Going-concern judgments: An experimental test of the self-fulfilling prophecy and forecast accuracy

Going-concern judgments: An experimental test of the self-fulfilling prophecy and forecast accuracy

Journal of Accounting and Public Policy 22 (2003) 401–432 www.elsevier.com/locate/jaccpubpol Going-concern judgments: An experimental test of the sel...

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Journal of Accounting and Public Policy 22 (2003) 401–432 www.elsevier.com/locate/jaccpubpol

Going-concern judgments: An experimental test of the self-fulfilling prophecy and forecast accuracy Robert R. Tucker a,*, Ella Mae Matsumura b, K.R. Subramanyam c a

c

Accounting & Taxation Area, Fordham University, 113 W. 60th Street, New York, NY 10023, USA b Department of Accounting & Information Systems, University of Wisconsin-Madison, 975 University Avenue, Madison, WI 53706, USA Marshall School of Business, University of Southern California, Los Angeles, CA 90089-0441, USA

Abstract Statement on Auditing Standards No. 59 requires auditors to assess whether substantial doubt exists about a clientÕs ability to remain a going concern. This study reports an experimental economic test of a game-theoretic model of that judgment. Competing behavioral predictions are based on loss avoidance, risk seeking, altruism, and adversarial play. We also examine how strategic dependence affects auditorsÕ and clientsÕ propensity to depart from equilibrium. The auditor conveys to the client a forecast on business survival and the intention to express a clean or going-concern opinion. The client can attempt to avoid a goingconcern opinion and its potential self-fulfilling prophecy effect by switching auditors. Several subjects played pure strategies consistent with loss avoidance, adversarial play, and risk seeking. Nevertheless, the experimental results support the modelÕs prediction that the first treatment variable, self-fulfilling prophecy, leads auditors to express fewer going-concern opinions and leads clients to switch auditors more frequently, particularly when the audit evidence has low forecast accuracy. The second treatment variable, forecast accuracy, also has a significant effect on subject behavior. However, in contrast to the modelÕs predictions, inaccurate forecasts did not lead auditors to express more clean opinions but led clients to switch auditors more frequently.  2003 Elsevier Inc. All rights reserved.

*

Corresponding author. Tel.: +1-201-670-4984; fax: +1-212-765-5573. E-mail address: [email protected] (R.R. Tucker).

0278-4254/$ - see front matter  2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jaccpubpol.2003.08.002

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Keywords: Experimental economics; Loss avoidance; Adversarial; Altruism; Auditing; Going concern opinions and self-fulfilling prophecy

1. Introduction The sensational Enron and WorldCom bankruptcies led congressional committees to ask why the auditors did not alert the public to the firmsÕ inherent riskiness. Weiss (2002) found that out of 228 bankrupt public companies, Enron and 95 other companies received clean opinions in the year prior to bankruptcy. The far-reaching consequences of such collapses justify research aimed at improving the quality of auditorsÕ going-concern judgments. Maintaining the professionÕs ethical standards of independence and integrity in the face of client pressure is particularly difficult with going-concern decisions because the judgment is complex, with unavoidable uncertainty. A key complication is the self-fulfilling prophecy effect, that is, when the auditorÕs public expression of doubt, in itself, hastens a companyÕs end, particularly one whose viability rests on trust and a high stock price, as did EnronÕs and WorldComÕs. Since client bankruptcy can also negatively affect the auditor, we test whether the auditorÕs judgment is affected when the going-concern report contributes to a self-fulfilling prophecy. We also examine how noise in the auditorÕs forecast of client viability affects the auditorÕs reporting ability. Recently, the Panel on Audit Effectiveness (2000, pp. 59–63) called for clearer guidance in defining a going-concern problem, procedures for evaluating the problem, and requirements for disclosing the problem. Clarifying and providing more detailed guidelines for auditorsÕ going-concern reporting should facilitate reducing noise in the auditorÕs forecast of client viability. We study the effect of decreasing the noise in a context where clients apply economic pressure and thereby challenge the auditorÕs independence. Our study involves experimental economic tests (Davis and Holt, 1993) of a game-theoretic modelÕs predictions. Only a few experimental economic studies examine a substantive auditor-reporting decision connected to possible auditor switching (e.g., Schatzberg (1994, pp. 33–55) and Mayhew (2000, pp. 599– 617)). Previous analytical studies using game theory to analyze auditor switching as a function of audit evidence and reporting include Dye (1991, pp. 347–374), Teoh (1992, pp. 1–23), and Lennox (2000, pp. 321–337). Unlike these studies, our study incorporates the self-fulfilling prophecy effect and examines strategic behavior before the auditor issues a report. Auditors and clients are more likely to confront the going concern question early in an annual audit as a result of the recent release of SAS No. 100 (AICPA, 2003) on interim financial reporting, which requires such a review with interim as well as year-end

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reports. In addition, after the reportÕs issuance, the auditorÕs and clientÕs range of strategic options and outcomes diminishes, making the issue less consequential. More closely related are the experimental study of Tucker and Matsumura (1998, pp. 179–217) and the analytical study of Matsumura et al. (1997, pp. 727–758). Our game-theoretic model builds on that of Matsumura et al., which assumes that subjects are risk neutral, they maximize only their own wealth, they never respond emotionally when the other playerÕs decision causes them to lose money, and they follow and anticipate high-level strategic thinking (Bloomfield, 1997, pp. 517–538). We develop and test competing predictions based on loss avoidance, risk seeking, adversarial play, and altruism to provide a perspective on the game-theoretic model and to aid in interpreting the results. Partly due to these alternative models, this study includes extensive descriptive and statistical analyses of individual subject behavior based on independent observations. Finally, this paper incorporates a test of strategic dependence. In our experiment, auditors convey to the client an intention to issue a clean or going-concern report based on a forecast judgment. Upon learning that a going-concern opinion is imminent, the client decides whether to switch auditors to obtain a positive probability of a clean opinion. The clientÕs credible threat to switch auditors complicates the auditorÕs reporting decision. The auditorÕs reporting judgment is complicated further by two factors: a self-fulfilling prophecy effect, and potential inaccuracy (noise) in the auditorÕs forecast. Specifically, if the auditorÕs going-concern report is self-fulfilling, then the game-theoretic results predict that the auditor will express fewer going-concern opinions to avoid losing an audit fee, and the client is more likely to switch auditors if a going-concern opinion is imminent. Moreover, an auditor is more likely to express a clean opinion as the accuracy of the auditorÕs forecast of client viability decreases. The paper contributes to the literature in several ways. Our tests reveal that the game-theoretic model is useful in interpreting many subjectsÕ behavior and in fully describing some subjectsÕ behavior. The competing predictions generated by alternative decision models also had notable explanatory power. These results suggest that one model alone is inadequate to aptly describe the variety of decision patterns exhibited. Specifically, the experimental results support the directional prediction that auditors express fewer going-concern opinions when the auditorÕs report is self-fulfilling. However, the percentage of going-concern opinions expressed far exceeded that predicted by the analytical model (72% versus 0%). In addition, clients who anticipated receiving a going-concern opinion switched auditors more frequently when that opinion was self-fulfilling, though not as frequently as predicted (40% versus 100%). Loss avoidance best explains these dramatic and surprising differences from predictions. If the relatively small experimental penalties for auditors and clients had this influence, it is worth considering whether the larger penalties faced by practicing

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auditors and clients might similarly make their reporting and switching decisions more conservative. Weaker forecast evidence affected behavior but not as predicted analytically. Auditors did not express more clean opinions, but clients did switch auditors more aggressively. Also, the experimental results strongly support BloomfieldÕs hypothesis that increases in strategic dependence lead players to play farther off-equilibrium. The remainder of the paper is organized as follows. Section 2 discusses the studyÕs two treatment variables. Section 3 presents the steps in the experiment, and Section 4 describes competing decision models. Section 5 states and discusses the major hypotheses and predictions. Sections 6 and 7 describe the experiment and the experimental results, respectively. The final section presents the paperÕs conclusions.

