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Prediction versus inducement and the informational efficiency ofgoing concern opinions∗
Joseph Gerakos†1, P. Richard Hahn2, Andrei Kovrijnykh3 and Frank Zhou4
1Tuck School of Business at Dartmouth College, United States2University of Chicago Booth School of Business, United States
3Arizona State University W.P. Carey School of Business, United States4The Wharton School, University of Pennsylvania, United States
October 31, 2016
Abstract
We examine two distinct channels through which going concern opinions can be associated withthe likelihood of bankruptcy: auditors have better access to information about their clients’bankruptcy risk and going concern opinions directly induce bankruptcies. Using a bivariateprobit model that addresses omitted variable bias arising from auditors’ additional information,we find support for both the information and inducement channels. The direct inducementeffect of receiving a going concern opinion is a 0.84 percentage point increase in the probabilityof bankruptcy for firms that do not have a going concern opinion in the prior year. Despite theinducement effect acting as a “self-fulfilling” prophecy, going concern opinions do not correctlypredict more bankruptcies than a statistical model based solely on observable data. This resultsuggests that auditors do not efficiently use information when generating going concern opinions.
∗We thank Kevin Chen (discussant), Chris Hansen, W. Robert Knechel, F. Asis Martinez-Jerez, Michal Matejka,workshop participants at the Public Company Accounting Oversight Board, the Tuck School, the Darden School,Chapman University, Caltech, the University of Florida, and conference participants at the 2016 European AccountingAssociation Annual Meetings and the 6th Workshop on Audit Quality for their comments.†Corresponding author. Mailing address: Tuck School of Business at Dartmouth College, 100 Tuck Drive, Hanover,
NH 03755, United States. E-mail address: [email protected]. Telephone number: +1 (603) 646-8965.
1 Introduction
Statement of Auditing Standards No. 59 requires auditors to opine on whether there is substan-
tial doubt regarding a client’s ability to continue operating as a “going concern” over the twelve
months following the balance sheet date. In forming this opinion, the auditor can use non-public
information obtained during the audit engagement as well as public information. Prior research
finds that going concern opinions have incremental explanatory power in bankruptcy prediction
models (e.g., Hopwood, McKeown, and Mutchler, 1989; Willenborg and McKeown, 2001; Gutier-
rez, Minutti-Meza, and Vulcheva, 2014). That is, a regression model that includes an indicator
for whether the client received a going concern opinion exhibits better predictive accuracy for
bankruptcy than regression models that exclude this variable.
The predictive value of going concern opinions can arise from two sources: the auditor’s superior
knowledge of the client’s bankurptcy risk or direct inducement of adverse events. Understanding
the relative importance of these two sources provides valuable insight into the efficacy of the current
auditing standards. For example, the transmission of the auditor’s additional information through
the issuance of a going concern opinion can be considered a useful attribute of the standard, while
direct inducement can distort the bankruptcy process by forcing healthy companies into bankruptcy
and vice versa. A statistical challenge in separating the two sources is that relevant variables are
unobservable, which leads to omitted variable bias. Namely, the explanatory power of going concern
opinions in a bankruptcy regression can arise from going concern opinions proxying for auditors’
superior knowledge of the client or from going concern opinions directly inducing bankruptcies.
The inducement effect operates through channels other than the going concern opinion providing
market participants with additional information. These channels include mechanical triggers such
1
as contractual clauses tied to the auditor’s opinion as well as strategic coordination of market
participants based on the auditor’s signal (e.g., suppliers refusing to sell on credit, clients refusing
to commit to the company’s products, and creditors tightening credit terms because they expect
other counter-parties of the company to act similarly).
We identify the inducement effect by exploiting the fact that any additional information pos-
sessed by the auditor must show up as an omitted variable not only in a bankruptcy prediction
regression, but also in a regression of going concern opinions on observable client characteristics.
Specifically, we use a bivariate probit model to jointly estimate these two regressions.1 The bivari-
ate probit model allows for direct estimation for the inducement effect. The effect of the auditor’s
additional information is isolated by a parameter that captures the correlation between the error
terms of the two regressions. The model therefore attributes any incremental predictive power of
the going concern opinion in the bankruptcy regression to the inducement effect.
We find support for both additional information and the direct inducement effect of going
concern opinions. A going concern opinion leads, on average, to a 0.84 percentage point increase
in the probability of bankruptcy for audit clients that did not receive a going concern opinion in
the prior year. Moreover, we estimate the bivariate probit correlation parameter to be 0.30, which
suggests the existence of additional information.
When we partition the sample, we find that the inducement effect is greater for large firms,
accelerated filers, and clients of Big 4 audit firms than for small firms, non-accelerated filers, and
clients of other audit firms. A going concern opinion, on average, leads to 6.42, 3.23, and 1.82
percentage point increases in the probability of bankruptcy for large firms, accelerated filers, and
1For descriptions of the bivariate probit model, see Heckman (1978), Freedman and Sekhon (2010), and Wooldridge(2010).
2
clients of Big 4 audit firms, compared with 0.28, 0.39, and 0.01 percentage point increases for
small firms, non-accelerated filers, and clients of other audit firms. Moreover, we find statistical
significant additional information for small firms, non-accelerated filers, and clients of other audit
firms, but not for large firms, accelerated filers, and clients of Big 4 audit firms, which is consistent
with the latter group receiving greater public scrutiny.
We also find that the inducement effect is stronger for firms with long term debt than those
without long term debt. If leverage is positively associated with creditors’ bargaining power, the
result suggests that a going concern opinion gives creditors additional bargaining power.
We next produce synthetic going concern opinions based solely on observable client characteris-
tics and what we know about the auditor’s going concern policy. We then use these synthetic going
concern opinions, along with the same observable client characteristics, to predict bankruptcies.
We find that including the synthetic going concern opinions in a bankruptcy prediction model sub-
stantially improves the predictive power. By construction, this incremental predictive power comes
exclusively from our understanding of how the auditor uses and packages observable information
to generate going concern opinions (e.g., the propensity to issue going concern opinions, any biases
that the auditor might have, and any other idiosyncrasies in the auditor’s use of observable client
characteristics). That is, the incremental predictive power can arise only because the auditor’s
actions have a direct effect on the client’s bankruptcy risk (i.e., the inducement effect), irrespective
of the going concern opinion’s information content. Note also that the incremental predictive power
can only arise if the auditor’s choice of firms that receive going concern opinion differs from the
firms that we would select based on the model.
We find that auditors correctly predict fewer bankruptcies than a statistical model that gener-
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ates the same number of going concern “indicators” based solely on observable data, which include
client characteristics. That is, despite having inducement and additional information working in
their favor, the audit industry does worse than a statistical model based on publicly observable
information.2
Our ability to correctly predict more bankruptcies than the audit industry with the same number
of going concern “indicators” provides insight into whether auditors use information efficiently when
issuing going concern opinions. Despite having the direct inducement effect making their predictions
self-fulfilling as well as superior access to the client’s liquidity or bankruptcy risk, the audit industry
performs worse than a model based solely on publicly observable client characteristics. This result
suggests that at least some auditors use information inefficiently when generating going concern
opinions. This inefficiency can arise either from auditors using “bad” models to generate going
concern opinions or from incentive problems arising from the auditor’s relation with the client
(e.g., Blay and Geiger, 2013). Moreover, in conjunction with the inducement effect, this result
suggests that auditors could inefficiently induce bankruptcies by issuing going concern opinions to
clients that are in “better” shape than other clients that do not receive an adverse opinion, and
vice versa.
2To compare the auditors with the statistical model, we hold the number of false positives (i.e., Type I errors)constant, and then compare the number of false negatives (i.e., Type II errors). This approach is equivalent toholding the number of issued opinions constant. Note that our bankruptcy predictors at this point are not the sameas the synthetic going concern opinions that we use to mimic the auditors’ behavior. These predictors efficiently useobservable information, which is not necessarily true for the auditors.
4
2 Disclosure of existing information versus generation of new in-
formation
Under current auditing standards, the auditor is required to discuss with management any
concerns about the entity’s risk of liquidation and evaluate the adequacy of management’s plans to
address such risk. The auditor is to take into account this likelihood when deciding whether to issue
a going concern opinion.3 Several studies find negative abnormal stock returns at the announcement
of a going concern opinion (e.g., Dopuch, Holthausen, and Leftwich, 1986; Jones, 1996; Menon and
Williams, 2010) and that returns are less negative at the announcement of bankruptcy if the audit
client previously received a going concern opinion (e.g., Chen and Church, 1996; Holder-Webb and
Wilkins, 2000).
There are three possible explanations for the above findings. First, going concern opinions
disclose to market participants non-public information that the auditor gleaned from its interaction
with the client. Second, contracts can include provisions based on going concern opinions. For
example, debt covenants are sometimes based on going concern opinions (Menon and Williams,
2016). The third possibility is that going concern opinions create new information. That is, market
participants form their beliefs about what others will do based on the going concern opinion (e.g.,
Morris and Shin, 2002). The second and third channels are traditionally grouped as the “self-
fulfilling prophecy” of going concern opinions (e.g., Tucker, Matsumura, and Subramanyam, 2003;
Guiral, Ruiz, and Rodgers, 2011; Carson, Fargher, Geiger, Lennox, Raghunandan, and Willekens,
3The going concern opinion determines whether the client’s financial statements are prepared on a going concernor liquidation basis. If financial statements are prepared on a liquidation basis, assets are to be written down toreflect liquidation values. In contrast, on a going concern basis, asset values are recorded under the assumption thatthe entity will continue operating in the normal course of business.
5
2013). In what follows, we refer to the first channel as additional information and the second and
third channels as the direct inducement effect.
Both the additional information and self-fulfilling channels can coexist. Hence, one cannot
claim that the incremental predictive value of the going concern opinion in a bankruptcy regression
is only due to the self-fulfilling channel (e.g., Geiger, Raghunandan, and Rama, 1998; Louwers,
Messina, and Richard, 1999; Gaeremynck and Willekens, 2003; Vanstraelen, 2003) or only due to
the additional information channel (e.g., Keller and Davidson, 1983; Blay, Geiger, and North, 2011).
3 Econometric model
We assume that auditors issue going concern opinions according to a random utility model:
GCi =
1 if Ui = f(xi) + νi ≥ 0
0 otherwise
(1)
where GCi is an indicator variable for whether the auditor issues client i a going concern opinion.
Ui is the auditor-specific utility (or score) for the issuance of a going concern opinion to client i
and xi represents a vector of client i’s characteristics observable to the researcher.
The function f(·) represents the auditor’s prediction model, which captures the auditor’s esti-
mate that client i will file for bankruptcy during the period along with any client i specific incentives
whether to issue a going concern opinion. Also included in f(·) is the audit client’s overall util-
ity/disutility of Type I versus Type II errors in the issuance of going concern opinions. The auditor’s
overall utility/disutility of Type I versus Type II errors can be captured with an intercept in f(·)
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that determines the threshold for issuing a going concern opinion. The error term νi represents
additional information held by the auditor as well as noise, both of which are unobservable to the
researcher. The separation of additional information from noise is an econometric challenge that
we discuss in what follows.
