lu and sivaramakrishnan - 2009 - mandatory audit firm rotation - fresh look versus poor knowledge

Mandatory audit firm rotation: Fresh look versus poor knowledge Tong Lu * , K. Sivaramakrishnan Bauer College of Business, University of Houston, Houston, TX 77204-6021, United States article info JEL classification: G31 G34 D82 Keywords: Auditor independence Auditor conservatism Audit quality Investment efficiency Auditor rotation abstract Our aim in this paper is to investigate the effects of mandatory audit firm rotation (MAR) on companies’ investment decision and auditor choice in a capital market setting. We compare a MAR regime with a non-MAR regime in a setting in which auditors’ independence and companies’ opinion shopping are real concerns. To capture auditor independence and opinion shopping, we model auditor biases (a conservative bias or an aggressive bias) and client firms’ incentives to engage auditors with desired biases. We find that when firms engage in opinion shopping, MAR improves investment efficiency for some firms but impairs investment efficiency for other firms. More generally, we contribute to the literature by demonstrating the real effects of auditing on corporate resource allocation decisions. Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction External auditors serve a valuable function in capital markets by lending credibility to financial statements issued by public companies, thereby reducing information risk. The sanctity of this audit role depends crucially on the nature of the auditor’s attestation. It has been argued that long-term auditor–client relationships can result in auditors becoming complacent and lax in their attestation roles. Lack of auditor independence from the client firm is also a matter of concern. One suggested avenue to address these concerns is to place term limits by enforcing mandatory audit firm rotation (MAR). Indeed, MAR has received much attention in legislative and regulatory circles recently, as reflected in a General Accounting Office study (GAO, 2003) required by Section 207 of the 0278-4254/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jaccpubpol.2009.01.006 * Corresponding author. Tel.: +1 7137430448; fax: +1 7137434828. E-mail address: tlu4@uh.edu (T. Lu). J. Account. Public Policy 28 (2009) 71–91 Contents lists available at ScienceDirect J. Account. Public Policy journal homepage: www.elsevier.com/locate/jaccpubpol Sarbanes-Oxley Act to look into its costs and benefits. However, there is little by way of systematic analysis in the literature as to whether MAR is at all desirable in the US corporate environment. In the paper, we present a theoretical model that evaluates the desirability of MAR relative to the current regime in which the decision to change an auditor is entirely voluntary. Opponents of MAR argue that a new auditor will not have the benefit of client-specific knowledge of a previous auditor (GAO, 2003). This poor knowledge of the new auditor hampers the effectiveness of the audit process and can result in a deadweight loss to society. Sunder (2003) goes even a step further to suggest removing the mandatory audit requirement in the first place, ‘‘leaving each firm to decide if it wishes to have an audit certificate accompany its reports.” On the other hand, proponents of MAR claim that a new auditor would bring a fresh look to the auditing task (Conference Board, 2003), and that it is an effective way of ensuring auditor independence and preventing ‘‘opinion shopping.” The focus of this paper is to model this classic trade-off between fresh look and poor knowledge to address the desirability of MAR in a setting in which auditor independence and opinion shopping are real concerns. To do so, however, we must first specify a criterion for evaluating the desirability of a regime, MAR or otherwise. We use investment efficiency as the criterion by analyzing the impact of an audit regime on corporate investment decisions, whose cash flow implications are ultimate interest to shareholders. A regime in which investment decisions come closest to first best investment levels (optimal investment levels in the absence of any informational asymmetries and agency problems) would be considered desirable. In any model of MAR, lack of auditor independence must potentially be an issue in the absence of MAR. The auditor independence standard requires that the auditor ‘‘must be without bias with respect to the client since otherwise he would lack that impartiality necessary for the dependability of his findings, however excellent his technical proficiency may be” (AU Section 220—Independence). We capture this aspect in our model by introducing auditors who may be biased in viewpoint (a conservative bias or an aggressive bias). There are two ways to introduce such a bias. One approach is to examine a setting in which the bias arises as a result of auditors’ incentives. A second approach is to assume that auditors are predisposed to biases in judgment, leading them to process information in a way that may or may not favor the client (Bazerman et al., 1997). By choosing between a conservative auditor and an