gietzmann and sen - 2002 - improving auditor independence through selective mandatory rotation [mar]

International Journal of Auditing Int. J. Audit. 6: 183-210 (2002) Received 2001 ISSN 1090–6738 Revised September 2001 Copyright © 2002 Management Audit Ltd. Accepted March 2002 Improving Auditor Independence Through Selective Mandatory Rotation Miles B. Gietzmann 1 *, Pradyot K. Sen 2 1 Department of Economics, University of Bristol, UK 2 Department of Accounting and Information Systems, University of Cincinnati, US When an auditor receives signicant fee income from one client it has often been suggested that reappointment concerns may dilute auditors incentives to maintain independence from management. A possible response to this issue could be to mandate the rotation of auditors. However this is costly since new auditors must repeatedly invest in learning a new clients accounting system. In this research we build a model to formally analyze this trade-off. We nd that the desirability of rotation depends critically upon characteristics of the audit market structure and to what extent an individual client dominates an auditors’ client portfolio dened in terms of total fees. We show that although rotation is costly, in audit markets with relatively few large clients (thin markets), the resulting improved incentives for independence outweigh the associated costs. Our research is timely because although historically it may not have been economically desirable to adopt mandatory rotation, currently with increased corporate merger activity taking place, for instance in the oil sector, markets may now have become sufciently thin to warrant the introduction of rotation. Key words: Auditor rotation, auditor independence, dominant client, multi-period game, sequential equilibrium. Correspondence to: Department of Economics, University of Bristol, 8 Woodlands Road, Bristol, BS8 1TN. E-mail: m.gietzmann@bristol.ac.uk SUMMARY A number of commentators on auditor rotation often quote the US report of the Quality Control Committee of the Securities and Exchange Commission (SEC) Practices section of the AICPA (1992). The study concluded that the frequency of audit failure was three times greater after the rst or second periodic audit than in successive periods. An additional inference from the study is that whether or not the auditor changes, defalcations going undetected are more likely in early years. The study has been used by some commentators to conclude that mandatory rotation is therefore more likely to expose the nancial community to more ‘new auditor ’ failures and hence on 184 M. B. Gietzmann and P. K. Sen Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) grounds of efciency and effectiveness should not be adopted. We question attempts to draw such conclusions on the basis of the AICPA report for the following reasons. It is our understanding that none of the sample rms in the US study changed their auditor in a systematic fashion as would be the case under a condition of mandatory rotation. Therefore, the audit failures occurred in rms where auditors were changed in the prior period for some non- legislative (non-mandatory) reason. The extant audit literature, see for example Teoh (1992) would suggest that at least some of these changes were motivated by weaker firms conducting opionion shopping or auditors dropping their high risk clients. For instance, it is conceivable that the reason there were increased failures in the early years is because the previously incumbent auditor recognized serious problems with the client (such as the going concern assumption) or, the observation of auditor change simply indicates audit rms removing the perceived ‘lemons’ from their portfolio. That is, the increased failure rate may not simply be the result of new auditor failures per se, but instead also the result of previous incumbents lack of desire to stay with certain risky clients. With these issues in mind we develop a model of auditor rotation which focuses upon the economic trade-offs facing auditors. We focus upon the incentives for a new auditor to provide sufcient effort to understand a client and the incentives for an incumbent auditor to be inuenced by reappointment concerns. We then define a set of circumstances which are supportive for the case for mandatory rotation. 1. INTRODUCTION ‘Another suggestion contained in the European Union’s Fifth Directive was that there should be an upper limit on the number of years for which an accounting rm could act as auditors to any given company. After a maximum of ve years, the company would have to find another auditor. This would mean the auditor would not have to worry about the effects of upsetting the directors because he would know he was going to be replaced after ve years anyway This proposal was also considered unacceptable by the accountancy profession on the grounds of time and cost. It could also be argued that an auditor is more likely to miss something during the early years of an appointment when he is relatively unfamiliar with the client. The proposal was certainly unpopular, although is not totally unworkable. In Italy, for example, an auditor cannot serve the same client for more than nine years. After this period has elapsed, he cannot be reappointed by the company for at least ve years.’ (Dunn pp.32, (1991)). ‘Independence is of paramount importance to the effectiveness of the audit function. Representatives of regulatory agencies, as well as critics of the public accounting profession and ineffective corporate governance, have questioned whether private sector auditors are sufciently independent of their clients in fact and appearance. To insure independence in Canada, among other controls, (1) the regulators may review the public accountants’ working papers and (2) two outside auditors are required to share responsibility for the audit with one of the two being rotated every two years.’ US GAO/AFMD-91-43 p48-49. A recent report by the Maastricht Accounting and Auditing Research Center (Buijink et al. (1996)) illustrated that within Europe, there exists a rich set of regulatory control mechanisms for auditors. This is in contrast to North America where the literature has predominantly focused upon auditors’ legal liability exposure (Nagarajan (1994), Balachandran (1993)), looking at whether the liability levels of US auditors may have become problematic in recent times. One of the principal research ndings of this paper is to argue that given structural changes in the market for audit services, it may now be benecial for another regulatory instrument (mandatory auditor rotation) to be given simultaneous consideration along with legal liability. Specically, consistent with informal arguments (Shank 1979, DeAngelo 1981a,b,) we establish that in audit markets with relatively few new client opportunities (thin markets), the application of rotation is economically desirable since the improved incentives for independence outweigh the additional cost associated with understanding a new client’s auditing system upon rotation. The simple intuition for this result is that when one client forms a signicant element of total fee income for an auditor, the auditor becomes more susceptible to managerial influence, endangering maintenance of Improving Auditor Independence Through Selective Mandatory Rotation 185 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) independence. Thus, in our view, the problem of auditor independence is not a systematic auditor-specic problem, rather it is embedded in the incentives of the specic auditor-client relationship and the entire audit market structure. If only liability levels are used to ensure independence, the best auditors which maintain independence, but which sometimes fail (for other reasons) face greater liability than is required to maintain their independence. Thus, under some circumstances, even the better auditors may prefer mandatory rotation if it led to a lower legal liability. Furthermore, we note that auditor rotation is used in a number of countries and these countries have lower legal liabilities for auditors 1 . For instance in Italy mandatory rotation exists for stock exchange listed companies and in Belgium and Canada for banks. In each of these cases it seems reasonable to argue that the audit markets could be characterized as thin 2 . In situations where independence is a concern, one possible alternative to rotation, would be to further increase the legal liability of the auditors. However, it is only recently that legislators in the US have enacted the Private Securities Litigation Reform Act 1995, which lowers the liability regime of auditors. This suggests that proposing increases in liability to further improve independence may not be constructive at this time. Instead, after the application of mandatory rotation in certain well defined situations, we show that auditors’ liability could in fact be further lowered without compromising independence, or increasing the cost to the client, while at the same time retaining sufcient incentives for better auditors to invest in learning costs for new clients. Our analysis provides a basic framework within which to better understand the performance of mandatory rotation so that its efcacy can be appraised relative to other policy instruments such as rotation of audit partners within partnerships and the use of audit committees to monitor the auditors to improve auditor independence. The paper is organized as follows. In Section 2 we characterize a representative client rm’s investment project that is subject to audit. Then we present a characterization of audit technology, along with managerial and auditor incentives. We characterize information processing in the dynamic setting and provide the equilibrium concepts used for our analysis. We, then analyze the case of period by period mandatory rotation in Section 3. In Section 4, we analyze the two-period audit game that represents a non-rotational regime and characterize the equilibria. Our main results are contained in Section 5. We establish that if audit markets are thin, independence can be maintained with a lower level of legal liability under mandatory rotation than when rotation is not mandated. The intuition here is that in thin markets without rotation, auditors’ reappointment concerns are so strong that liability levels need to be signicant to maintain independence. In contrast, in more developed audit markets with many potential new clients, auditors’ potential gains from maintaining a reputation for independence outweigh the gains from reappointment with a specific client. Exploiting this incentive, regulators can reduce liability, relying on auditors’ self-interested concern to maintain independence. Our results, therefore, arise because in a sufciently thin market, self-interested reputation concerns are muted by the fact that there are relatively few new clients and that opportunities to replace the existing client base are limited no matter how good an auditor’s reputation. In such a setting without mandatory rotation, the legal liabilities must not only balance the cost of effort, it must also balance the auditors’ compromising incentives associated with the loss of current business, lest the report becomes unfavorable. Indeed, if overall liability reduction is deemed to be desirable from a societal perspective, mandatory rotation is clearly benecial where the market for audit services is dominated by a few large clients who are solicited by all the audit firms. In Section 6 we outline some empirical evidence from countries where auditor rotation is in effect and discuss regulators current policy debate on mandatory auditor rotation in Section 7. We present our concluding comments in Section 8. 