The effect of going concern opinions: Prediction versus inducement * Joseph Gerakos † 1 , P. Richard Hahn 1 , Andrei Kovrijnykh 2 and Frank Zhou 1 1 University of Chicago Booth School of Business, United States 2 Arizona State University W.P. Carey School of Business, United States November 14, 2015 Abstract We examine two distinct channels through which going concern opinions can be associated with the likelihood of bankruptcy: auditors have better access to information about their clients’ bankruptcy risk and going concern opinions directly induce bankruptcies. Using a bivariate probit model that addresses omitted variable bias arising from auditors’ additional information, we find support for both the information and inducement channels. The direct inducement effect of receiving a going concern opinion is a 8.6 percentage point increase in the probability of bankruptcy conditional on previously receiving a going concern opinion, and a 0.8 percentage point increase for clients that did not receive a going concern opinion in the prior year. Despite the direct effect acting as a “self-fulfilling” prophecy, going concern opinions do not predict more bankruptcies than a statistical model based solely on observable data. * We thank Chris Hansen, Patricia Ledesma, and Michal Matˇ ejka for their comments. † Corresponding author. Mailing address: University of Chicago Booth School of Business, 5807 South Woodlawn Avenue, Chicago, IL 60637, United States. E-mail address: [email protected]. Telephone number: +1 (773) 834-6882.
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The effect of going concern opinions: Prediction versusinducement∗
Joseph Gerakos†1, P. Richard Hahn1, Andrei Kovrijnykh2 and Frank Zhou1
1University of Chicago Booth School of Business, United States2Arizona State University W.P. Carey School of Business, United States
November 14, 2015
Abstract
We examine two distinct channels through which going concern opinions can be associated with
the likelihood of bankruptcy: auditors have better access to information about their clients’
bankruptcy risk and going concern opinions directly induce bankruptcies. Using a bivariate
probit model that addresses omitted variable bias arising from auditors’ additional information,
we find support for both the information and inducement channels. The direct inducement
effect of receiving a going concern opinion is a 8.6 percentage point increase in the probability
of bankruptcy conditional on previously receiving a going concern opinion, and a 0.8 percentage
point increase for clients that did not receive a going concern opinion in the prior year. Despite
the direct effect acting as a “self-fulfilling” prophecy, going concern opinions do not predict more
bankruptcies than a statistical model based solely on observable data.
∗We thank Chris Hansen, Patricia Ledesma, and Michal Matejka for their comments.†Corresponding author. Mailing address: University of Chicago Booth School of Business, 5807 South Woodlawn
Avenue, Chicago, IL 60637, United States. E-mail address: [email protected]. Telephone number:+1 (773) 834-6882.
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 or direct inducement of adverse events. Understanding the relative importance of these
two sources provides valuable insight into the efficacy of the current audit standards. A statistical
challenge in separating the two sources is that the relevant variables are unobservable, which leads
to correlated omitted variable bias. Namely, the explanatory power of going concern opinions
in a bankruptcy regression can arise from going concern opinions proxying for auditors’ private
information or from direct inducement of bankruptcies by going concern opinions. The direct effect
operates through channels other than providing additional information. These channels include
mechanical triggers such 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).
1
We identify the direct effect by exploiting the fact that any additional information possessed 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 This joint estimation
leads to an efficiency gain. Even more valuable in this setting, the bivariate probit model allows
for direct estimation for the inducement effect provided that the auditor’s additional information is
drawn from a continuous distribution. 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. Hence,
any incremental predictive power of the going concern opinion in the bankruptcy regression is due
to the direct inducement effect.
We find support for both the additional information hypothesis and the direct inducement
effect of going concern opinions. However, the economic magnitude of the inducement effect varies
with whether the client received a going concern opinion in the previous year. In terms of economic
magnitude, for the sample of audit clients that received a going concern opinion in the previous year,
a going concern opinion leads to a 8.6 percentage point increase in the probability of bankruptcy.
For clients that did not receive a going concern opinion in the prior year, a going concern opinion
leads to a 0.8 percentage point increase in the probability of bankruptcy.
To demonstrate the empirical importance of this direct effect, we mimic the auditor’s role in
inducing bankruptcies while suppressing the auditor’s additional information channel. We do so
by producing synthetic going concern opinions based solely on observable client characteristics and
what we know about the auditor’s going concern policy. We then use these synthetic going concern
1For descriptions of the bivariate probit model, see Heckman (1978), Freedman and Sekhon (2010), and Wooldridge(2010).
2
opinions, along with the same observable client characteristics, to predict bankruptcies and find
that including the synthetic going concern opinions in a bankruptcy prediction model substan-
tially 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). Interestingly, auditors predict fewer bankruptcies than our statistical model based
solely on observable data, which includes client characteristics and auditor behavior.2
Our ability to 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. The auditors have the direct inducement effect on their side as well as
superior access to the client’s bankruptcy risk. Nonetheless, the industry does 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 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.
2Note that our bankruptcy predictors at this point are not the same as the synthetic going concern opinionsthat we use to mimic the auditors’ behavior. These predictors efficiently use observable information, which is notnecessarily true for the auditors.
3
2 Disclosure of existing information versus generation of new in-
formation
Under the current standard, 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,
2012). 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,
2013). In what follows, we refer to the second and third channels as the direct inducement effect.
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.
4
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 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 going concern model, which captures the auditor’s estimate 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 utility/disutility of type I versus
type II errors in the issuance of going concern opinions. The error term νi represents additional
information held by the auditor as well as noise, both of which are unobservable to the researcher.
We then express the bankruptcy probability of client i in terms of the same observable charac-
5
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. The function h(·) captures
the impact of client i’s characteristics, xi, on the likelihood of bankruptcy, while ξi represents
unobservable factors as well as the contribution of GCi (i.e., the inducement effect).
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
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
6
observable covariates x derived by applying a nonlinear classification method to the previous year’s
going concern and bankruptcy data. It is useful to consider this model from the perspective of an
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 going concerns. To the extent that a going
concern 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. Fortunately, an inducement effect can be
accommodated 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
and ζi captures unobserved covariation due to unmeasured confounding (i.e., additional information
used by the auditor in generating the going concern opinion).
3.1 Informational efficiency
In addition to the direct effect of receiving a going concern opinion, we also examine the infor-
mational efficiency of going concern opinions. We define going concern opinions as being informa-
tionally 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
7
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, one can conclude that the actual going concern opinions are informationally inefficient.
That is, for the average probability of bankruptcy to be higher for the same number of clients when
using a 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 be possible 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 private information of the auditor 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.
8
4 Empirical implementation
In our empirical implementation, we assume joint normality. 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 (εg, εb) 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. This model was introduced by Heckman (1976,
1978), and 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,i
Sb,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.
4.1 Identification and estimation for bivariate probit models
The identification of parameters in bivariate probit models has a confusing literature. The
treatment in Heckman (1978) derives the bivariate probit model from a system of simultaneous
9
equations. Section 3 of Heckman (1978), page 949, provides a proof that the associated reduced
form parameters of the model are identified without any exclusion restrictions. This identification
follows from the functional form of the probit likelihood, and indeed Heckman (1978) contains a
section devoted to maximum likelihood estimation.
Heckman (1978) also treats the continuous (non-binary response) version of the same structural
system; in that case, exclusion restrictions are necessary for identification and estimation can
proceed by a two-stage least squares procedure without specifying a likelihood function. Evans and
Schwab (1995) study an applied problem using the binary response formulation of the Heckman
(1978) model, but do not assume the probit formulation and rather proceed to estimate parameters
using an OLS based procedure. In this context, the role of an exclusion restriction is ambiguous
as Altonji et al. (2005) point out; in fact, the two step procedure applied to the binary response
setting gives inconsistent estimates.