2. Issues 2.1. The self-fulfilling prophecy effect A unique aspect of the going-concern decision is that a going-concern report may actually contribute to the demise of an otherwise viable client. Early evidence on this effect was obtained primarily through experimentation (Kida, 1980, pp. 506–523), surveys and interviews (Mutchler, 1984, pp. 17–30; Williams, 1984, pp. 12–19; Carmichael and Pany, 1993, pp. 35–58), and professional observation, (Bell, 1991, pp. 14–20). Dopuch et al. (1986, pp. 93–117) provided empirical evidence that going-concern opinions are associated with a significant decline in stock price on average. Others have attempted to document the selffulfilling prophecy effect empirically. Pryor and Terza (1999) and George et al. (1996) find a positive and significant self-fulfilling prophecy effect and provide additional evidence on its strength and immediacy. One purpose of our study is to determine the ramifications of this effect for the strategic interaction between the auditor and client with regard to reporting and auditor-switching behavior. 2.2. Noise in assessing the client’s going-concern status This study operationalizes noise by varying the level of inaccuracy in the auditorÕs going-concern forecast. Future uncertainty only partially accounts for the noise in the auditorÕs forecast of client viability. Noise might also arise should the auditor collect insufficient or unreliable evidence, misinterpret results, or misinterpret the professionÕs objective as evidenced by the betweenauditor inconsistency in interpreting subjective phrases such as ‘‘substantial doubt exists’’ found in US Statement on Auditing Standards No. 59. Evidence also exists that auditors consider factors other than those needed to satisfy

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professional standards, such as size (Pryor and Terza, 1999; Louwers, 1998, pp. 143–156), default status even when it is not well correlated with business termination (Chen and Church, 1992, pp. 30–49; Louwers, 1998, pp. 143–156), and the auditorÕs potential loss function (Hopwood et al., 1994, pp. 409–432). The noise variable merits study for at least two reasons. First, this variable is the variable most controllable by practitioners and the accounting profession as a whole. Second, the effect is socially significant. For example, noise may partially explain WeissÕ (2002) finding that 42.1% of the public companies that went bankrupt during 2001 and the first half of 2002 received clean opinions on their prior annual report. Empirical evidence suggests that auditors render more going-concern opinions the clearer their audit and reporting responsibilities (Raghunandan and Rama, 1995, pp. 50–63), and the less ambiguous the probability of bankruptcy (McKeown et al., 1991, pp. 1–13).

3. Sequence of steps in the game-theoretic model and experiment Our 2 · 2 between-subjects experiment involves two treatments: a self-fulfilling prophecy effect and forecast inaccuracy. Each game involves strategic interaction between two players assuming the roles of auditor and client. The game tree depicted in Fig. 1 supplements the narrative below by providing a concise graphical overview of the game and experiment, and Table 1 provides a more complete definition of the variables used below. All variables or parameter values, information, and payoffs relevant to a particular cell were common knowledge to the auditor and client. The steps of each game in the experiment closely parallel the steps in our game-theoretic model. 3.1. Initial state determination The computer plays the role of nature and determines the clientÕs future state––business termination (B) or survival (S)––which is unknown to the client and auditor at the beginning of the game. In the experiment, the prior probabilities of the two states are equal, 1 which suggests that this is a high-risk engagement. 3.2. Audit forecast judgment During the course of an audit, the auditor accumulates evidence that provides the basis for an imperfect forecast judgment of the clientÕs viability. The 1

We assume the auditor can a priori identify clients in financial distress. Within this subset of high-risk clients, P ðBÞ ¼ 0:5 might be reasonable.

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Fig. 1. Sequence of events given a forecast.

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Table 1 Summary of variables and parameters Auditor payoffs AFS ¼ $1:35 AFB ¼ $0:00 D ¼ $0:05 Ca ¼ $0:60

Cb ¼ $0:80 Client payoffs PV ¼ $0:90

L ¼ $0:70

SW ¼ $0:20

Probabilities P ðBÞ ¼ 0:5 e

pClean ¼ 0:50 pFail

sf

psf

Present value of future quasi-rents anticipated from a surviving client. Present value of future quasi-rents anticipated from a defunct client. Expected cost of client dismissal. This represents a reputational cost and potential loss of the current yearÕs audit fee. Cost of reputation damage and possible legal implications from incorrectly issuing a going-concern report. Reputation damage would include the loss of or decrease in fees from existing and prospective clients. Legal costs and reputation damage resulting from incorrectly issuing a standard report when a going-concern report was appropriate. Present value of future payoffs to the client from managing a surviving firm. This encompasses managerial compensation including stock options, increased reputation, and goodwill from managing a successful business. Loss in benefits to the client from receiving a going-concern report only when the firm survives. This includes reductions in stock price, increased probability of management takeover, and loss of reputation in the labor market. Transaction cost from auditor change. This includes both actual cost of auditor change (switch) and the adverse reputational effect in financial markets. The prior probability of business termination known to both the incumbent auditor and the client. The probability a binary forecast received by the incumbent auditor is incorrect. Let B denote business termination, S denote business survival, yB denote a forecast suggesting business termination, and yS denote a forecast suggesting survival. We assume PrðyS jBÞ ¼ PrðyB jSÞ ¼ e and PrðyB jBÞ ¼ PrðyS jSÞ ¼ 1  e. In the experiment, the level of error in the binary forecast is either high, eH ¼ 0:45 (in cells EH -NoSFP and EH -SFP), or low, eL ¼ 0:35 (in cells EL -NoSFP and EL -SFP). The probability that the alternative auditor will issue a clean opinion. Generic term for the unperturbed posterior probability of business termination. That is, pFail may represent pBB ¼ PrðBjyBB Þ, pSB ¼ PrðBjySB Þ, or pss ¼ PrðBjySS Þ, where pBB indicates the auditor combined two forecasts yielding a joint forecast of business termination. The perturbation in the posterior probability of business termination induced by the self-fulfilling prophecy. In the experiment, the self-fulfilling prophecy effect was either high, sf H ¼ 0:4 (in cells EL -SFP and EH -SFP), or low, sf L ¼ 0 (in cells EL -NoSFP and EH -NoSFP). The perturbed posterior probability of business termination, given a goingconcern decision in conjunction with a self-fulfilling prophecy effect. In the experiment, this probability is operationalized as pSf ¼ minf1; pFail þ sf H g ¼ minf1; pFail þ 0:4g.

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client knows the auditorÕs forecast, y, as it seems reasonable that the auditor would justify the appropriateness of a going-concern opinion to the client. On the other hand, if the auditor intends to issue a clean opinion, the clientÕs information set is irrelevant, as there is no reason to switch auditors. We combine two forecasts of S or B to generate three imperfect forecasts, ySS , yBS , and yBB (labeled forecasts 1, 2, and 3, respectively), with ySS suggesting client survival, yBB suggesting business termination, and yBS providing a neutral middle case. 2 The neutral case depicts a challenging audit where the auditorÕs evidence cannot predict client survival. In such a setting, the auditor is more likely to manifest the effects of economic incentives and strategic considerations. The forecast is imperfect because the two underlying forecasts comprising it are inaccurate with probability e. We assume the underlying forecasts are statistically independent, conditional on the true underlying state. One of the two treatments in the experiment is the level of forecast inaccuracy. The level depends on the error in the binary forecasts and is either high, eH ¼ 0:45, or low, eL ¼ 0:35. As defined in Table 1 and shown in Fig. 1, pfail denotes the generic posterior probability of business termination for a given forecast. 3 3.3. Auditor’s reporting decision Based on the auditorÕs forecast, P ðBÞ, the payoffs, the level of self-fulfilling prophecy effect, and an expectation of the clientÕs response, the auditor privately expresses to the client an intention to render either a clean or goingconcern opinion. The computer network relays this intention, displaying it on the clientÕs computer screen. The self-fulfilling prophecy effect occurs only if the client retains an auditor who issues a going-concern opinion. Our model assumes that this effect increases the probability of business termination to pSf > pFail . The experiment operationalizes this increase in probability by increasing the self-fulfilling

2 This characterization also permits a test of a recent proposal by Weiss (2002) to the United States Senate that called for three levels of going-concern report: (1) clean, (2) warning, and (3) going-concern. 3 If the forecast inaccuracy is high, then the posterior probability of business termination, given forecast 1 (ySS ), is computed as follows:

P ðySS jBÞ ¼ e2H ¼ 0:452 ¼ 0:2025 and P ðySS jSÞ ¼ ð1  eH Þ2 ¼ 0:552 ¼ 0:3025 P ðBjySS Þ ¼

P ðySS jBÞP ðBÞ e2H P ðBÞ ¼ P ðySS jBÞP ðBÞ þ P ðySS jSÞP ðSÞ e2H P ðBÞ þ ð1  eH Þ2 ð1  P ðBÞÞ

ð1Þ

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Table 2 Probabilities of business termination given different levels of forecast noise

Forecast 1 Forecast 2 Forecast 3

EL -NoSFP P(Bjforecast)

EL -SFP P(Bjforecast, GCR)

EH -NoSFP P(Bjforecast)

EH -SFP P(Bjforecast, GCR)