2. THE AUDIT GAME: A STOCHASTIC INVESTMENT PROJECT AND STRATEGIC INCENTIVES In the following subsections we develop our model of the audit game using standard game theoretic constructs which help us understand how the strategic behavior of an auditor is 186 M. B. Gietzmann and P. K. Sen Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) determined. However, before presenting the formal modelling assumptions we shall set out some of the conceptual limitations of this economic approach. We argue that although the model makes somewhat simple assumptions about the motivation of auditors, the derived model provides us with predictions which allow us to clearly identify regulatory implications under one polar extreme assumption about self- interested selfish auditors. That is while ultimately research needs to be conducted to capture more complex auditor behavior, the results with the simplied assumptions need to be established so that one can then see how sensitive they are to subsequent behavioral modications. Modelling the auditor as an economic agent In the following model we shall assume that auditors’ desire to maintain independence is determined by economic forces such as present and future fee income. However, it has sometimes been argued that some auditors lack independence for no apparent economic reasons and that conversely some other auditors have historically made signicant nancial sacrices to maintain independence. Obviously there is a complex mix of economic, pschological and other reasons why an auditor behaves in a particular fashion and hence our model should be seen as a polar extreme which simply concentrates on economic factors. While admitting therefore that the model only captures part of the setting in which auditors actually operate, we think it is also important to stress that with the increasing size, internationaliza- tion and commoditization of auditing, economic factors have become increasingly important to auditors working in the eld. In fact some would argue that it is the dominant factor. Indeed, factors such as fee income and repeat business have become increasingly applied in internal performance appraisal when auditors look to be promoted within an audit partnership. Thus given this increasing use of such economic performance measures at every stage of the promotion and renumeration phases of an auditor’s career, it is hard to defend any assumption that such economic factors are of minor importance 3 . Another concern reects whether an auditor’s desire to maintain independence is a fixed binary choice or determined more on a case by case basis related to economic factors. That is, is an auditor always independent no matter how important the client is, or could the auditor consider compromising his or her independence only if a client was ‘sufciently’ important. We try to address this complex issue by developing a model of implicit collusion in which an auditor does not simply flip from being totally independent to alternatively conspiring with a client to hide information once some critical economic cutoff is reached. Instead in our model the auditor switches from diligently looking for defalcation to not looking so hard for defalcation. However, if it is found in the latter case it is immediatedly acted upon. That is we do not assume that auditors switch from being completly independent to completly non independent but instead that at the margin they simply don’t try as hard when they are under increasing nancial pressure. Finally it is sometimes argued that a (fee) size based metric for independence is problematic. One possible reason for this is that taking the economic model to its extreme it should be client assignment protability that is the driving force, not fee, since some large assignments may be so complex and labour intensive that the assignment is not as protable as a medium sized niche sector assignment. However, while recognizing that this is a limitation of the model, basing the model on assignment protability will severly limit empirical testability since such profitability is not disclosed. Moreover, the magnitude of client by client fees is often seen as a good proxy for the ability of an audit partnership to sell on lucrative consulting services such as management consulting and taxation advice. Thus while it is true to say that size alone does not soley determine an auditor’s incentives to maintain independence it is an important factor 4 . Thus given these important caveats let us now turn to the formal model specication. We assume there are three risk-neutral players in the game; an owner (shareholder), manager and an (external) auditor. The owner has an investment project which the manager oversees (manages) on a day-to-day basis. Since some auditors need to invest in client-relation specic skills that augment their audit technology Improving Auditor Independence Through Selective Mandatory Rotation 187 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) (outlined below), we shall forthwith describe the owners’ investment project simply as ‘the project’ and reserve ‘investment’ for the auditor’s technological investment required to understand the accounting system of a specic client. The essential strategic interaction in the game is as follows. We assume that a conict of interest exists between the manager and the owner because the manager is an empire builder 5 who wants the project always to continue and the owner only wants the project to continue, if it is expected to be protable. Given the stochastic nature of the project and the owners awareness of the managers’ incentives, the owner may nd it valuable to