This paper has provided both an analytical solution and a simple approximation method for producing near-optimal audit strategies in a strategic audit setting with some inherently honest auditees and a pre-announced strategy.
6.1. Segmentation strategy
Segmentation of the auditee population should be used whenever adequate data is available. Segmentation has the effect that high fraud segments will be audited at the critical audit level 1/(1 + π), whereas the low fraud segment will be left unaudited.
Segmentation preferably can be combined with the use of an information strategy in which the auditor announces the audit strategy with sufficient notice for the auditee to incorporate this information into his/her fraud decision. In Appelgren (2017), the population was split into two segments, a smaller high-risk segment with about 17% fraudulent persons and a larger segment with about 8% fraudsters. The sequential game simulation model was applied on both segments as well as on the total population. As expected, segmentation resulted in a lower total cost.
6.2. All auditees potentially dishonest versus some inherently honest auditees
The cases with all dishonest auditees (AN and AP) are included here mainly for historical reasons. They are less realistic since they generate much higher levels of fraud compared to what is observed empirically, as noted by Erard and Feinstein (1994a). Therefore, we have concentrated on the cases with some honest auditees (HN and HP).
With the introduction of a social penalty motivating some auditees to abstain from fraud, new models with all potentially dishonest auditees may become more attractive.
6.3. Non-announced strategy versus pre-announced strategy
There are numerous situations where a pre-announced strategy is not feasible. In audits of financial statements, it seems unlikely that an auditor would want to declare an audit strategy in advance. This explains the extensive use of non-announced strategies in the strategic audit literature in the accounting field. There may also be regulatory restrictions or professional standards that prevent auditors from pre-announcing the audit strategy. The discussion below is therefore limited to situations where pre-announced strategies are possible.
In some papers from the accounting literature, prior distributions of important variables are assumed to be known, for instance in Shibano (1990, page 116), Matsumura and Tucker (1992, page 755), Bloomfield (1995, pages 72–73), and Caplan (1999, page 105). The assumption of such distributions means that there is a population of auditees from which such distributions can be measured, unless it is stated that those distributions are subjectively assessed by the auditor, as in Newman et al. (2001).
The existence of such populations seems more likely for some types of audits, such as expense account auditing in large organizations, than for other audit types, such as financial statement audits. When such populations exist, it is advantageous to use pre-announced audit strategies if they are permitted.
The strategies studied in this paper are based on utility-maximizing auditees. There are arguments for and against modelling pre-announced audit strategies in this setting. An argument for a pre-announced strategy is the general result that the utility for the first player in a sequential game with perfect information is higher or equal to the utility of the same player in a simultaneous-move game. An argument against pre-announced strategies is that auditors may be unwilling to disclose their audit strategy since they feel that this would provide the auditees with too much information. This may be especially true in cases where the perception of the auditees is that the audit density is higher than the actual level. Therefore, models of pre-announced strategies may have limited external validity. It is probable, however, that productive results can be obtained by informing the auditees of the general shape of the audit rate function, such as “the audits will be concentrated on taxpayers declaring the lowest incomes” or “the audits will be concentrated on auditees claiming the highest claim amounts.”
6.4. Analytical solution versus simulation method
In the pre-announced strategy case, the simulation model is a straightforward method that generates near-optimal audit strategies. Variations of the model are easily implemented, for instance with auditees having concave utility functions, with partially discrete distributions of the true value of the control variable, and with a mix of fraud and errors.
A prerequisite for all models described in this paper is that the probability distribution of the true value of the control variable is known. Since the accuracy of an empirically-derived distribution is limited, there is no need for very accurate calculations of optimal audit rate functions, supporting the use of a simple method generating near-optimal solutions.
The results from the tax audit example in Section 5.2 indicate that the simple two-parameter approach is only marginally inferior to the more complex model with three or four parameters. This is not necessarily true for all true-income distributions.
6.5. Social penalty
A disadvantage with the sequential game model as well as with the Erard and Feinstein model is that dishonest auditees will always cheat, i.e., there is no set of parameters that will induce the auditee to abstain from fraud. This is due to the penalty being proportional to the fraud amount in the model. In line with Alm (2013), future research should include the construction of models where the proportion of honest taxpayers is calculated endogenously, possibly with the introduction of a social penalty that is not strictly proportional to the fraud amount.
Social penalty can be introduced as a deterministic or stochastic variable, dependent or independent of the fraud amount, which is added when fraud is detected. It has the effect that an auditee may abstain from fraud, in contrast to the models where the share of potentially fraudulent auditees is determined exogenously. Thus, the introduction of an endogenous social penalty can replace the exogenous assumption of some inherently honest auditees. An example of social penalty is found in Dionne et al. (2009), which introduces a moral cost with a known probability distribution.
In addition to the introduction of a social penalty, Alm (2013) also promoted the development of models which consider group behaviour.