0.23 0.50 0.77

0.63 0.90 1.00

0.40 0.50 0.60

0.80 0.90 1.00

GCR ¼ auditor issues a going-concern report; B ¼ business termination; forecast 1 ¼ ySS , forecast 2 ¼ yBS , and forecast 3 ¼ yBB ; EL -NoSFP: Low forecast error, no self-fulfilling prophecy; EL -SFP: Low forecast error, self-fulfilling prophecy; EH -NoSFP: High forecast error, no self-fulfilling prophecy; EH -SFP: High forecast error, self-fulfilling prophecy. * If the self-fulfilling prophecy effect is absent, then P(Bjforecast) is unaffected by the auditorÕs report. ** Given a self-fulfilling prophecy effect (sf H ¼ 0:4 in the experiment), P(Bjforecast, GCR) ¼ P(BjforecastÞ þ 0:4, or 1, whichever is smaller, that is, with a self-fulfilling prophecy, the selffulfilling prophecy with sf ¼ sf H ¼ 0:4 implies that PðBjforecast; GCRÞ ¼ minf1; PðBjforecastÞ þ 0:4g. *** The computation of this probability is provided in Eq. (1) in footnote 3. The other P(Bjforecast) probabilities are computed similarly.

prophecy variable, sf, from sf L ¼ 0:0 to sf H ¼ 0:4. When the self-fulfilling prophecy variable is set at sf H ¼ 0:4, P ðBjySS Þ in Eq. (1) in footnote 3, will be perturbed from 0.4 to 0.8. The generic perturbed probability, psf , is the smaller of one or (pFail þ sf H ). 4 The experimentÕs four cells, EL -NoSFP, EL -SFP, EH -NoSFP, and EH -SFP, result from crossing two levels of forecast inaccuracy (eL ¼ 0:35 or eH ¼ 0:45) with the two levels of self-fulfilling prophecy effect (sf L ¼ 0:0 or sf H ¼ 0:4). Subjects received the forecast number and the associated probability of business termination reported in Table 2. The auditorÕs penalties for inaccurate reporting, Ca (i.e., penalty for incorrectly issuing a going-concern report) and Cb (i.e., penalty for incorrectly issuing a standard report), promote error avoidance. Note that these payoffs represent expected values. One interpretation of Ca and Cb is that Ca ($0.60) includes a high probability of a relatively small penalty (e.g., loss of client fees), and Cb ($0.80) includes a low probability of a large penalty resulting from an audit failure. Two incentives potentially decrease auditor objectivity. First, clean opinions ensure that the auditor does not suffer the expected cost of dismissal by the

4 Characterizing the self-fulfilling prophecy effect as additive is useful for illustration and is roughly consistent with the findings of George et al. (1996); however, it is not suggested that it is perfectly descriptive. A fruitful area for future empirical and analytical research is to define more precisely the functional form of the sf variable or, possibly, to create a model that endogenizes the effect.

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client, D ¼ $0:05. Second, if the opinion tends to be self-fulfilling, rendering a clean opinion makes it more likely that the auditor will receive audit fees from a surviving client (AFS ¼ $1:35) rather than from a defunct client (AFB ¼ $0). AFS and AFB represent the present value of future quasi-rents anticipated from a surviving and defunct client, respectively. However the client defines audit quality, the AF variables reflect the auditorÕs reputation for delivering such quality of service but do not include the expected long-term implications of this periodÕs report. 3.4. The client’s switching decision and the potential successor auditor’s decision We assume the client becomes aware of the auditorÕs intention in sufficient time to engage another auditor and thus prevent the incumbent auditorÕs decision from becoming public. 5 If the auditor declares the intention to render a clean opinion, the game ends, as it is presumed that the client will retain the auditor. Otherwise, the client decides whether to accept the opinion and retain the auditor or incur the cost to replace the auditor and obtain a second opinion from an alternative auditor, played by the computer. The clientÕs strategy will depend on the auditorÕs forecast, the switching cost (SW ¼ $0:20), and the probability that an alternative auditor will issue a clean opinion, pClean ¼ 0:5. 6 A surviving client must also consider the potential selffulfilling prophecy effect, the present value of managing a viable firm

5 SAS No. 59 requires that auditors inquire with management regarding any mitigating factors which would allow the company to remain a going concern, and SAS No. 100 requires that auditors address the going concern issue when involved with interim reports. Professional regulations (AICPA, 1986, 1997) and SEC 8-K (SEC FRR 34, 1989) requirements to the contrary, in a high-risk audit situation, the client might act strategically to inhibit the free flow of information between auditors, possibly through threat of legal action (e.g., the Lincoln Savings and Loan case (Knapp, 2001, pp. 57–70)). Moreover, because the incumbent auditor does not actually issue an opinion in our scenario, remaining silent entails less legal risk. 6 pClean ¼ 0:5 seems reasonable given that KPMG gave clean opinions on 57% of the publicly listed companies they audited that went bankrupt (Weiss, 2002). Some of the justifications for modeling the second auditorÕs decision as independent include: (1) The clientÕs perception of finding another auditor with different reporting behavior is overly optimistic. (2) Though the auditorÕs forecast is common knowledge, the client need not agree with the auditorÕs perception. (3) The client, now alert to the audit professionÕs perspective, anticipates manipulating the evidence obtained by the successor auditor, (4) The client believes a subpopulation of auditors exist who lack competence (i.e., ability, knowledge, work effort, audit approach) (Williams, 1988, pp. 243–261; St. Pierre and Anderson, 1984, pp. 242–263), lack independence (Barnes and Huan, 1993, pp. 223– 238), interpret subjective elements of the accounting standards differently, or possess different risk preference or marketing strategies, or (5) despite professional standards and SEC requirements to disclose the reasons for the switch in an 8-K, a free flow of communication may not exist between predecessor and successor auditors.

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(PV ¼ $0:90) and the cost (L ¼ $0:70) associated with erroneously receiving a going-concern opinion from either the current or the successor auditor. If the client terminates operations, the present value of future payoffs is normalized to zero (PV ¼ $0) for simplicity. 3.5. Payoff distribution At the conclusion of each game, the computer displays the payoff screens, which convey all decisions made, the cash payoff for the game, and the cumulative cash payoff totaling all completed games. Also displayed are the random numbers generated to determine the clientÕs outcome as well as the outcome itself both before and after the self-fulfilling prophecy effect. Table 3 shows all possible cash payoffs for both players and panel C of Table 4 reports the equilibrium predictions based on the parameters used in this study.

4. Competing decision models One objective of this research is to investigate the relative predictive power of other decision models. Kachelmeier (1996) and Kachelmeier and King (2002, pp. 219–232) suggest that the benefits of experimentation are more fully tapped if one considers both the economic incentives of a strategic model and the behavioral forces that might challenge these incentives. To this end, treatment manipulations and economic incentives were purposely not designed to smother strong behavioral tendencies, which, though contrary to equilibrium prediction, might reflect behaviors exhibited by real world auditors. The first four alternative decision models predict auditor–client behaviors that are independent of treatment level or forecast type, as follows, where ‘‘Going Concern’’ indicates that the auditor intends to issue a going-concern report: Decision model

AuditorÕs opinion

ClientÕs decision

Loss avoidance Adversarial Altruism Risk seeking

Going concern Going concern Clean Clean

Retain Switch Retain Switch

The fifth alternative decision model, ‘‘follow the forecast,’’ assumes subjects base their decisions only on the forecast received, ignoring economic incentives.

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Failed

Survived

Failed

Survived

Failed

Survived

Failed

Survived

AuditorÕs Report GCR ¼ going-concern report ClientÕs decision New AuditorÕs Report

Clean N/A N/A

Clean N/A N/A

GCR Switch Clean

GCR Switch Clean

GCR Switch GCR

GCR Switch GCR

GCR Retain N/A

GCR Retain N/A

Audit fee (AF)

Dismissal cost (D)

Cost of Type I error (Ca )

Cost of Type II Error (Cb ) AuditorÕs cash payoff

$0.00

$1.35

$0.00

$1.35

)$0.05

)$0.05

)$0.05

)$0.05

)$0.80 )$0.80

$1.35

)$0.05

)$0.05

)$0.05

)$0.05

$0.00

$0.75

ClientÕs cross payoff (PV)

Cost of AuditorÕs Type I Error (L) Switching cost (SW) ClientÕs net cash payoff

$0.00

$0.90

$0.00

$0.90

$0.00

$0.00

$0.90

)$0.20 )$0.20

)$0.20 $0.70

)$0.20 )$0.20

$0.90 )$0.70

$0.00

$0.90 )$0.70 )$0.20 $0.00

$0.00

$0.20

)$0.60

GCR ¼ auditor issues a going-concern report. * The probability of the clientÕs outcome is affected by the audit report issued in the self-fulfilling prophecy cells EL -SFP and EH -SFP.

