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“Accounting Theory as a Bayesian Discipline”

David Johnstone writes:

The Bayesian logic of probability, evidence and decision is the presumed rule of reasoning in analytical models of accounting disclosure. Any rational explication of the decades-old accounting notions of “information content”, “value relevance”, “decision useful”, and possibly conservatism, is inevitably Bayesian. By raising some of the probability principles, paradoxes and surprises in Bayesian theory, intuition in accounting theory about information, and its value, can be tested and enhanced. Of all the branches of the social sciences, accounting information theory begs Bayesian insights. This monograph lays out the main logical constructs and principles of Bayesianism, and relates them to important contributions in the theoretical accounting literature. The approach taken is essentially “old-fashioned” normative statistics, building on the expositions of Demski, Ijiri, Feltham and other early accounting theorists who brought Bayesian theory to accounting theory. Some history of this nexus, and the role of business schools in the development of Bayesian statistics in the 1950–1970s, is described. Later developments in accounting, especially noisy rational expectations models under which the information reported by firms is endogenous, rather than unaffected or “drawn from nature”, make the task of Bayesian inference more difficult yet no different in principle. The information user must still revise beliefs based on what is reported. The extra complexity is that users must allow for the firm’s perceived disclosure motives and other relevant background knowledge in their Bayesian models. A known strength of Bayesian modelling is that subjective considerations are admitted and formally incorporated. Allowances for perceived self-interest or biased reporting, along with any other apparent signal defects or “information uncertainty”, are part and parcel of Bayesian information theory.

I don’t know anything about accounting, except that I used to have a convenient approach to doing my taxes where every one in awhile I’d send the IRS a check, based on my guess of what I owed them. They’d keep track of things so that each year my tax bill would account for my payments. Once I didn’t send them enough and they fined me something like $50.

In any case, it makes sense to me that uncertainty should be considered fundamental to accounting. I’ve always thought of accounting as arithmetic, but real-world accounting is full of uncertainty and combination of different sources of information, so, yeah, Bayes.

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