employ an independent auditor to attest 6 the ‘state’ of the project. However, the independence of the auditor may be compromised since economic incentives exist such that the auditor may also prefer the project to continue and be reappointed as the auditor again. That is, rather than suggest that the auditor would ever collude directly with management, we propose a model in which the auditor simply may not ‘try too hard’ to nd evidence which casts the project in a negative light; which we describe as implicit collusion by the auditor. Thus in our model setting 7 we dene an auditor as maintaining independence as an auditor that does not implicitly collude. The formal analysis is presented as follows. In the rst subsection we shall concentrate only upon the nature of the project, temporarily assuming that the manager is non selsh and carries out duties purely in the interests of the owner. In the second subsection we will relax the naive incentives assumption and focus upon the economic incentives of management and auditors and how self interest may lead them to behave strategically in their own interests resulting in non-maintenance of independence by the auditor. The project We shall assume the project can be classied as intrinsically either a good, g project or a bad, b project, and at the beginning of the game the owner assumes that the (unconditional) probability that the project is good is p(g) (bad with probability (1-p(g))). We shall assume that the project has just generated an annual return of Y and at issue is whether to continue with the investment project or liquidate it and also whether to continue with the incumbent auditor or not. If the state of the project were good, it will generate an annual return of Y for the next two periods 8 , which has a net present value (to the owner) of V g . If the project were bad it would generate an annual return Y each period if it remained in progress. However, in every period, there is a probability w that it will suffer nancial distress 9 and this is evaluated by the owner as having an expected net present value of V b . We further assume that all period project state realizations are independent. That is: Y Y V g = Y + ––––– + –––––– 1 + r (1 + r) 2 ’ and 1 – w 1 – w 2 V b = Y + –––––– Y + –––––– Y. 1 + r ( 1 + r ) In order to generate a potential demand for an auditor to attest the state of the project we shall also assume that if the owner was informed that the project state was bad (before it suffered nancial distress), market opportunities exist such that the owner can immediately liquidate the project for a value L by diverting the assets of the project to some alternative unrelated use such that: V g > L > V b (1) i.e., the owner would prefer to keep with good projects and liquidate bad ones. However, without any audit, the owner stays with the project because: p(g)V g +(1 – p(g))V b > L, (2) that is, without any information about the state of the project, it is not desirable to liquidate it. The audit technology, liability, direct and reputational fees We shall assume that since audit technology is imperfect, audits do not perfectly reveal the underlying project state. To reflect this we introduce tilda notation to differentiate the auditors’ report on the state of the project, from the intrinsic states, g and b. That is we let: ~ g = auditor reports the project is good ~ b = auditor reports the project is bad. Furthermore we assume a good project never generates a bad signal 10 but a bad project can generate a good signal. Next in order to generate the possibility of different strategic responses by different 188 M. B. Gietzmann and P. K. Sen Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) auditors, we need to introduce auditor heterogeneity into our model. Recalling that it is often argued in the literature that initial audit engagements may involve signicant relation specic start-up costs (Arens and Loebbecke 1976 p. 100, De Angelo 1981 p. 35), we assume there are two (unobservable) types of auditors. These two types of auditors are labelled M and N and they differ as follows. At the beginning of an audit assignment, type M auditors make a client- specific investment in detection technology, denoted I, that is not observable to the investor 11 resulting in the chance of an audit detecting a bad project being d M . In contrast, the type N auditors do not have the ability to improve their audit detection probability which remains xed at d N . The relation specific investment is productive in the sense that it increases the probability of an auditor detecting a bad state, with: 1 > d M > d N > 0. (3) Then let the proportion of Type M auditors in the economy be denoted m Î (0,1) and for notational convenience we shall subsequently write the detection probability to be d m , where d m Î [d M , d N ]. We further assume that the auditor is independent in the sense of Magee and Tseng (1990) such that the auditors report what they observe and do not strategically misrepresent their findings 12 . What they however do provide strategically is their effort. That is auditors always report what they see but when they do not maintain independence they do not provide (extra) effort 13 to detect whether the state is bad. We assume the auditor is paid an audit fee F per period for performing the audit 14 . We also assume that the audit fee F is sufciently large to cover the auditor’s operating costs so that both types of auditors can participate and the market for audit services does not break down with the decision to collude following in a trivial fashion. Furthermore, when performing audit-detection duties, auditors incur (xed) effort cost of e every period regardless of their type. If the project fails (suffers nancial distress) after the auditor reports ~ g then the auditor