separating the probability of committing and detecting
TRANSCRIPT
Separating the Probability of Committing and Detecting Restatements:
Evidence from Auditor Attributes and Accounting Quality
Preliminary Draft: Please do not cite or quote without authors’ permission
Jane Barton - Baruch College
Brian Burnett - Biola University
Katherine Gunny - University of Colorado - Denver
Brian P. Miller - Indiana University – Bloomington
April 2017
ABSTRACT
Empirically measuring accounting quality has proven difficult as many accrual based measures
can be confounded with other economic factors. To address these concerns, many researchers have
instead relied on the existence of restatements to measure accounting quality. Although examining
the probability of a restatement has tremendous intuitive appeal as it provides a directly observable
outcome of poor accounting quality, the inferences from these models are limited since only
misstatements that are detected can be observed. As such, the probability of a restatement
examined in most prior models is the product of two latent probabilities (i.e., misstatement
commission and misstatement detection). We demonstrate the importance of separating these
latent probabilities by showing that when using traditional probability models that do not account
for these separate processes, Big N auditors are actually more likely to be associated with a future
restatement. However, when we employ an empirical model that separates the underlying latent
processes, we find evidence that Big N clients are less likely to be associated with misstatement
commission. Further, conditional on that misstatement occurring, a Big N auditor is more likely to
detect the misstatement. This evidence supports the notion that it is important to separate these
latent probabilities to mitigate potential incorrect inferences that may be derived from traditional
probability models.
We are grateful for discussions and helpful comments from Joseph Schroeder. Brian Miller gratefully acknowledges
financial support from the PwC Faculty Fellowship.
1
1. Introduction
A substantial literature examines the various governance and oversight measures of accounting
quality. Many of these studies rely on accrual-based measures of accounting quality. Given
concerns that many of these accrual based measures are associated with other economic factors
(e.g., growth), many researchers have instead relied on the existence of restatements as a measure
of accounting quality.1 The use of restatements has tremendous intuitive appeal as a proxy for
accounting quality, since financial statement restatements capture misstatements with a high
degree of accuracy. Specifically, a restatement provides clear evidence that the financial
statements as originally filed with the Securities and Exchange Commission (SEC) were not in
accordance with Generally Accepted Accounting Principles (GAAP).
Despite the significant benefits of examining the probability of restatement using traditional
logistic models, interpretations of these models are clouded by partial observability. In particular,
only misstatements that are committed and subsequently detected (i.e., restatements) are
observable. Partial observability prevents researchers from observing the probability of a
misstatement, and instead only allows only for the visibility of detected misstatements. This
probability of detected misstatement (or restatement) is the product of two latent probabilities: the
probability of misstatement commission and the probability of misstatement detection.
Traditional logistic models ignore this underlying partial observability problem, which may
potentially lead to incorrect inferences. In particular, many variables of interest have opposing
effects on the probability of misstatement commission and the probability of misstatement
detection. Although this distinction may seem subtle, in reality these distinctions can have
significant policy implications. For instance, while certain regulatory policies may be designed to
1 See discussion of the implications of growth on accrual measures provided by Kothari, Leone, and Wasley (2005).
2
decrease the likelihood that a misstatement occurs (e.g., executive certification of financial
statements), other policies may instead be designed to increase the likelihood of detection (e.g.,
SEC investigation resources). A researcher using traditional logistic models documenting a net
increase (or decrease) in the existence of restatement activity may incorrectly interpret that
evidence to indicate a policy failure (or success).
To address these shortcomings in traditional logistic and probit models, we propose a bivariate
probit model with partial observability that examines the two underlying latent processes
separately. 2 The challenge with implementing this model in many settings is distinguishing
between the two latent processes. Fortunately, prior fraud and restatement research (e.g., Beneish
1999 and Dechow et al. 2011) provides a distinct set of variables separately designed to capture 1)
incentives and ability to manipulate financial statements and 2) financial statement distortions that
indicate misstatement is likely to have occurred. Based on this work, we include variables that
capture incentives to manipulate financial statements in our model of the probability of
misstatement commission, and separately include variables designed to indicate a misstatement is
likely to have occurred in our model of the probability of misstatement detection following
occurrence.