aggressive auditor, client firms can potentially align auditor bias with their own reporting incentives. Both approaches to modeling auditor attestation constitute interesting avenues to pursue. In the text, we pursue the latter approach because it allows us to incorporate auditor bias in a tractable man- ner and focus squarely on our primary objective of examining the desirability of MAR in terms of its impact on corporate investment decisions. That is, our focus is not so much on the source of auditor bias as it is to examine the consequences of auditor bias. In Appendix 2, we introduce auditor incentives and show how auditor biases are endogenized. Specifically, we assume that auditors can be one of two types: conservative or aggressive (Krishnan, 1994). When faced with uncertainty, conservative auditors tend to err on the side of understatement, while aggressive auditors tend to err on the side of overstatement. If a firm desires, say, an aggressive auditor and the incumbent auditor is aggressive, then the firm can retain the incumbent; otherwise, the firm can shift to a new auditor who is aggressive. In other words, we are essentially examining the demand for auditor bias by clients. We assume that a firm, which has private knowledge of its prospect (i.e., the probability of its future financial condition), chooses an observable investment level to maximize its expected stock price conditional on the firm’s audited accounting report, net of the investment cost. Under MAR, the firm must pick a new auditor, but has the discretion to choose between a conservative and an aggressive new auditor. In the absence of MAR (hereafter, the non-MAR regime), the firm has an additional option of retaining the incumbent auditor. Firms are often known to engage in opinion shopping (Lennox, 2000). Opinion shopping refers to a firm’s incentive to switch auditors to secure a more favorable audit opinion ex post (i.e., after the incumbent auditor proposes an audit opinion). In general, opinion shopping compromises the quality of external audits. Clearly, opinion shopping is a potential issue in the non-MAR regime because auditor switches are entirely voluntary in this regime. However, even under MAR, the firm can potentially 72 T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 wait till it privately learns its financial condition and then exercise its discretion in choosing between a conservative and an aggressive new auditor. Thus, our model presents us with a unique opportunity to examine how opinion shopping incentives might affect the desirability of MAR—an issue that has not received much attention in the debate over MAR. In our model, the incumbent auditor has a knowledge advantage over the new auditor in the sense that the incumbent auditor can detect the true financial condition with a higher probability; equivalently, the new auditor suffers from poor knowledge. However, to the extent that the chosen new auditor is of a different type from the incumbent auditor, the new auditor brings a fresh look to the audit task. Using this structure, we examine the equilibrium effects of MAR on companies’ investment decisions and auditor choices. We find that, when the incumbent auditor is aggressive, MAR results in a switch to a conservative auditor more frequently than in the non-MAR regime, and when the incumbent auditor is conservative, MAR results in a switch to an aggressive auditor more frequently than in the non-MAR regime. Thus, if the purpose of imposing MAR is to bring in fresh look, it would clearly be achieved. More importantly, to the extent that opinion shopping is a real concern, we find that it has important implications for the desirability of MAR from an investment efficiency standpoint. To establish this result, we first ignore opinion shopping and assume that firms switch auditors ex ante, i.e., before privately observing their financial condition. In this ex ante auditor choice setting in which opinion shopping is not an issue, we show that MAR always impairs investment efficiency. Next, we introduce opinion shopping by allowing firms to switch auditors ex post, i.e., after privately learning their financial condition. In this ex post auditor choice setting, firms that have received an unfavorable report from the incumbent auditor have a natural incentive to seek a favorably biased opinion from a new auditor. Such an opinion shopping incentive drastically alters the implications of MAR for investment efficiency. In particular, it is no longer the case that MAR always impairs investment efficiency. Given an aggressive incumbent auditor, MAR impairs corporate investment efficiency for firms with good prospects but improves corporate investment efficiency for firms with bad prospects. In contrast, given a conservative incumbent auditor, MAR impairs corporate investment efficiency for firms with bad prospects but improves corporate investment efficiency for firms with good prospects. To our knowledge, our study is the first to highlight the impact of opinion shopping on the desirability of MAR. The intuition for the above results is as follows. In the ex ante auditor choice