Accordingly, textbook summaries of the bivariate probit model equivocate on the necessity of
an exclusion restriction (Wooldridge, 2010, Chapter 15). To be clear, if one assumes the bivariate
probit formulation, then an exclusion restriction is not necessary. If one wants to fit an index model
for bivariate binary responses without making distributional assumptions, an exclusion restriction
may, however, be necessary.
In our model specification, we do not use an underlying simultaneous equation model. We
therefore do not require an exclusion restriction to estimate the parameters of the model. As we
show in the simulations, while imposing a valid exclusion restriction (forcing some βj = 0) increases
statistical efficiency, imposing an invalid exclusion restriction can produce badly biased estimates
of the parameter of interest, γ.
10
4.2 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,i
Sb,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)
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 value of 0, 0.5, 1, 2 and ρ takes values of 0, 0.3, 0.6. We use these values for
γ and ρ because hen γ = 1 and ρ = 0.3, the marginal and conditional distributions of bankruptcy
and going concern using the simulated sample are close to those of the actual data.
For each γ−ρ pair, we examine three scenarios: (1) no exclusion restriction, (2) a valid exclusion
11
restriction, (3) an invalid exclusion restriction. In the case of a valid exclusion restriction, we
draw the 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 assume that it is correlated with the
error term of the bankruptcy equation (correlation coefficient is arbitrarily set to be 0.20).
The results from the simulation are presented in Table 1 and Figures 1, 2, and 3. 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 estimates have large confidence intervals (see Table 1). This is consistent with Heckman (1978)
and Wilde (2000) who show that the identification of of γ and ρ does not depend on the existence of
an exclusion restriction. Moreover, note that there is a negative relation between ρ and γ. Second,
with a valid exclusion restriction, the sampling distribution is much tighter, suggesting efficiency
improvement. Third, with an invalid exclusion restriction, all of the estimates of γ are biased,
except when ρ = 0.
5 Data and variable measurement
For our analysis, we combine data from Audit Analytics, Compustat, and BankruptcyData.com.
Our sample period is 2000–2011 and is constrained by the availability of auditing 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 2011 (the end of sample period). This
database includes the date of the bankruptcy filing, the date that the bankruptcy is resolved (e.g.
12
liquidation, reorganization, dismissal, etc.), and other bankruptcy related variables. To ensure ac-
curacy, we manually collect CIK client identifiers for each bankrupt client from the Electronic Data
Gathering, Analysis, and Retrieval system (EDGAR) of the Securities and Exchange Commission
and collect liquidation information from CRSP, which leads to 1,930 unique bankruptcy filings of
public traded clients between 2000 and 2011. We truncate our bankruptcy data at 2000 due to the
availability of auditing 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 fees 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 entity’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 case 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;
13
7. Non-audit fees: the fraction of non-audit fees to total fees paid to an auditor;
8. Years client: the number of years a client stays with an auditor in the sample.
We drop observations with missing values of the control variables. After merging datasets
and applying filters, we are left with 72,580 client-year observations. The sample includes 794
bankruptcies and 11,696 going concern opinions. Table 2 provides details of how we construct the
sample.
Table 3 provides descriptive statistics for the full sample, for the subsamples of clients that did
or did not receive a going concern opinion in the prior year, and for the subsample of clients filing
for bankruptcy. First, on average, only 1.1% of clients went bankrupt in our sample. The issuance
of going concern opinion, however, is at a higher rate of 13.1%, 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 subsamples, clients not receiving 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 (7.3% versus 82.1%). This finding is consistent with such clients having
lower bankruptcy probability than clients that received a going concern opinion in the prior year
(0.7% versus 2.9%).
Many clients that received going concern opinions do not end up filing 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 12.74%
while the Type II error rate (not receiving a going concern opinion and going bankrupt) is 29.72%.
For clients that did not receive a going concern opinion in the prior year, the Type I error rate is
3.29% and the Type II error rate is 39.40%. In contrast, for clients that received a going concern
opinion in the prior year, the Type I error rate is 81.69% and the Type II error rate is 3.18%.
The 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
14
going concern opinion was issued in the prior year. A first time going concern opinion is likely
to be more informative than a second time going concern opinion, especially given that auditors
are likely to be more conservative following a prior going concern opinion. However, the removal
of a going concern opinion following a prior going concern opinion could be a strong indicator of
financial soundness.
6 Results
6.1 Bankruptcy prediction
We first examine the explanatory power of our bankruptcy prediction models. Researchers do
not observe all information observed by the client’s auditor and lenders. Information observed by
both the client’s auditor and lenders but unobserved by researchers enters 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 despite the correlated
error terms, it is, nonetheless, worth controlling for as many observable factors as possible for three
reasons. First, reducing the noise of error terms makes the estimator more efficient, which increases
the power of empirical tests. Second, to the extent that we control for information observed by the
auditor, we reduce the correlation between the two error terms. Such reductions limit the need for
us to rely on the assumption that error terms follow joint normal distribution. In the limit, if we
observed and controlled for all information observed and used by the auditor, we identify the causal
effect of a going concern opinion on bankruptcy with just the bankruptcy equation and without
imposing distributional assumption on error terms. Third, a linear model can be misspecified,
which is likely to bias the estimates. In particular, the inducement effect results in a discontinuity
for which a linear model would not be able to account.
Our measure of the direct inducement effect is based on the premise that a going concern
opinion results in higher likelihood of bankruptcy holding everything else constant. Suppose an
auditor implements a threshold rule when issuing going concern opinions, as informational efficiency
15
dictates. That is, all clients with a probability of bankruptcy higher than the threshold receive a
going concern opinion, and no other client does. Once the going concern opinions are released, the
probability of bankruptcy will increase for all clients above the threshold due to the inducement
effect (i.e. updated market beliefs, mechanically triggered covenants, credit rationing, etc.). In
the same vein, the probability of bankruptcy will decrease for all clients below the threshold. This
results in the discontinuity at the going concern opinion threshold. However, if we manage to rank
the clients by the probability of bankruptcy according to the auditor’s beliefs, we would be able
to “imitate” the inducement effect by generating an indicator variable equal to one for all clients
above the threshold that we believe the auditor would use. These sorts of non-linearities are well
captured by randomForest, which looks for classification thresholds that best describe the data
(Hastie, Tibshirani, and Friedman, 2009).
One way to address these issues is to include interaction terms and higher order terms as
additional control variables. However, this is likely to be inefficient because we lack theory to guide
us in the choice of interactions and orders. Instead, we use randomForest to construct measures of
going concern and bankruptcy likelihood based on information observed by researchers. Random
forests take into account non-linear relations between outcome variables (i.e., going concern opinion
and bankruptcy) and predictor variables, thereby reducing within-sample classification error.
We estimate randomForest using information from prior years and use it to predict going con-
cern opinions and bankruptcies in the current year. This procedure ensures that we do not use
information unavailable to auditors. 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, return on asset, the natural logarithm of closing stock price for the fiscal
period.
To show that randomForest does as well in predicting outcome variables as a logit regression,
we follow prior literature and plot ROC curves. A ROC curve plots the true positive rate against
the false positive rate (Type I error) as researchers vary the threshold used to classify outcome.
In the case of bankruptcy prediction, the ROC curve plots the percentage of correctly predicted
16
bankruptcies among actual bankruptcies against the percentage of incorrectly predicted bankruptcy
among non-bankruptcies. A ROC curve further skewed to the upper left corner is indicative of
better predictive performance.
Figures 4, 5, and 6 plot various ROC curves using different specifications and outcome variables.
Figure 4 shows that randomForest does marginally better in predicting bankruptcy than logit. The
triangle represents the auditors’ overall error rate. It is below the ROC curve produced by our
randomForest model. Hence, we also do better than auditors in predicting bankruptcy.