This distinction is further aided by the fact that restatements, by definition, are misstatements
that occur in one period and then are subsequently discovered in the following period. This
provides the opportunity for several additional variables that are distinct between the two latent
processes in our setting. For instance, the existence of large stock price decreases and abnormally
2 This bivariate probit was introduced by Poirier (1980) and has been used in prior economic and finance literatures
primarily to examine various aspects of predictors of fraudulent behavior (Wang, Winton, and Yu 2010; Wang
2013; Dyck, Morse and Zingales 2013). We build on these papers by examining all accounting misstatements as our
focus is primarily on auditor detection, where auditors should be responsible for detecting all material misstatements
(i.e., errors and irregularities).
3
high volatility increases that often occur subsequent to the misstatement period but prior to its
detection are unlikely to be associated with the likelihood of misstatement occurrence in the prior
period, but likely increase scrutiny leading to a higher likelihood of detection of a misstatement if
one has occurred. Combined, these factors help us distinguish between the latent processes of
misstatement commission and detection.
We use auditor attributes to illustrate the importance of distinguishing these two latent
processes. In particular, in our primary tests we focus on disentangling whether misstatements are
more likely to be committed by Big N clients and, conditional on a misstatement occurring,
whether a Big N auditor is more likely to detect said misstatement. Examining Big N auditors has
important economic implications in the sense that these auditors charge a premium largely for their
ability to provide higher quality audits (Palmrose 1986; Simon and Francis 1988). However, it is
not clear whether these auditors merely have higher quality clients with a lower incidence of
misstatements, or whether they indeed provide higher quality audits and therefore are more likely
to detect misstatements.
We demonstrate the importance of separating these latent probabilities by showing that when
using a traditional probit model that does not account for these separate processes Big N auditors
are actually more likely to be associated with a future restatement. Without separating the
underlying latent probabilities this evidence could be interpreted in multiple ways. On the one
hand, this evidence could be consistent with a somewhat counterintuitive result where Big N
auditors provide lower quality audits because their clients are more likely to commit misstatements
that subsequently result in restated financial statements. On the other hand, this evidence could be
interpreted in a more traditional manner to indicate that Big N auditors are superior in detecting
misstatements. Due to partial observability, it is difficult to distinguish between these alternatives
4
without separating the latent probabilities of misstatement commission and misstatement
detection.
When we employ our bivariate probit methodology to separate the underlying latent processes,
we find that the Big N clients are less likely to be associated with misstatement commission. This
evidence is consistent with Big N auditors providing higher quality audits and thereby reducing
the likelihood of potential undetected misstatements in the financial statements as originally filed.
Alternatively, this evidence could be interpreted as Big N auditors selecting higher quality audit
clients, where there is a lower likelihood of misstatement. Although these alternatives are difficult
to disentangle in the first model, the benefit of the bivariate probit is that is it allows us to
distinguish these alternatives when we examine the probability of detection of a misstatement
conditional on a misstatement occurring. In particular, the evidence from our second model shows
that conditional on a misstatement occurring, there is an increase in the probability of a Big N
auditor detecting that misstatement. In additional analyses, we provide evidence that the results in
these primary tests are robust to comparing Big 4 auditors to their 2nd tier counterparts (i.e. Crowe
Horwarth LLP, BDO USA LLP, Grant Thornton LLP, and McGladrey LLP) and not just to
comparing to small auditors. Combined, the evidence suggests that Big N auditors have higher
audit quality in the sense that they are more adept at catching misstatements once those
misstatements have occurred.