We then express the bankruptcy probability of client i in terms of the same observable charac-
teristics xi:
Bi =
1 if Si = h(xi) + ξi ≥ 0
0 otherwise
(2)
where Bi represents an indicator variable for the bankruptcy of client i and Si represents the client’s
bankruptcy score. The function h(·) captures the impact of client i’s observable characteristics, xi,
on the likelihood of bankruptcy, while ξi represents unobservable factors as well as the contribution
of GCi (i.e., the inducement effect).4
Our econometric analysis revolves around modeling the going concern and bankruptcy scores,
f(xi)+νi and h(xi)+ ξi. Estimation of f(xi) and h(xi) must account for the fact that unmeasured
factors can induce dependence between the error terms νi and ξi. Our approach is to use a bivariate
probit model that includes a parameter, ρ, which captures correlation between the two error terms.
Intuitively, ρ captures the unmeasured correlation, allowing f(·) and h(·) to be estimated properly.
Two difficulties emerge when implementing this approach. First, we allow the functions f(·) and
h(·) to be non-linear. Non-linear functions pose computational challenges within the bivariate probit
setting; essentially the likelihood function can become highly multimodal making joint estimates
of ρ and the two functions unstable. We address this difficulty by first deploying a dimension
4It is important to point out that ξi captures factors (i.e., additional information and the inducement effect) thatare unobservable to the researcher. We are not assuming that the inducement effect is stochastic.
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reduction technique, which reduces our nonlinear bivariate probit model to a better behaved linear
version. Formally, our approach can be expressed as
Ui = f(xi) + νi = β0 + β1f(xi) + β2h(xi) + εi, (3)
Si = h(xi) + ξi = α0 + α1h(xi) + α2f(xi) + ζi. (4)
where f(·) and h(·) are understood as nonlinear transformations and dimension reductions of the
observable covariates x derived by applying a nonlinear classification method to the previous year’s
going concern and bankruptcy data. It is helpful to consider this model from the perspective of a
new auditor who is formulating their going concern model. From this vantage, equation (4) says
that an auditor forms their going concern utility as a linear combination of two regression models,
one which forecasts bankruptcies and one which forecasts the previous auditor’s going concern
opinions. To the extent that a going concern opinion is a bankruptcy forecast, we use the same
formulation for the bankruptcy score.
Equation (4), however, does not explicitly account for the possibility of a self-fulfilling or in-
ducement effect of receiving a going concern opinion. However, an inducement effect can be ac-
commodated by including GCi explicitly as a predictor in the bankruptcy score equation.
Ui = f(xi) + νi = β0 + β1f(xi) + β2h(xi) + εi, (5)
Si = h(xi) + ξi = α0 + α1h(xi) + α2f(xi) + γGCi + ζi. (6)
With this formulation, estimates of γ capture the inducement effect, while the correlation between εi
8
and ζi captures unobserved covariation due to unmeasured confounding (i.e., additional information
used by the auditor in generating the going concern opinion).
4 Empirical implementation
In our empirical implementation, we assume joint normality of the latent errors. We make the
normality assumption to facilitate estimation, but, as we discuss further, it is not strictly necessary
for identification. Specifically, we assume that the error terms (εi, ζi) are jointly normal with means
equal to zero and covariance matrix
Σ = cov
εζ
=
1 ρ
ρ 1
. (7)
The parameter ρ reflects the degree of dependence between the error terms, which we interpret as
the extent of an auditor’s additional information. Heckman (1976, 1978) introduced this model,
and it has been used more recently in Altonji, Elder, and Taber (2005).
Equivalently, we can express the model in terms of (Ug, Sb), which we call the going concern
utility and the bankruptcy score.
Ug,iSb,i
iid∼N (µ,Σ), µ =
β0 + β1f(xi) + β2h(xi)
α0 + α1h(xi) + α2f(xi) + γGCi
, Σ =
1 ρ
ρ 1
. (8)
This bivariate, continuous distribution implies a distribution over the observed binary data (Gi, Bi)
via expressions (1) and (2).
The parameters of the bivariate probit model are identified without imposing any exclusion
9
restrictions when estimation is via maximum likelihood (Heckman (1978) page 949). This result
may not hold if other, non-normal, error distributions are assumed; we conjecture that a similar
result would hold for symmetric, unimodal error distributions. We show below via simulations that
imposing a valid exclusion restriction (forcing some betaj to be equal to zero) increases statistical
efficiency, but that imposing an invalid exclusion restriction can produce badly biased estimates of
the parameter of interest, γ.
4.1 Simulation
We conduct a simulation study based on synthetic data to examine how bivariate probit models
identify parameters with and without exclusion restrictions. Within each simulation, we generate
10,000 observations in which we know the true parameters and then estimate the parameters using
bivariate probit. We ran the simulation 200 times varying the levels of inducement effect γ, the
extent of unobserved (to the researcher) information ρ, and the existence of a valid exclusion
restriction. These simulations allow us to recover the sampling distribution of our estimator and
visualize consistency of our estimates.
We simulate data using the following model,
Ug,iSb,i
iid∼N (µ,Σ), µ =
β0 + β1xi
α0 + α1xi
, Σ =
1 ρ
ρ 1
. (9)
We then generate bankruptcy and going concern opinions using a binary indicator function
G = 1{Ug,i ≥ 0
};
B = 1{Sg,i ≥ −γG
}.
(10)
10
We assume the following values for the underlying parameters: σ = 1, β1 = −1, α1 = 0.2,
β0 = −1.6, α0 = −2.6. In addition, we generate the observable covariate x1 as a draw from
N (0, 1). The γ takes values of 0, 0.5, 1, and 2 and ρ takes values of 0, 0.3, and 0.6. We use these
values for γ and ρ, because when γ = 1 and ρ = 0.3 the marginal and conditional distributions
of bankruptcies and going concern opinions using the simulated sample are close to those of the
actual data.
For each γ − ρ pair, we examine three scenarios: no exclusion restriction, a valid exclusion
restriction, and an invalid exclusion restriction. In the case of a valid exclusion restriction, we draw
the excluded variable independently from N (0, 1) and include it as an additional covariate in the
going concern equation. Because we draw the variable independently, the exclusion restriction is
satisfied. In the case of an invalid exclusion restriction, we also draw from N (0, 1) and include it
as an additional covariate in the going concern equation, but set its correlation with the error term
of the bankruptcy equation to 0.20.
Table 1 and Figures 1, 2, and 3 present the results from the simulation. The takeaways from
the simulation are as follows. First, when we do not impose an exclusion restriction, the sampling
distributions of γ and ρ have a mean and median that are close to the true value, although the esti-
mates have large confidence intervals (see Table 1). This result is consistent with Heckman (1978)
and Wilde (2000) who show that the identification of γ and ρ does not depend on the existence
of an exclusion restriction. Second, with a valid exclusion restriction, the sampling distribution is
tighter, suggesting an efficiency improvement. Third, with an invalid exclusion restriction, all of
the estimates of γ are biased, except when ρ = 0, which is equivalent to the auditor not possessing
additional information.
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5 Informational efficiency
In addition to the direct effect of receiving a going concern opinion, we examine the informational
efficiency of going concern opinions. We define going concern opinions as being informationally
efficient if the ranking of clients according to the auditor’s going concern random utility model is
the same as the ranking by the probability of bankruptcy conditional on all information available
to the auditor. In other words, if client i receives a going concern opinion, then all clients that are
more likely to go bankrupt than client i should also receive a going concern opinion. If this is the
case, the auditor’s problem can be reduced to choosing a bankruptcy probability threshold such
that all of its clients with a bankruptcy probability above the threshold receive a going concern
opinion.
Because the going concern opinion is a binary signal, informational efficiency does not imply
that the going concern opinion will be a sufficient statistic for the prediction of bankruptcy. In fact,
other firm characteristics can provide incremental information about the probability of bankruptcy.
In other words, even if all auditors are informationally efficient in generating going concern opin-
ions and use the identical threshold, the conversion of the auditor’s ranking to a binary signal
necessarily leads to an information loss for users. However, if one can generate a binary statistic
that systematically predicts more bankruptcies, holding the number of “going concern opinions”
constant (or the number of Type I or Type II errors constant), one can conclude that the actual
going concern opinions are informationally inefficient.5 (In what follows, we refer to such binary
statistics as “synthetic going concern opinions.”) That is, for the average probability of bankruptcy
5Given bankruptcies are rare, we lack sufficient power to test for statistical differences between the performanceof auditors and the performance of our model. In what follows, we can only evaluate whether the model accuratelypredicts more bankruptcies than actual going concern opinions.
12
to be higher for the same number of clients when using synthetic going concern opinions, some of
the clients issued a going concern opinion by the auditor were replaced by clients with a higher
probability of bankruptcy. Such a replacement would not lead to a higher probability under an
informationally efficient ranking.
In producing such an alternative ranking, the researcher is at a disadvantage relative to the
auditor for two reasons. First, the auditor’s private information can only be inferred from the
actual going concern opinion, which is a binary signal. Second, the inducement effect works in
favor of the auditor’s prediction, making recipients (non-recipients) of going concern opinions more
(less) likely to go bankrupt.
6 Data and variable measurement
For our analysis, we combine data from Audit Analytics, Compustat, and BankruptcyData.com.
Our sample period is 2000–2014 and is constrained by the availability of audit and bankruptcy data.
Our source of bankruptcy data comes from BankruptcyData.com of New Generation Research,
which covers all bankruptcies of public traded clients between 1986 and 2014 (the end of sample
period). This database includes the date of the bankruptcy filing, the date that the bankruptcy is
resolved (e.g., liquidation, reorganization, dismissal, . . . ), and other bankruptcy related variables.
Because the bankruptcy data identify each firm using EIN (Employer Identification Number), which
can be missing from Compustat, to ensure accuracy, we manually collect CIK identifiers for each
bankrupt client from the Electronic Data Gathering, Analysis, and Retrieval System (EDGAR) of
the Securities and Exchange Commission. We further complement bankruptcy data by collecting
13
liquidation information from CRSP. These constraints lead to 2,648 unique bankruptcy filings of
public traded clients between 2000 and 2014.
We truncate our bankruptcy data at 2000 due to the availability of audit data. We obtain audit
fees, auditor identity, and going concern opinions from Audit Analytics, which starts in 2000. The
coverage of audit fee data increases after 2002, which results in a mild loss of observations when
we merge audit fee data with audit opinions data (see Table 2). We then merge Audit Analytics
with our bankruptcy data and Compustat.