In Figure 5, we show 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 predict more
bankruptcies with the same number of synthetic going concern opinions. This result provides
strong evidence against the informational efficiency of auditors’ going concern opinions. Finally,
in Figure 6, we plot the ROC curve for going concern opinion. In this specification, randomForest
does better than logit in predicting going concern opinions.
6.2 Bivariate probit
We next present our estimates of the auditor’s additional information, ρ, and the inducement
effect, γ. For all regressions, we bootstrap and cluster the standard errors at the client-level. It
is well-known that 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 appears not to present such
a troublesome case. All standard errors are bootstrapped in our analysis and the estimates are
stable suggesting that we do not have many local modes. While it could be the case that all of our
bootstrap subsamples resulted in similar local modes, this appears unlikely.
All regressions include year fixed effects to control macroeconomic factors that can affect the
issuances of going concern opinions and bankruptcies, and auditor fixed effects to control for auditor-
specific tendencies to issue going concern opinions and select certain types of clients. The control
17
variables include: the natural logarithm of total assets, the ratio of of debt to total assets, the
ratio of short-term investments to total assets, the ratio of cash to total assets, return on asset, the
natural logarithm of closing stock price for the fiscal period. We generate predictive probabilities
of bankruptcy and going concern using randomForest, and then transform them using an inverse
normal kernel and include them as control variables. Our randomForest estimates use the same
control variables as the control variables used in estimating the linear probit model.
We include both the going concern and bankruptcy scores in the bankruptcy equation and the
going concern equation. We do so to address the possibility that past going concern and bankruptcy
scores are informative about the current going concern and bankruptcy likelihoods.
Our main results are consistent with both the additional information and direct inducement
channels. Table 4 shows that the estimated effect of going concern opinion on the likelihood of
bankruptcy reduces by about 30% (from 0.914 to 0.635) when we allow going concern opinions
to reflect auditors’ additional information unobserved by researchers (column 4). Any additional
information used by the auditor should also predict bankruptcy. The error terms of the going
concern and the bankruptcy equations are significantly and positively correlated, which is consistent
with the existence of auditors’ additional information. After accounting for auditors’ additional
information, the coefficient on going concern opinion reflects the inducement effect. The receipt
of a going concern opinion increase the client’s bankruptcy likelihood by 1.49 percentage points, a
large effect in light of the unconditional bankruptcy rate of 1.1%.
We next partition the sample based on whether clients received a going concern opinion in
the prior year. Going concern opinions can “induce” bankruptcy through two channels. First
time going concern opinions could contain more information than repeated going concern opinions
because auditors tend to be more conservative following the issuance of first time going concern
opinion. However, removal of going concern opinion could be a strong signal of financial soundness.
Table 6 presents estimates for clients that received a going concern opinion in the prior year.
First, when we do not allow for unobserved common information in the simple probit presented
in the second column, γ is positive and significant. In specification (3), we estimate a bivariate
18
probit that allows for additional information, but does not include the going concern opinion in the
bankruptcy equation. For this specification, ρ is significantly positive, suggesting that auditors have
additional information. However, when we include the going concern opinion in specification (4),
we find even stronger evidence of the inducement effect—γ increases from 1.030 in column (2) to
1.847 in specification (4). In terms of economic significance, a going concern opinion increases
bankruptcy by about 8.6 percentage points.
We next examine the subsample of clients did not receive a going concern opinion in the previous
year. For this sample, we again find evidence for inducement in specification (4), although the
magnitude of γ drops to 0.573, which implies that a going concern opinion increases the probability
of bankruptcy by about 0.78 percentage points.
To evaluate the distribution of the economic magnitude of going concern opinion, we calculate
each client’s partial effect—the change in predicted probability of bankruptcy for each client given
its observables for moving from receiving no going concern opinion to receiving a going concern
opinion holding the observable information constant. We first present the histogram of partial
effects for clients that received a going concern opinion in the prior year. Figure 7 plots the
distribution of partial effects for audit clients that received a going concern opinion in the prior
year. Being issued a going concern opinion a second time is, on average, leads to a 8.6 percentage
point increase in bankruptcy probability. In Figure 8, 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 0.78 percentage point in increase in the probability of bankruptcy.
Many clients in our sample are audited by Big 4 auditors. An important question is whether
the effect of going concern opinion on the likelihood of bankruptcy different for Big 4 and non-Big 4
auditors. If the function of going concern opinion is to provide incremental information to market
participants, we could expect the magnitude to be smaller for a going concern opinion issued by a
Big 4 auditor because clients of Big 4 auditors are typically larger and less opaque, thereby leaving
less room for incremental additional information. Alternatively, if Big 4 auditors could generate
higher quality audits that lead to more additional information. If this is the case, we would expect
19
that the direct effect of a going concern opinion would be larger for Big 4 auditors. Table 7 presents
results for Big 4 clients, and Table 8 presents results for non-Big 4 clients. Compared with the full
sample results, the magnitudes of the inducement effect, γ, are smaller for Big 4 audit firms.
20
REFERENCES
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21
Freedman, D., Sekhon, J., 2010. Endogeneity in probit response models. Political Analysis 18,
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22
Horowitz, J., 1998. Semiparametric methods in econometrics. Springer, New York, NY.
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23
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Cambridge, Massachusetts, second ed.
24
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Figure 1: Identification of the bivariate probit when ρ = 0.To evaluate the performance of bivariate probit model in identifying model parameters, we simulate10,000 observations assuming the following data generating process,(
Ug
Sb
)iid∼N (µ,Σ), µ =
(β0 + β1xα0 + α1x
), Σ =
(1 ρρ 1
).
G = 1{Ug ≥ 0
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B = 1{Sg ≥ −γG
}.
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Figure 2: Identification of the bivariate probit when ρ = 0.3.We evaluate the performance of bivariate probit model in identifying model parameters. We simulate10,000 observations assuming the following data generating process,(
Ug
Sb
)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, α0 = −2.6. Each figure corresponds to the case whenρ = 0.3 and γ = 0, 0.5, 1, 2. Circles represent the case with no exclusion restriction, triangles the casewith exclusion restriction and plus signs the case with bad exclusion restriction. We obtain samplingvariation by repeating the simulation above 200 times.
26
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● no exclusionexclusionbad exclusion
Figure 3: Identification of the bivariate probit when ρ = 0.6.We evaluate the performance of bivariate probit model in identifying model parameters. We simulate10,000 observations assuming the following data generating process,(
Ug
Sb
)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, α0 = −2.6. Each figure corresponds to the case whenρ = 0.6 and γ = 0, 0.5, 1, 2. Circles represent the case with no exclusion restriction, triangles the casewith exclusion restriction and plus signs the case with bad exclusion restriction. We obtain samplingvariation by repeating the simulation above 200 times.
27
0.0 0.2 0.4 0.6 0.8 1.0
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● Random ForestLogit
Figure 4: ROC Curve for Bankruptcy Prediction. This figure plots ROC curves to evaluate theperformance of randomForest and logit in predicting bankruptcy one year ahead. The horizontal axisis the false positive rate (i.e., predicting false bankruptcy) and the vertical line is the true positive rate(i.e., predicting true bankruptcy). A ROC curve that further skews to the upper left corner indicatesbetter predictive performance. The solid round dots represent random forest. The hollow diamonddots represent logit. The solid triangle corresponds to the predictive performance using auditor’s goingconcern opinion as bankruptcy predictor.
