Introduction
It is perhaps little known that accounting and mathematics have been connected for
more than 500 years ago. In 1494, Luca Pacioli published his mathematics compendium
Summa de Arithmetica, Geometria, Proportioni et Proportionalita consisting of
615 pages. “[T]he only significant part of the book that has ever been translated to
English” was the 27-page treatise on bookkeeping, which defines the hour of birth
of accounting. So to speak the study of double entry accounting was developed in
concert with linear algebra. Beyond the joint development, which becomes apparent
in Pacioli’s book, there are several reasons why accounting offers a very good
application for mathematical techniques and mathematical knowledge. First, accounting
phenomena cannot be understood best by just observing them. For generating
predictions and interpretations [analytical] theory is required.Second, formalizing
economic arguments by means of a mathematical model results in a more rigorous
presentation. With accounting and auditing becoming international, it is more important
than ever to have a common ground for discussion that is not hampered by any
language barriers. This common ground is provided by mathematical and analytical
methods, like agency theory or game theory. Third, accounting and auditing are
highly regulated by national and international standards. If standard setting processes
comprise strategic behavior by and strategic interactions (in the sense of game theory)
between companies, investors and auditors then our analysis of these interactions may
benefit from game theoretical models. More generally, accounting theory cannot only
rely on normative standards.
The objective of this special issue of OR Spectrum is to emphasize the impacts
of accounting and auditing regimes on the behavior of rational agents acting in this
environment. The set of papers presented here covers auditing, financial accounting,
managerial accounting, and tax accounting highlighting the importance of strategic
behavior in all these sub-disciplines of accounting.
2 Auditing—audit regulation and auditor reputation
The first paper, authored by Wuchun Chi, contributes to audit regulation theory. It
analyzes the impacts of mandatory auditor rotation on the possibility of collusion
between manager and auditor. The advantage of changing the audit company after a
pre-specified period of time is to avoid familiarity between the client and the auditor.
The disadvantage is that gains resulting from learning effects are lost. Whether
the net-effect is positive or negative is unclear. In this context, analytical modeling is
applied for two reasons: First, the standard-oriented, normative debate left unnoticed
certain drawbacks of mandatory audit regulation. Second, only very few countries
implemented mandatory audit rotation, implying that empirical data is lacking. Thus,
modeling is the most adequate way of gaining deeper insights. The model compares
the optimal audit committee investigation strategy and the optimal audit fees in a rotation
and a non-rotation regime. The author concludes that under a rotation-regime the
audit committee adopts a more aggressive investigation strategy, i.e. more effort is
provided. Further, audit fees will be higher compared with a non-rotation regime.
The paper by Jochen Bigus is the second paper contributing to audit regulation.
Here, auditor liability’s interaction with potential reputation losses and overcompensation
is analyzed. The paper distinguishes between (individual) economic losses and
social losses showing that even in the absence of punitive damages, i.e. only the real
economic loss is compensated, reputation and overcompensation induce an excessive
care level provided by the auditor, i.e., the audit effort exceeds the overall optimum.
However, this effect can be alleviated by a properly defined liability cap. Interestingly,
standard setters started discussing to abandon liability caps a few years ago, but have
only been able to agree that limited liability has beneficial effects.
3 Incentive effects of corporate governance and financial accounting
If auditing is seen as a corporate governance device, then the paper by Thorsten
Döscher and Gunther Friedl bridges the gap between the audit papers presented above
and the following contributions from financial accounting. Assuming that the board
of directors has a major influence on managerial compensation, the authors investigate
the question whether CEOs have the power to influence both level and structure
of their own compensation directly or indirectly. For this purpose, a principal-agent
model is designed, where the shareholders as principal contract both the board of
directors and the CEO. The latter can influence the firm value by spending individual
effort, whereas the former tries to learn about the manager’s ability. By doing
so, the board helps in adjusting the compensation parameters more properly. By initiating
collusive behavior, the CEO has the opportunity to influence the board by
persuading the board not to convey this information. As expected, shareholders adjust
the optimal contracts to prevent the agents from colluding. In contrast to conventional
wisdom, this may cause a highly skilled manager’s compensation to decrease
in equilibrium.
In analytical models, accounting is often interpreted as an information device,
providing performance measures for contracting purposes. However, the appropriateness
of accounting data might change with the set of available information
sources. This is why a partial equilibrium view of the world might generate misleading
results. The paper by Mirko Heinle and Christian Hofmann builds upon
this effect when investigating the consequences of publicly reported soft information
from a contracting perspective. They present a model where the set of
performance measures which is observable to investors is changed in the compared
settings. Accordingly, aggregation of information in prices is altered, inducing
different optimal incentive rates and different payoffs to the principal. If soft
information is available to investors, a less congruent market price can result,
leading to inefficient effort allocations of the agent and leaving the principal
worse-off.
A similar problem is modeled by Anja De Waegenaere and Jacco Wielhouwer.
They consider a principal-agent setting where the manager selects an accounting
method from a set of accounting options. Hence, the manager directly influences his
performance measure. Focusing on the degree of discretion, the paper demonstrates
that the minimum degree of discretion may be necessary for contracting. This is an
interesting result, because negotiation theory suggests that enlarging the negotiation
space should simplify the contracting. However, the argument presented here works
slightly different: With a sufficiently small degree of reporting flexibility, incentive
problems are mitigated, allowing for lower bonus payments and leaving the principal
better off. With a sufficiently high level of accounting flexibility, incentive problems
are increased, but compensation risk is decreased, implying that the net-effect
on the principal’s payoff is unclear. Introducing limited liability the manager’s payoff
always improves, but the principal only benefits, if accounting choices are limited.