According to Auditing Standard No. 15, Audit Evidence, the auditor has a responsibility to
evaluate whether there is substantial doubt about the client’s ability to continue as a going concern
for a reasonable period of time, not to exceed one year beyond the date of the financial statement
audit. We therefore code the bankruptcy indicator to one if bankruptcy occurs within one year
after the signature date of the audit report. In cases of clients emerging from bankruptcy, we reset
bankruptcy to zero. In the regressions, we include the following control variables, which are similar
to those used by DeFond, Raghunandan, and Subramanyam (2002):
1. Log(Assets): the natural log of total assets;
2. Leverage: the ratio of total liabilities to total assets;
3. Investment: the ratio of short-term investments to total assets;
4. Cash: the ratio of cash and equivalent to total assets;
5. ROA: return on assets;
6. Log(Price): the natural log of the client’s stock price;
7. Intangible assets: the ratio of intangible assets to total assets;
8. R&D: the ratio of research & development expenditures to sales;
9. R&D missing: an indicator for missing research & development expenditures;
10. No S&P rating: a indicator for the existence of a S&P rating;
14
11. Rating below CCC+: a indicator for S&P rating below CCC+;
12. Rating downgrade: rating downgrade from above CCC+ to CCC+ or below;
13. Non-audit fees: the ratio of non-audit fees to total audit fees;
14. Non-audit fees missing: an indicator for missing non-audit fees;
15. Years client: the number of years of a client-auditor relation.
After merging datasets and applying filters, we are left with 88,545 client-year observations.
The sample includes 1,201 bankruptcies and 12,589 going concern opinions. Table 2 describes how
we construct the sample.
Table 3 provides descriptive statistics for the full sample, for the subsamples of clients that did
and did not receive a going concern opinion in the prior year, and for the subsample of clients filing
for bankruptcy. First, on average, only 1.4% of clients in our sample filed for bankruptcy. Going
concern issuance, however, is at a higher rate of 14.2%, which is consistent with auditors being
concerned about litigation risk. Compared with the full sample, clients filing for bankruptcy are
smaller, more highly levered, make smaller investments, hold less cash, have lower ROA, have lower
stock price, and have a higher chance of receiving a going concern opinion.
Next, looking into the subsamples, clients that did not receive a going concern opinion in the
prior year have a lower chance of receiving a going concern opinion than clients that received a
going concern opinion in the prior year (3.9% versus 81.6%). This finding is consistent with such
clients having lower bankruptcy probability than clients that received a going concern opinion in
the prior year (1.0% versus 2.9%). Many clients that received going concern opinions did not file
for bankruptcy. However, bankrupt clients have much higher probability of receiving going concern
opinions. For the full sample, the Type I error rate (receiving a going concern opinion and not
going bankrupt) is 13.6% while the Type II error rate (not receiving a going concern opinion and
going bankrupt) is 37.39%.
For clients that did not receive a going concern opinion in the prior year, the Type I error rate
is 3.4% and the Type II error rate is 49.1%. In contrast, for clients that received a going concern
opinion in the prior year, the Type I error rate is 81.3% and the Type II error rate is 18.4%. The
15
stark difference of between the Type I and Type II error rates across the two sub-samples suggests
that the incentive to issue a going concern opinion likely differs depending on whether a going
concern opinion was issued in the prior year.
7 Estimation
We do not observe all of the information about the client that is available to the auditor. Infor-
mation relevant for bankruptcy prediction that is available to the client’s auditor could potentially
enter the error terms of both the bankruptcy equation and the going concern equation, causing
them to be correlated. Although the bivariate probit can identify the direct effect of going concern
opinions even when the error terms are correlated, it is, nonetheless, worth controlling for as many
observable factors as possible for several reasons. First, controlling for additional factors can reduce
the variance of the error terms, thereby increasing the efficiency of the estimator and the power
of the statistical tests. Increasing efficiency is especially important in our setting given the low
frequency of bankruptcies. Second, to the extent that we control for public information observed
and used by the auditor, we can reduce the correlation between the two error terms. In this case,
any remaining correlation can be interpreted as evidence of the auditor’s additional information.
In practical implementation, there is a possibility that we omit a publicly observed predictor
of bankruptcy that the auditor uses. Such an omitted predictor would then be interpreted as
the auditor’s additional information. Identifying such variables would improve the quality of our
prediction model.
Our measure of the inducement effect is based on the premise that a going concern opinion
results in a higher likelihood of bankruptcy holding everything else constant. Suppose an auditor
implements a threshold rule when issuing going concern opinions, as informational efficiency dic-
tates. That is, all clients with a probability of bankruptcy higher than the threshold receive a going
concern opinion, while no client below the threshold does. Once the going concern opinions are
issued, the probability of bankruptcy will increase discretely for all clients above the threshold due
to the inducement effect (i.e., updated market beliefs, mechanically triggered covenants, credit ra-
16
tioning, . . . ). In the same vein, the probability of bankruptcy will decrease discretely for all clients
below the threshold. These changes in the probability of bankruptcy will result in a discontinuity
at the going concern opinion threshold.
A linear model would not be able to account for the discontinuity resulting from the inducement
effect. One way to address this issue is to include interaction terms and higher order terms as
additional control variables. However, this approach is likely inefficient because we lack theory
to guide the choice of interactions and higher orders. These sorts of non-linearities are, however,
well captured by Random Forests, which looks for classification thresholds that best describe the
data. Random Forests take into account non-linear relations between outcome variables (i.e.,
going concern opinions and bankruptcy) and predictor variables, thereby reducing within-sample
classification error (Hastie, Tibshirani, and Friedman, 2009). We therefore use Random Forests
to construct measures of going concern and bankruptcy likelihood based on information observed
by researchers. We estimate Random Forests using information only from prior years to predict
going concern opinions and bankruptcies in the current year, thereby ensuring that we do not use
information unavailable to auditors. In the Random Forests regressions, we use the same predictors
as in the bivariate probit regressions.
To show that Random Forests do as well as probit in predicting outcome variables, we follow
prior literature and plot ROC curves. A ROC curve plots the false positive rate (Type I error) on
the x-axis and the true positive rate on the y-axis as the threshold used to classify outcomes varies.
In the case of bankruptcy prediction, the ROC curve plots the percentage of correctly predicted
bankruptcies among actual bankruptcies on the y-axis and the percentage of incorrectly predicted
bankruptcy among non-bankruptcies on the x-axis. A ROC curve further skewed to the upper left
corner indicates better predictive performance.
Figure 4 compares the performance of Random Forests and probit in predicting one year ahead
bankruptcies. The ROC curve for probit is below the ROC curve for Random Forests in the
relevant range, indicating that Random Forests have superior predictive power for bankruptcies. In
17
addition, the Random Forests ROC curve is above the solid dot that represents the actual predictive
performance of auditors’ going concern opinions.
In Figure 5, we plot ROC curves for the prediction of going concern opinions. Random Forests
better predict going concerns opinions—the ROC curve for Random Forests is above the ROC
curve for probit in the relevant range.
To illustrate the usefulness of Random Forest, in Figure 6, we compare the predictive perfor-
mance of actual going concern opinions and our synthetic bankruptcy and going concern scores
when they are included in bankruptcy prediction models. We generate synthetic going concern
and bankruptcy scores by using publicly available information from the previous year (i.e., out of
sample) and Random Forests estimates. We then include the synthetic going concern scores and
bankruptcy scores along with other observables in Random Forests bankruptcy prediction models
and then compare their ROC curves. The ROC curves demonstrate that, based solely on publicly
available information, one can correctly predict the same number bankruptcies (i.e., true positives)
with fewer synthetic going concern opinions than the actual number of going concern opinions.
Equivalently, one can correctly predict more bankruptcies with the same number of synthetic going
concern opinions. In addition, when we include the actual going concern opinion in the Random
Forest in addition to the scores and observables, we further improve the bankruptcy prediction.
Including the actual going concern use the auditor’s private information that researchers do not
observe. This result provides strong evidence against the informational efficiency of auditors’ going
concern opinions. Otherwise, improvement will not be possible.
In Table 4, we compare the predictive performance of actual and synthetic going concern opin-
ions when they are used to predict bankruptcy. We generate predictive bankruptcy probabilities
by using publicly available information from the previous year (i.e., out of sample) and Random
Forests estimates, and transform the probabilities into bankruptcy scores using an inverse standard
normal kernel.6 For each auditor-year pair, we issue the same number of going concern opinions
6We only use observable firm characteristics and do not any information related to going concern opinions, includingthe going concern scores.
18
as the actual number of going concern opinions issued by that auditor, according to the clients’
bankruptcy scores.
For Big 4 clients, the synthetic going concern opinions generate similar Type I errors to those of
the actual going concern opinions, with about 0.1% difference. Relative to the actual going concern
opinions, the synthetic going concern opinions are associated with lower Type II errors for Ernst &
Young and Deloitte but higher Type II errors for PwC and KPMG. For other auditors, the model
does better in predicting bankruptcy than the actual going concern opinions. For example, the
Type I(II) error rate is 0.336 (0.224) using synthetic going concern opinions compared with 0.365
(0.280) using actual going concern opinions.
We next present our bivariate probit estimates. For all regressions, we bootstrap the standard
errors, because maximum likelihood estimates of the bivariate probit model can be unstable (i.e.,
many local modes), especially when there is a large number of predictor variables (Meng and
Schmidt, 1985; Freedman and Sekhon, 2010). Fortunately, our data appear not to present such a
troublesome case. The bootstrap standard error estimates are stable suggesting that we do not
have many local modes.7
In addition to the predictor variables, all regressions include year fixed effects to control macroe-
conomic factors that can affect the issuances of going concern opinions and bankruptcies, one-digit
SIC industry fixed effects to control for industry specific relations between going concerns and
bankruptcies, and auditor fixed effects to control for auditor-specific tendencies to issue going con-
cern opinions and select certain types of clients.
We also generate predictive probabilities of bankruptcy and going concern opinions using Ran-
dom Forests, and then transform them into scores using an inverse normal kernel. Our Random
Forests estimates use the same predictor variables described above. In the bivariate probit spec-
ifications, we include both the going concern and bankruptcy scores in the bankruptcy equation
and the going concern equations. We do so to address the possibility that past going concern and
bankruptcy scores are informative about current going concern and bankruptcy likelihoods.
7While it could be the case that all of our bootstrap subsamples resulted in similar local modes, this appearsunlikely.
19
Our main results provide evidence for both the additional information and direct inducement
channels. Table 5 presents probit estimates of the relation between observables and the two bi-
nary variables of interest: going concern opinion and bankruptcy. In first two columns, we present
independent probit estimates that do not allow for correlation between the error terms. In the
bankruptcy regression, the positive and significant coefficient on the going concern opinion demon-
strates that going concern opinions are relevant for bankruptcy prediction. In this specification,
however, one cannot distinguish between the inducement channel and the additional information
channel—the coefficient on going concern opinion captures both channels.
We next estimate bivariate probit models, which allow the errors to be correlated. In model (3),
we jointly estimate the going concern opinion and bankruptcy filing regressions but do not include
the actual going concern opinion in the bankruptcy regression. We see that the errors are strongly
correlated. However, interpreting this correlation as evidence of the auditor’s additional informa-
tion is problematic because in this specification the correlation parameter, ρ, also captures the
inducement effect.