28
0.0 0.2 0.4 0.6 0.8 1.0
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Figure 5: Going Concern Opinion in Bankruptcy Prediction. This figure plots ROC curvesto evaluate the usefulness of including going concern opinions in bankruptcy prediction models. Thehorizontal axis is the false positive rate (i.e., predicting false bankruptcy) and the vertical line is thetrue positive rate (i.e., predicting right bankruptcy). A ROC curve that further skews to the upper leftcorner indicates better predictive performance. The hollow diamond dots represent the randomForestmethod including the going concern opinion as a predictor variable. The solid round dots representrandomForest excluding the going concern opinion as a predictor variable. The solid triangle correspondsto the predictive performance using auditor’s going concern opinion as bankruptcy predictor.
29
0.0 0.2 0.4 0.6 0.8 1.0
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Figure 6: ROC Curve for Predicting Going Concern Opinions. This figure plots ROC curvesthat evaluate the performance of random forecast and logit in predicting going concern opinions. Thehorizontal axis is the false positive rate (i.e., predicting a going concern opinion when the client doesnot receive a going concern opinion), and the vertical line is the true positive rate (i.e., predicting agoing concern opinion and the client receives a going concern opinion). The further the ROC skewsto the upper left corner the better predictive performance. The dots represent randomForest and thehollow diamonds represent logit.
30
Partial Effects of Going Concern Opinion (%)
Den
sity
0 5 10 15 20 25
0.00
0.05
0.10
0.15
0.20
Figure 7: Histogram of partial effects of a going concern opinion for clients that received agoing concern opinion in the prior year. We generate the partial effects of a going concern opinionusing the bivariate probit estimates of the randomForest specification for clients that received goingconcern opinion in the prior year. For each observation, we hold constant the going concern score andbankruptcy score and vary going concern opinion. The horizontal axis is the percentage point differenceof the bankruptcy probability when going concern opinion = 1 and when going concern opinion = 0.
31
Partial Effects of Going Concern Opinion (%)
Den
sity
0 5 10 15
0.0
0.2
0.4
0.6
0.8
Figure 8: 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 randomForest 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.
32
Table 1: Simulation results
In this table, we examine the properties of bivariate probit. We simulate data using the following model.(Ug
Sb
)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, α0 = −2.6. The observable covariate x is drawn from N(0, 1).The true γ takes value from 0, 0.5, 1, 2 and ρ takes value from 0, 0.3, 0.6. For each γ, ρ pair, we examinethree cases: (1) no exclusion restriction, (2) valid exclusion restriction, (3) invalid exclusion restriction.To create a valid exclusion restriction, we draw from N (0, 1) and use it as an additional covariate onlyin the going concern equation. To create an invalid exclusion restriction, we draw from N(0, 1) butassume that it is correlated with the error term of the bankruptcy equation (correlation coefficient isarbitrarily set to be 0.20). We generate 10,000 observations for each parameter combination and thenestimate the parameters using bivariate probit. We obtain the sampling distribution of γ and ρ byrunning the simulation 200 times and report the summary statistics in the table.
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 −0.039
33
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, and Bankruptcy.com. The sampleperiod used in estimation is 2000–2011.
Filter Number Percent
Audit Analytics: Opinions 1999–2013 219, 839 100%Requiring GVKEY 112, 651 51%Drop multiple auditors 112, 363 51%Merge with Compustat 94, 580 43%Keep between 2000-2011 87, 949 40%After dropping missing values 72, 580 33%
Compustat 1999–2013 123, 452 100%Merge with Audit Analytics 94, 289 76%Keep between 2000-2011 87, 949 71%After dropping missing values 72, 580 59%
Bankruptcy.com 2000–2011 1, 930 100%Merge with Audit Analytics 1, 265 66%After dropping missing values 794 41%
34
Table 3: Summary statistics
This table presents summary statistics for the variables used in our analysis. Definitions of all variablescan be found in Section ??. Panel A presents summary statistics for the entire sample. Panel B presentssummary statistics for clients that did not receive a going concern opinion in the prior year. Panel Cpresents summary statistics for clients that received a going concern opinion in the prior year. Panel Dpresents summary statistics for clients that filed for bankruptcy within 12 months after receiving a goingconcern opinion. Years Client is the number of years the company has been a client of its audit firm inthe sample. The sample period is 2000–2011.
Panel A: Full sample
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 72,580 0.011 0.104 0.000 0.000 0.000 0.000 0.000Going concern 72,580 0.136 0.342 0.000 0.000 0.000 0.000 1.000Log(Assets) 72,580 5.369 2.717 0.614 3.427 5.502 7.227 9.768Leverage 72,580 0.630 0.614 0.089 0.301 0.546 0.817 1.271Investment 72,580 0.054 0.129 0.000 0.000 0.000 0.035 0.340Cash 72,580 0.185 0.223 0.003 0.027 0.088 0.265 0.701ROA 72,580 −0.176 0.652 −1.128 −0.124 0.008 0.051 0.158Log(Price) 72,580 2.141 1.259 0.086 1.051 2.293 3.179 4.002Years Client 67,384 4.259 2.870 1.000 2.000 3.000 6.000 10.000Non-audit fees 67,384 0.223 0.207 0.000 0.052 0.170 0.338 0.653
Panel B: Conditional on not receiving a going concern opinion in the prior year
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 55,475 0.007 0.085 0.000 0.000 0.000 0.000 0.000Going concern 55,475 0.037 0.189 0.000 0.000 0.000 0.000 0.000Log(Assets) 55,475 5.953 2.424 2.022 4.268 5.980 7.537 10.001Leverage 55,475 0.554 0.353 0.099 0.303 0.534 0.777 0.954Investment 55,475 0.060 0.132 0.000 0.000 0.001 0.045 0.359Cash 55,475 0.195 0.224 0.005 0.032 0.098 0.282 0.706ROA 55,475 −0.066 0.383 −0.590 −0.044 0.013 0.058 0.159Log(Price) 55,475 2.407 1.144 0.322 1.552 2.580 3.304 4.060Years client 54,246 4.730 2.867 1.000 2.000 4.000 6.000 10.000Non-audit fees 54,246 0.215 0.193 0.000 0.059 0.169 0.321 0.610
35
Panel C: Conditional on receiving a going concern opinion in the prior year
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Bankruptcy 7,524 0.029 0.168 0.000 0.000 0.000 0.000 0.000Going concern 7,524 0.821 0.383 0.000 1.000 1.000 1.000 1.000Log(Assets) 7,524 1.819 1.910 0.004 0.343 1.266 2.647 5.952Leverage 7,524 1.233 1.386 0.056 0.344 0.756 1.483 4.938Investment 7,524 0.018 0.078 0.000 0.000 0.000 0.000 0.098Cash 7,524 0.133 0.198 0.000 0.007 0.044 0.166 0.619ROA 7,524 −0.918 1.313 −3.902 −1.211 −0.468 −0.108 0.165Log(Price) 7,524 0.475 0.632 0.010 0.058 0.207 0.647 1.808Years client 6,518 3.270 2.235 1.000 2.000 3.000 4.000 8.000Non-audit fees 6,518 0.128 0.169 0.000 0.000 0.056 0.198 0.500
Panel D: Conditional on filing for bankruptcy
PercentileVariable N Mean SD 5th 25th 50th 75th 95th
Going concern 794 0.703 0.457 0.000 0.000 1.000 1.000 1.000Log(Assets) 794 4.967 2.510 0.892 3.054 4.945 6.711 9.075Leverage 794 1.153 0.916 0.273 0.708 0.955 1.275 2.918Investment 794 0.034 0.090 0.000 0.000 0.000 0.022 0.236Cash 794 0.132 0.176 0.001 0.020 0.064 0.163 0.556ROA 794 −0.628 1.009 −2.508 −0.767 −0.283 −0.071 0.032Log(Price) 794 0.798 0.798 0.020 0.182 0.542 1.198 2.469Years Client 648 3.710 2.557 1.000 2.000 3.000 5.000 9.000Non-audit fees 648 0.242 0.219 0.000 0.053 0.197 0.380 0.689
36
Tab
le4:
Goi
ng
con
cern
ind
uce
db
ankru
ptc
y—
full
sam
ple
Inth
ista
ble
,w
eex
amin
ew
het
her
au
dit
or’
sgo
ing
con
cern
opin
ion
has
pre
dic
tive
pow
erfo
rban
kru
ptc
yb
eyon
din
form
atio
nav
aila
ble
tob
oth
cred
itors
an
dau
dit
ors.