expects to incur litigation liability of a , that is, nancial distress acts as a trigger 15 for litigation (Alexander (1991)) and the auditor just breaks even on other assignments 16 . At this stage it is important to stress that if we assumed that direct liability concerns were the only force incentivizing auditors to maintain independence, we may be criticized for being too severe on auditors. Indeed auditors are also motivated by a concern to maintain their reputation and not simply by litigation costs. Since developing a fully endogenized model of formation and maintenance of auditor reputation is outside the scope of this research, we concentrate only on one aspect of the entire reputational concerns: the concern to protect the future fees. We assume existence for such a concern, and denote the additional fees (possibly through additional assignments) to a ‘reputed’ auditor as f. Our analysis then allows f to vary parametrically so as to be applicable to different market settings which give rise to different values for reputation maintenance f. Also note that the process that generates the reputational fees f in our model is economically rational. We assume the total audit market per surviving auditor to grow in period 2. Since the independence and type of auditors are unobservable, investors in the second period select only from those auditors who have a good ‘track record’ in that their clients did not suffer nancial distress in the rst period. Since d M > d N , type M auditors are more likely to survive in the second period. Therefore, it is rational for the clients to impute a reputation of competence (better audit detection technology) on the average to the surviving auditors, who are rewarded with incremental business (reputational gain) of f in the second period 17 . Having established the payoff variables, let us now characterize the auditor’s strategy. Both the auditor types, i.e., who do and do not invest in additional audit detection technology respectively, have a choice whether or not to provide some minimum effort (which we shall normalize to take the value 0 ) or alternatively provide additional (xed) effort e > 0 when trying to ascertain the state 18 , that is: e > 0 = personal (xed) cost to the auditor of providing effort to ascertain the state in every period e = 0 = normalized cost of providing minimum effort. We assume the manager is an empire builder deriving positive utility from project continuance and faces limited liability 19 . When the state is good, the manager is indifferent about auditors’ behavior. When the state of the world is bad, the manager prefers the auditor to Improving Auditor Independence Through Selective Mandatory Rotation 189 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) provide minimum detection effort 20 and hence the decision to set e = 0 can be described as auditor collusion with management, whereas setting e > 0 maintains independence 21 , that is: e > 0 Þ auditor maintains independence (4) e = 0 Þ auditor implicitly colludes. There now remains one necessary detail; the length of the audit game. We shall consider two possibilities. In the immediately following section we assume that mandatory rotation is in place and hence we model the audit game as a one-period game. In the next section we assume that the auditors of rms, who do not suffer nancial distress, can be reappointed. We model the simplest setting in which reappointment can occur, a two-period setting 22 . 3. MANDATORY ROTATION: THE SINGLE PERIOD AUDIT GAME Mandatory auditor rotation can be viewed as an arrangement where the auditor-client relationship is limited by law to a nite number of years. For mathematical simplicity we shall dene the length of time of such a limitation as one period. Thus, whether or not the client experiences nancial distress, the engagement comes to an end. In a mandatory rotation setting, since rehiring cannot take place, a reputation based upon observation of rehiring can not now be established. Thus, by construction, there is no possibility of a reputational gain 23 of f. We assume that the sequence of strategic moves and the associated pay-offs of the players (game tree) are summarized in Figure 1. Note that the nodes A and A’ (equivalently B and B’) are informationally equivalent. Similarly, nodes 1, 2, 3 and 4 are informationally equivalent to the nodes 1’, 2’, 3’, and 4’ respectively. Starting from the left assuming the project has just commenced:  Nature chooses the state of project s Î [g, b], g for good and b for bad, with respective prior probabilities p(g) and 1 – p(g).  Nature also chooses the auditor types whereby m Î (0, 1) is the proportion of type M auditors who are capable of investing an amount I in the client-specic skills. PERIOD 1 F – I – e F – I F – e F F – I – e F – I – e – a F – I – e F – I F – I – a F – e F – e – a F – e F F – a Project g Project b Invest m Not Invest (1-m) Invest m Not Invest (1-m) Work (1 – C 1 ) Collude C 1 Work (1 – C 1 ) Collude C 1 Work (1 – C 1 ) Not Detect 1 – d 1 Not Detect 1 – d 1 Detect d 1 Survive 1 - W Fail W Survive 1 - W Fail W Survive 1 - W Fail W Survive 1 - W Fail W Detect d 1 Collude C 1 Work (1 – C 1 ) Collude C 1 B’ A’ A B 1 2 3 4 1’ 2’ 3’ 4’ Figure 1: 190 M. B. Gietzmann and P. K. Sen Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)  The investors decide to hire an auditor 24 and pay a fee F, provided that the auditor produces decision-relevant information (that is, satises the conditions of Observation 1 to be set out). Since investors can not observe the auditor type, it is as if nature assigns auditors to projects.  The auditor chooses an implicit collusion strategy l Î [c, nc] where c stands for colluding (e = 0) and nc stands for not colluding (e > 0). Let c M , c N denote the probability of colluding with management by investing types M and N respectively. For the sake of notational convenience, we write the collusion probability to be c m , where c m Î [c M , c N ].  