Models (1), (2), and (3) provide a baseline for interpreting model (4), which presents the
main results of this study. One can view models (2) and (3) as two extremes in which both the
inducement and additional information channels are captured by single parameters—the coefficient
on the going concern opinion in model (2) and ρ in model (3). In model (4), we separate these effects
by including the going concern opinion in the bankruptcy regression and allowing the error terms
to be correlated. In this specification, ρ captures the continuous relation between the probability
of bankruptcy and the probability of receiving a going concern opinion arising from unobserved
variable entering the error terms of both regressions. Whereas, the coefficient on the going concern
opinion captures the discrete jump in the probability of bankruptcy arising from the receipt of a
going concern opinion.
In model (4), the estimated effect of a going concern opinion on the likelihood of bankruptcy
reduces by about one-third compared to model (2) (0.914 versus 0.635) and correlation between
the error terms reduces by about two-thirds compared to model (3) (0.438 versus 0.163). These
20
reductions are consistent with the intuition that both the inducement and additional information
channels are present, but captured by two different parameters.
When we move from the independent probits to the bivariate probits, the coefficients on the
control variables are relatively stable. One exception is the coefficient on the going concern score.
In model (3), it is larger than in models (2) and (4). A potential explanation for this increase
is that the going concern score proxies for the inducement effect when the actual going concern
opinion is not included among the regressors.
To evaluate the economic magnitude of the inducement effects, we calculate each client’s partial
effect—the change in predicted probability of bankruptcy, given each client’s observable character-
istics, for moving from receiving no going concern opinion to receiving a going concern opinion
holding the observable characteristics constant. In Figure 7, we present the histogram of partial
effects for clients that did not receive a going concern opinion in the prior year. The mean partial
effect for this sample is a 0.84 percentage point in increase in the probability of bankruptcy. We
report the distribution of the marginal effects in the first row of Table 6.
Many clients in our sample are audited by Big 4 firms. An important question is whether
the effect of going concern opinions on the likelihood of bankruptcy differs for Big 4 and non-
Big 4 firms. If the function of the going concern opinion is to provide incremental information
to market participants, we would expect the correlation between the error terms to be smaller
for clients of Big 4 firms because they are typically larger and less opaque, thereby leaving less
room for incremental additional information. On the other hand, if Big 4 audits are higher quality,
then one would expect more additional information than for non-Big 4 firms. Also, because of
higher perceived quality, debt contracts with audit-related covenants are more likely to require
Big 4 audits (Menon and Williams, 2016), which would result in larger inducement effect. Table 7
presents results separately for Big 4 clients, and non-Big 4 clients. Overall, the inducement effect is
larger in magnitude for Big 4 than for non-Big 4 clients, while the additional information channel
is more important for non-Big 4 clients.
Aside from auditor characteristics, we next examine how the inducement effects vary with firm
21
characteristics. We find that the inducement effects are significant for large firms (Table 8) and
accelerated filers (Table 9). For accelerated filers, the coefficient on the going concern opinion
(1.193) is 3.5 times as large as that for the sample pooling all firms (0.341). Separately examining
non-accelerated filers generates an insignificant negative coefficient on the going concern opinion
(−0.033). We find similar results when we separately examine firms that had assets above or below
the median assets in the prior year. The average marginal effect associated with changing a going
concern opinion to zero to one for accelerated filers is 3.23%, compared with 0.84% for pooling
accelerated and non-accelerated filers.
To further provide evidence where the inducement effects come from, we partition our sample
based on whether a firm is an accelerated filer and employs a Big 4 auditor. The results in Table 10
shows that inducement effects are significant only for firms that are accelerated filers and employ
Big 4 auditors. The average marginal effect associated with changing a going concern opinion to
zero to one for accelerated filers that employ Big 4 auditor is 5.33%.
We finally examine how inducement effects vary with the level of debt. Table 11 shows that the
inducement effects are not statistically significant at the 5% for firms with and without long term
debt. However, the coefficient on the going concern opinion for firms that have long term debt is
significantly larger than that for firms that have no long term debt. Examining the bootstrapping
results suggests that the coefficient on the going concern opinion is positive for 92% of the time for
firms that have long term debt, compared with 42% for firms that do not have long term debt.
8 Robustness
As a robustness check, we control for whether the client violated a debt covenant in the year of
the audit. To do so, we use the covenant violation data compiled by Nini, Smith, and Sufi (2013),
which covers covenant violations between 1997 and 2007. Merging our data with the covenant
violation data results in a loss of 58% observations in our sample, leaving us only 406 bankruptcy
cases for the estimation. We find that after controlling for covenant violation, the coefficient on
going concern opinion in the bivariate probit specification attenuates to 0.229 compared with 0.341
22
for the full sample. The 95% confidence interval becomes wider, [−0.341, 0.828] compared with
[0.001, 0.658] for the full sample. Despite this, over 93% of the bootstrapped coefficients are larger
than zero. The results appear to be driven by a loss of power arising from the reduction in sample
size. A sufficient sample size is important for our tests, because we use bankruptcies, which are
relatively rare. To demonstrate that this is reduction in power from the smaller sample size, we
estimate a simple probit of bankruptcy prediction model and and find that covenant violation is
not statistically significantly associated with future bankruptcy. If covenant violations drive the
estimated inducement effect, then we should expect that they are significantly related to bankruptcy
in a simple probit regression. The results above collectively suggest that the small sample size likely
causes of the insignificance of the going concern opinion in the bivariate probit model that includes
covenant violation as an additional control. In spite of the statistical insignificance, the economic
magnitude of the inducement effect remains similar to our main results.
9 Conclusion
Statement of Auditing Standards No. 126 does not provide an explicit criterion for evaluating
an auditor’s performance in generating going concern opinions. In fact, the standard explicitly
recognizes the inherent uncertainty that the auditor faces with respect to the client’s ability to
continue operating as a going concern and states that “the auditor cannot predict such future
conditions or events.” Therefore, the standard rules out the possibility of evaluating the auditor’s
performance based on any particular going concern opinion that the auditor issues.
The criterion that we propose uses all going concern opinions by audit firms and is based on the
premise that the efficient use of information by the auditor would result in the issuance of going
concern opinions to the clients with the highest bankruptcy risk given the information available to
the auditor. We present evidence that one can issue binary forecasts of bankruptcy that are superior
to those generated by audit firms in aggregate. That is, model generated going concern opinions
correctly predict more bankruptcies than the same number of going concern opinions generated by
audit firms. This finding is inconsistent with the efficient use of information by auditors.
23
When comparing the model generated going concern opinions with those issued by the auditors,
one should take into account two factors that work against the model generated opinions. First,
the model generated opinions use only a subset of information available to auditors and therefore a
priori one should expect the model to be less accurate. Another factor that works in the auditors’
favor is the inducement effect. As we show, the inducement effect is present and significantly affects
the predictive power of auditors’ going concern opinions.
What are the drivers of auditors’ inefficient use of information? This is an important question
because the combination of the inducement effect and auditors’ inefficient use of information can
distort the bankruptcy process in the sense that liquid companies are forced into bankruptcy and
illiquid companies delay filing for bankruptcy. However, this is a challenging question, especially
with respect to identifying auditor biases. To address this question, one needs to go beyond
regressing auditors’ errors on client characteristics, because errors are more likely for the marginal
client (i.e., a client whose bankruptcy likelihood is close to the auditor’s going concern threshold)
and the marginal client likely differs from the average client.
24
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Figure 1: Identification of the bivariate probit when ρ = 0.To evaluate the performance of the bivariate probit model in identifying the model parameters, wesimulate 10,000 observations from the following data generating process,(
UgSb
)iid∼N (µ,Σ), µ =
(β0 + β1xα0 + α1x
), Σ =
(1 ρρ 1
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G = 1{Ug ≥ 0
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B = 1{Sg ≥ −γG
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We assume that β1 = −1, α1 = 0.2, β0 = −1.6, and α0 = −2.6. These parameter values matchthe empirical rates of bankruptcy and going concern opinions. We set ρ = 0, which is equivalent toassuming that auditors possess no additional information. Each figure corresponds to γ = 0, 0.5, 1,and 2. Circles represent the case with no exclusion restriction, triangles represent the case of a validexclusion restriction, and plus signs represent the case of a “bad” exclusion restriction (i.e., the variableused as an instrument is correlated with the error term). We repeat each simulation 200 times.
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● no exclusionexclusionbad exclusion
Figure 2: Identification of the bivariate probit when ρ = 0.3.To evaluate the performance of the bivariate probit model in identifying the model parameters, wesimulate 10,000 observations from the following data generating process,(
UgSb
)iid∼N (µ,Σ), µ =
(β0 + β1xα0 + α1x
), Σ =
(1 ρρ 1
).
G = 1{Ug ≥ 0
};
B = 1{Sg ≥ −γG
}.
We assume β1 = −1, α1 = 0.2, β0 = −1.6, and α0 = −2.6. These parameter values match the empiricalrates of bankruptcy and going concern opinions. We set ρ = 0.3, which is equivalent to assumingthat auditors possess some additional information. Each figure corresponds to γ = 0, 0.5, 1, and 2.Circles represent the case with no exclusion restriction, triangles represent the case of a valid exclusionrestriction, and plus signs represent the case of a “bad” exclusion restriction (i.e., the variable used asan instrument is correlated with the error term). We repeat each simulation 200 times.
30
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● no exclusionexclusionbad exclusion
Figure 3: Identification of the bivariate probit when ρ = 0.6.To evaluate the performance of the bivariate probit model in identifying the model parameters, wesimulate 10,000 observations from the following data generating process,(
UgSb
)iid∼N (µ,Σ), µ =
(β0 + β1xα0 + α1x
), Σ =
(1 ρρ 1
).
G = 1{Ug ≥ 0
};
B = 1{Sg ≥ −γG
}.
We assume β1 = −1, α1 = 0.2, β0 = −1.6, and α0 = −2.6. These parameter values match the empiricalrates of bankruptcy and going concern opinions. We set ρ = 0.6, which is equivalent to assuming thatauditors possess significant additional information. Each figure corresponds to γ = 0, 0.5, 1, and 2.Circles represent the case with no exclusion restriction, triangles represent the case of a valid exclusionrestriction, and plus signs represent the case of a “bad” exclusion restriction (i.e., the variable used asan instrument is correlated with the error term). We repeat each simulation 200 times.