Mod
el1
an
d2
are
sim
ple
pro
bit
regr
essi
ons.
Mod
el3
and
4ar
eb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
(1)
Goi
ng
Con
cern
,an
ind
icato
rfo
rw
het
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art,
(2)
Ban
kru
ptc
y,an
ind
icat
orfo
rw
het
her
acl
ient
wen
tb
ankru
pt
wit
hin
one
yea
rof
the
issu
an
ceof
aud
itor
’sgo
ing
con
cern
opin
ion
.E
xp
lan
ator
yva
riab
les
are
Goi
ng
Con
cern
Sco
re,
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
Ban
kru
ptc
yS
core
,p
red
icti
vesc
ore
ofa
clie
nt
goin
gb
ankru
pt.
To
crea
teG
oin
gC
once
rnS
core
(Ban
kru
ptc
yS
core
)fo
rcl
ienti
yeart,
we
pool
all
dat
afr
omyea
r1
toye
art−
1an
du
sera
nd
omF
ores
tto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
n(g
oin
gban
kru
pt)
.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
scor
eso
that
on
eu
nit
chan
geco
rres
pon
ds
toch
ange
inon
est
andar
dd
evia
tion
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
ass
ets,
the
rati
oof
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,re
turn
onas
set,
the
nat
ura
llo
gari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms,
wh
ich
cap
ture
sin
form
atio
nsh
ared
by
cred
itors
(wh
od
eter
min
eb
an
kru
ptc
y)
and
aud
itor
s(w
ho
issu
ego
ing
conce
rnop
inio
ns)
.W
eal
soin
clu
de
yea
rfi
xed
effec
tsan
dau
dit
orfi
xed
effec
ts.
We
ob
tain
the
sam
pli
ng
dis
trib
uti
onth
rough
boot
stra
pp
ing.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
bel
owth
ees
tim
ate
s.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tep
rob
itB
ivar
iate
pro
bit
Vari
able
sG
oin
gC
on
cern
Ban
kru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
y
Goin
gco
nce
rn0.
914
0.63
5[0
.809
,1.
023]
[0.4
79,
0.77
6]G
oin
gco
nce
rnsc
ore
0.79
70.
080
0.79
20.
214
0.79
60.
119
[0.7
62,
0.8
32]
[0.0
30,
0.13
1][0
.756
,0.
828]
[0.1
65,
0.26
6][0
.760
,0.
830]
[0.0
62,
0.17
5]B
an
kru
ptc
ysc
ore
0.0
350.
314
0.03
40.
301
0.03
40.
305
[0.0
08,
0.0
60]
[0.2
51,
0.37
7][0
.009
,0.
059]
[0.2
39,
0.36
3][0
.008
,0.
06]
[0.2
43,
0.36
9]L
og(
Ass
ets)
−0.
184
0.41
0−
0.18
80.
351
−0.
186
0.39
5[−
0.2
16,−
0.1
50]
[0.3
65,
0.45
6][−
0.22
0,−
0.15
4][0
.307
,0.
396]
[−0.
218,−
0.15
3][0
.349
,0.
441]
Lev
erage
0.03
50.
060
0.03
20.
079
0.03
40.
071
[0.0
19,
0.0
51]
[0.0
29,
0.09
2][0
.016
,0.
049]
[0.0
48,
0.11
1][0
.018
,0.
050]
[0.0
40,
0.10
2]In
vest
men
ts0.
032
−0.
018
0.03
2−
0.01
60.
032
−0.
017
[0.0
15,
0.0
49]
[−0.
053,
0.02
0][0
.015
,0.
048]
[−0.
050,
0.01
9][0
.014
,0.
048]
[−0.
052,
0.01
9]C
ash
−0.
072
0.04
1−
0.07
10.
026
−0.
071
0.03
4[−
0.0
87,−
0.0
55]
[0.0
05,
0.07
6][−
0.08
7,−
0.05
5][−
0.00
9,0.
058]
[−0.
087,−
0.05
5][−
0.00
4,0.
070]
RO
A−
0.08
1−
0.03
9−
0.08
2−
0.06
2−
0.08
2−
0.04
9[−
0.09
9,−
0.0
62]
[−0.
084,−
0.00
1][−
0.10
1,−
0.06
4][−
0.10
4,−
0.02
3][−
0.10
0,−
0.06
3][−
0.09
3,−
0.01
2]L
og(
Pri
ce)
−0.
162
−0.
185
−0.
163
−0.
219
−0.
163
−0.
196
[−0.1
93,−
0.1
28]
[−0.
240,−
0.13
0][−
0.19
4,−
0.12
9][−
0.27
5,−
0.16
2][−
0.19
3,−
0.12
8][−
0.25
2,−
0.14
0]ρ
0.43
80.
163
[0.3
92,
0.48
2][0
.096
,0.
233]
Pse
ud
oR
20.6
210.
322
0.57
70.
578
Ob
serv
ati
on
s647
1264
712
6471
264
712
6471
264
712
37
Tab
le5:
Cli
ents
that
did
not
rece
ive
goin
gco
nce
rnop
inio
nin
the
pre
vio
us
year
Inth
ista
ble
,w
eex
amin
ew
het
her
au
dit
or’
sgo
ing
con
cern
opin
ion
has
pre
dic
tive
pow
erfo
rban
kru
ptc
yb
eyon
din
form
atio
nav
aila
ble
tob
oth
cred
itors
an
dau
dit
ors.
Mod
el1
an
d2
are
sim
ple
pro
bit
regr
essi
ons.
Mod
el3
and
4ar
eb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
(1)
Goi
ng
Con
cern
,an
ind
icato
rfo
rw
het
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art,
(2)
Ban
kru
ptc
y,an
ind
icat
orfo
rw
het
her
acl
ient
wen
tb
ankru
pt
wit
hin
one
yea
rof
the
issu
an
ceof
aud
itor
’sgo
ing
con
cern
opin
ion
.E
xp
lan
ator
yva
riab
les
are
Goi
ng
Con
cern
Sco
re,
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
Ban
kru
ptc
yS
core
,p
red
icti
vesc
ore
ofa
clie
nt
goin
gb
ankru
pt.
To
crea
teG
oin
gC
once
rnS
core
(Ban
kru
ptc
yS
core
)fo
rcl
ienti
yeart,
we
pool
all
dat
afr
omyea
r1
toye
art−
1an
du
sera
nd
omF
ores
tto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
n(g
oin
gban
kru
pt)
.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
scor
eso
that
on
eu
nit
chan
geco
rres
pon
ds
toch
ange
inon
est
andar
dd
evia
tion
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
ass
ets,
the
rati
oof
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,re
turn
onas
set,
the
nat
ura
llo
gari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms,
wh
ich
cap
ture
sin
form
atio
nsh
ared
by
cred
itors
(wh
od
eter
min
eb
an
kru
ptc
y)
and
aud
itor
s(w
ho
issu
ego
ing
conce
rnop
inio
ns)
.W
eal
soin
clu
de
yea
rfi
xed
effec
tsan
dau
dit
orfi
xed
effec
ts.