The auditor reports the audit nding non- strategically 25 , denoted as ~ s Î [ ~ g, ~ b].  In the case the auditor colludes and nature chose b, there is a probability w that the project will then suffer nancial distress and end in the period. However, there is also a 1–w probability that the project will not suffer nancial distress in the period.  In the case the auditor does not collude and nature chooses b, there is a probability d m that the auditor will detect the state is bad and hence the project is ended as a result of the auditors’ discovery. However, there is also a probability of 1 – d m that the bad state is not detected and hence following the audit report there is a probability of w that the project then suffers nancial distress and probability 1 – w that it will not.  The investor decides to act after receiving the audit report (continues or divests from the project); the nancial distress is determined then through nature’s move. We denote this event as the (imperfect) state realization and denote it as q . Although we discuss the above game in continuous strategies, we restrict our analysis only to pure strategies, i.e., whether the auditors collude or not. That is, the admissible values of c m for this analysis are either 0 or 1. Before we characterize the equilibria, we need another consistency check. In any equilibrium, the investors must have a demand for auditing, such that the information generated by audit has a strictly positive value. We establish such a condition in Observation 1 below. Investors demand for audit information We assume that investors decision of whether or not to hire an auditor is based upon an evaluation of whether the auditor generates decision relevant information. In this particular context this pertains to the extent to which audit information leads investors to revise beliefs concerning the state of the investment project g or b. Thus letting r (g| ~ g) denote the (Bayesian) revised belief of the investor after observing a good audit report ~ g for the rst period but before the nature’s draw determining nancial distress, we rst note that if the state is bad the probability that the auditor will not detect it is given by: n (d m , c m , m) = {m[1 – d M (1 – c M )] + (1 – m) [1 – d N (1 – c N )} and hence the unconditional probability of a good report p( ~ g) is given by: p( ~ g) = p(g) + n (d m , c m , m)(1 – p(g)) For instance in the case of type M auditors and c M = 0 (implying no collusion takes place) the chance of non detection is simply given by (1 – d M ). In contrast with collusion c M = 1, this probability becomes 1. Thus the required conditional expectation for investors is given by: p(g) r (g| ~ g) = –––––––––––––––––––––––– (5) p(g) + u (d m , c m , m)(1 – p(g)) . and so when an investor is considering the incremental benet of employing an auditor, this necessitates a comparison between: the expected payoff with an audit information conditioned strategy: – if receive audit report ~ g continue with the investment expecting to earn r (g| ~ g)V g + (1 – r (g| ~ g))V b – F = [ (6) – if receive audit report ~ b, liquidate the investment earning L – F to the expected payoff without audit information (given by (2)) p(g)V g + (1 – p(g))V b . Thus we have: Observation 1: (Condition for positive demand for auditors under rotation) Audit information has value to investors provided: p( ~ g)( r (g| ~ g)V g + (1 – r (g| ~ g))V b ) + (1 – r ( ~ g))L – F>p(g)V g + (1 – p(g))V b (7) Proof: Follows from the denition of the value of information. Improving Auditor Independence Through Selective Mandatory Rotation 191 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) Turning now to consider the characterization of equilibria, we note that for every equilibrium, we need to verify that (7) holds given the parameters specied under that equilibrium. Equilibrium Under Mandatory Rotation It is clear that there are three possible candidates for equilibrium in the above one-period game. A pooling equilibrium, where both (investment) types do not collude which we denote as the Full Compliance (FC) Equilibrium. A separating equilibrium where only type M auditors do not collude but type N auditors collude, which we denote as the Partial Compliance (PC) equilibrium. Another pooling equilibrium candidate is where both types collude, which we denote as the No Compliance (NC) Equilibrium. We use the concept of the Bayesian-Nash- sequential equilibrium (Kreps and Wilson 1982) adapted to our situation 26 . We show that the only two possible equilibria that can exist in the game described above are a PC equilibrium and a FC equilibrium. An NC equilibrium cannot exist because under the belief structure induced by NC strategies, there is no demand for auditing. Theorem 1 sets out the conditions for existence of the FC and the PC equilibria. Theorem 1 (Existence of FC and PC equilibria) Let the fee in the audit market be set to at least offset the operating costs of a Type M auditor. Let a R denote the legal liability under the mandatory rotational regime. The only possible equilibria of the single period audit game discussed above are a PC equilibrium and an FC equilibrium. An NC equilibrium cannot exist. A PC equilibrium would exist if: p M a R º d M w(1 – p(g)) a R  e  d N w(1 – p(g)) a R º p N a R . (8) Alternatively, a FC equilibrium would exist, if instead, p N a R º d N w(1 – p(g)) a R  e. (9) and, I  (d M – d N ) (1 – p(g))w a R . (10) Proof: See Appendix. From (8) we see that assuming type M auditors have no incentive to collude, if effort cost for a type N auditor is large relative to the probability of liability p N , such auditors will