31
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Figure 4: ROC curves for bankruptcy prediction. This figure plots ROC curves to evaluate theperformance of Random Forests and probit in predicting one year ahead bankruptcies. The x-axis isthe false positive rate (i.e., incorrectly predicting that the client will file for bankruptcy) and the y-axisis the true positive rate (i.e., correctly predicting that the client will file for bankruptcy). A ROC curvethat further skews to the upper left corner indicates better predictive performance. The solid rounddots represent random forest. The hollow diamond dots represent probit. The stand-alone solid dotcorresponds to the predictive performance obtained from just using actual going concern opinions as abankruptcy predictor. The predictor variables include the natural logarithm of total assets, the ratioof debt to total assets, the ratio of short-term investments to total assets, the ratio of cash to totalassets, return on assets, the natural logarithm of closing stock price for the fiscal period, the numberof years of an auditor-client relation, R&D divided by sales, an indicator for missing R&D, fraction ofnon-audit fees in total audit fees, an indicator for missing audit fees, intangible assets divided by totalassets, an indicator for the S&P credit rating being CCC+ or below, an indicator for a S&P creditrating downgrade, an indicator for no S&P credit rating, and indicator variables for each of the Big 4auditors, Grant Thornton, and BDO.
32
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Figure 5: ROC curves for predicting going concern opinions. This figure plots ROC curvesthat evaluate the performance of random forecast and probit in predicting going concern opinions. Thex-axis is the false positive rate (i.e., incorrectly predicting that the client will receive a going concernopinion), and the y-axis is the true positive rate (i.e., correctly predicting that the client will receivea going concern opinion). The further the ROC skews to the upper left corner the better predictiveperformance. The dots represent Random Forests and the hollow diamonds represent probit. Thepredictor variables include the natural logarithm of total assets, the ratio of debt to total assets, theratio of short-term investments to total assets, the ratio of cash to total assets, return on asset, thenatural logarithm of closing stock price for the fiscal period, the number of years of an auditor-clientrelation, R&D divided by sales, an indicator for missing R&D, fraction of non-audit fees in total auditfees, an indicator for missing audit fees, intangible assets divided by total assets, an indicator for a S&Pcredit rating being CCC+ or below, an indicator for a S&P credit rating downgrade, an indicator for noS&P credit rating, and indicator variables for each of the Big 4 auditors, Grant Thornton, and BDO.
33
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●
● With going concern scoresWith actual going concern opinions
Figure 6: The performance of including actual going concern opinions in bankruptcy pre-diction models. This figure plots ROC curves to evaluate the usefulness of including actual goingconcern opinions in bankruptcy prediction models. The x-axis is the false positive rate (i.e., incorrectlypredicting that the client will file for bankruptcy) and the y-axis is the true positive rate (i.e., correctlypredicting that the client will file for bankruptcy). A ROC curve that further skews to the upper leftcorner indicates better predictive performance. The hollow diamonds represent Random Forests pre-dictions that include the actual going concern opinions as one of the predictor variables. The solid dotsrepresent Random Forests predictions that exclude actual going concern opinions as one of the predictorvariables. The stand-alone solid dot corresponds to the predictive performance obtained from just usingactual going concern opinions as a bankruptcy predictor. Other predictor variables include the naturallogarithm of total assets, the ratio of debt to total assets, the ratio of short-term investments to totalassets, the ratio of cash to total assets, return on asset, the natural logarithm of closing stock price forthe fiscal period, the number of years of an auditor-client relation, R&D divided by sales, an indicatorfor missing R&D, fraction of non-audit fees in total audit fees, an indicator for missing audit fees,intangible assets divided by total assets, an indicator for a S&P credit rating being CCC+ or below,an indicator for a S&P credit rating downgrade, an indicator for no S&P credit rating, and indicatorvariables for each of the Big 4 auditors, Grant Thornton, and BDO.
34
Marginal effects (%)
Den
sity
0 5 10 15
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Figure 7: Histogram of partial effects of a going concern opinion for clients that did notreceive a going concern opinion in the prior year. We generate the partial effects of a goingconcern opinion using the bivariate probit estimates of the Random Forests specification for clients thatdid not receive a going concern opinion in the prior year. For each observation, we hold constant thegoing concern score and bankruptcy score and vary going concern opinion. The horizontal axis is thepercentage point difference of the bankruptcy probability when going concern opinion == 1 and whengoing concern opinion == 0.
35
Table 1: Simulation results
In this table, we examine the properties of bivariate probit. We simulate data using the following model:(UgSb
)iid∼N (µ,Σ), µ =
(β0 + β1xα0 + α1x
), Σ =
(1 ρρ 1
).
Bankruptcy and going concern opinions are generated using a binary indicator function
G = 1{Ug ≥ 0
},
B = 1{Sg ≥ −γG
}.
We assume that β1 = −1, α1 = 0.2, β0 = −1.6, and α0 = −2.6. We draw the observable covariatex from N (0, 1). The true γ takes values from (0, 0.5, 1, 2) and ρ takes values from (0, 0.3, 0.6). Foreach γ, ρ pair, we examine three cases: (1) no exclusion restriction, (2) a valid exclusion restriction,(3) an invalid exclusion restriction. To create a valid exclusion restriction, we draw from N (0, 1) anduse the realization as an additional covariate only in the going concern equation. To create an invalidexclusion restriction, we draw from N (0, 1) but correlate the draw with the error term of the bankruptcyequation (correlation coefficient is arbitrarily set to be 0.20). We generate 10,000 observations for eachparameter combination and then estimate the parameters using bivariate probit. We obtain the samplingdistribution of γ and ρ by running the simulation 200 times and report the summary statistics in thetable.
γ ρTrue γ/True ρ/Method
Mean Sd 2.5% 50% 97.50% Mean Sd 2.5% 50% 97.50%
(0/0/no exclusion) 0.009 0.900 −1.237 0.030 1.534 −0.035 0.348 −0.702 −0.012 0.675(0/0/exclusion) −0.020 0.327 −0.701 −0.004 0.622 0.014 0.212 −0.382 0.004 0.403(0/0/bad exclusion) −0.014 0.211 −0.443 −0.019 0.377 0.005 0.178 −0.370 0.019 0.294(0.5/0/no exclusion) 0.566 0.414 −0.178 0.583 1.420 −0.022 0.217 −0.438 −0.032 0.383(0.5/0/exclusion) 0.529 0.211 0.126 0.538 0.928 −0.013 0.141 −0.294 −0.006 0.266(0.5/0/bad exclusion) 0.504 0.137 0.253 0.511 0.742 0.001 0.118 −0.239 0.001 0.231(1/0/no exclusion) 1.034 0.305 0.447 1.018 1.591 −0.010 0.149 −0.306 −0.011 0.280(1/0/exclusion) 1.025 0.159 0.732 1.014 1.351 −0.008 0.106 −0.214 −0.005 0.184(1/0/bad exclusion) 1.009 0.099 0.814 1.010 1.173 −0.003 0.081 −0.158 −0.005 0.161(2/0/no exclusion) 2.027 0.265 1.479 2.033 2.483 −0.011 0.121 −0.224 −0.017 0.264(2/0/exclusion) 2.016 0.114 1.824 2.013 2.233 0.000 0.063 −0.106 −0.005 0.124(2/0/bad exclusion) 2.012 0.086 1.861 2.007 2.173 −0.001 0.054 −0.100 −0.003 0.106(0/0.3/no exclusion) 0.041 0.522 −0.946 0.030 1.085 0.277 0.282 −0.244 0.271 0.811(0/0.3/exclusion) −0.029 0.227 −0.577 −0.019 0.396 0.311 0.147 0.026 0.306 0.595(0/0.3/bad exclusion) 0.652 0.143 0.389 0.658 0.907 −0.105 0.127 −0.369 −0.104 0.119(0.5/0.3/no exclusion) 0.528 0.424 −0.325 0.559 1.276 0.285 0.208 −0.108 0.268 0.728(0.5/0.3/exclusion) 0.501 0.177 0.128 0.519 0.853 0.302 0.119 0.096 0.300 0.518(0.5/0.3/bad exclusion) 1.172 0.114 0.929 1.171 1.376 −0.083 0.091 −0.248 −0.082 0.086(1/0.3/no exclusion) 1.017 0.367 0.164 1.049 1.622 0.290 0.167 0.005 0.273 0.648(1/0.3/exclusion) 1.010 0.144 0.725 1.003 1.285 0.297 0.088 0.124 0.300 0.448(1/0.3/bad exclusion) 1.696 0.099 1.505 1.697 1.886 −0.077 0.069 −0.231 −0.079 0.044(2/0.3/no exclusion) 2.001 0.347 1.328 2.004 2.631 0.298 0.137 0.056 0.293 0.565(2/0.3/exclusion) 2.003 0.111 1.785 2.008 2.213 0.304 0.054 0.207 0.306 0.417(2/0.3/bad exclusion) 2.735 0.091 2.569 2.726 2.917 −0.068 0.052 −0.165 −0.066 0.028(0/0.6/no exclusion) 0.051 0.444 −0.676 0.071 0.919 0.570 0.215 0.109 0.590 0.900(0/0.6/exclusion) 0.013 0.177 −0.278 0.010 0.372 0.586 0.104 0.373 0.601 0.755(0/0.6/bad exclusion) 1.518 0.175 1.185 1.517 1.873 −0.244 0.117 −0.473 −0.245 −0.029(0.5/0.6/no exclusion) 0.533 0.424 −0.217 0.541 1.330 0.583 0.177 0.203 0.599 0.880(0.5/0.6/exclusion) 0.511 0.149 0.256 0.502 0.813 0.594 0.080 0.434 0.598 0.735(0.5/0.6/bad exclusion) 2.095 0.148 1.819 2.096 2.384 −0.215 0.086 −0.396 −0.214 −0.064(1/0.6/no exclusion) 1.043 0.390 0.275 1.014 1.854 0.581 0.145 0.303 0.592 0.843(1/0.6/exclusion) 1.010 0.134 0.761 1.013 1.257 0.599 0.058 0.501 0.597 0.711(1/0.6/bad exclusion) 2.677 0.138 2.423 2.685 2.983 −0.190 0.066 −0.321 −0.194 −0.067(2/0.6/no exclusion) 2.039 0.381 1.303 2.046 2.698 0.585 0.109 0.387 0.589 0.783(2/0.6/exclusion) 2.008 0.111 1.807 2.002 2.225 0.601 0.044 0.520 0.603 0.682(2/0.6/bad exclusion) 3.849 0.130 3.602 3.839 4.123 −0.141 0.052 −0.229 −0.145 −0.03936
Table 2: Sample selection
This table summarizes our sample construction process. The unit of observation is the client-year. Oursample consists of the intersection of Compustat, Audit Analytics, CRSP, and Bankruptcy.com. Thesample period used in estimation is 2000–2014.
Filter Number Percent
Audit Analytics: Opinions 2000–2014 247,297 100%Require GVKEY 128,750 52%Drop multiple auditors 128,391 52%Merge with Compustat 108,205 44%After dropping missing values 88,545 36%
Compustat 1999–2015 160,107 100%Merge with Audit Analytics 2000–2014 108,205 68%After dropping missing values 88,545 55%
Total bankruptcy cases 2,648 100%Merge with Audit Analytics 1,558 66%After dropping missing values 1,201 45%
37
Table 3: Summary statistics
This table presents summary statistics for the variables used in our analysis. Panel A presents summarystatistics for the entire sample. Panel B presents summary statistics for clients that did not receive agoing concern opinion in the prior year. Panel C presents summary statistics for clients that received agoing concern opinion in the prior year. Panel D presents summary statistics for clients that filed forbankruptcy within 12 months after receiving a going concern opinion. The sample period is 2000–2014.