We next control for and separately examine the impact of other auditor attributes on the
commission of misstatements and detection of restatements. In particular, we control for both
office size (Francis and Yu 2009) and industry specialization (Ferguson, Francis, and Stokes 2003;
Francis, Reichelt and Wang 2005) and note that while our findings are not altered by the inclusion
of these other auditor attributes, both variables also provide several additional unique insights. In
5
particular, when using traditional probability models we find no evidence that auditors at larger
offices are more likely to be associated with restatements. When we separate the two latent
probabilities, we find evidence similar to that found for the Big N auditor variable in that we find
clients of larger offices are less likely to commit a misstatement, but conditional on a misstatement
occurring, auditors at larger offices are more likely to detect a restatement. Combined, this
evidence suggests that the two latent probabilities likely offset when using traditional approaches
leading to an incorrect inference that office size does not play a significant role in the misstatement
or restatement detection process.
In addition to our examination of office size, we also examine industry specialization. Our
examination of industry specialist auditors shows that when traditional probability models are
employed, industry specialists are associated with a greater likelihood of restatement. However,
when we employ the bivariate probit model, we find only modest evidence of an increase in
restatement detection for industry specialist auditors. This evidence provides only weak support
that industry specialization results in higher audit quality as measured by restatement detection.
In our final set of tests, we revisit the notion that Big N auditors are more likely to detect
misstatements by providing additional evidence on the length of time it takes to detect a
misstatement after an auditor switch. To ensure that the misstatement itself did not lead to an
auditor switch (Hennes, Leone, and Miller 2014), we limit our sample to only those observations
where the auditor switch occurs after the end of the restatement period as well as after the
disclosure of the restatement. We find that amongst firms with Big N auditors during the
restatement period, those misstatements where the Big N auditor switched to another Big N auditor
(i.e. lateral switches) were detected on average over 100 days quicker (over 30% faster) than cases
where the Big N auditor switched to a non-Big N auditor (i.e. downgrades). This difference is not
6
only economically significant, but also statistically significant for both the mean and median
difference. Further, this evidence continues to hold at conventional significance levels in in a
multivariate regression analysis.
In sum, the evidence in this study highlights the importance of separating the latent processes
of misstatement commission and detection in the Big N auditor setting. As discussed in more detail
in the following section, these findings shed light on prior studies that examine the link between
Big N auditors and restatements. However, more importantly this study provides a useful tool and
highlights the importance of separating these underlying latent processes when examining other
governance and oversight measures of accounting quality using restatements.
The remainder of the paper proceeds as follows. Section 2 reviews the academic literature on
audit quality proxies and bivariate probit models. Section 3 presents our motivation and hypothesis
development. Section 4 discusses our research design and primary results. Section 5 discusses our
additional analyses. Section 6 concludes.
2. Literature Review
2.1 Bivariate Probit Models
Though bivariate probit models have not been previously used in the restatement literature,
they have been used in prior literature primarily to examine fraud. In particular, Wang (2013)
demonstrates that certain factors found to be insignificant in fraud models using traditional probit
approaches (e.g. R&D intensity) have a significant impact on the latent processes of fraud
commission and fraud detection, but that their significant effects cancel out in these traditional
probit models. She also provides evidence that active aquirers are less likely to commit fraud but
more likely to be detected if they commit fraud. In addition, she shows that variables such as
analyst coverage are negatively associated with fraud commission, but positively associated with
7
fraud detection. Relatedly, Wang, Winton, and Yu (2010) also use a bivariate probit model to
examine how firms’ incentives to commit fraud vary with investor beliefs. In particular, the
propensity to commit fraud increases when investors are more optimistic about industry
prospects, but decreases when beliefs are extremely high. Our study adds to this emerging
literature by expanding these fraud models to examine all types of restatements. In particular, our
interest lies in audit quality, where auditors are responsible for the prevention and detection of all
material misstatements regardless of whether the restatement was due to an error or an
irregularity (Hennes, Leone, and Miller 2008). As discussed in more detail later in the
manuscript, this required us to modify the bivariate probit models used in prior literature to
account for all types of restatements.
2.2 Audit Quality Proxies
A substantial literature examines the various governance and oversight measures of
accounting and audit quality, where many of these studies rely on accrual based metrics.