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Table 3 Payoff possibilities for both players

Table 4 Optimal strategies and expected returns by forecast and cell

Client

Auditor

EH -NoSFP Client

EH -SFP

Pair

Auditor

Auditor

Client

Auditor

1

Clean opinion GCR-switch GCR-retain

0.86 )0.05 0.58

0.69 0.22 0.15

0.86 )0.5 0.28

0.69 0.18 0.07

0.49 )0.5 0.45

0.54 0.13 0.12

0.49 )0.05 0.15

0.54 0.09 0.04

2

Clear opinion GCR-switch GCR-retain

0.28 )0.05 0.38

0.45 0.08 0.10

0.28 )0.05 0.08

0.45 0.03 0.02

0.28 )0.05 0.38

0.45 0.08 0.10

0.28 )0.05 0.08

0.45 0.03 0.02

3

Clear opinion GCR-switch GCR-retain

)0.31 )0.05 0.17

0.21 )0.07 0.05

)0.31 )0.05 0.00

0.21 )0.10 0.00

0.06 )0.05 0.30

0.36 0.02 0.08

0.06 )0.05 0.00

0.36 )0.02 0.00

Panel B: Summary of the optimal strategies for the client receiving a going-concern opinion EL -SFP Forecast EL -NoSFP 1 Switch Switch 2 Retain Switch 3 Retain Retain Panel C: Summary of the equilibrium auditor/client strategy pairs 1 Clean opinion Clean opinion 2 GCR-Retain Clean opinion 3 GCR-Retain GCR-Retain

Client

EH -NoSFP

EH -SFP

Switch Retain Retain

Switch Switch Retain

Clean opinion GCR-Retain GCR-Retain

Clean opinion Clean opinion Clean opinion

413

GCR ¼ auditor issues a going-concern report; EL -NoSFP: Low forecast error, no self-fulfilling prophecy; EL -SFP: Low forecast error, self-fulfilling prophecy; EH -NoSFP: High forecast error, no self-fulfilling prophecy; EH -SFP: High forecast error, self-fulfilling prophecy. Forecast 1 ¼ ySS , forecast 2 ¼ yBS , and forecast 3 ¼ yBB . * Nash equilibrium.

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Panel A: Expected returns for each strategy pair by forecast and cell EL -SFP Forecast Auditor/client strategy EL -NoSFP

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Table 5 Predictions of auditor and client behavior by cell and decision model Game Theory

Loss avoidance

Risk seeking

Adversarial

Altruism

Forecast 1 Auditor EL -NoSFP EL -SFP EH -NoSFP EH -SFP

Clean(2) Clean(1) Clean(4) Clean(3)

GC(3) GC(4) GC(1) GC(2)

Clean(2) Clean(1) Clean(4) Clean(3)

GC(2) GC(1) GC(4) GC(3)

Clean(2) Clean(1) Clean(4) Clean(3)

Client EL -NoSFP EL -SFP EH -NoSFP EH -SFP

Switch(2)a Switch(1)a Switch(4)a Switch(3)a

Retain(3) Retain(4) Retain(1) Retain(2)

Switch(2) Switch(1) Switch(4) Switch(3)

Switch(1) Switch(3) Switch(2) Switch(4)

Retain(1) Retain(3) Retain(2) Retain(4)

Forecast 2 Auditor EL -NoSFP EL -SFP EH -NoSFP EH -SFP

GC Clean GC Clean

GC(1) GC(2) GC(1) GC(2)

Clean(2) Clean(1) Clean(2) Clean(1)

GC(2) GC(1) GC(2) GC(1)

Clean(2) Clean(1) Clean(2) Clean(1)

Client EL -NoSFP EL -SFP EH -NoSFP EH -SFP

Retaina;b Switcha Retaina Switcha

Retain(1) Retain(2) Retain(1) Retain(2)

Switch(2) Switch(1) Switch(2) Switch(1)

Switch(1) Switch(2) Switch(1) Switch(2)

Retain(1) Retain(2) Retain(1) Retain(2)

Forecast 3 Auditor EL -NoSFP EL -SFP EH -NoSFP EH -SFP

GC(1) GC(2) GC(3) Cleanb

GC(1) GC(2) GC(3) GC(4)

Clean(4) Clean(3) Clean(2) Clean(1)

GC(4) GC(3) GC(2) GC(1)

Clean(4) Clean(3) Clean(2) Clean(1)

Client EL -NoSFP EL -SFP EH -NoSFP EH -SFP

Retain(1)a Retain(2)a Retain(3)a Retain(4)a

Retain(1) Retain(2) Retain(3) Retain(4)

Switch(4) Switch(3) Switch(2) Switch(1)

Switch(2) Switch(4) Switch(1) Switch(3)

Retain(2) Retain(3) Retain(1) Retain(4)

GC ¼ Going-concern opinion; (1) ¼ highest predicted average for all cells; (2) ¼ second highest, etc. a Predictions of client switching behavior presume the auditor expressed a going concern opinion. b Rankings are not given because the decision makerÕs strategy changes across cells.

The loss avoidance and risk seeking models relax the game-theoretic modelÕs assumption that the players are risk neutral. The adversarial and altruism decision models are motivated by prior experimental studies of

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bargaining games (e.g., the Ultimatum and Dictator games (Boles et al. (2000)) that find that subjects do not act in the assumed egoistic manner. Instead, they consider the other playerÕs outcomes. Moreover, apparent emotional reactions to perceived unfairness, altruism and retaliation, lead to non-Nash solutions (Guth et al., 1982, pp. 367–388; Forsythe et al., 1994, pp. 347–369). Davis and Holt (1993) summarize the literature on Ultimatum and Dictator games and conclude that strategic considerations do affect the first moverÕs generosity, but they are not the whole story. This experiment bears some similarity to the Ultimatum game in that the auditor has first-mover advantage and the client can retaliate at some cost by switching auditors, suggesting that similar forces could affect the strategic interaction in this experiment. Though the experimental treatments do not affect the predicted behavior of these alternative decision models, the propensity to behave in the predicted manner varies in intensity among the four cells in our experiment. Table 5 reports the intensity by designating (1) as the highest predicted average and (4) as the lowest. For example, holding the noise level constant, the SFP makes a going-concern opinion more likely for an adversarial auditor and less likely for a loss-avoiding auditor. For comparison, Table 5 includes the game-theoretic predictions. The predicted client strategies presuppose that the auditor declared an intention to issue a going-concern opinion because experimentally, the client has no decision otherwise. 4.1. Loss avoidance Loss avoidance is a likely characterization of many real-world auditors whose financial and human capital are tied up in the firm and who do not want to forfeit their investment in reputation by issuing an erroneous opinion. Experimentally, subjects are uncertain regarding the other playerÕs utility function, level of rationality, and decision model. This uncertainty in conjunction with a strong desire to avoid losing money can lead some players to exhibit loss-avoiding behavior (Tversky and Kahneman, 1992). For simplicity, suppose loss-avoiding subjects seek to minimize their maximum loss. We develop the predictions for auditor and client using the following procedure: (1) We predict that the auditor will avoid the largest absolute dollar loss ()$0.80) in Table 3 by always expressing a going-concern opinion. Similarly, upon receiving a going-concern opinion, clients retain the auditor, as switching exposes them to the largest absolute dollar loss of )$0.20. (2) Given the decision and forecast, we use panels A and B of Table 4 to rank the desirability of the decision across cells. (3) If two cells have identical expected returns, we break the tie by minimizing the opportunity

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loss of this decision versus the alternative anticipating the other partyÕs trembling hand. 7 4.2. Risk seeking Audit failures sometimes result from risk seeking behavior by auditors as well as clients. Audit partners, such as Jose Gomez in the ESM Government Securities case (Knapp, 2001, pp. 15–28) or David Duncan and Joseph Berardino in the Enron case (CNN/Money, 2002) were aware of the risks to their careers and their firmsÕ reputations, yet they accepted those risks. Even if less common, risk-seeking behavior warrants consideration because it could lead an auditor to underweight the consequences of an audit failure and emphasize the gains (e.g., higher audit and consulting fees, status in firm) derived from accepting the client-preferred position. For simplicity, we assume the riskseeking individual always prefers the decision that makes possible the largest payoff. Consequently, regardless of forecast, the auditor always prefers to express a clean opinion, and the client who receives a going-concern opinion always switches auditors (see Table 3). 8