setting, the capital market knows that the firm has not yet learned its financial condition, so auditor switching is not viewed negatively by the market. Therefore, a firm that desires a switch to improve its investment efficiency will do so whether in a MAR regime or in a non-MAR regime; however, a firm that does not wish to switch is forced by MAR to switch, which results in a deterioration of its investment efficiency. In brief, in an ex ante auditor choice setting, MAR impairs investment efficiency for some firms without improving investment efficiency for others. However, in the ex post auditor choice setting, the market knows that the firm privately knows its financial condition at the time of switching, and is therefore cognizant of its motives to switch. The consequent negative market reaction would prevent some firms—those firms that would otherwise switch auditors in the ex ante setting to improve investment efficiency—from switching auditors. On the other hand, MAR forces all firms to switch, and so the market cannot tell which firms are opinion shopping and which are not. 1 Consequently, MAR would enable some firms to improve their investment efficiency by making ‘‘desirable” switches, but in the meantime, MAR would impair other firms’ investment efficiency by forcing them to make ‘‘undesirable” switches. In related research, Elitzur and Falk (1996) (hereafter, EF) focus on the effect of MAR on the auditor’s planned audit quality and employ a multi-period framework. EF find that the level of planned audit quality will diminish over time under MAR. In contrast, we focus on auditor biases and employ a one-period framework. Gietzmann and Sen (2002) (hereafter, GS) find that MAR should only be imposed in thin markets where a few clients dominate the auditor’s client portfolio, whereas we find that the desirability of 1 We thank an anonymous referee for pointing out this argument on the market’s beliefs under MAR. T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 73 MAR depends on the client prospect and the auditor bias. Our study differs from theirs in important ways. First, GS focus exclusively on auditor aggressiveness, whereas we study both aggressive and conservative auditor biases. Second, GS concentrate on the auditor’s work/shirk decision while we examine the client’s investment decision and auditor choice, and the capital market price. Kornish and Levine (2004) (hereafter, KL) model a contractual setting where the auditor serves two clients, an audit committee and a manager; we study a market setting, where the client firm chooses its auditor in light of its expected capital market price. KL argue that the audit committee can use dis- missal threats to discipline the auditor and therefore MAR is detrimental because it reduces the effectiveness of such a threat. We find that whether MAR is desirable depends on the client prospect and the auditor bias. Dopuch et al. (2001) study MAR in an experimental setting. While they assume exogenous benefits to the firm from financial reports, we derive them endogenously by incorporating a capital market. They focus on auditor aggressiveness; we study both aggressiveness and conservatism. Their experimental results show that MAR decreases investment but we show that MAR may either increase or decrease investment, depending on the client prospect and the auditor bias. The paper proceeds as follows: Section 2 describes our model. In Section 3, we investigate the capital market’s pricing of the firm and the corporate investment decision given a particular auditor type. We then analyze the client firm’s auditor choice under both MAR and non-MAR regimes and identify implications for the investment decision. We do so first in an ex ante case in Section 4 and then in an ex post case in Section 5. Finally, Section 6 concludes. 2. Model 2.1. Technology and sequence of events Given our purpose of evaluating the desirability of MAR using investment efficiency as the criterion, our model centers on a firm’s investment decision. The firm chooses an investment level repre- sented by k. The cost of the investment is 1 2 k 2 . The investment yields a return gk at some future point in time if the financial condition (i.e., the state of nature) is good ðgÞ, which occurs with probability k;it yields a return of zero if the financial condition is bad ðbÞ, with probability 1 À k. The parameter g > 0 captures the productivity of the investment in monetary terms in the good state. The firm has private knowledge of its financial prospect, k, and its financial condition (g or b) once it is realized. Once the financial condition is realized, the firm prepares a report subject to an audit. The auditor discovers privately the true financial condition with probability q and approves or disapproves the client-proposed report. With probability q, the auditor accumulates conclusive evidence about the client’s financial condition, g or b; with probability 1 À q, the auditor accumulates inconclusive evidence, denoted by i. We call q audit quality. The audited accounting report is either G or B, where G signifies ‘‘good” and B signifies ‘‘bad.” Conditional on the audited accounting report and other available information, the market prices the firm at m. Finally, the return to investment, gk or 0, is realized. As a benchmark, we first consider the case in which the firm can credibly commit to choose its auditor before it learns the realized financial condition (g or b). We refer to this benchmark as the ex ante auditor choice setting. The following time line presents the sequence of events in this setting: Time line 1:  Nature determines the realization of firm prospect, k, which is privately learned by the firm.  