Economic Sufficiency and Statistical Sufficiency in the Aggregation of Accounting Signals - Amershi, Amin H.; Banker, Rajiv D.; Datar, Srikant M. (The Accounting Review, 1990)
[Management accountants are often required to construct measures of performance of individual managers by aggregating several accounting numbers (signals). We show that the same method of aggregation will rarely be used for evaluating the performance of different managers. Instead, the method of aggregation will vary with the specific preference functions of individual managers and the corresponding action choices induced by the owner. Such an optimal aggregate always exists but is not, in general, a sufficient statistic for the individual signals with respect to the agent's effort. We further show that, in most cases, using all the information in the sufficient statistic makes the principal strictly worse off. The analysis provides insights into a different statistical approach for evaluating nonsufficient aggregates based on the signal to noise ratio of the individual signals that are aggregated.]