Panel A: Full sample
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 88,545 0.014 0.116 0.000 0.000 0.000 0.000 0.000Going concern 88,545 0.142 0.349 0.000 0.000 0.000 0.000 1.000Log(Assets) 88,545 5.299 2.690 0.586 3.387 5.385 7.174 9.695Leverage 88,545 0.668 5.016 0.081 0.282 0.506 0.735 1.313Investment 88,545 0.054 0.129 0.000 0.000 0.000 0.031 0.341Cash 88,545 0.194 0.226 0.002 0.029 0.100 0.282 0.713ROA 88,545 −0.231 6.988 −1.181 −0.144 0.009 0.058 0.163Log(Price) 88,545 2.135 1.300 0.086 1.001 2.236 3.195 4.067Intangible assets 88,545 0.125 0.182 0.000 0.000 0.031 0.189 0.538R&D 88,545 0.409 3.265 0.000 0.000 0.000 0.067 0.936R&D missing 88,545 0.457 0.498 0.000 0.000 0.000 1.000 1.000No S&P rating 88,545 0.784 0.411 0.000 1.000 1.000 1.000 1.000S&P rating below CCC+ 88,545 0.006 0.079 0.000 0.000 0.000 0.000 0.000S&P rating downgrade 88,545 0.011 0.102 0.000 0.000 0.000 0.000 0.000Non-audit fees 88,545 0.190 0.202 0.000 0.012 0.129 0.295 0.614Non-audit fees missing 88,545 0.081 0.272 0.000 0.000 0.000 0.000 1.000Years client 88,545 4.576 3.485 1.000 2.000 4.000 6.000 12.000
Panel B: Conditional on not receiving a going concern opinion in the prior year
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 69,266 0.010 0.099 0.000 0.000 0.000 0.000 0.000Going concern 69,266 0.039 0.193 0.000 0.000 0.000 0.000 0.000Log(Assets) 69,266 5.893 2.389 2.039 4.211 5.875 7.496 9.912Leverage 69,266 0.521 0.378 0.092 0.284 0.493 0.697 0.955Investment 69,266 0.059 0.134 0.000 0.000 0.000 0.041 0.361Cash 69,266 0.204 0.227 0.004 0.035 0.112 0.299 0.718ROA 69,266 −0.070 0.579 −0.602 −0.056 0.019 0.065 0.163Log(Price) 69,266 2.407 1.193 0.315 1.493 2.552 3.328 4.134Intangible assets 69,266 0.134 0.183 0.000 0.000 0.044 0.209 0.543R&D 69,266 0.397 3.323 0.000 0.000 0.000 0.061 0.693R&D missing 69,266 0.456 0.498 0.000 0.000 0.000 1.000 1.000No S&P rating 69,266 0.750 0.433 0.000 0.000 1.000 1.000 1.000S&P rating below CCC+ 69,266 0.006 0.076 0.000 0.000 0.000 0.000 0.000S&P rating downgrade 69,266 0.012 0.110 0.000 0.000 0.000 0.000 0.000Non-audit fees 69,266 0.197 0.191 0.000 0.040 0.148 0.298 0.590Non-audit fees missing 69,266 0.029 0.168 0.000 0.000 0.000 0.000 0.000Years client 69,266 5.216 3.512 1.000 2.000 4.000 7.000 12.000
38
Panel C: Conditional on receiving a going concern opinion in the prior year
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 10,571 0.029 0.167 0.000 0.000 0.000 0.000 0.000Going concern 10,571 0.816 0.387 0.000 1.000 1.000 1.000 1.000Log(Assets) 10,571 1.805 1.845 0.003 0.339 1.287 2.718 5.578Leverage 10,571 1.644 12.799 0.044 0.303 0.717 1.434 4.959Investment 10,571 0.020 0.085 0.000 0.000 0.000 0.000 0.103Cash 10,571 0.142 0.209 0.000 0.007 0.047 0.177 0.657ROA 10,571 −1.103 3.959 −4.009 −1.238 −0.479 −0.115 0.157Log(Price) 10,571 0.508 0.655 0.005 0.062 0.227 0.703 1.914Intangible assets 10,571 0.088 0.181 0.000 0.000 0.000 0.072 0.543R&D 10,571 0.554 3.025 0.000 0.000 0.000 0.139 2.193R&D missing 10,571 0.445 0.497 0.000 0.000 0.000 1.000 1.000No S&P rating 10,571 0.983 0.131 1.000 1.000 1.000 1.000 1.000S&P rating below CCC+ 10,571 0.010 0.100 0.000 0.000 0.000 0.000 0.000S&P rating downgrade 10,571 0.007 0.081 0.000 0.000 0.000 0.000 0.000Non-audit fees 10,571 0.105 0.164 0.000 0.000 0.000 0.153 0.469Non-audit fees missing 10,571 0.132 0.339 0.000 0.000 0.000 0.000 1.000Years client 10,571 3.279 2.470 1.000 2.000 3.000 4.000 8.000
Panel D: Conditional on filing for bankruptcy
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 1,201 1.000 0.000 1.000 1.000 1.000 1.000 1.000Going concern 1,201 0.626 0.484 0.000 0.000 1.000 1.000 1.000Log(Assets) 1,201 4.939 2.458 0.865 3.195 4.934 6.601 8.979Leverage 1,201 1.094 1.463 0.127 0.631 0.889 1.190 2.516Investment 1,201 0.043 0.142 0.000 0.000 0.000 0.014 0.238Cash 1,201 0.146 0.209 0.001 0.020 0.065 0.161 0.658ROA 1,201 −0.601 2.326 −2.218 −0.708 −0.226 −0.050 0.037Log(Price) 1,201 0.909 0.883 0.031 0.223 0.626 1.335 2.660Intangible assets 1,201 0.110 0.180 0.000 0.000 0.010 0.153 0.534R&D 1,201 0.425 2.445 0.000 0.000 0.000 0.019 1.365R&D missing 1,201 0.541 0.499 0.000 0.000 1.000 1.000 1.000No S&P rating 1,201 0.771 0.420 0.000 1.000 1.000 1.000 1.000S&P rating below CCC+ 1,201 0.102 0.303 0.000 0.000 0.000 0.000 1.000S&P rating downgrade 1,201 0.086 0.280 0.000 0.000 0.000 0.000 1.000Non-audit fees 1,201 0.147 0.195 0.000 0.000 0.058 0.243 0.556Non-audit fees missing 1,201 0.253 0.435 0.000 0.000 0.000 1.000 1.000Years client 1,201 3.524 2.947 1.000 1.000 2.000 5.000 10.000
39
Table 4: Type I and Type II errors—model v.s. auditors
In this table, we report Type I errors (predicting false bankruptcy) and Type II errors (predicting falsenon-bankruptcy) using actual going concern opinions as bankruptcy predictors and using our modelgenerated going concern opinions as bankruptcy predictors. For year t, we pool all data from year 1 toyear t − 1 and use Random Forests to forecast the propensity of filing bankruptcy. We then issue thesame number of going concern opinions as a given auditor according to the ranking of the predictivebankruptcy probability of the auditor’s clients year t. Predictor variables include: the natural logarithmof total assets, the ratio of debt to total assets, the ratio of short-term investments to total assets, theratio of cash to total assets, return on asset, the natural logarithm of closing stock price for the fiscalperiod, the number of years of an auditor-client relation, R&D divided by sales, an indicator for missingR&D, the ratio of non-audit fees to total audit fees, an indicator for missing audit fees, intangible assetsdivided by total assets, an indicator for the S&P credit rating being CCC+ or below, an indicator fora S&P credit rating downgrade, an indicator for no S&P credit rating, and indicator variables for eachof the Big 4 auditors, Grant Thornton, and BDO.
Error rateAuditor E&Y DT KPMG PwC GT BDO Others
Model Type I 0.035 0.035 0.041 0.033 0.067 0.133 0.336Model Type II 0.383 0.364 0.392 0.388 0.458 0.435 0.224Actual Type I 0.036 0.037 0.042 0.032 0.072 0.140 0.365Actual Type II 0.400 0.479 0.284 0.339 0.604 0.484 0.280
40
Tab
le5:
Goi
ng
con
cern
opin
ion
san
db
ankru
ptc
yfi
lings
Inth
ista
ble
,w
eex
am
ine
goin
gco
nce
rnop
inio
ns
and
ban
kru
ptc
yfi
lin
gsfo
rfi
rms
that
did
not
rece
ive
ago
ing
con
cern
opin
ion
inth
ep
rior
year
.M
od
els
(1)
an
d(2
)ar
ep
rob
itre
gre
ssio
ns
esti
mat
edin
dep
end
entl
y.M
od
els
(3)
and
(4)
are
biv
aria
tep
robit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
anin
dic
ator
for
wh
eth
era
clie
nt
rece
ives
ago
ing
con
cern
opin
ion
inye
art
and
anin
dic
ator
for
wh
eth
erth
ecl
ient
file
dfo
rb
ankru
ptc
yw
ith
inon
eye
arof
the
bal
ance
shee
td
ate
.E
xp
lan
ator
yva
riab
les
incl
ud
ego
ing
con
cern
scor
ew
hic
his
ap
red
icti
vesc
ore
ofa
clie
nt
rece
ivin
ggo
ing
con
cern
opin
ion
an
db
an
kru
ptc
ysc
ore
whic
his
ap
red
icti
vesc
ore
for
the
clie
nt
fili
ng
for
ban
kru
ptc
y.T
ocr
eate
the
scor
esfo
rcl
ienti
inye
art,
we
pool
all
dat
afr
omye
ar1
toye
art−
1an
du
seR
and
omF
ores
tsto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
nor
fili
ng
for
ban
kru
ptc
y.W
eu
seth
ein
vers
est
an
dar
dn
orm
al
cum
ula
tive
dis
trib
uti
onfu
nct
ion
totr
ansf
orm
the
pre
dic
tive
pro
bab
ilit
yto
scor
eso
that
one
un
itch
ange
corr
esp
on
ds
toa
one
stan
dard
dev
iati
onch
ange
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
asse
ts,
the
rati
oof
deb
tto
tota
lass
ets,
the
rati
oof
short
-ter
min
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,th
ere
turn
onas
sets
,th
en
atu
ral
loga
rith
mof
clos
ing
stock
pri
cefo
rth
efisc
alp
erio
d,
the
nu
mb
erof
yea
rsof
the
aud
itor
-cli
ent
rela
tion
ship
,R
&D
div
ided
by
sale
s,an
ind
icat
orfo
rm
issi
ng
R&
D,
the
rati
oof
non
-au
dit
fees
toto
tal
aud
itfe
es,
anin
dic
ator
for
mis
sin
gau
dit
fees
,in
tan
gib
leas
sets
div
ided
by
tota
las
sets
,an
ind
icat
orfo
rth
eS
&P
cred
itra
tin
gb
ein
gC
CC
+or
bel
ow,
an
ind
icat
orfo
ran
S&
Pcr
edit
rati
ng
dow
ngr
ade,
anin
dic
ator
for
no
S&
Pcr
edit
rati
ng.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms.