collude. However once (9) is satised, they would not. Notice also that improved audit technology of type M auditors requires that d M > d N , which precludes the possibility that a type M auditor would collude when a type N auditor nds it optimal to maintain independence (not collude). The condition (10) ensures that whenever a type M auditor nds it economical to work, a type N auditor also nds it economical to work. That is, if fees are set to just make type M auditors indifferent about participation we need to ensure that type N auditors’ participation constraint is also satised. In the Appendix we show that this corresponds to requiring that the differential gains from investment are not too large relative to the cost of investment and leads to the condition (10). In other words, one cannot separate the types by offering a differential fee schedule and ‘pricing out’ the less efficient auditor. In this respect, it is interesting to note that in economies characterized by a high level of good projects (p(g) ® 1), the right-hand side of (10) would tend to get smaller and the participation condition for the Type N auditor are more likely to be satised. The intuition of Theorem 1 is that for a type m auditor, the benet of providing costly effort e is that the expected liability (1 – p(g))w a R is reduced by a factor d m , that is, the reduction in expected liability compensates for the additional personal effort cost where p m is the probability of liability reduction. Depending on how large is the d N parameter compared to d M , we will have either a PC or an FC equilibrium. It also follows that everything else being equal, the liabilities required to induce an FC equilibrium will be greater than that required to induce a PC equilibrium, as discussed in Corollary 1 below. Corollary 1 (Liability needs to be higher to insure FC existence as compared to what is required for PC existence) If a R is chosen to satisfy: e e ––– > a R > ––– (11) p N p M a PC equilibrium will follow. However, if a R is increased so that the left inequality of (11) is violated, then an FC equilibrium will follow. Proof: Follows straightforward from Theorem 1. The importance of Corollary 1 is that it allows us to examine bounds on the liability level a R which, under mandatory rotation, induces desirable auditor behavior completely or at least, partially. The intuition for the (11) 192 M. B. Gietzmann and P. K. Sen Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002) requirement is that if liability levels are sufciently high, an auditor will always provide maximum effort no matter what their type is and an FC equilibrium will follow. However, the liability required to induce an FC equilibrium will always be more than adequate for the type M auditors. This is somewhat undesirable since the legal system may not want to appear too harsh to the most skilled service providers. If the legal liability is set just about to induce independence from the type M auditors, a PC equilibrium will result because the liability will not be adequate to preclude collusion by the type N auditors. Thus, our conjecture is that under mandatory rotation, if liability was set to insure existence of a FC equilibrium, the type M auditors would complain about ‘excessive’ legal liability. It is also worth noting that apart from the systemic operating risk characteristics w and p(g), the required liability level under mandatory rotation is functionally dependent upon only two sets of parameters: the audit technology d m and effort cost e. This is important because in the following subsection when rotation is no longer mandated, a third set of parameters, current fees F relative to future fees f (that can be earned only through survival and building of reputation), also effect the determination of necessary liability levels in the various equilibria. In particular, we will focus upon when the interaction between these two parameters reinforces auditors’ incentives to maintain independence (as is often claimed by the profession) or alternatively weakens incentives. It will then be in the later class of cases that mandating rotation will have a role to play. 4. NO MANDATORY ROTATION: THE TWO-PERIOD AUDIT GAME In this section, we allow auditors to be reappointed for another term and hence potentially extend the auditing game to a second period. In so doing, we specifically bring attention to the fact that auditors’ behavioral strategy [c, nc] may be inuenced by a desire for reappointment. In particular if management is inuential in the reappointment decision, an auditor may balance the trade-off between loss of reputation and legal liability and the improved prospects of continuation of future audit fees when deciding to collude 27 . Therefore we need to consider carefully whether the incentive effects of a xed level of legal liability are reduced when such additional reappointment concerns arise. As we shall see, it will depend upon characteristics of the audit market, and liability levels may need to be increased or alternatively could be decreased in order to maintain incentives. Before commencing the formal analysis, it is important to stress that an addition of a second period, per se, does not necessarily give rise to different conclusions concerning auditor strategic behavior. In particular, if the participants were certain that one more period exists in the game, they would play the second period as if it were a one period game, and by backward induction, arrive at the solution of the rst period, which would be no different. What makes a difference in our model is that the likelihood that the auditor may ‘enter’ a second period game is in part influenced by the strategies and inferences adopted by the auditor, the investor, and the manager in the rst play of the game. That is, the auditor can never be certain that a second period will take place. As before, let us commence by setting out the circumstances under which the audit game will continue 28 to a second period. This will of course depend on the underlying state of the project hence:  if the state of the project is good: regardless of what the auditor does, the game continues to a second period provided the investor values a second audit report.  