The firm makes an investment of k units and chooses its auditor.  The firm observes the realized financial condition (state), g or b.  The audited accounting report, G or B, is issued.  The capital market prices the firm at m.  The return to investment, gk or 0, is realized. In practice, however, there is no mechanism by which a firm can credibly commit to choose its auditor ex ante. A more realistic model is one which allows for a tactical auditor switch by the firm, 74 T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 i.e., when the firm has the discretion to choose its auditor ex post, that is, when the firm can potentially engage in opinion shopping. However, the ex ante setting allows us to first examine the desirability of MAR in the absence of opinion shopping, which we then use to evaluate the impact of opinion shopping on the desirability of MAR. The following time line presents the sequence of events when opinion shopping is present: Time line 2:  Nature determines the realization of firm prospect, k, which is privately learned by the firm.  The firm makes an investment of k units.  The firm observes the realized financial condition (state), g or b.  The audited accounting report, G or B, is proposed by the incumbent auditor.  The firm either retains its incumbent auditor or switches to a new auditor.  The capital market prices the firm at m.  The return to investment, gk or 0, is realized. 2.2. Preferences We focus exclusively on the conflict between two generations of shareholders and assume that the firm is run by a manager who wishes to boost the price of the firm in the capital market. Such a man- agerial incentive may come from stock-based compensation contracts. This assumption is also in keeping with other models in accounting and finance that focus on inter-generational shareholder conflicts (see, for example, Dye, 1985; Fishman and Hagerty, 1989). 2 The firm chooses an investment of k and an auditor to maximize the price prospective shareholders will be willing to pay, less the investment cost. The prospective shareholders in a competitive capital market will receive the eventual return to investment, less the price they pay for the firm. Thus, the social welfare is maximized when the return on investment (the eventual return to investment less the investment cost) is maximized. 3 2.3. Audit function Given the information asymmetry between the current and prospective shareholders regarding the realized state of nature, auditing plays a crucial role of reducing information risk in support of a trade. The auditor can be one of two types: aggressive ðAÞ or conservative ðCÞ. 4 Auditor conservatism is a well-understood term in the auditing and accounting literatures. An auditor is said to be conservative when he or she is more inclined to err toward approving a bad report, B, when faced with uncertainty regarding the true state (that is, when the auditor accumulated inconclusive evidence, i). On the other hand, an aggressive auditor is more inclined to err toward approving a good report, G, when faced with the same uncertainty. 5 2 We also relax this assumption to introduce an element of internal agency conflict (‘‘empire building”). The results are qualitatively similar and available upon request. 3 That is, we assume here that it is the firm that incurs the investment cost. Alternatively, we can assume that the new shareholders incur the investment cost. It does not change the investment decision, k, because in either case, the investment is chosen to maximize the expected eventual return to investment less the investment cost. When the investment cost is incurred by the firm, the firm maximizes its expected price (which is the expected eventual return to investment) less the investment cost; when the investment cost is incurred by the new shareholders, the firm maximize s its expected price, which equals the expected eventual return to investment less the investment cost. 4 Auditor decisions can be modeled here (see the next footnote); that is, we can model auditors as strategic players. We choose to do so in Appendix 2 to streamline the analysis in the text. 5 We show in Appendix 2 how auditor conservatism/aggressiveness can be endogenized. In brief, we show that auditor conservatism/aggressiveness is determined by a trade-off faced by the auditor. That trade-off is summarized by a ‘‘fee/liability ratio.” Therefore, outside investors can use this ratio to infer whether the auditor is conservative or aggressive. In other words, even though we assume in the text that auditor conservatism/aggressiveness