Theoretically, higher discretionary accruals represent managerial manipulation over the earnings
reporting process. However, in practice, there are many problems with using discretionary
accruals as a proxy for accounting and audit quality as it is extremely difficult to parse out which
accruals are truly biased. For instance, Hribar and Collins (2002) note that there is significant
measurement error present in many discretionary accruals models which can lead to incorrect
inferences in accounting research. Similarly, Kothari, Leone, and Wasley (2005) demonstrate
issues with growth that often confound interpretations of discretionary accruals models.
In contrast, restatements have long been regarded as the most direct and observable measure
of audit quality. Restatements have intuitive appeal as by definition they represent an audit
failure, or an instance in which an auditor issued an unqualified opinion on financial statements
that were materially misstated. Consistent with this notion, restatements have been described as
8
“the most visible indicator of improper accounting” (Schroeder 2001 p. 1627). Further, auditing
researchers have noted that “the existence of a client restatement provides more compelling
evidence of low-quality audits than earnings quality metrics” (Francis, Michas, and Yu 2013). As
previously discussed the issue with the traditional approach to using restatements as a proxy for
audit quality is that traditional probit models do not account for the fact that many variables of
interest have opposing effects on the probability of misstatement commission and the probability
of misstatement detection.
3. Motivation
3.1 Big N Auditors and Restatements
The primary focus of this paper is to illustrate the importance of separating the probability of
misstatement commission and the probability of misstatement detection. To do so, we examine
whether Big N auditors provide higher accounting quality as proxied for by restatements. This
setting provides an important research question, where theoretically one would expect higher Big
N researchers would provide accounting quality but prior empirical work is mixed.
In her seminal work, DeAngelo (1981) notes that bigger auditors are capable of providing a
more efficient and effective audit as they possess certain economies of scale relative to their
competition, for example, with respect to employee training. DeAngelo (1981) also proposes that
Big N auditors have greater incentives to provide higher quality audits in order to maintain their
reputations and reduce risk of loss. In particular, Big N auditors have bigger reputations to lose,
more clients (and associated future audit fees) to lose, and deeper pockets to plunder in the event
of potential future litigation.
Despite these strong arguments for Big N auditors being associated with higher quality
accounting, empirical evidence on the relationship between Big N auditors and restatements is
9
mixed. For ease of exposition, we summarize in chronological order some of the prior papers that
examine this relationship in Appendix A. It is important to note that most of this mixed evidence
on the relation between Big N auditors and restatements arise from studies that do not intend to
directly test this relation, but that include Big N as a control variable in a restatement model
designed to address another research question. As such, sample selection in terms of type of
restatement examined, firm characteristics, and time periods examined vary greatly across these
studies and likely account for many of differences documented in prior literature.
A quick review of the papers summarized in Appendix A reveals that three studies find at least
some evidence of a significantly negative relationship between Big N and restatements (Lobo and
Zhao 2013; Francis et al. 2013; Eshelman and Guo 2014). In contrast, DeFond, Lim, and Zang
(2016) in a limited sample of income-decreasing restatements document a positive and significant
relation between Big N and restatements. The remaining papers examining restatements report an
insignificant coefficient on Big N. DeFond, Erkens, Zhang (2016) is the most recent in this line of
studies that fail to document a significant relationship between Big N and restatement. Despite the
fact that this study documents a strong Big N effect with respect to the vast majority of their audit
quality metrics (e.g., absolute discretionary accruals, income increasing discretionary accruals,
going concern opinions), they fail to find consistent evidence of a relationship between Big N
auditors and restatements across several different matching procedures. We contend that the
inability of this and other papers to find a significant coefficient on Big N auditors likely stems
from the underlying probability of misstatement commission and the probability of misstatement
detection offsetting each other when using traditional logistic and probit models.
In sum, despite the strong arguments for Big N auditors leading to higher accounting quality,
the evidence is mixed. We believe this mixed evidence is due to combining the probability of
10
misstatement commission and the probability of misstatement detection. Based on the arguments
laid out in DeAngelo (1981), we believe that Big N auditors will be less likely to allow their clients
to misstate their initial financial statements. Further, we also believe that these Big N auditors
conditional on a misstatement occurring, these auditors will be more likely to detect that
misstatements. More formally, when we separate these probabilities using the bivariate probit
model, we hypothesize the following (in alternative form):
H1a: Big N auditors are negatively associated with the probability of misstatement
commission.