We
als
oin
clu
de
yea
rfi
xed
effec
ts,
one
dig
itS
ICin
du
stry
fixed
effec
ts,
and
aud
itor
fixed
effec
ts.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rvals
bel
owth
ees
tim
ates
that
are
bas
edon
boot
stra
pp
ing.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tep
rob
itB
ivar
iate
pro
bit
Goin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yV
ari
able
sop
inio
nfi
ling
opin
ion
fili
ng
opin
ion
fili
ng
Goin
gco
nce
rn0.
873
0.34
1[0
.777
,0.
977]
[0.0
01,
0.65
8]G
oin
gco
nce
rnsc
ore
0.73
00.
085
0.71
60.
196
0.72
40.
145
[0.6
53,
0.8
01]
[0.0
02,
0.16
5][0
.642
,0.
787]
[0.1
09,
0.28
3][0
.648
,0.
796]
[0.0
41,
0.25
2]B
an
kru
ptc
ysc
ore
0.1
070.
390
0.10
20.
366
0.10
40.
377
[0.0
52,
0.1
63]
[0.2
79,
0.49
8][0
.049
,0.
158]
[0.2
56,
0.47
4][0
.049
,0.
161]
[0.2
58,
0.48
9][0
.172,
0.5
41]
[0.1
78,
0.57
3][0
.19,
0.56
2][0
.206
,0.
591]
[0.1
83,
0.55
5][0
.196
,0.
59]
ρ0.
477
0.30
4[0
.431
,0.
525]
[0.1
42,
0.48
2]
Con
trol
vari
able
sY
esY
esY
esY
esA
ud
itor
FE
Yes
Yes
Yes
Yes
Ind
ust
ryF
EY
esY
esY
esY
esY
ear
FE
Yes
Yes
Yes
Yes
Pse
ud
oR
20.4
460.
352
0.39
40.
395
Ob
serv
atio
ns
69,
259
69,2
5969
,259
69,2
59
41
Table 6: Marginal effects of going concern opinions
This table reports the distribution of marginal effects associated with a going concern opinion issuance.Each row represents one sample. For a given sample, we use the estimates of the bivariate probit modelbased on that sample and compute the change in bankruptcy probability associated with changing goingconcern opinion from zero to one, holding constant other covariates.
Mean Q1 Median Q3
GC = 0 Prior Year 0.84% 0.02% 0.21% 0.90%Accelerate = 0 0.39% 0.01% 0.13% 0.44%Accelerate = 1 3.23% 0.36% 1.13% 3.67%Big4 = 0 0.01% 0.00% 0.01% 0.02%Big4 = 1 1.82% 0.09% 0.43% 1.88%Large = 1 6.42% 1.21% 3.07% 7.94%Large = 0 0.28% 0.00% 0.08% 0.30%Leverage ≥ 0.67 0.65% 0.02% 0.18% 0.81%Leverage ≥ 0.33 & Leverage < 0.67 1.84% 0.28% 0.84% 2.30%No Long Term Debt −0.07% −0.05% −0.01% 0.00%With Long Term Debt 0.78% 0.04% 0.18% 0.78%Accelerate = 1 & Big 4 = 1 5.33% 0.78% 2.19% 6.43%Accelerate = 1 & Big 4 = 0 1.06% 0.02% 0.26% 1.12%Accelerate = 0 & Big 4 = 1 0.90% 0.03% 0.23% 0.91%Accelerate = 0 & Big 4 = 0 −0.84% −0.94% −0.26% −0.02%
42
Table 7: Going concern opinions and bankruptcy filings—Big 4 vs Non-Big 4 clients
In this table, we examine going concern opinions and bankruptcy filings allowing for differential effects forBig 4 and Non-Big 4 clients, using bivariate probit regressions. The dependent variables are an indicatorfor whether a client receives a going concern opinion in year t and an indicator for whether the client filedfor bankruptcy within one year of the balance sheet date. Explanatory variables include going concernscore which is a predictive score of a client receiving going concern opinion and bankruptcy score whichis a predictive score for the client filing for bankruptcy. To create the scores for client i in year t, we poolall data from year 1 to year t−1 and use Random Forests to forecast the propensity of receiving a goingconcern opinion or filing for bankruptcy. We use the inverse standard normal cumulative distributionfunction to transform the predictive probability to score so that one unit change corresponds to a onestandard deviation change. Other predictor variables include: the natural logarithm of total assets,the ratio of debt to total assets, the ratio of short-term investments to total assets, the ratio of cashto total assets, the return on assets, the natural logarithm of closing stock price for the fiscal period,the number of years of the auditor-client relationship, R&D divided by sales, an indicator for missingR&D, the ratio of non-audit fees to total audit fees, an indicator for missing audit fees, intangible assetsdivided by total assets, an indicator for the S&P credit rating being CCC+ or below, an indicator foran S&P credit rating downgrade, an indicator for no S&P credit rating. ρ is the correlation betweentwo error terms. We also include year fixed effects, one digit SIC industry fixed effects, and auditorfixed effects. We present the mean estimates and 95% confidence intervals below the estimates that arebased on bootstrapping.
(1) (2)Big 4 Non-Big 4
Going concern Bankruptcy Going concern BankruptcyVariables opinion filing opinion filing
Going concern 0.725 −0.065[0.185, 1.155] [−0.546, 0.457]
Going concern score 0.642 0.179 0.852 0.203[0.519, 0.774] [0.058, 0.336] [0.755, 0.937] [0.034, 0.391]
Bankruptcy score 0.045 0.269 0.097 0.374[−0.038, 0.125] [0.13, 0.417] [0.026, 0.168] [0.203, 0.564]
ρ 0.160 0.456[−0.081, 0.443] [0.196, 0.686]
Control variables Yes YesAuditor FE Yes YesIndustry FE Yes YesYear FE Yes Yes
Pseudo R2 0.413 0.347Observations 47,789 20,482
43
Table 8: Going concern opinions and bankruptcy filings—client size
In this table, we examine going concern opinions and bankruptcy filings allowing for differential effectsfor large and small clients, using bivariate probit regressions. A client is large if its assets in the prioryear are larger than the median asset value among firms that did not receive a going concern opinion inthe prior year. The dependent variables are an indicator for whether a client receives a going concernopinion in year t and an indicator for whether the client filed for bankruptcy within one year of thebalance sheet date. Explanatory variables include going concern score which is a predictive score of aclient receiving going concern opinion and bankruptcy score which is a predictive score for the clientfiling for bankruptcy. To create the scores for client i in year t, we pool all data from year 1 to year t−1and use Random Forests to forecast the propensity of receiving a going concern opinion or filing forbankruptcy. We use the inverse standard normal cumulative distribution function to transform thepredictive probability to score so that one unit change corresponds to a one standard deviation change.Other predictor variables include: the natural logarithm of total assets, the ratio of debt to total assets,the ratio of short-term investments to total assets, the ratio of cash to total assets, the return on assets,the natural logarithm of closing stock price for the fiscal period, the number of years of the auditor-clientrelationship, R&D divided by sales, an indicator for missing R&D, the ratio of non-audit fees to totalaudit fees, an indicator for missing audit fees, intangible assets divided by total assets, an indicatorfor the S&P credit rating being CCC+ or below, an indicator for an S&P credit rating downgrade,an indicator for no S&P credit rating. ρ is the correlation between two error terms. We also includeyear fixed effects, one digit SIC industry fixed effects, and auditor fixed effects. We present the meanestimates and 95% confidence intervals below the estimates that are based on bootstrapping.
(1) (2)Asset ≤50% Asset > 50%
Going concern Bankruptcy Going concern BankruptcyVariables opinion filing opinion filing
Going concern 0.171 1.255[−0.294, 0.64] [0.593, 1.796]
Going concern score 0.812 0.282 0.403 0.161[0.727, 0.889] [0.081, 0.464] [0.205, 0.638] [0.038, 0.292]
Bankruptcy score 0.091 0.371 0.147 0.2[0.032, 0.148] [0.193, 0.57] [−0.02, 0.351] [0.06, 0.351]
ρ 0.349 −0.037[0.095, 0.597] [−0.305, 0.276]
Control variables Yes YesAuditor FE Yes YesIndustry FE Yes YesYear FE Yes Yes
Pseudo R2 0.351 0.420Observations 34,630 34,630
44
Table 9: Going concern opinions and bankruptcy filings—accelerated filers
In this table, we examine going concern opinions and bankruptcy filings for audit clients allowing fordifferential effects based on whether the client is an accelerated filer, using bivariate probit regressions.The dependent variables are an indicator for whether a client receives a going concern opinion in year tand an indicator for whether the client filed for bankruptcy within one year of the balance sheet date.Explanatory variables include going concern score which is a predictive score of a client receiving goingconcern opinion and bankruptcy score which is a predictive score for the client filing for bankruptcy.To create the scores for client i in year t, we pool all data from year 1 to year t − 1 and use RandomForests to forecast the propensity of receiving a going concern opinion or filing for bankruptcy. We usethe inverse standard normal cumulative distribution function to transform the predictive probability toscore so that one unit change corresponds to a one standard deviation change. Other predictor variablesinclude: the natural logarithm of total assets, the ratio of debt to total assets, the ratio of short-terminvestments to total assets, the ratio of cash to total assets, the return on assets, the natural logarithmof closing stock price for the fiscal period, the number of years of the auditor-client relationship, R&Ddivided by sales, an indicator for missing R&D, the ratio of non-audit fees to total audit fees, an indicatorfor missing audit fees, intangible assets divided by total assets, an indicator for the S&P credit ratingbeing CCC+ or below, an indicator for an S&P credit rating downgrade, an indicator for no S&P creditrating. ρ is the correlation between two error terms. We also include year fixed effects, one digit SICindustry fixed effects, and auditor fixed effects. We present the mean estimates and 95% confidenceintervals below the estimates that are based on bootstrapping.
