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

Abstract

The 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.

The impact of depreciation-type adjustments on the distribution of accounting earnings

“…See Willett (1988) and Gibbins and Willett (1997). The role of the variance in differentiating earnings distributions across alternative earnings functions is not considered in this paper due to the focus on the distributional form of earnings and the need to contain the length of the material.…”

“…A review of the theory and its applications is contained in Gibbins and Willett (1997). A brief but comprehensive report on computer experiments investigating these and other issues is to be found in Gibbins et al,(l998), which in addition contains a basic statement of the role of accounting numbers in economic models and theories.…”

“…The underlying and general concern of this literature, whether it employs methods based upon mathematical analysis, computer experiments, archival data analysis, case studies or historical and comparative research, is how it is possible to gain an improved knowledge of the technical measurement aspects of accounting numbers. Such knowledge is viewed as a prerequisite to a better understanding of their 'information value' (Milburn, 1994) and 'decision relevance' (Gibbins and Willett, 1997). …”

The Relationship Between Accounting Profit and Economic Income

“…A genuine or "true" surplus can only arise with an increase in the net amount of the money consideration of relevant transactions changing property rights of the entity. Transactions provide the fundamental measurements underpinning the general system for external financial reporting (Littleton, 1933;Paton and Littleton, 1940;Ijiri, 1967;Willett, 1987Willett, , 1988Salvary, 1992;Gibbins and Willett, 1997).…”

A Statistical Activity Cost Analysis of the Relationship Between Physical and Financial Aspects of Fixed Assets

“…In accounting, a rational framework which provides such an interpretation of costs is Statistical Activity Cost Analysis (SACA) due to Willett (1987Willett ( , 1988Willett ( , 1991 and extended by Gibbins & Willett (1997) and Falta & Wolff (2004). To date, applications of this framework to aspects of reliability theory, maintenance or life-cycle analysis have been limited (Falta, 2005).…”