7 In this case, the auditorÕs opportunity loss is the difference between the auditorÕs expected returns for (1) expressing a clean opinion and being retained and (2) expressing a going concern opinion and being retained or replaced in accordance with the clientÕs assumed decisions. For example, if the auditor receives forecast 2 and the client responds as indicated in panel B of Table 4, then the auditorÕs opportunity loss for cell EL -NoSFP is ð0:28  0:38 ¼ 0:10Þ, since the clientÕs optimal strategy is to retain. However, in cell EL -SFP, the client finds switching optimal; thus, the opportunity loss is much higher ð0:28  ð0:05Þ ¼ 0:33Þ. No further criterion exists to break the ties because both NoSFP cells, EH -NoSFP and EL -NoSFP, provide identical expected returns, as do the two SFP cells. The rankings for all forecasts are determined with similar logic. For forecast 1, we use this procedure and find that the EL cells are tied ð0:86  ð0:05Þ ¼ 0:91Þ and EH cells are tied ð0:49  ð0:05Þ ¼ 0:54Þ. In contrast to the forecast 2 situation, we are able to use a further procedure to distinguish between the tied cells (NoSFP and SFP), given the forecast inaccuracy. We assume that some clients exhibit a ‘‘trembling hand’’––that is, upon receiving a going concern opinion, they will retain the auditor at least some of the time. Alternatively, we can assume that the loss-avoiding auditor perceives the client to be like-minded, and therefore the client seeks to avoid the loss of $0.20 that results only if they switch (see Table 3). For example, in the forecast 1 case, the opportunity loss would be ð0:86  0:58 ¼ $0:28Þ for cell EL -NoSFP and ð0:86  0:28 ¼ 0:58Þ for cell EL -SFP. 8 If the auditor were to express a clean opinion, of course the client would prefer to retain; however, experimentally, the client makes decisions only if the auditor expresses a going concern opinion. Consequently, our prediction of client behavior is that they will switch auditors, making possible the $0.70 payoff (Table 5).

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4.3. Adversarial decision model Subjects might engage in adversarial play if they hold the other player accountable, perceive the other player to be unfair or insensitive to their outcome, or seek to deter unwanted behavior. In general, an auditor who wishes to hurt the client will propose a going-concern opinion and the clientÕs retaliates by switching auditors. More emotional play is anticipated in the self-fulfilling prophecy cells because the auditorÕs decision affects the clientÕs outcome. Though curtailed by recent legislation, clients still can penalize the auditor by declining to purchase non-audit services as well. This partial loss of potentially lucrative fees would allow the client to apply pressure on an on-going basis. Loss-avoiding and adversarial auditors both choose to express going-concern opinions regardless of forecast type (see Table 5). However, the experimental treatments have the opposite effect on their level of desire. The SFP only makes the adversarial auditor more likely to give a going-concern opinion because it causes greater loss to the client (see Table 4). Like the risk-seeking client, the adversarial one always prefers to switch auditors in the face of a going-concern opinion. However, the criteria used to arrive at the decision rule differ, and the models predict different levels of enthusiasm for the decision rule across cells (see Table 5). For example, the adversarial clientÕs desire increases when (1) no SFP exists and (2) forecast error is low for forecast 1 or high for forecast 3. 9 4.4. Altruistic decision model Other subjects may consider the other playerÕs welfare but act altruistically. In the real world, clients are under no professional duty to remain independent of their auditor and frequently choose auditors who they know and like. As auditor tenure lengthens and the client hires professionals from their audit firm (e.g., Enron), this bond can deepen. Becker (1976) and Farnell (2002) provide several reasons why altruism, helping another at a cost to oneself, persists in equilibrium in the survival of the fittest. Like the risk-seeking auditor, the

9

We determined these predictions by evaluating the most negative effect on the other player according to the expected returns in Table 4. If the negative effect on the auditorÕs expected returns was the same for two cells, then the clientÕs level of desire was determined by his own expected return. Consider the clientÕs ranking of this strategy for forecast 3 (i.e., 2, 4, 1, 3) in Table 5. The auditorÕs economic expected loss should the client switch rather than retain is ð0:17  ð0:05Þ ¼ 0:22Þ in cell EL -NoSFP, ð0  ð0:05Þ ¼ 0:05Þ in cell EL -SFP, ð0:30  ð0:05Þ ¼ 0:35Þ in cell EH NoSFP, and ð0  ð0:05Þ ¼ 0:05Þ in cell EH -SFP. One rationale for behaving adversarially is to motivate the opponent to change strategies. Though the same loss is meted out in cells EH -SFP and EL -SFP, the adversarial client prefers EH -SFP because it is more likely the auditor will change strategy since changing would increase the auditorÕs expected return.

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altruistic auditor will always give a clean opinion, and the altruistic client will always retain the auditor. However, the altruistic auditorÕs preference for this decision strategy (see Table 5) depends on the strategyÕs effect on the clientÕs expected returns. Specifically, this desire increases if the SFP exists or if forecast 3Õs error is high. The altruistic client always retains the auditor, thus enabling the auditor to avoid the sure loss stemming from dismissal. To the extent the clients consider their own payoff in addition to the auditorÕs, retention is more likely in cells without the SFP and, in the case of forecast 3, when the forecast error is high. 4.5. Follow the forecast A final decision model captures the behavior of a highly professional auditor or one that is naive. Specifically, the model assumes subjects do not base their reporting judgments on economic incentives and strategic consequences in their reporting judgments, but rather, merely follow the forecast. That is, if the forecast predicts that the client will terminate operations, the auditor expresses a going-concern opinion. Conversely, if the forecast predicts survival, the auditor expresses a clean opinion. Finally, when the forecast is neutral, the auditor randomizes between clean and going-concern opinions, which we define as a reporting average between 0.4 and 0.6 (where 1 ¼ clean opinion and 0 ¼ going-concern opinion).

5. Hypotheses 5.1. Self-fulfilling prophecy H1 and H2 test the effect of the self-fulfilling prophecy (SFP) on the initial auditorÕs reporting decision and on the clientÕs decision to switch auditors. Three cell-to-cell comparisons of equilibrium predictions, 10 reported in panel C of Table 4, form the basis for testing H1. Forecast 2 provides two contrasts. The auditor expresses an intention to issue a going-concern opinion in the noSFP cells, EL -NoSFP and EH -NoSFP, but expresses a clean opinion in the SFP cells, EL -SFP and EH -SFP. Similarly, in the high forecast error condition for forecast 3, the auditor expresses a going-concern opinion in EH -NoSFP and a clean opinion in EH -SFP. These three contrasts form the basis for H1. If any 10

The equilibrium predictions are based on the experimentÕs operationalizing the self-fulfilling prophecy effect by increasing the self-fulfilling prophecy variable, sf, from 0 to 0.4. If sf ¼ sf H ¼ 0:4, then the generic perturbed probability is the smaller of one or (pFail þ sf H ), that is, the smaller of one or pSf . The variable sf corresponds to pSf  pFail .

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auditors manifest altruistic or risk-seeking behavior (i.e., expresses clean opinions) in NoSFP cells or loss avoidance and adversarial behavior (i.e., expresses going-concern opinions) in SFP cells, then this will mute the effect of the SFP. H1: The auditor will express more clean opinions when a going-concern opinion contributes to a self-fulfilling prophecy (sf H ¼ 0:4) than when it does not (sf L ¼ 0:0). In general, increases in the self-fulfilling prophecy variable (sf H ) make it more likely the client will switch auditors. Referring to Eq. (A.1) in the appendix, as pSf increases, ^ pclean decreases under the reasonable condition that the clientÕs expected return from operating a surviving company exceeds the expected loss resulting from receiving a going-concern opinion, that is, PV > L, a condition that holds in this experiment ($0.90 > $0.70). Further, as ^pClean decreases, it is less likely that the condition for auditor retention, pClean < ^pClean , will hold. Of course, the auditor forms rational expectations about the clientÕs decision and can avoid dismissal by expressing a clean opinion. For the parameters in this experiment, the client is not predicted to switch in equilibrium (see panel of Table 4). However, if other players employ a different decision model, then the playerÕs best response is to play off-equilibrium also. For example, consider the clientÕs optimal strategies in panels A and B of Table 4. For forecast 2, if the auditor expresses a going-concern opinion, the clientÕs optimal response is to switch auditors in the SFP cells, but retain them in the NoSFP cells. These two contrasts in predictions form the basis for H2. On the contrary, if subjects exhibit loss avoidance or altruism, then they will always retain the auditor despite the SFP effect. In addition, clients playing adversarial or risk-seeking strategies will switch even when no SFP effect exists. Consequently, the manifestation of these alternative decision models will work for the null hypothesis and against the alternative stated below. H2: Given that the auditor expresses a going-concern opinion, the client will switch auditors more often when such an opinion contributes to a self-fulfilling prophecy (sf H ¼ 0:4) than when it does not (sf L ¼ 0:0). 5.2. Noise The purpose of H3 below is to investigate the effect of forecast noise on the auditorÕs reporting decision. In general, as noise increases, the auditor expresses fewer going-concern opinions because noise lowers the posterior probability of business termination (pFail ) making it less likely that expression (A.2) will hold. Intuitively, with less precise evidence, the auditorÕs decision process might be more influenced by economic incentives. For forecast 3, the

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contrast between the equilibrium predictions in cells EL -SFP (going-concern opinion) and EH -SFP (clean opinion), found in panel C of Table 4, form the basis for testing H3. Regardless of treatment, auditors exhibiting loss avoidance or adversarial behavior would always express a going-concern opinion, whereas altruistic or risk-seeking auditors would express a clean opinion. Consequently, these competing predictions work against H3 stated below: H3: The auditor will issue more going-concern opinions as the forecast error decreases.