is directly observable, this assumption is innocuous in that auditor conservatism/aggressiveness can be inferred. T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 75 Fig. 1 illustrates auditor conservatism/aggressiveness and the resultant audited accounting reports. Referring to Fig. 1, if the report G is approved by a conservative auditor, it is fully informative because it is revealing of the true state g. However, when there is uncertainty, the conservative auditor only allows the report B and therefore B is noisy. Similarly, if the report B is issued by a firm whose auditor is aggressive, it is fully informative because it is revealing of the true state b. However, when there is uncertainty, the aggressive auditor approves the report G and therefore G is noisy. From the above discussion, we can see that auditor conservatism or auditor aggressiveness is not always bad: auditor conservatism may produce a type I error while auditor aggressiveness may produce a type II error. Under certain conditions, one is better; under other conditions, the other is better. (We are going to identify those conditions in Sections 4 and 5.) As shown in Sections 4 and 5, because different firms in different conditions demand for different types of auditors, both conservatism and aggressiveness will stay in equilibrium and neither will disappear or be regulated out. With the introduction of two types of auditors, now we define ‘‘fresh look:” Definition. An auditor switch results in a fresh look when the new auditor type is not the same as the old auditor type. We assume that the incumbent auditor has the advantage of client-specific knowledge over the new auditor, or equivalently, the new auditor has ‘‘poor knowledge.” We capture this knowledge dif- ference through the audit quality, q. On the other hand, an incumbent auditor may not be able to see ‘‘correctly” in her audit process because of her ‘‘coziness” with the client due to her long tenure. A new auditor instead is not plagued with this problem and comes with a fresh look which may increase the probability of detecting the client’s financial condition (state). We can represent these two effects on the audit quality through qð a ; bÞ, where a represents poor knowledge and b represents fresh look. We assume that dq d a < 0 and dq db > 0; that is, a poorer knowledge decreases audit quality but a fresher look increases audit quality. Empirical evidence indicates that the effect of poor knowledge dominates the effect of fresh look (see, for example, Myers et al., 2003; Stanley and DeZoort, 2007). Therefore, we assume that dq d a       > dq db       . 6 Thus, we have the following (the subscript I refers to the incumbent auditor and the subscript N refers to the new auditor): Definition. Poor knowledge of the new auditor relative to the incumbent auditor implies q I > q N . 7 λ λ −1 q −q1 q −q1 g b g b i i state audit evidence GG G G B B BB audited accounting reports given given auditor auditor conservatism aggressiveness Fig. 1. Auditor conservatism and auditor aggressiveness. 6 We thank an anonymous reviewer for this way of modeling the poor knowledge and fresh look effects and for the empirical reference. 7 Under a MAR regime, the incumbent auditor may boost up her audit quality towards the end of her tunure in order to ‘‘clean up skeletons in her closet.” This is consistent with our assumption that q I > q N . We thank an anonymous reviewer for rasing up this issue. 76 T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 We can characterize an auditor fully by the tuple fT; q j g, where T 2fC; Ag and j 2fI; Ng. The following table presents the various auditing scenarios along the poor knowledge and fresh look dimensions: (MAR denotes mandatory audit firm rotation.) The client’s auditor choice Incumbent fC; q I g Incumbent fA; q I g Retain the incumbent auditor (infeasible under MAR) fC; q I gfA; q I g Switch to a conservative new auditor fC; q N gfC; q N g Switch to an aggressive new auditor fA; q N gfA; q N g Clearly, in the non-MAR setting, the firm can choose to retain the incumbent auditor, whether conservative or aggressive, or hire a new auditor, either conservative or aggressive. In the MAR setting, the firm does not have the option of retaining the incumbent auditor, but it can still choose either a conservative or an aggressive auditor to be the new auditor. 3. Investment We begin our analysis by examining the complete information case in which the firm’s financial prospect, k, is public knowledge. Let us first consider the case of an aggressive auditor. As Fig. 1 implies, by Bayes’ theorem, the market price conditional on the audited report is given by m A G ¼ k 1 Àð1 À kÞq gk and m A B ¼ 0; where the superscript A denotes the aggressive auditor and the subscripts G and B denote the audited reports. Referring to the structure in Fig. 1, we can calculate the expected market price given an aggressive auditor as P ðGjAÞm A G þ PðBjAÞm A B ¼½1 Àð1 À kÞq k 1 Àð1 À kÞq gk ! ¼ kgk: Similarly, as Fig. 1 implies, with a conservative auditor, the market price conditional on the audited report is given by m C G ¼ gk and m C B ¼ kð1 À qÞ 