H1b: Conditional on a misstatement occurring, Big N auditors are positively associated with
the probability of misstatement detection.
3.2 Industry Expertise and Office Size and Restatements
Our next set of predictions relates to other measures of auditor quality: industry expertise and
office size. Theoretically, industry specialists should be linked to higher quality audits as they have
a better understanding of the specific economic and accounting complexities underlying their
clients. Consistent with this notion, industry specialist auditors have been shown in experimental
research to be superior at detecting errors when operating within their own specialization (Owhoso,
Messier, and Lynch 2002). More recent archival research has documented a strong negative
association between industry specialist auditors and restatements in simple probit models,
including Romanus, Maher, and Fleming (2008) and Chin and Chi (2009).
Office size has also been a strong indicator of audit quality in accounting research. Specifically,
larger offices are indicative of higher quality. Potential mechanisms behind this superior quality
include larger offices having better in-house expertise and knowledge-sharing (Francis and Yu
2009). Further, larger offices possess enhanced independence as larger offices are less likely to be
beholden to any one client (Choi, Kim, Kim and Zang 2010). Francis et al. (2013) provides
empirical evidence consistent with larger offices resulting in fewer restatements specifically for
11
clients of Big 4 auditors and the four largest non-Big 4 audit firms. However, they do not provide
evidence of a significant association between office size and restatements regardless of auditor.
These prior literatures on industry specialist auditors and auditor office size address important
questions, but they do not address the partial observability problem. As such, it is unclear whether
prior findings are driven by a lower likelihood of misstatement occurrence or lower detection rates
by these auditors. We address this issue using our bivariate approach, and make the following
predictions:
H2a: Industry specialist auditors (and larger auditor offices) are negatively associated with
the probability of misstatement commission.
H2b: Conditional on a misstatement occurring, industry specialist auditors (and larger auditor
offices) are positively associated with the probability of misstatement detection.
4. Research Design and Results
4.1 Sample
Table 1 summarizes the sample selection process. We begin with 84,793 firms in the
Compustat Annual database between 2003 and 2013. We exclude firm-years prior before 2003 to
mitigate the confounding influences of SOX and Arthur Andersen. We end our sample in 2013
(i.e., fiscal year-ends through May 31, 2014) to allow sufficient time for a restatement to be
disclosed. We require each observation to have an audit opinion in the Audit Analytics database
which yields a sample of 63,340 firm-years. Next, we exclude restatements for which the auditor
during the restatement period and the auditor during the announcement of the restatement are
different. This eliminates the possibility that auditor switches are influencing our results.3 We then
delete observations without the necessary data to calculate our control variables (from Compustat,
3 In untabulated results, we find our results are robust when we do not exclude these restatement observations.
12
Center for Research in Security Prices (CRSP), or Audit Analytics).4 These steps result in a sample
of 36,306 firm-years, including 3,319 firm-year restatement observations and 1,924 unique
restatements.
4.2 Research Design
A restatement is a result of a two-step process. First, a firm must violate GAAP when issuing
their financial statements. Second, the violation of GAAP in the firm’s financial statements must
be detected. Audit quality should influence both processes, but in opposite directions. Specifically,
higher audit quality should lead to (1) fewer violations of GAAP in issued financial statements
(i.e., lower misstatement frequency) and (2) increased detection given a violation of GAAP has
occurred (i.e., higher restatement frequency).
To disentangle the influence of audit quality on these two distinct processes (i.e., the propensity
to violate GAAP and the propensity to detect a misstatement given a violation in GAAP has
occurred), we use a partial observability bivariate probit framework (Poirier 1980). This method
is used in several corporate fraud papers including Wang et al. (2010), Wang (2013), and Dyck,
Morse and Zingales (2013). The method simultaneously estimates two equations with binary
dependent variables when it is only possible to observe the product of the two binary dependent
variables. As previously discussed, we take this approach because we cannot directly observe
violations of GAAP that occur, only those that are subsequently detected. We simultaneously
estimate the probability of committing a misstatement and the probability of detection of
misstatement given that a misstatement occurred.