5.3. Strategic dependence Bloomfield (1997) finds that players have more difficulty determining their optimal strategies when the optimality of their decision is highly dependent on the other playerÕs decision. Such a situation exists in this experiment, motivating H4. For forecasts 2 and 3, when forecasts are inaccurate and the selffulfilling prophecy is in effect, the auditor and client have much higher expected returns if they cooperate (clean opinion-retain) than if they do not (goingconcern-switch). Bloomfield finds that both auditor and manager play farther from equilibrium when strategic dependence is greater. We measure the distance between the equilibrium or comparative static prediction and the auditorÕs and clientÕs decisions and then compare this measure for the cells with the lowest (EL -NoSFP) and highest strategic dependence (EH -SFP). We compute this distance by subtracting the analytical modelÕs prediction (1 ¼ clean; 0 ¼ going-concern; 1 ¼ switch; 0 ¼ retain) from each subjectÕs average to calculate a revised average. H4: Auditor reporting averages and client switching averages will be farther from predicted when strategic dependence is high than when it is low.

6. Subjects and experimental procedures The subject pool consisted of 160 students at a large Midwestern university. For each of the four experimental cells, we conducted a 212 hour session with a cohort of 10 subjects (five assigned to the auditorÕs role and five to the clientÕs role). After completing a subject consent form, subjects received the written instructions, which the experimenter read aloud. After answering clarifying questions, the experimenter administered a pre-experiment questionnaire to test the subjectsÕ understanding of the instructions and to correct any remaining misconceptions. Roles were rotated during the two practice sequences of 25 games, and no cash was paid. In all other respects, these practice rounds

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were identical to the subsequent 30-game experimental sequence. Subjects played the same role throughout the experimental sequence but were randomly re-paired with someone playing the opposite role at the beginning of each game. Through a post-experiment questionnaire, subjects provided demographic data and described their thought processes. The experimenter guaranteed that no one would owe the experimenter money. Endowments of $2.40 for auditors and $0.60 for clients were therefore given at the beginning of the sequence. Payoffs for the session ranged from $3.75 to $23.50. These payoffs and the expected payoffs from each decision were deemed sufficient to make the incentive salient to subjects and to dominate inconsequential, non-economic influences.

7. Experimental results Several measures were taken to promote independence among the 30 periods of the experimental sequence so as to more closely mirror the modelÕs single period structure. Nonetheless, for the purpose of statistical analysis, we define an independent observation as a subjectÕs average response during the 30-period sequence. Because each auditor encounters several realizations of forecast 1, 2, and 3 during the sequence, each has 3 averages. For each forecast, we base our analysis of auditor reporting on 80 observations (20 subjects · 4 cells). The client was able to respond only when the auditor expressed a going-concern opinion. For forecast 1, only 41 auditors expressed going-concern opinions; consequently, we obtained only 41 switching averages. Eighty switching averages are available for forecasts 2 and 3. To measure the strength of the treatment effects and their interaction, we model subject behavior using regression and two sample comparison t-tests and report the results in Table 6. The non-parametric Mann–Whitney tests generated similar results, and the interaction terms were not significant and therefore are not reported. Table 7 shows reporting and switching averages and provides statistics on the number of subjects playing pure or randomized strategies. To detect any learning or other behavioral changes during the 30game sequence, we divided the data into two 15-game periods and re-ran all statistical tests. The tests revealed no period effect. Tables of individual subject behavior are available from the authors by request. 7.1. Hypotheses H1 and H2: the self-fulfilling prophecy effect We first consider forecast 3. The results reported in Tables 6 (panel A) and 7 support hypothesis H1, which predicts that, in equilibrium, auditors form fewer going-concern opinions when issuing such an opinion increases the prospect of client demise. The SFP effect and the concurrent potential loss of

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Table 6 Regression results on client switching and auditor reporting Panel A: Auditor Reporting Model Reporting average ¼ b0 þ b1 ðForecast inaccuracyÞ þ b2 ðself-fulfilling prophecyÞ þ e where: high (low) forecast inaccuracy cells were coded 1 (0), sf H ¼ 0:4 (sf L ¼ 0) cells were coded 1 (0), and clean (going-concern) opinions were coded 1 (0) Forecast 3 Data

Intercept Forecast inaccuracy Self-fulfilling prophecy

Expected sign

Coefficient

t-Statistic

Significance level

+ +

0.15 )0.001 0.078

3.93 )0.01 1.74

0.000 0.99 0.04

Panel B: Client Switching Model Switching average ¼ b0 þ b1 ðForecast inaccuracyÞ þ b2 ðself-fulfilling prophecyÞ þ e where switching (retaining) decisions were coded 1 (0) Forecast 2 Data

Intercept Forecast inaccuracy Self-fulfilling prophecy

Expected sign

Coefficient

t-Statistic

Significance level

+

0.35 0.05 0.13

5.66 0.77 1.92

0.000 0.44 0.03

Coefficient

t-Statistic

Significance level

0.17 0.19 0.02

3.76 3.76 0.43

0.000 0.000 0.66

Forecast 3 Data Expected sign Intercept Forecast inaccuracy Self-fulfilling prophecy

The data upon which the client switching averages are based were gathered by auditor rather than by client. The coefficients of regressions for the auditor or client observing Forecast 1 or auditors observing Forecast 2 are not statistically significant nor are any interaction terms; consequently, these are not reported. * p-value based on a one-tailed test.

the engagement and audit fees cause the auditor to express a clean opinion, though the auditorÕs evidence (i.e., forecast 3) suggests client bankruptcy. Specifically, a t-test of the reporting averages for forecast 3 between the high error cells, EH -NoSFP ¼ 0.13 and EH -SFP ¼ 0.28 (see Table 7), revealed a significant difference in the predicted direction ðp ¼ 0:02Þ, that is, an increase in the SFP increased the dependent variable, percentage of clean opinions. Moreover, the percentage of clean opinions for the SFP cells (EL -SFP (0.21) and EH -SFP (0.28)) was significantly higher than in the NoSFP cells (EL NoSFP (0.17) and EH -NoSFP (0.13)) (i.e., SFP ¼ 0:245 > NoSFP ¼ 0:15, at p ¼ 0:04). These results support H1. Still, the reporting averages for cells EL NoSFP, EL -SFP, EH -NoSFP, and EH -SFP (i.e., 0.17, 0.21, 0.13, and 0.28)

Cell

Auditor

Client

Number with a pure strategy

Reporting average

Number with a pure strategy GT

R

Randomized

SW

Switching average

GT

GC

Clean

FTF

Forecast 1 EL -NoSFP EL -SFP EH -NoSFP EH -SFP

16 12 13 13

0 0 0 1

16 12 13 13

16 12 13 12

0.93 0.88 0.90 0.82

3 7 4 6

3 2 5 4

3 7 4 6

0 1 1 5

0.60 0.82 0.38 0.52

Forecast 2 EL -NoSFP EL -SFP EH -NoSFP EH -SFP

0 1 0 3

0 0 0 0

3 1 1 3

2 4 3 3

0.65 0.64 0.66 0.64

7 4 4 5

7 7 4 4

5 4 4 5

8 9 12 11

0.40 0.44 0.37 0.59

Forecast 3 EL -NoSFP EL -SFP EH -NoSFP EH -SFP

7 9 9 0

7 9 9 5

0 0 0 0

7 9 9 5

0.17 0.21 0.13 0.28

11 9 8 6

11 9 8 6

1 0 0 1

8 11 12 13

0.19 0.17 0.34 0.40

Clean ¼ Clean opinion; GC ¼ Going-concern Opinion; SW ¼ Switch auditors; R ¼ Retain auditor; GT ¼ Game Theoretic Decision Model; Randomized ¼ Randomized strategy; FTF ¼ Follow the Forecast Model; (1) ¼ highest predicted average for all cells; (2) ¼ second highest predicted average for all cells, etc. * Auditor reporting average assumes 1 ¼ Clean opinion and 0 ¼ going-concern opinion. ** Client switching average assumes 1 ¼ Switch auditors and 0 ¼ retain the auditor.

