New Light on Accrual, Aggregation and Allocation, Using an Axiomatic Analysis of Accounting Numbers' Fundamental and Statistical Character

he general nature of basic accounting measurement procedures is analysed from the perspective of their representational faithfulness rather than, as is normally nowadays done, from the perspective of relevance to user decision models. The character of accounting numbers is examined using an axiomatic framework based in statistical theory to demonstrate that statistical properties of the numbers are created by the process of preparing, constructing, the numbers. These properties, deriving from the process of constructing the numbers, are there regardless of the uses to which the numbers may be put, and therefore knowledge of them informs not only preparers of the numbers but also those who decide whether and how to disclose them to others, and those who make use of them for any purpose. The article argues, with axiomatic analysis and examples, that accounting numbers are statistics having properties such as distribution and variance that affect their usefulness in general and that may be examined separately from any use. Such an examination is helpful partly because it then avoids confounding the understanding of accounting measures' technical nature with issues of disclosure choice and use. The necessary axiomatic framework is presented briefly to establish its perspective on measurement questions, then the value of the framework for examining vexing accounting issues is illustrated with examinations of accrual accounting and matching, cross-sectional and time-series allocation, and accounting-relevant market values.