1 À kq gk; where the superscript C denotes the conservative auditor. Therefore, the expected market price given a conservative auditor is P ðGjCÞm C G þ PðBjCÞm C B ¼ kq½gkþð1 À kqÞ kð1 À qÞ 1 À kq gk ! ¼ kgk: Thus, the expected market price is the same under either auditor type, and the firm will choose k to maximize the expected price less the investment cost, kgk À 1 2 k 2 . From the corresponding first-order condition, the first best investment level is k FB ðkÞ¼kg: ð1Þ Thus, when information is symmetric, neither the auditor biases (C or A) nor the differential knowledge between the incumbent auditor and the new auditor (q I or q N ) matters. We next analyze the case in which the firm prospect (i.e., the probability of the state), k, is private information to the firm. We analyze this case in three parts. In the remaining portion of this section, we examine the firm’s optimal investment given the auditor’s type. We then investigate the firm’s optimal auditor choice in the next two sections. Because the firm makes its investment decision based on its private information ðkÞ, the choice of k is informative to the market in that the market can potentially infer k from k. Let b k denote the market’s inference. For a particular level of k, the market infers that the firm prospect is b k, and we use kð b kÞ to T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 77 refer to that level of investment that triggers the market’s inference, b k. Denote the firm’s expected payoff by Vð b k; kÞ when a type k firm pretends its type to be b k by investing kð b kÞ. We are interested in equilibria in which the market correctly infers the true k from the firm’s investment choice k: 8 Let VðkÞVðk; kÞ represent the firm’s expected payoff when the firm type is revealed fully through the investment policy kðkÞ. The firm would implement any feasible fully-revealing schedule kðkÞ only when it is incentive compatible. Definition. A fully-revealing investment schedule kðkÞ is incentive compatible if VðkÞVðk; kÞ P Vð b k; kÞ 8k; b k: ð2Þ For now, we will not specify whether the auditor is incumbent or new, but will address this issue at the end of this section. 3.1. The optimal investment given an aggressive auditor Let us consider the case in which the firm is with an aggressive auditor. As Fig. 1 implies, the market prices conditional on the audited reports of G and B are given by, respectively m A G ¼ b k 1 Àð1 À b kÞq gk and m A B ¼ 0; ð3Þ where b k represents the market’s inference about k. With these market prices, we can calculate the firm’s expected payoff at the time of the investment decision as Vð b k; kÞ¼ ½1 Àð1 À kÞq |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} probability of report G b k 1 Àð1 À b kÞq gkð b kÞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} market price given report G À 1 2 k 2 ð b kÞ |fflfflfflffl{zfflfflfflffl} cost of investment : ð4Þ We now state the main result on the equilibrium investment schedule with an aggressive auditor. Proposition 1. For a firm with an aggressive auditor: (A) The equilibrium investment schedule kðkÞ solves the differential equation: ½kðkÞÀkgk 0 ðkÞ¼ 1 À q 1 Àð1 À kÞq gkðkÞð5Þ with the boundary condition kð0Þ¼0, (B) k 0 ðkÞ > 0, and (C) kðkÞ P k FB ðkÞ. 3.2. The optimal investment given a conservative auditor Refer to Fig. 1. By Bayes’ theorem, with a conservative auditor, the market prices conditional on the audited reports of G and B are given by, respectively m C G ¼ gk and m C B ¼ b kð1 À qÞ 1 À b kq gk: ð6Þ With these market prices, we can calculate the firm’s expected payoff at the time of the investment decision as Vð b k; kÞ¼ kq |{z} probability of report G gkð b kÞ |fflffl{zfflffl} market price given report G þð1 À kqÞ |fflfflfflfflffl{zfflfflfflfflffl} probability of report B b kð1 À qÞ 1 À b kq gkð b kÞ |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} market price given report B À 1 2 k 2 ð b kÞ |fflfflffl{zfflfflffl} cost of investment : ð7Þ 8 We show at the end of Appendix 1 that a pooling equilibrium does not exist. We thank an anonymous reviewer for checking out whether a pooling equilibrium exists. 78 T. Lu, K. Sivaramakrishnan / J. Account. Public Policy 28 (2009) 71–91 As before, we restrict our attention to the set of investment schedules that are fully-revealing and state the main result with respect to properties of the equilibrium investment schedule with a conservative auditor. Proposition 2. For a firm with a conservative auditor: (A) The equilibrium investment schedule kðkÞ solves the differential equation: ½kðkÞÀkgk 0 ðkÞ¼ 1 À q 1 À kq gkðkÞð8Þ with the boundary condition kð0Þ¼0, (B) k 0 ðkÞ > 0, and (C) kðkÞ P k FB ðkÞ. Propositions 1(C) and 2(C) together establish that, irrespective of whether the auditor in place is conservative or aggressive, overinvestment results. To understand the reason for overinvestment, consider a simple case in which the private information k can take one of two possible values— low and high. To maximize its expected price, the low k firm has an incentive to mimic the high k firm. To do so, the low type firm must make a large investment because a larger investment