We
ob
tain
the
sam
pli
ng
dis
trib
uti
onth
rough
boot
stra
pp
ing.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
bel
owth
ees
tim
ate
s.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tep
rob
itB
ivar
iate
pro
bit
Vari
able
sG
oin
gC
on
cern
Ban
kru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
y
Goin
gco
nce
rn0.
975
0.47
3[0
.877
,1.
085]
[0.0
93,
0.89
7]G
oin
gco
nce
rnsc
ore
0.57
80.
108
0.56
90.
217
0.57
50.
158
[0.5
24,
0.6
35]
[0.0
35,
0.18
1][0
.514
,0.
627]
[0.1
43,
0.29
4][0
.520
,0.
631]
[0.0
70,
0.25
1]B
an
kru
ptc
ysc
ore
0.0
740.
230
0.07
30.
200
0.07
30.
214
[0.0
35,
0.1
13]
[0.1
56,
0.31
0][0
.034
,0.
113]
[0.1
29,
0.27
6][0
.034
,0.
113]
[0.1
36,
0.29
6]L
og(
Ass
ets)
−0.
035
0.35
0−
0.04
40.
316
−0.
040
0.33
7[−
0.0
77,
0.00
8][0
.292
,0.
408]
[−0.
086,
0.00
1][0
.259
,0.
371]
[−0.
083,
0.00
3][0
.278
,0.
398]
Lev
erage
0.01
80.
128
0.01
90.
152
0.01
80.
145
[−0.0
07,
0.04
8][0
.078
,0.
185]
[−0.
006,
0.04
8][0
.100
,0.
21]
[−0.
006,
0.04
8][0
.089
,0.
204]
Inve
stm
ents
0.05
2−
0.02
70.
052
−0.
016
0.05
2−
0.02
2[0
.027,
0.0
76]
[−0.
076,
0.02
2][0
.027
,0.
076]
[−0.
063,
0.02
9][0
.027
,0.
076]
[−0.
07,
0.02
6]C
ash
−0.
081
−0.
019
−0.
083
−0.
046
−0.
082
−0.
034
[−0.
108,−
0.0
52]
[−0.
069,
0.03
0][−
0.11
0,−
0.05
6][−
0.09
3,0.
001]
[−0.
109,−
0.05
3][−
0.08
7,0.
017]
RO
A−
0.25
1−
0.09
5−
0.25
5−
0.17
5−
0.25
3−
0.13
7[−
0.30
0,−
0.2
06]
[−0.
166,−
0.02
9][−
0.30
4,−
0.20
9][−
0.24
4,−
0.10
9][−
0.30
2,−
0.20
8][−
0.22
0,−
0.06
6]L
og(
Pri
ce)
−0.
190
−0.
296
−0.
192
−0.
325
−0.
191
−0.
314
[−0.
251,−
0.1
33]
[−0.
386,−
0.21
0][−
0.25
2,−
0.13
4][−
0.41
9,−
0.24
0][−
0.25
2,−
0.13
3][−
0.40
9,−
0.22
4]ρ
0.52
20.
281
[0.4
78,
0.56
9][0
.062
,0.
480]
Pse
ud
oR
20.4
430.
377
0.40
10.
401
Ob
serv
ati
on
s546
4554
645
5464
554
645
5464
554
645
38
Tab
le6:
Cli
ents
that
rece
ived
goin
gco
nce
rnop
inio
nin
the
pre
vio
us
year
Inth
ista
ble
,w
eex
amin
ew
het
her
au
dit
or’
sgo
ing
con
cern
opin
ion
has
pre
dic
tive
pow
erfo
rban
kru
ptc
yb
eyon
din
form
atio
nav
aila
ble
tob
oth
cred
itors
an
dau
dit
ors.
Mod
el1
and
2ar
esi
mp
lep
rob
itre
gres
sion
s.M
od
el3
and
4ar
eb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
(1)
Goi
ng
Con
cern
,an
ind
icato
rfo
rw
het
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art,
(2)
Ban
kru
ptc
y,an
ind
icat
orfo
rw
het
her
acl
ient
wen
tb
ankru
pt
wit
hin
one
yea
rof
the
issu
an
ceof
aud
itor
’sgo
ing
con
cern
opin
ion
.E
xp
lan
ator
yva
riab
les
are
Goi
ng
Con
cern
Sco
re,
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
Ban
kru
ptc
yS
core
,p
red
icti
vesc
ore
ofa
clie
nt
goin
gb
ankru
pt.
To
crea
teG
oin
gC
once
rnS
core
(Ban
kru
ptc
yS
core
)fo
rcl
ienti
yeart,
we
pool
all
dat
afr
omyea
r1
toye
art−
1an
du
sera
nd
omF
ores
tto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
n(g
oin
gban
kru
pt)
.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
scor
eso
that
on
eu
nit
chan
geco
rres
pon
ds
toch
ange
inon
est
andar
dd
evia
tion
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
ass
ets,
the
rati
oof
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,re
turn
onas
set,
the
nat
ura
llo
gari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms,
wh
ich
cap
ture
sin
form
atio
nsh
ared
by
cred
itors
(wh
od
eter
min
eb
an
kru
ptc
y)
and
aud
itor
s(w
ho
issu
ego
ing
conce
rnop
inio
ns)
.W
eal
soin
clu
de
yea
rfi
xed
effec
tsan
dau
dit
orfi
xed
effec
ts.
We
ob
tain
the
sam
pli
ng
dis
trib
uti
onth
rough
boot
stra
pp
ing.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
bel
owth
ees
tim
ate
s.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tepro
bit
Biv
aria
tep
rob
itV
ari
able
sG
oin
gC
on
cern
Ban
kru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
y
Goin
gco
nce
rn1.
030
1.84
7[0
.889
,1.
185]
[1.5
26,
2.31
0]G
oin
gco
nce
rnsc
ore
0.49
30.
092
0.49
70.
164
0.48
9−
0.05
0[0
.429,
0.5
64]
[−0.
032,
0.21
6][0
.435
,0.
565]
[0.0
52,
0.27
6][0
.428
,0.
558]
[−0.
189,
0.08
2]B
an
kru
ptc
ysc
ore
0.0
200.
199
0.01
70.
241
0.02
40.
161
[−0.
034,
0.0
76]
[0.0
67,
0.33
0][−
0.03
7,0.
074]
[0.1
11,
0.36
8][−
0.03
0,0.
077]
[0.0
42,
0.28
1]L
og(
Ass
ets)
−0.
202
0.60
7−
0.18
80.
547
−0.
214
0.60
2[−
0.2
81,−
0.1
28]
[0.4
54,
0.75
3][−
0.26
7,−
0.11
3][0
.399
,0.
682]
[−0.
294,−
0.13
7][0
.462
,0.
736]
Lev
erage
0.04
80.
095
0.04
50.
083
0.05
20.
086
[0.0
14,
0.0
82]
[0.0
27,
0.16
0][0
.010
,0.
079]
[0.0
19,
0.14
2][0
.018
,0.
085]
[0.0
16,
0.15
1]In
vest
men
ts0.0
450.
041
0.04
50.
039
0.04
70.
031
[0.0
05,
0.0
85]
[−0.
028,
0.11
0][0
.005
,0.
083]
[−0.
026,
0.10
5][0
.008
,0.
086]
[−0.
035,
0.09
7]C
ash
−0.
163
0.04
1−
0.16
20.
034
−0.
164
0.07
0[−
0.1
97,−
0.1
27]
[−0.
027,
0.10
8][−
0.19
6,−
0.12
7][−
0.02
9,0.
098]
[−0.
199,−
0.12
8][0
.003
,0.
137]
RO
A−
0.09
50.
018
−0.
095
0.00
6−
0.09
40.
037
[−0.1
28,−
0.0
59]
[−0.
056,
0.08
0][−
0.12
8,−
0.05
9][−
0.06
3,0.