if the state of the project is bad: the game progresses to the second period if the investor values a second audit report and if in the rst period the auditor: – colludes and the project survives; – does not collude, does not detect the state and the project survives; [ – does not collude, detects the state and the investor liquidates. In the last alternative, although the auditor loses the current assignment fee F, it would continue to earn its normal fee f during the second period. Clearly the remaining possibilities are that the game does not proceed to a second period because the firm suffers financial distress without any warning from the auditor. Our [...]... cation and rearrangement of terms in (28) and (29) yields (16) and (15) respectively Given that a FC-2 equilibrium is about to follow, the auditors must nd their optimal rst period strategy along the paths that lead to the FC-2 equilibria There are two ways an FC-2 equilibrium can be reached The FC-1, FC-2 equilibrium Int J Audit 6: 18 3-2 10 (2002) Improving Auditor Independence Through Selective Mandatory. .. the following Proposition 4 Int J Audit 6: 18 3-2 10 (2002) 199 Improving Auditor Independence Through Selective Mandatory Rotation Proposition 4: (Type M auditors have more incentives to protect reputation for independence) Whenever a Type N auditor has a non-zero incentive to protect her reputation for independence, so will a Type M auditor Proof: The non-zero incentive implies that for both the types,... Jersey Balachandran, B., (1993), Introduction: Auditors’ Legal Liability in the United States, Journal of Economics and Management Strategy, 2:3, 33 3-3 38 Barca, F., (1995), On Corporate Governance in Italy: Issues, Facts and Agenda, Fondasione Mettei Series Int J Audit 6: 18 3-2 10 (2002) 207 Improving Auditor Independence Through Selective Mandatory Rotation Buijink, W., S Maijoor, R Meuwissen, and A van... any equilibrium involving PC-2, thus eliminating two more candidates34 In the following Theorem 2, we characterize the remaining two equilibria (FC-1,FC-2 and PC1,FC-2) that now become the principal focus of Int J Audit 6: 18 3-2 10 (2002) 195 Improving Auditor Independence Through Selective Mandatory Rotation our analysis Before doing so we note that since we are now in a two-period game we need to drop... regimes, rotation versus non -rotation, and examine more completely the role of the current and the future period’s fee in determining auditors’ independence 5 MINIMUM LEVELS OF LIABILITY THAT INSURE AUDITOR INDEPENDENCE, WITH AND WITHOUT ROTATION In this section we compare the equilibria under the two regimes and derive implications pertaining to auditors’ independence in each of Copyright © 2002 Management... non-rotational regime and instead add a subscript 2 to indicate that it is the second period liability Theorem 2 (Existence of FC-1,FC-2 and PC1,FC-2 equilibria in the two-period setting) FC-1,FC-2 equilibrium conditions: Let the audit fees be set to at least offset the operating costs of the Type M auditors Let a1 and a2 denote that legal liability levels in period 1 and period 2 respectively An FC-1,FC-2... that rotation always improves auditors’ incentives to maintain independence and always decreases audit quality Additional research into a number of related topics will further re ne our understanding of the potential ef cacy of mandated rotation For instance, consideration of whether rotating partners or audit teams within audit rms may Int J Audit 6: 18 3-2 10 (2002) 203 Improving Auditor Independence Through. .. Arthur Anderson audit of Delorean Following the failure of the automotive project, Arthur Anderson faced not only potential litigation from investors in the venture, but was also banned for a period from bidding for any consulting projects with the UK government which in our notation corresponds to a loss of f Int J Audit 6: 18 3-2 10 (2002) Improving Auditor Independence Through Selective Mandatory Rotation. .. level of investment I supported by mandatory rotation regime is lower than the investment supported in the reappointment regime Proof: It is suf cient if we prove our claim in the case with zero concern for reputation, i.e., where the concern for reputation exactly offset the Int J Audit 6: 18 3-2 10 (2002) 197 Improving Auditor Independence Through Selective Mandatory Rotation concern for reappointment... Conversely, it can be argued that non-negative reputation is suf cient to induce a1 < aR Thus, in a thin market, mandatory rotation reduces the liability by removing the reappointment concerns In a developed audit market, however, that would not be true because mandatory rotation would not allow development of reputation, which supports auditor independence Introducing mandatory rotation in such a situation . the auditor. Our Improving Auditor Independence Through Selective Mandatory Rotation 193 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 18 3-2 10 (2002) assumption (3) ensures that non-colluding. 6: 18 3-2 10 (2002) Received 2001 ISSN 1090–6738 Revised September 2001 Copyright © 2002 Management Audit Ltd. Accepted March 2002 Improving Auditor Independence Through Selective Mandatory Rotation Miles. Proposition 4. Improving Auditor Independence Through Selective Mandatory Rotation 199 Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 18 3-2 10 (2002) Proposition 4: (Type M auditors have