(1) (2)Non-accelerated filers Accelerated filers
Going concern Bankruptcy Going concern BankruptcyVariables opinion filing opinion filing
Going concern −0.033 1.193[−0.697, 0.631] [0.634, 1.672]
Going concern score 0.797 0.154 0.587 0.154[0.698, 0.893] [−0.055, 0.371] [0.431, 0.742] [0.031, 0.285]
Bankruptcy score 0.075 0.465 0.089 0.237[0.009, 0.151] [0.269, 0.673] [−0.017, 0.206] [0.097, 0.385]
ρ 0.457 −0.104[0.106, 0.776] [−0.37, 0.169]
Control variables Yes YesAuditor FE Yes YesIndustry FE Yes YesYear FE Yes Yes
Pseudo R2 0.323 0.404Observations 17,939 44,994
45
Tab
le10
:G
oin
gco
nce
rnop
inio
ns
and
ban
kru
ptc
yfi
lin
gs–B
ig4
and
Acc
eler
ated
file
r
Inth
ista
ble
,w
eex
amin
ego
ing
con
cern
opin
ion
san
db
an
kru
ptc
yfi
lin
gs
all
owin
gfo
rd
iffer
enti
al
effec
tsfo
rw
het
her
afi
rmh
as
aB
ig4
au
dit
or
an
dis
an
acce
lera
ted
file
r,u
sin
gb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
an
ind
icato
rfo
rw
het
her
acl
ient
rece
ives
agoin
gco
nce
rnop
inio
nin
yeart
an
dan
ind
icat
orfo
rw
het
her
the
clie
nt
file
dfo
rb
ankru
ptc
yw
ithin
on
eye
ar
of
the
bala
nce
shee
td
ate
.E
xp
lan
ato
ryva
riab
les
incl
ud
egoin
gco
nce
rnsc
ore
wh
ich
isa
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
op
inio
nan
db
an
kru
ptc
ysc
ore
wh
ich
isa
pre
dic
tive
score
for
the
clie
nt
fili
ng
for
ban
kru
ptc
y.T
ocr
eate
the
scor
esfo
rcl
ienti
inye
art,
we
pool
all
dat
afr
om
year
1to
yea
rt−
1an
du
seR
an
dom
Fore
sts
tofo
reca
stth
ep
rop
ensi
tyof
rece
ivin
ga
goin
gco
nce
rnop
inio
nor
fili
ng
for
ban
kru
ptc
y.W
eu
seth
ein
vers
est
an
dard
norm
al
cum
ula
tive
dis
trib
uti
on
fun
ctio
nto
tran
sform
the
pre
dic
tive
pro
bab
ilit
yto
score
soth
at
one
un
itch
ange
corr
esp
ond
sto
aon
est
and
ard
dev
iati
on
chan
ge.
Oth
erp
red
icto
rva
riab
les
incl
ud
e:th
en
atu
ral
logari
thm
of
tota
lass
ets,
the
rati
oof
deb
tto
tota
las
sets
,th
era
tio
ofsh
ort-
term
inve
stm
ents
toto
tal
ass
ets,
the
rati
oof
cash
toto
tal
ass
ets,
the
retu
rnon
ass
ets,
the
natu
ral
logari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
,th
enu
mb
erof
year
sof
the
aud
itor-
clie
nt
rela
tion
ship
,R
&D
div
ided
by
sale
s,an
ind
icato
rfo
rm
issi
ng
R&
D,
the
rati
oof
non
-au
dit
fees
toto
tal
aud
itfe
es,
anin
dic
ator
for
mis
sin
gau
dit
fees
,in
tan
gib
leass
ets
div
ided
by
tota
lass
ets,
an
ind
icato
rfo
rth
eS&
Pcr
edit
rati
ng
bei
ng
CC
C+
or
bel
ow,
an
ind
icat
orfo
ran
S&
Pcr
edit
rati
ng
dow
ngr
ade,
anin
dic
ato
rfo
rn
oS
&P
cred
itra
tin
g.ρ
isth
eco
rrel
ati
on
bet
wee
ntw
oer
ror
term
s.W
eals
oin
clu
de
yea
rfi
xed
effec
ts,
one
dig
itS
ICin
du
stry
fixed
effec
ts,
and
audit
or
fixed
effec
ts.
We
pre
sent
the
mea
nes
tim
ate
san
d95%
con
fid
ence
inte
rvals
bel
owth
ees
tim
ate
sth
at
are
bas
edon
boot
stra
pp
ing.
(1)
(2)
(3)
(4)
Acc
eler
ate
&B
ig4
Acc
eler
ate
&N
on
Big
4A
ccel
erate
=0
Big
4=
1A
ccel
erate
=0
Big
4=
0G
oin
gco
nce
rnB
an
kru
ptc
yG
oin
gco
nce
rnB
an
kru
ptc
yG
oin
gco
nce
rnB
an
kru
ptc
yG
oin
gco
nce
rnB
an
kru
ptc
yV
ari
ab
les
op
inio
nfi
lin
gop
inio
nfi
lin
gG
oin
gco
nce
rn1.5
43
0.4
09
−0.0
16
−0.3
47
[0.8
35,
2.2
19]
[−0.6
32,
1.2
94]
[−0.6
8,
1.3
01]
[−1.1
03,
0.3
69]
Goin
gco
nce
rnsc
ore
0.5
02
0.1
69
0.7
76
0.1
55
0.6
22
0.3
44
0.8
06
0.0
89
[0.3
05,
0.6
88]
[0.0
33,
0.3
35]
[0.4
68,
1.0
5]
[−0.0
79,
0.4
23]
[0.4
48,
0.7
98]
[0.0
22,
0.6
29]
[0.6
92,
0.9
13]
[−0.1
23,
0.3
87]
Ban
kru
ptc
ysc
ore
0.0
51
0.2
40.1
30.1
30.0
50.2
12
0.0
96
0.5
84
[−0.0
72,
0.1
86]
[0.0
54,
0.4
23]
[−0.1
08,
0.3
75]
[−0.0
96,
0.4
03]
[−0.0
73,
0.1
76]
[−0.0
23,
0.4
72]
[0.0
11,
0.1
82]
[0.3
08,
0.8
78]
ρ−
0.2
66
0.1
94
0.5
25
0.5
81
[−0.5
87,
0.0
81]
[−0.2
87,
0.7
37]
[−0.1
32,
0.8
84]
[0.2
09,
0.9
26]
Contr
ol
vari
ab
les
Yes
Yes
Yes
Yes
Au
dit
or
FE
Yes
Yes
Yes
Yes
Ind
ust
ryF
EY
esY
esY
esY
esY
ear
FE
Yes
Yes
Yes
Yes
Pse
ud
oR
20.4
07
0.4
57
0.3
43
0.3
27
Ob
serv
ati
on
s37,6
70
6,6
98
7,1
47
10,5
50
46
Tab
le11
:G
oin
gco
nce
rnop
inio
ns
and
ban
kru
ptc
yfi
lin
gs–t
he
exis
ten
ceof
lon
gte
rmd
ebt
Inth
ista
ble
,w
eex
am
ine
goi
ng
con
cern
op
inio
ns
and
ban
kru
ptc
yfi
lin
gsal
low
ing
for
diff
eren
tial
effec
tsfo
rw
het
her
afi
rmh
asou
tsta
nd
ing
lon
gte
rmd
ebt,
usi
ng
biv
aria
tep
rob
itre
gre
ssio
ns.
We
div
ide
firm
sin
totw
osa
mp
les
bas
edon
wh
eth
era
firm
has
lon
gte
rmd
ebt,
for
firm
sth
atd
idn
ot
rece
ive
agoi
ng
con
cern
inth
ep
rior
year
.T
he
dep
end
ent
vari
able
sar
ean
ind
icat
orfo
rw
het
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art
an
dan
indic
ator
for
wh
eth
erth
ecl
ient
file
dfo
rb
ankru
ptc
yw
ith
inon
eye
arof
the
bal
ance
shee
td
ate.
Exp
lan
ator
yva
riab
les
incl
ud
ego
ing
con
cern
score
wh
ich
isa
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
ban
kru
ptc
ysc
ore
wh
ich
isa
pre
dic
tive
scor
efo
rth
ecl
ient
fili
ng
for
ban
kru
ptc
y.T
ocr
eate
the
scor
esfo
rcl
ienti
inye
art,
we
pool
all
dat
afr
omye
ar1
toye
art−
1an
du
seR
and
omF
ores
tsto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
agoi
ng
con
cern
opin
ion
orfi
lin
gfo
rb
ankru
ptc
y.W
eu
seth
ein
vers
est
and
ard
nor
mal
cum
ula
tive
dis
trib
uti
onfu
nct
ion
totr
ansf
orm
the
pre
dic
tive
pro
bab
ilit
yto
score
soth
aton
eu
nit
chan
geco
rres
pon
ds
toa
one
stan
dar
dd
evia
tion
chan
ge.
Oth
erp
red
icto
rva
riab
les
incl
ud
e:th
en
atu
ral
loga
rith
mof
tota
las
sets
,th
era
tio
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
ves
tmen
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,th
ere
turn
on
ass
ets,
the
nat
ura
llo
gari
thm
ofcl
osin
gst
ock
pri
cefo
rth
efi
scal
per
iod
,th
enu
mb
erof
year
sof
the
aud
itor
-cli
ent
rela
tion
ship
,R
&D
div
ided
by
sale
s,an
ind
icat
orfo
rm
issi
ng
R&
D,
the
rati
oof
non
-au
dit
fees
toto
tal
aud
itfe
es,
anin
dic
ator
for
mis
sin
gau
dit
fees
,in
tan
gib
leas
sets
div
ided
by
tota
lass
ets,
anin
dic
ator
for
the
S&
Pcr
edit
rati
ng
bei
ng
CC
C+
orb
elow
,an
ind
icat
orfo
ran
S&
Pcr
edit
rati
ng
dow
ngra
de,
an
ind
icat
or
for
no
S&
Pcr
edit
rati
ng.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms.
We
also
incl
ud
eye
arfi
xed
effec
ts,
one
dig
itS
ICin
du
stry
fixed
effec
ts,
and
aud
itor
fixed
effec
ts.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
sb
elow
the
esti
mat
esth
atar
eb
ased
on
boot
stra
pp
ing.
(1)
(2)
No
lon
gte
rmd
ebt
Wit
hlo
ng
term
deb
tG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yV
ari
able
sop
inio
nfi
lin
gop
inio
nfili
ng
Goin
gco
nce
rn0.
033
0.34
7[−
0.58
0,1.
004]
[−0.
127,
0.78
6]G
oin
gco
nce
rnsc
ore
0.8
340.
353
0.63
50.
112
[0.7
24,
0.9
43]
[0.0
82,
0.59
7][0
.53,
0.73
6][0
.008
,0.
224]
Ban
kru
ptc
ysc
ore
0.10
60.
297
0.11
40.
261
[0.0
15,
0.1
98]
[0.1
10,
0.50
3][0
.047
,0.
189]
[0.1
49,
0.38
1]
ρ0.
514
0.31
7[−
0.03
3,0.
786]
[0.0
93,
0.56
2]
Contr
olva
riab
les
Yes
Yes
Au
dit
orF
EY
esY
esIn
du
stry
FE
Yes
Yes
Yea
rF
EY
esY
es
Pse
ud
oR
20.
419
0.39
3O
bse
rvati
on
s17
,794
51,3
87
47