064]
[−0.
125,−
0.05
8][−
0.03
0,0.
094]
Log(
Pri
ce)
−0.
186
−0.
096
−0.
185
−0.
120
−0.
184
−0.
047
[−0.2
54,−
0.1
16]
[−0.
198,
0.00
7][−
0.25
2,−
0.11
6][−
0.21
7,−
0.02
1][−
0.25
4,−
0.11
6][−
0.15
8,0.
057]
ρ0.
373
−0.
528
[0.2
88,
0.47
8][−
0.81
7,−
0.30
4]P
seu
doR
20.
318
0.23
50.
294
0.29
7O
bse
rvati
on
s748
574
8574
8574
8574
8574
85
39
Tab
le7:
Big
4cl
ients
Inth
ista
ble
,w
eex
am
ine
wh
eth
erau
dit
or’s
goin
gco
nce
rnop
inio
nh
asp
red
icti
ve
pow
erfo
rban
kru
ptc
yb
eyon
din
form
atio
nav
aila
ble
tob
oth
cred
itor
san
dau
dit
ors
.M
od
el1
and
2ar
esi
mp
lep
rob
itre
gres
sion
s.M
od
el3
and
4ar
eb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
(1)
Goin
gC
on
cern
,an
ind
icat
or
for
whet
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art,
(2)
Ban
kru
ptc
y,an
ind
icat
orfo
rw
het
her
acl
ient
wen
tb
ankru
pt
wit
hin
one
yea
rof
the
issu
an
ceof
aud
itor
’sgo
ing
con
cern
opin
ion
.E
xp
lan
ator
yva
riab
les
are
Goi
ng
Con
cern
Sco
re,
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
Ban
kru
ptc
yS
core
,p
red
icti
vesc
ore
ofa
clie
nt
goin
gb
ankru
pt.
To
crea
teG
oin
gC
once
rnS
core
(Ban
kru
ptc
yS
core
)fo
rcl
ienti
yeart,
we
pool
all
dat
afr
omyea
r1
toye
art−
1an
du
sera
nd
omF
ores
tto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
n(g
oin
gban
kru
pt)
.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
scor
eso
that
on
eu
nit
chan
geco
rres
pon
ds
toch
ange
inon
est
andar
dd
evia
tion
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
ass
ets,
the
rati
oof
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,re
turn
onas
set,
the
nat
ura
llo
gari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms,
wh
ich
cap
ture
sin
form
atio
nsh
ared
by
cred
itors
(wh
od
eter
min
eb
an
kru
ptc
y)
and
aud
itor
s(w
ho
issu
ego
ing
conce
rnop
inio
ns)
.W
eal
soin
clu
de
yea
rfi
xed
effec
tsan
dau
dit
orfi
xed
effec
ts.
We
ob
tain
the
sam
pli
ng
dis
trib
uti
onth
rough
boot
stra
pp
ing.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
bel
owth
ees
tim
ate
s.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tep
rob
itB
ivar
iate
pro
bit
Vari
able
sG
oin
gC
on
cern
Ban
kru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
y
Goin
gco
nce
rn1.
059
0.57
3[0
.930
,1.
183]
[0.2
94,
0.86
6]G
oin
gco
nce
rnsc
ore
0.68
70.
104
0.67
40.
253
0.68
20.
164
[0.6
09,
0.7
60]
[0.0
15,
0.19
0][0
.598
,0.
752]
[0.1
62,
0.34
5][0
.605
,0.
756]
[0.0
65,
0.27
4]B
an
kru
ptc
ysc
ore
0.0
130.
259
0.01
40.
218
0.01
30.
239
[−0.0
39,
0.06
4][0
.171
,0.
351]
[−0.
038,
0.06
4][0
.135
,0.
302]
[−0.
039,
0.06
3][0
.150
,0.
330]
Log(
Ass
ets)
−0.
134
0.36
2−
0.13
90.
299
−0.
137
0.34
0[−
0.1
83,−
0.0
89]
[0.3
00,
0.42
1][−
0.18
9,−
0.09
2][0
.243
,0.
353]
[−0.
187,−
0.09
1][0
.284
,0.
397]
Lev
erage
0.06
70.
146
0.06
40.
183
0.06
50.
171
[0.0
31,
0.1
05]
[0.0
87,
0.20
8][0
.028
,0.
101]
[0.1
27,
0.24
6][0
.030
,0.
103]
[0.1
15,
0.23
3]In
vest
men
ts0.
019
−0.
035
0.01
9−
0.03
20.
019
−0.
035
[−0.0
08,
0.04
6][−
0.09
0,0.
022]
[−0.
009,
0.04
7][−
0.08
4,0.
020]
[−0.
009,
0.04
7][−
0.08
9,0.
021]
Cash
−0.
089
−0.
019
−0.
092
−0.
044
−0.
091
−0.
033
[−0.
121,−
0.0
58]
[−0.
077,
0.04
2][−
0.12
4,−
0.06
1][−
0.09
8,0.
012]
[−0.
122,−
0.05
9][−
0.09
1,0.
030]
RO
A−
0.14
3−
0.02
8−
0.14
7−
0.08
0−
0.14
5−
0.05
5[−
0.18
9,−
0.1
01]
[−0.
097,
0.03
3][−
0.19
2,−
0.10
4][−
0.14
9,−
0.02
0][−
0.19
2,−
0.10
3][−
0.12
7,0.
008]
Log(
Pri
ce)
−0.
340
−0.
274
−0.
347
−0.
359
−0.
344
−0.
317
[−0.
419,−
0.2
67]
[−0.
381,−
0.17
8][−
0.42
6,−
0.27
5][−
0.46
8,−
0.25
9][−
0.42
3,−
0.27
2][−
0.42
6,−
0.21
4]ρ
0.54
00.
270
[0.4
89,
0.58
9][0
.128
,0.
396]
Pse
ud
oR
20.5
080.
438
0.45
70.
458
Ob
serv
ati
on
s395
6039
560
3956
039
560
3956
039
560
40
Tab
le8:
Non
-Big
4cl
ients
Inth
ista
ble
,w
eex
am
ine
wh
eth
erau
dit
or’s
goin
gco
nce
rnop
inio
nh
asp
red
icti
ve
pow
erfo
rban
kru
ptc
yb
eyon
din
form
atio
nav
aila
ble
tob
oth
cred
itor
san
dau
dit
ors
.M
od
el1
and
2ar
esi
mp
lep
rob
itre
gres
sion
s.M
od
el3
and
4ar
eb
ivar
iate
pro
bit
regr
essi
ons.
Th
ed
epen
den
tva
riab
les
are
(1)
Goin
gC
on
cern
,an
ind
icat
or
for
whet
her
acl
ient
rece
ives
ago
ing
con
cern
opin
ion
inye
art,
(2)
Ban
kru
ptc
y,an
ind
icat
orfo
rw
het
her
acl
ient
wen
tb
ankru
pt
wit
hin
one
yea
rof
the
issu
an
ceof
aud
itor
’sgo
ing
con
cern
opin
ion
.E
xp
lan
ator
yva
riab
les
are
Goi
ng
Con
cern
Sco
re,
pre
dic
tive
scor
eof
acl
ient
rece
ivin
ggo
ing
con
cern
opin
ion
and
Ban
kru
ptc
yS
core
,p
red
icti
vesc
ore
ofa
clie
nt
goin
gb
ankru
pt.