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Table 7 Auditor reporting and client switching behavior

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varied considerably from the modelÕs equilibrium point predictions (0, 0, 0, 1, respectively). The predicted behavior overshoots the mark in anticipating the extent to which auditors will succumb to client pressure. Krishnan et al. (1996) find empirical evidence that auditors treat switchers more conservatively in issuing an audit opinion. The alternative decision models investigated provide a potential explanation for KrishnanÕs finding and for the difference between predicted and actual behavior, particularly the disparity in EH -SFP. Of the decision models proposed, more auditors displayed a pure strategy consistent with loss avoidance or adversarial models than that of the gametheoretic model, as seen by comparing the number of going-concern and clean opinions to the modelsÕ predictions in Table 7. Given the pattern of goingconcern averages across cells, this seems driven more by loss aversion than by an adversarial strategy. Though no auditor chose altruism or risk seeking as a pure strategy, 10 auditors had reporting averages of 0.5 or higher (1 ¼ clean; 0 ¼ going-concern) and 50 of the 80 were non-zero. Moreover, five of these 10 were in cell EH -SFP, the cell in which the model predicted clean opinions. Also note that the number of clean opinions expressed in cell EH -SFP may have been further suppressed by the aggressive switching behavior of clients (predicted ¼ 0, actual ¼ 0.4, where 1 ¼ switch and 0 ¼ retain). Future experiments that allow repeated play, face-to-face contact, longer periods of interaction, and elements of cooperation could increase the probability of observing altruistic behavior. For forecast 2 data, the auditorsÕ reporting average was nearly identical across cells (0.65). Therefore, the main effect and two simple effects were not significant and do not support H1. Before concluding complete absence of a treatment effect, one needs to examine the clientsÕ behavior and consider the interactive nature of the game. Note that forecast 2 implies a 50% probability of business termination (without a SFP effect) across all cells. Without an informative forecast, auditors were more susceptible to other influences such as client pressure, economic incentives, and concern for othersÕ welfare. To consider the effect of client pressure, first examine Fig. 1 and the auditorÕs expected returns reported in panel A of Table 4 for the non-SFP cells (EL NoSFP and EH -NoSFP) given forecast 2. These expected returns hold in equilibrium if the client retains the auditor. However, as seen in Table 7, the forecast 2, NoSFP switching average of 39% differs from the equilibrium prediction of 0%. Since this switching average was relatively constant throughout the sequence, it is reasonable that auditors held this expectation of client behavior. Given the clientsÕ behavior and the expected return alternatives found in panel A of Table 4, the non-aggressive auditor would be better off expressing a clean rather than a going-concern opinion in the NoSFP cells because this provides the greater expected return of 0:28 > 0:21 ¼ ðð0:05Þð0:39Þ þ ð0:38Þð0:61ÞÞ, where 0.21 is the expected return from declaring an intention to express a going-concern opinion based on the probabilities

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in the experiment. 11 Consequently, the auditorsÕ departure from equilibrium play in the NoSFP cells (65.5% actual versus 0% clean opinions predicted) can be interpreted in two ways: (1) as a rational response to off-equilibrium, aggressive switching behavior by the client, and/or (2) as auditor altruism or riskseeking. Few auditors adopted a pure strategy; however, all eight that did followed strategies consistent with altruism or risk seeking (see Table 7). The risk-seeking model seems more apt, for if the auditors had been altruistic, one would expect a similar number of subjects manifesting this behavior across forecast levels. Instead, Table 7 reports that the numbers of subjects adopting a pure strategy of clean opinions were 54, 8, and 0 for forecast 1, 2, and 3, respectively, which reflects reasoning mindful of strategic self-interest. Relative to the equilibrium prediction, we observe an excess of clean opinions in cells without the self-fulfilling prophecy due to the realization and anticipation that clients would act adversarially, and a shortage of clean opinions in cells with the self-fulfilling prophecy due to loss avoidance or adversarial play by auditors. Considering that the reporting average in all cells was approximately 0.65, it would seem that the naive follow-the-forecast model, which predicts reporting averages between 0.4 and 0.6 for forecast 2, would be most predictive. However, although most auditors randomized their strategies, they tended to favor one opinion over the other. As a result, only 15% of the reporting averages fell between 0.4 and 0.6. Though the forecasts were highly significant in predicting aggregate reporting behavior, the followthe-forecast model provides little additional explanation or understanding of individual behavior. Studying the audit reports of public companies, Weiss (2002) also found a ‘‘dramatic difference’’ in individual audit firm performance in alerting investors to bottom-line problems. We can also examine the clientsÕ response to the off-equilibrium play of the auditors. Consider hypothesis H2. In the case of forecast 2, clients anticipating a going-concern opinion will switch auditors in the SFP cells (cells EL -SFP and EH -SFP) but will retain otherwise (see Table 4). The regression results in panel B of Table 6 support hypothesis H2. Clients switched auditors more frequently in SFP cells than in non-SFP cells (also see Table 7; SFP ¼ 0.515 ¼ (0.44 + 0.59)/2 > NoSFP ¼ 0.385 ¼ (0.40 + 0.37)/2, at p ¼ 0:03). Note that it is largely the simple effect of the SFP when the forecast error is high that drives this result (EH -SFP ¼ 0:59 > EH -NOSFP ¼ 0:37 at p < 0:001).

11 Using this probability and the auditorÕs expected returns for GCR-switch and GCR-retain with forecast 2 in panel A of Table 2, an auditorÕs expected return from declaring an intention to express a going-concern opinion was ((expected return from replacement)(probability the client will switch) + (expected return from retention)(probability the client will retain the auditor)) ¼ (()0.05)(0.39) + (0.38)(1)0.39)) ¼ 0.2123.

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In conclusion, the SFP effect did affect subject behavior. With forecast 3, the self-fulfilling prophecy led auditors to express more clean opinions to avoid the loss of clients and client fees, thus supporting hypothesis H1. However, with forecast 2, auditors did not respond to the SFP as predicted. Thus, the second test of H1 failed to reject the null. One explanation is that clients were more aggressive in switching auditors than predicted in the no-SFP cells (cells EL NoSFP and EH -NoSFP). Consequently, the auditor expressed more clean opinions in these cells as a rational response to the off-equilibrium play of the client, an effect possibly reinforced by auditor risk seeking. Clients switched auditors more frequently when going-concern opinions were self-fulfilling, and this effect was strongest in the high-forecast-error cells. This result supports hypothesis H2. It also suggests that clients facing the SFP are more likely to switch auditors if they perceive that support for the auditorÕs opinion is weak. 7.2. Hypothesis H3: accuracy of audit forecasts of client’s business termination Hypothesis H3 predicts that the auditor will issue more clean opinions when the support for the opinion is weaker, that is, when the forecast is more inaccurate. This did not occur. On average, forecast inaccuracy did not lead auditors to express more of the client-preferred clean opinions. For forecast 2, forecast accuracy is irrelevant because it is non-predictive, implying a 50% probability of business termination across all cells; consequently, the investigation of the effects of forecast inaccuracy focuses on forecast 3 data. The analytical model predicts that auditors will express more clean opinions when forecasts are inaccurate. As reported in Table 7, the difference between the reporting averages for cells EL -SFP and EH -SFP (0.21 and 0.28) was not significant (p ¼ 0:25); consequently, hypothesis H3 is not supported. The average of clean opinions for cell EH -SFP, though nominally higher than for cells EL -SFP and EH -NoSFP in the predicted direction, is at some distance from the predicted equilibrium (EH -SFP ¼ 0.28 versus 1.00 predicted) and deserves some explanation. Many subjects exhibited loss avoidance. As reported in Table 7, 30 of the 80 auditors played a pure strategy of always expressing a going-concern opinion upon observing forecast 3. The auditorsÕ pattern of reporting averages across cells is more consistent with the intensities predicted for loss avoidance than for adversarial play. Also, written responses from the post-experiment questionnaires and feedback from discussions with subjects during the post-experiment debriefing period suggest that several subjects played to avoid large losses. Loss avoidance could mute the effect of the treatments in cell EH -SFP in the following manner. If the auditor expresses the non-equilibrium going-concern opinion, the deepest downside risk is )$0.05, if dismissed by the client. On the other hand, expressing a clean opinion exposes the auditor to a downside risk

