When Debit=Credit, The Balance Constraint in Bookkeeping, Its Causes and Consequences for Accounting

42 Pages Posted: 30 Jun 2020

See all articles by Sander Renes

Sander Renes

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); University of Mannheim - SFB 884 Political Economy of Reforms

Date Written: June 11, 2020

Abstract

This paper studies the balance constraint (debit=credit) in bookkeeping, its causes and its consequences for accounting. Balance in the ledger is shown to: 1) imply balance in journal entries and vice versa; 2) link the value definitions in the earnings statement and balance sheet; 3) have direct implications for valuation puzzles encountered in accounting, like accounting for OCI or stock-based compensation, and the difference between earnings or balance-sheet approaches to valuation. These system-wide effects on accounting highlight a design question: why do we have the balance constraint in bookkeeping? Backward-engineering shows 6 axioms that logically lead to double-entry bookkeeping. The balance constraint follows from the existence of a residual account: owner's equity. A class of equivalently powerful record keeping systems is shown to exist. These systems use double-entry bookkeeping without the monetary-unit assumption and can be used to record other outputs of the organization, like societal impact. These systems can be implemented in relational databases, a blockchain, or a different technology all together. The discussion covers links with other mathematical descriptions of bookkeeping and potential avenues for future research in the mathematics of bookkeeping.

Keywords: Axioms for bookkeeping, duality, bookkeeping system design, mathematics of record keeping

JEL Classification: M40, M49, Y80

Suggested Citation

Renes, Sander, When Debit=Credit, The Balance Constraint in Bookkeeping, Its Causes and Consequences for Accounting (June 11, 2020). Available at SSRN: https://ssrn.com/abstract=3624726 or http://dx.doi.org/10.2139/ssrn.3624726

Sander Renes (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

University of Mannheim - SFB 884 Political Economy of Reforms ( email )

L13, 17
Mannheim, 68131
Germany

HOME PAGE: http://www.sanderrenes.com

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