal and interpret these weights through the signals’ sensitivity and precision in the joint distribution. The characterization shows that linear aggregation is optimal for a broad class of situations.

Abstract

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.