Accounting information, aggregation, and discriminant analysis

Aggregation is a pervasive theme in accounting. The preparation of financial statements involves extensive aggregation – information regarding several transactions is summarized using a few account balances. In this article, we study linear, double-entry aggregation rules. The level of aggregation (transactions versus account balance information) affects a decision maker's ability to discriminate between two entities. We show that the orientation of the discriminant function relative to the row space and the nullspace (two fundamental subspaces) of the double-entry matrix determines the information loss due to aggregation. In addition, we observe that an interdependency in account balances is introduced by the double-entry process. The cause and effect property (debit and credit) translates into a negative covariance being introduced among account balances; this, in turn, affects the decision maker's optimal use of information. Finally, in discussing benefits to aggregation, we present an example in which adopting a double-entry aggregation rule serves as a commitment device for the owner.