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of )$0.80. Though the auditorÕs expected return from expressing a clean opinion ($0.06) exceeds that for a going-concern opinion ($0), a loss avoiding subject might prefer to express a going-concern opinion and avoid the larger downside risk. Analogizing to the professional setting, risk-averse auditors would forego higher expected returns and would not yield to client pressure but would express a going-concern opinion if their evidence suggested it was appropriate. The client equilibrium behavior in the experiment was not expected to be affected by forecast 3Õs accuracy. However, clients did switch auditors more aggressively in high-error cells. As Table 7 reports, the combined switching average for the low-error cells (the average of EL -NoSFP (0.19) and EL -SFP (0.17)), is less than that for the high-error cells (EH -NoSFP (0.34) and EH -SFP (0.40))(low error ¼ 0.18 < high error ¼ 0.37; p < 0:001 in a two-tailed test). The effect was also strong for both contrasts: EL -NoSFP ¼ 0:19 < EH -NoSFP ¼ 0:34 (p ¼ 0:03) and EL -SFP ¼ 0:17 < EH -SFP ¼ 0:40 (p < 0:01), where both are two-tailed tests. The model aids in explaining these results. Panel A of Table 4 permits a comparison between the low- and high-error cells for forecast 3. Specifically, the expected returns were lower (i.e., )0.07 and )0.10 versus 0.02 and )0.02) and the opportunity loss higher (i.e., 0.12 and 0.10 versus 0.06 and 0.02, respectively). As the model predicted, most clients did not switch auditors. However, for those that did, the pattern of switching averages across cells most closely resembles the ranking predicted by the risk-seeking model. Consequently, given some risk seeking or off-equilibrium play by subjects, we would expect less auditor switching in cells with low forecast error. 7.3. Hypothesis H4: strategic dependence We find strong support for hypothesis H4 in that auditorsÕ and clientsÕ decisions were generally much farther from equilibrium when strategic dependence was high than when it was low. We computed a measure of the distance of each subjectÕs average from that predicted by the analytical model. We performed t-tests comparing the overall revised averages for the high-strategicdependence cell (i.e., EH -SFP) with that in the low-strategic-dependence cell (i.e., EL -NoSFP). The t-tests for both auditor and client strategic dependence using forecast 3 data were highly significant. Forecast 1 data were sparse for clients, so the test was run only on auditor data and was significant (p ¼ 0:04). The results for forecast 2 were mixed. The auditorÕs results did not support strategic dependence and the client results were only partially supportive. One explanation is that the forecast error did not change, thus reducing the level in strategic dependence. When the No-SFP cell data were pooled with the SFP cell data for forecast 2, the test for strategic dependence was marginally significant (p ¼ 0:06). Awareness that the auditorÕs expected return is quite

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dependent on the clientÕs decisions forewarns the profession of the heightened need for professional skepticism in high-strategic-dependence situations.

8. Conclusions This paper uses experimental economic methods to investigate the relative predictive power of a game-theoretic model vis-a-vis other decision models, namely loss avoidance, risk seeking, adversarial, and altruistic. The gametheoretic model analyzes the strategic interaction between the auditor and a risky client when the auditor chooses whether to express a going-concern opinion and the client decides whether to switch auditors. We investigate the effects of the self-fulfilling prophecy and the reliability of the auditorÕs forecast of client viability on the decisions of both auditor and client. We also tested BloomfieldÕs (1997) hypothesis that strategic dependence leads subjects to play farther from equilibrium. Our experimental results indicate that both auditor and client decisions are affected by the self-fulfilling prophecy effect, but depend on the nature of the auditorÕs evidence. When the auditorÕs evidence provided a non-informative prediction about client viability, the self-fulfilling prophecy effect manifested itself through the behavior of the client rather than that of the auditor. In contrast, when informative evidence suggested business termination, clean opinions occurred more frequently in cells with the self-fulfilling prophecy than without it, but occurred far less frequently than the game-theoretic model predicted. The loss avoidance model aids in explaining this result. Most auditors chose not to ‘‘cave in’’ by giving the client-preferred clean opinion, thus demonstrating a willingness to sacrifice expected returns in order to minimize losses. This should be a welcome result for the accounting profession, particularly since real-world auditors face far greater penalties from rendering inappropriate clean opinions than those to which our subjects were exposed. Consistent with the loss avoidance model but inconsistent with our equilibrium prediction, auditors obtaining evidence suggesting business termination did not express more clean opinions when forecast accuracy decreased. Such evidence did affect client behavior, however, as clients switched more aggressively. Though contrary to prediction, the model remains useful in interpreting this result, because this departure from equilibrium play occurred more frequently in high forecast error cells, where the expected costs of such departures were lower. Though few clients always switched, many who did switch exhibited a pattern consistent with risk seeking. Clients may also have experienced less dissonance in dismissing an auditor whose evidence was weak. In summary, the results suggest that the game-theoretic model is descriptive of many subjectsÕ behaviors and is useful in interpreting the behavior of other subjects even if they played far off the equilibrium path. Of the competing

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models, loss avoidance occurred most frequently, and led auditors and clients to be more conservative in their reporting and switching behavior. Consistent with risk seeking behavior, 13% of the auditors expressed clean opinions over 50% of the time despite evidence to the contrary. On the other hand, adversarial and altruistic models did not appear descriptive. Forecasts were attended to, but the follow-the-forecast model provided little additional insight into individual auditor behavior. Finally, supporting BloomfieldÕs strategic-dependence hypothesis, we find that subjects do play farther from equilibrium when their payoffs are more dependent on othersÕ decisions. Left for future research is the redesign of the model resulting from the experimental results and a more precise, endogenous characterization of the selffulfilling prophecy. Modeling auditor–client differences in their forecasts of bankruptcy would permit one to view switching behavior in a different way. Also warranting research is the explicit consideration of reputation effects on strategic decision-making in repeated play setting which would allow subjects greater opportunity to cooperate or retaliate. Moreover, this would increase the likelihood of detecting altruistic and adversarial behaviors. The experiment revealed that a significant number of subjects attempted to avoid large losses, and a smaller number focused more on the upside reward and than on the downside risk. The risk takers liberally expressed clean opinions despite evidence to the contrary. Regardless of frequency, the consequences of such risktaking behavior and resultant audit failures justify further examination. Future models should encompass all risk preferences and might examine how ethical standards, sanctions, and compunctions interact with risk preferences to decrease the frequency of audit failures.

Acknowledgements The Graduate School of the University of Wisconsin-Madison and the University of Illinois at Chicago provided funding for this project. The authors also wish to acknowledge the helpful comments of Paul Beck, Brian Mayhew, David Smith, Tony Steele, and the workshop participants at the University of Illinois at Champaign-Urbana and the University of Illinois at Chicago.

Appendix A A.1. Equilibrium strategy sets The analysis that follows is a variation of that in Matsumura et al. (1997, pp. 727–758). For simplicity, we assume both players are risk neutral. If the

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incumbent auditor intends to issue a clean opinion, the client has no incentive to switch auditors and, thus, retains the incumbent (see Fig. 1). Alternatively, if the incumbent auditor expresses a going-concern opinion, we derive the auditor/client pure strategy Nash (subgame perfect) equilibrium strategies by beginning with the clientÕs decision and using backward induction to determine the auditorÕs reporting decision. At node 1 in Fig. 1, the client compares the expected payoffs of replacing the auditor with that of retaining the auditor. Thus, the clientÕs optimal strategy is to retain the auditor if ðSWÞðpsf Þð1  pClean Þ þ ðPV  SW  LÞð1  psf Þð1  pClean Þ þ ðSWÞðpFail ÞðpClean Þ þ ðPV  SWÞð1  pFail ÞðpClean Þ < ðPV  LÞð1  psf Þ; pClean ¼ pClean < ^

or

SW : Lð1  psf Þ þ ðpsf  pFail ÞðPVÞ

ðA:1Þ

At node 2, the incumbent auditorÕs optimal reporting strategy depends on the clientÕs optimal strategy at node 1. If expression (A.1) holds, the client will retain the incumbent auditor even if that auditor expresses a going-concern opinion. The auditor will do so if the expected return exceeds that from expressing a clean opinion, that is, if ðpSf ÞðAFB Þ þ ð1  psf ÞðAFs  Ca Þ > pFail ðAFB  Cb Þ þ ð1  pFail ÞAFs ; or Ca ð1  ðpsf  pFail ÞÞ þ ðpsf  pFail ÞðAFS  AFB Þ : pFail > Ca þ Cb

ðA:2Þ

If expression (A.1) does not hold, then the client will replace the incumbent auditor who expresses a going-concern opinion, which the auditor will do if and only if  D > pFail ðAFB  Cb Þ þ ð1  pFail ÞAFs ; AFS þ D pFail > : AFS þ Cb  AFB

or ðA:3Þ

The right-hand side of Eq. (A.1) contrasts the costs of switching (numerator) with the costs of not switching (denominator). Intuitively, if the probability of receiving a clean opinion from a replacement auditor becomes large relative to the cost of switching, the client prefers to switch. The intuition behind expression (A.2) is that the auditor will express a going-concern opinion if the probability of business termination (left-hand side) becomes large relative to the cost of rendering a going-concern opinion. The right-hand side of expression (A.2) compares the cost of rendering a going-concern opinion (numerator) to the total costs of both type I and II errors (denominator).

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