implies a more favorable firm prospect in the eyes of the market (that is, kð b kÞ is increasing in b k). How- ever, the low k firm also realizes that it has a lower chance of producing a favorable audited report than the high k firm (see Fig. 1). Hence, the low k firm might not reap the full benefits from mimicking but surely would bear the full cost of mimicking. Thus, by overinvesting enough, the high k firm effectively deters the low k firm from mimicking and so reveals its type through k in equilibrium. Thus far, we have not distinguished between an incumbent auditor and a new auditor. Propo- sitions 1 and 2 apply equally to incumbent and new auditors with the use of appropriate audit quality ðqÞ to express (5) and (8)—an incumbent auditor discovers the true realized state with probability q I and a new auditor does so with probability q N , with q I > q N . Specifically, the investment schedules for a firm with an incumbent auditor and for a firm with a new auditor are as follows: Investment schedule for a firm With an aggressive auditor With a conservative auditor With an incumbent auditor ½kðkÞÀkgk 0 ðkÞ¼ 1Àq I 1Àð1ÀkÞq I gkðkÞ½kðkÞÀkgk 0 ðkÞ¼ 1Àq I 1Àkq I gkðkÞ With a new auditor ½kðkÞÀkgk 0 ðkÞ¼ 1Àq N 1Àð1ÀkÞq N gkðkÞ½kðkÞÀkgk 0 ðkÞ¼ 1Àq N 1Àkq N gkðkÞ 4. Ex ante auditor choice In this section, we analyze the benchmark case in which the firm chooses its auditor before the realization of its financial condition (state), g or b (refer to time line 1 in Section 2). Recall that in the non-MAR regime, the firm has the discretion to retain the incumbent auditor, whether conservative or aggressive, or switch to a new auditor, whether conservative or aggressive. In contrast, the firm must switch auditors under MAR, but has the option to hire either a conservative or aggressive auditor to replace the incumbent auditor. Thus, in comparing the two regimes, we have a number of different combinations to consider. 4.1. Auditor choice given an aggressive incumbent auditor In a non-MAR regime, given an aggressive incumbent auditor, the firm can choose to keep the aggressive incumbent auditor, or hire either an aggressive or conservative auditor. The following proposition characterizes the firm’s auditor choice. T. Lu, K. Sivaramakrishnan / J. Account. Public Policy 28 (2009) 71–91 79 Proposition 3 (Ex ante auditor choice). In a non-MAR regime, a firm with an aggressive incumbent auditor retains its auditor if k P k Ã and switches to a conservative new auditor if k 6 k Ã , where k Ã  1 1 þ q I 1Àq I 1Àq N q N < 1 2 . To understand this result, recall from Proposition 1 that there is always overinvestment in equilibrium. Overinvestment is a costly way of credibly revealing firm type; but a more informative audited report reduces the signaling burden on investment. Now the question is: Which type of auditor can help improve the informativeness of audited reports? As Fig. 1 implies, conservative attestation may produce understatements (with probability kð1 À qÞ), whereas aggressive attestation may produce overstatements (with probability ð1 À kÞð1 À qÞ). Thus, the likelihood of misstatement is lower with a conservative auditor for a firm with poorer prospects (i.e., a firm with lower k) but for a firm with better prospects (higher k), the likelihood of misstatement is lower with an aggressive auditor. In addition, a new auditor’s poor knowledge ðq N < q I Þ increases the likelihood of misstatement and so reduces the informativeness of financial reporting, and therefore, other things being equal, poorer knowledge increases overinvestment. Therefore, we have the following: Remark 1 (1) Firms with poorer prospects prefer conservative auditors, whereas firms with better prospects prefer aggressive auditors. (2) Among the same type of auditors, firms prefer incumbent to new auditors. Conventional wisdom might indicate that good firms seek more reputable auditors and ‘‘more reputable” means ‘‘more conservative,” i.e., Proposition 3 and Remark 1 might appear counterintuitive. We interpret reputable auditors as those who minimize the likelihood of misstatements. A conservative auditor may send false alarms (the type I error) while an aggressive auditor may be unduly opti- mistic (the type II error). Therefore, when choosing between a conservative auditor and an aggressive auditor, the firm must trade off these two errors. For a good firm, undue optimism is not a concern because that firm’s fundamental is truly good, but a false alarm is damaging. For that reason, a good firm prefers an aggressive auditor. So, indeed, as one might think, good firms seek more reputable auditors, but not in the sense that the chosen auditor is conservative; rather, the auditor is ‘‘reputable” in the sense that she minimizes the likelihood of misstatements. Thus, as Proposition 3 demonstrates, with an aggressive incumbent auditor, a firm with a high k will retain its incumbent auditor because she is aggressive but a firm with a low k will switch to a conservative auditor. λ )( λ FB k ),;( N qCk λ ),;( I qAk λ 0 1 0 g k * λ firm investment financial prospec t ),;( N qAk λ 2 1 optimal investment given a conservative new auditor optimal investment given an aggressive new auditor optimal investment given an aggressive incumbent auditor first best investment ),;( I qAk λ ),;( N qAk λ ),;( N qCk λ )( λ FB k Fig. 2. Equilibrium investment given alternative auditor choices (the case of an aggressive incumbent auditor). 