To
crea
teG
oin
gC
once
rnS
core
(Ban
kru
ptc
yS
core
)fo
rcl
ienti
yeart,
we
pool
all
dat
afr
omyea
r1
toye
art−
1an
du
sera
nd
omF
ores
tto
fore
cast
the
pro
pen
sity
ofre
ceiv
ing
goin
gco
nce
rnop
inio
n(g
oin
gban
kru
pt)
.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
scor
eso
that
on
eu
nit
chan
geco
rres
pon
ds
toch
ange
inon
est
andar
dd
evia
tion
.O
ther
pre
dic
tor
vari
able
sin
clu
de:
the
nat
ura
llo
gari
thm
ofto
tal
ass
ets,
the
rati
oof
ofd
ebt
toto
tal
asse
ts,
the
rati
oof
shor
t-te
rmin
vest
men
tsto
tota
las
sets
,th
era
tio
ofca
shto
tota
las
sets
,re
turn
onas
set,
the
nat
ura
llo
gari
thm
of
closi
ng
stock
pri
cefo
rth
efi
scal
per
iod
.ρ
isth
eco
rrel
atio
nb
etw
een
two
erro
rte
rms,
wh
ich
cap
ture
sin
form
atio
nsh
ared
by
cred
itors
(wh
od
eter
min
eb
an
kru
ptc
y)
and
aud
itor
s(w
ho
issu
ego
ing
conce
rnop
inio
ns)
.W
eal
soin
clu
de
yea
rfi
xed
effec
tsan
dau
dit
orfi
xed
effec
ts.
We
ob
tain
the
sam
pli
ng
dis
trib
uti
onth
rough
boot
stra
pp
ing.
We
pre
sent
the
mea
nes
tim
ates
and
95%
con
fid
ence
inte
rval
bel
owth
ees
tim
ate
s.
(1)
(2)
(3)
(4)
Pro
bit
Pro
bit
Biv
aria
tep
rob
itB
ivar
iate
pro
bit
Vari
able
sG
oin
gC
on
cern
Ban
kru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
yG
oin
gco
nce
rnB
ankru
ptc
y
Goin
gco
nce
rn0.
680
0.60
4[0
.534
,0.
834]
[0.3
66,
0.83
0]G
oin
gco
nce
rnsc
ore
0.84
10.
147
0.84
20.
251
0.84
10.
158
[0.7
93,
0.8
89]
[0.0
74,
0.21
5][0
.794
,0.
89]
[0.1
83,
0.32
2][0
.793
,0.
889]
[0.0
86,
0.23
2]B
an
kru
ptc
ysc
ore
0.0
470.
220
0.04
70.
221
0.04
70.
219
[0.0
15,
0.0
82]
[0.1
35,
0.30
6][0
.015
,0.
080]
[0.1
37,
0.30
9][0
.015
,0.
082]
[0.1
33,
0.30
4]L
og(
Ass
ets)
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41
Appendix
A causal interpretation of γ
Having presumed a particular parametric model for the distribution of the data (G,B) condi-
tional on covariates x, we would like additional license for the interpretation that ρ captures the
contribution of auditor’s additional information on bankruptcy likelihood, while γ captures the
contribution of inducement effects on bankruptcy likelihood.
To justify this interpretation, we turn to the causal analysis framework of Pearl (2000). In
Pearl’s framework, the inducement effect would be written as
Pr(B = 1 | x, do(G = 1))− Pr(B = 1 | x, do(G = 0)), (11)
where do(G = 1) denotes the intervention of issuing a going concern, regardless of the data gener-
ating process.
Denote by A the auditor’s additional information. Suppressing the covariates x, the relationship
between G and B can be expressed using the following causal diagram.
A
G?
- B
-
This diagram asserts several causal assumptions. First, the issuance of a going concern does
not cause the existence of auditor’s additional information: there is no arrow running from G
to A. Second, bankruptcies cannot cause going concerns: there is no arrow running from B to G.
42
Similarly, bankruptcies do not cause the creation of auditor’s additional information for predicting
bankruptcy: there is no arrow from B to A. All of these assumptions follow straightforwardly from
a temporal ordering—auditor’s first procure information concerning bankruptcy propensity (A),
they then issue going concern opinions (G) and then clients either go bankrupt or not (B).
Because A disconnects alternative routes from B to G and no directed path exists from G to A, A
is said to satisfy the back-door criterion (Pearl, 2000), and we can compute Pr(B = 1 | x, do(G = 1))
via the expression:
Pr(B = 1 | x, do(G = 1)) =
∫Pr(B = 1 | x, A = a,G = 1)p(a)da, (12)
where p(a) is the marginal density of the random variable A.
The difficulty, of course, is that A is unobserved in our problem so p(a) can never be estimated
from data. However, we can re-express the bivariate probit model directly in terms of A in order to
derive expression (12) in terms of (ρ, γ, α, β). This allows us to see how the function form dictates
the causal estimand in (11). Specifically we re-write (8), conditional on A, as:
Ug,i
Sb,i
iid∼N(µ,Σ), µ =
β0 + β1xi + ηgA
α0 + α1xi + ηbA
, Σ =
vg 0
0 vb
, (13)
where A ∼ N(0, 1), vg = 1 − η2g , vb = 1 − η2b and ρ = ηgηb. Although this representation is non-
unique in (ηg, ηb, vg, vb), it turns out that expression (12) will not depend on these values. This can
43
be seen by direct calculation:
Pr(B = 1 | x, do(G = 1)) =
∫Pr(B = 1 | x, A = a,G = 1)Na(0, 1)da,
=
∫1− Φ(0; γ + α0 + α1x + ηba)Na(0, 1)da,
=
∫1−
∫ 0
−∞Nw(γ + α0 + α1x + ηba, vb)dwNa(0, 1)da,
= 1−∫ 0
−∞
∫Nw(γ + α0 + α1x + ηba, vb)Na(0, 1)dadw,
= 1−∫ 0
−∞Nw(γ + α0 + α1x, 1)dw,
= 1− Φ(0; γ + α0 + α1x),
= Φ(γ + α0 + α1x).
(14)
Here Φ(0;µ) denotes the CDF of a normal distribution with mean µ and variance 1, evaluated at
0. A similar calculation can be done for Pr(B = 1 | x, do(G = 0)), allowing us to recover our causal
estimand as Φ(γ + α0 + xα1) − Φ(α0 + xα1). In other words, fitting a bivariate probit model to
the data (G,B,x), coupled with the causal assumptions encoded in diagram 6.2, implies a causal
inducement effect that can be written in terms of α and γ (and not including ρ or β).
The causal analysis above is in terms of all parameters fixed. It is still crucial, therefore, that
α and γ are estimated jointly with ρ and β for their estimates to be valid. Also, as the parameters
of the model will be estimated using the observed covariates x, we require that the distribution
assumed for A accounts for any association between the measured predictors x and the unobserved
auditor information. Above, we have assumed, as is standard in the bivariate probit literature, that
A is independent of x (that is, x is exogenous). It is possible to conduct a sensitivity analysis to
this (likely implausible) assumption, by obtaining effective bounds on the treatment effect in the
44
more realistic case that x is endogenous (i.e., unobserved auditor information is correlated with the
observed predictor variables).
With this causal interpretation fleshed out, it is now easier to spot how the distribution assump-
tions determine our estimates. Specifically, the backdoor calculation (12) highlights two separate
aspects of the bivariate probit specification—the shape of the Gaussian link Φ(·) and the implied
linear dependence on the auditor’s additional information, γG+ ηA+ xβ. The linear dependence
structure of the Gaussian model is defensible if the observable covariates capture most of the rel-
evant information for predicting bankruptcies so that the relative importance of observable client
characteristics is large compared to the auditor’s additional information. If the impact of the ad-
ditional information relative to the measured covariates is relatively small, a linear approximation
should suffice. The probit link, on the other hand, is without strong justification. It is a matter
of ongoing work to adapt semi-parametric single-index models (Horowitz, 1998, Chapter 2) to this
task, essentially forming a bivariate Gaussian copula model for endogenous binary predictors.
45
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