3.3 Case II: No Fraud is Detected in Period One
3.3.6 Client Opinion Shopping versus Incumbent Resignation
Comparison across Cases
The preceding results show that for high auditor-client pre-alignments an auditor switch is always more likely to occur due to opinion shopping, both after a clean no
fraud report and a qualified fraud report, while the contrary holds for low auditor-client pre-alignments. The actual thresholds for this expected behavior will, however, depend on the specific parameter values, and not much can be said from the preceding analysis as to how the two cases compare.
It would, therefore, be o f interest to determine how these upper and lower bounds compare across the two cases, and if for any given set of parameter values opinion shopping is more likely to occur after a fraud report than after a no-fraud report.
This would be consistent with empirical studies that have found a positive association between a client’s propensity to switch auditors and the receipt of a qualified report.
See, for example, Chow and Rice [1982], and Sarhan et al. [1991].
Proposition 3.9 states that the probability of observing an auditor switch due to client opinion shopping after a qualified (fraud) report is always greater than after a clean (no-fraud) report, for any set of parameter values for which an auditor switch be feasible in both cases.
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Proposition 3.9: For any combination o f parameter values
<Q,9,Y\,and y2, such that y 2 > Y 2>and y2 > Y 2, we have that:
P r (a s |D FI ,y2 > Z 2)> Pr(05|£)NF^'Yi > Y l )
This result is consistent with our intuition regarding the causes that trigger client opinion shopping, and that ultimately lead to auditor replacement. Causes for opinion shopping are commonly associated with some form of auditor-client disagreement over an accounting matter, a going concern opinion or a qualified report.67
There will exist many cases where a specific combination of parameter values results in a situation where a switch is only feasible in one o f the two cases, which implies that the above result is not applicable. In these situations, a comparison across cases is meaningless. Such cases will, however, have an effect on the overall frequency of expected auditor switches in each of the two scenarios.
The result of Proposition 3.9, that client opinion shopping is more likely to occur after a qualified fraud report than after a clean no-fraud report, will play an important role in determining the desirability and efficiency o f retention and rotation rules.
Proposition 3.10 states that precisely the opposite holds for low type incumbent resignations. That is, the probability of observing an auditor switch due to a low type incumbent resignation after a clean (no-fraud) report is always greater than after a
67 See, for example, Chow and Rice [1982], Sarhan et al. [1991], and Matsumura et al. [1994],
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qualified (no-fraud) report, for any set o f parameter values for which an auditor switch be feasible in both cases.
Proposition 3.10: For any combination o f param eter values co, 9, yx, and y 2, such that y 2 > y , and y 2 >yz,we have that:
Pr(/Z?|Z)JVF | , y 2 > y 2) > Pt(zr|z)f j , y 2 > yz)
Propositions 3.9 and 3.10 together suggest that client opinion shopping will occur with more frequency after a qualified fraud report, while low type incumbent resignation with more frequency after a clean no-fraud report. The comparisons made in Propositions 3.9 and 3.10 are only meaningful for parameter values such that an auditor switch will take place both after a fraud and a no fraud report. That is, when y 2 > y^ and y 2 > y 2. For any other combination of parameter values, auditor switches will either never occur or they will occur only after one of the two cases.
The different possibilities of observing auditor switches are represented schematically in Figure 3.4.
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Scenario 4
Switches are observed in equilibrium.
Low type incumbents resign both after detecting fraud and after not detecting fraud, which allows fraudulent clients to always engage in
opinion shopping and replace a high type incumbent.
Scenario 2
Auditor switches observed only after a no fraud report Low type incumbents resign, and fraudulent clients engage in opinion shopping if incumbent is high type.
&(®)
Scenario 3
Scenario 1
No switches will be observed in equilibrium. Low type incumbents never resign which precludes fraudulent clients from engaging in
opinion shopping.
(0
Auditor switches observed only
after a fraud report Low type incumbents
resign, and fraudulent clients engage in
opinion shopping if incumbent is high type.
Figure 3.4: Auditor switch scenarios
It has also been determined that auditor-client pre-alignment plays a key role in determining the most probable cause o f auditor switches in both cases. It can be shown that the pre-alignment thresholds Q)1 ,a jl ,Q)11, and W '1, compare as follows:
0) ' < a)11, and Ho1 < aj!/, with G)/l > W ! being feasible.
The implication that a " > W is feasible, is that for given parameter values, and in particular for “high” auditor-client pre-alignments, it is feasible that a low type resignation be the most probable cause of an auditor switch should no-fraud be detected even when client opinion shopping would be the most probable cause should fraud be
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detected. That is, the notion o f a “high” auditor-client pre-alignment may have different meaning in both cases.
This difference can be seen schematically when comparing Figures 3.2 and 3.3, which are reproduced below as Figure 3.5.
Figure 3.5: Comparison o f Figures 3.2 and 3.3
In the next section, mandatory retention and rotation rules are introduced into the analysis. I will explore possible reasons for adoption o f these rules, what effects they have on the overall fraud detection probability and under what conditions these rules are efficient.
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3.4 Mandatory Rotation and Retention Rules
In this section, mandatory rotation and retention rules are imposed on client firms and auditors. Without these rules, auditors and clients follow the first and second period engagement behavior described in the preceding sections, which will be referred to in the rest o f this chapter as the deregulated audit market.
Mandatory rotation and retention rules are two forms of regulation that impose time limits on the auditor-client engagement. These two forms o f regulation are, however, quite different both in terms of the engagement limitations they impose, and in the nature of the alleged problem they try to solve. Typically either mandatory auditor rotation rules or mandatory auditor retention rules are suggested or imposed, but a few countries have passed regulation where both rules coexist.
A brief overview o f these rules and their implications follows.