80 T. Lu, K. Sivaramakrishnan /J. Account. Public Policy 28 (2009) 71–91 [...]... incidence of fresh look: more firms switch from aggressive to conservative À Â ÃÁ auditors In a non-MAR regime, for firms with poorer prospects k 2 kÃ ; 1 , the benefit from the incum2 bent auditor’s good knowledge exceeds the benefit from a fresh look, and so the firm would like to retain its incumbent auditor However, when MAR is imposed, the incumbent’s good knowledge is lost, and now only the ‘ fresh look ... from the incumbent auditor’s 2 good knowledge exceeds the benefit from a fresh look, and so the firm would like to retain its incumbent auditor However, when MAR is imposed, the incumbent’s good knowledge is lost, and now only the ‘ fresh look matters Therefore, such firms with better prospects switch to an aggressive auditor 83 T Lu, K Sivaramakrishnan / J Account Public Policy 28 (2009) 71–91 (Remark... their preferred auditors under the guise of mandatory auditor rotation However, for firms with better financial prospects ðk > kÃ Þ, investment inefficiency is minimized with their (aggressive) incumbent auditors, but MAR forces them to switch to a new auditor with poor client-specific knowledge, thereby impairing those firms’ investment efficiency 5.2 Auditor choice given a conservative incumbent auditor Next... 5.1 Auditor choice given an aggressive incumbent auditor In a non-MAR regime, given an aggressive incumbent auditor, the firm can choose to keep the aggressive incumbent auditor, or hire either an aggressive or conservative auditor The following proposition characterizes the firm’s auditor choice: Ex ante auditor choice Given an aggressive incumbent auditor: non-MAR MAR Given a conservative incumbent auditor:... λ** retain non-MAR MAR switch to aggressive retain non-MAR Ex post auditor choice Given an aggressive incumbent auditor: retain switch to conservative switch to aggressive Given a conservative incumbent auditor: retain non-MAR MAR switch to conservative switch to aggressive Fig 4 Auditor choices in ex ante and ex post cases 1 λ 84 T Lu, K Sivaramakrishnan / J Account Public Policy 28 (2009) 71–91 Proposition... firms with poorer prospects switch to a conservative auditor (Remark 1) On the other hand, in the region k P 1, MAR essentially results in a switch 2 from an incumbent aggressive auditor to a new aggressive auditor (Remark 1) Thus, in this region, there is loss in investment efficiency due to poor knowledge without even the benefit of the fresh look 4.2 Auditor choice given a conservative incumbent auditor... different values of k choose the same level of investment Appendix 2 The auditor’s decisions In this appendix, we endogenize the auditor’s two decisions: audit quality (audit effort) and attestation We first discuss the auditor’s attestation decision (i.e., whether to approve or disapprove the client preferred report, G) and then discuss the auditor’s audit quality decision (i.e., what level of q the auditor... incumbent auditor Proceeding along similar lines as in the case of the aggressive incumbent auditor above, we state the following proposition: Proposition 5 In a non-MAR regime, a firm with a conservative incumbent auditor retains its auditor if 1 1 > k 6 kÃÃ and switches to an aggressive new auditor if k P kÃÃ , where kÃÃ qN 1 þ 1Àq 1ÀqI 2 q N I 82 T Lu, K Sivaramakrishnan / J Account Public Policy 28 (2009) ... course, in reality, client firms may switch auditors because they have grown to a size that the incumbent auditor lacks a capacity to handle We do not introduce this factor into our model 85 T Lu, K Sivaramakrishnan / J Account Public Policy 28 (2009) 71–91 Given a conservative auditor, only the firm receiving an audit report B has an incentive to switch auditors and such a firm can have either a financial... effect does not exist, only the fresh look matters 5 Ex post auditor choice (opinion shopping) In this section, we analyze the firm’s ex post auditor choice under both MAR and non-MAR regimes By ex post auditor choice or opinion shopping, we refer to the situation in which the firm chooses its auditor after the realization of the state (g or b) and conditional on the incumbent auditor’s proposed report, G . Mandatory audit firm rotation: Fresh look versus poor knowledge Tong Lu * , K. Sivaramakrishnan Bauer College of Business, University of Houston, Houston, TX 7720 4-6 021, United States article. where a represents poor knowledge and b represents fresh look. We assume that dq d a < 0 and dq db > 0; that is, a poorer knowledge decreases audit quality but a fresher look increases audit quality following table presents the various auditing scenarios along the poor knowledge and fresh look dimensions: (MAR denotes mandatory audit firm rotation. ) The client’s auditor choice Incumbent fC; q I g

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