Accounting information, aggregation, and discriminant analysis

Aggregation is a pervasive theme in accounting. The preparation of financia l statements involves extensive aggregation-information regarding several t ransactions is summarized using a few account balances. In this article, we study Linear, double-entry aggregation rules. The level of aggregation (tr ansactions versus account balance information) affects a decision maker's a bility to discriminate between two entities. We show Brat the orientation o f the discriminant function relative to the row space and the nullspace (tw o fundamental subspaces) of the double-entry matrix determines the informat ion loss due to aggregation. In addition, we observe that an interdependenc y in account balances is introduced by the double-entry process. The cause and effect property (debit and credit) translates into a negative covarianc e being introduced among account balances; this, in turn, affects the decis ion maker's optimal use of information. Finally, in discussing benefits to aggregation, we present an example in which adopting a double-entry aggrega tion rule serves as a commitment device for the owner.