4 We include all misstatements from audit analytics. Our results (untabulated) are robust to only including annual
earnings restatements.
13
Two conditions must be met for identification of the bivariate probit model with partial
observability. The first condition is that the model for the estimation of the probability of
committing a misstatement and the model of the estimation of the probability of detecting a
misstatement given that one occurred cannot contain the exact same variables. Fortunately, prior
fraud and restatement research (e.g., Beneish 1999 and Dechow et al. 2011) provides a distinct set
of variables separately designed to capture 1) incentives and ability to manipulate financial
statements and 2) financial statement distortions that indicate a misstatement is likely to have
occurred. This work suggests variables capturing the incentives and ability of firms to manipulate
their financial statements in the model of the probability of misstatement commission and variables
designed to detect financial statement distortions in the model of detection of a misstatement given
one has occurred.
Further, the fact that misstatements are identified in the period subsequent to the commission
of the misstatement further aids identification of the model. Unexpected, large decreases in stock
price and abnormally high volatility in the subsequent period increase the likelihood of the
detection of prior period misstatements. The litigation literature finds firms with abnormally poor
stock price performance and unexpectedly high volatility face higher litigation risk (e.g., Jones
and Weingram 1996). Importantly, these large stock price decreases and abnormal volatility in the
year following the period misstated are unlikely to be associated with misstatement commission
in the prior period, but highly likely to be associated with its subsequent detection. The second
condition for identification of the bivariate probit model with partial observability is that the
explanatory variables in the models must exhibit substantial variation. Our inclusion of continuous
variables in both models provides this variation and improves identification (Poirier 1980).
4.2.1 Determinants of the Propensity to Violate GAAP: “P(Misstatement)”
14
We model the determinants of the propensity to violate GAAP based on prior literature (e.g.,
Dechow et al. 2011; DeFond et al. 2016a; DeFond et al. 2016b), as follows:
P(Misstatement) = 01 + 1Big4it + 2LogMVit + 3Litigationit + 4ActIssueit + 5BMit
+ 6Leverageit + 7ROAit + 8Lossit +9Mergerit + 10Segmentsit + 11ForeignOpsit
+ 12QReturnit + 13QVolatilityit + 14AssetTurnoverit + 15Currentit + . (1a)
Appendix B provides detailed definitions of all variables used throughout our study. We begin
with discussing control variables that proxy for the ability and incentive to engage in earnings
management. Size (LogMV) controls for any size effects. We include litigation risk (Litigation) to
control for whether the firm operates in a high-risk industry, defined as industries with SIC codes
2833-2836, 3570-3577, 3600-3674, 5200-5961, and 7370 (LaFond and Roychowdhury 2008). We
expect a negative coefficient because high-litigation industries should increase the costs of
engaging in earnings management. Firms raising external financing also have incentives to
manipulate accounting numbers and information, therefore we include ActIssue.
Book-to-Market (BM) controls for growth companies, and Leverage controls for firms near
debt constraints because these firms may have increased incentives to manage earnings. We
include contemporaneous ROA, Loss, and QReturn to controls for the effect of performance on the
likelihood of misstatements. Financially distressed firms face greater capital market pressures and
are more likely to manipulate the financial statements and related disclosures in response to these
pressures. We expect Loss to be positively associated with the likelihood of misstatements and
ROA and QReturn to be negatively associated with the likelihood of misstatements. We include an
indicator variable to control for the effect of mergers and acquisitions (Merger). We include
Segments and ForeignOps to control for accounting complexity which is correlated with the ability
and flexibility to engage in earnings management. Therefore, we expect Segments and ForeignOps
15
to be positively associated with misstatements. We include the decile rank of the firm’s monthly
stock return volatility calculated over the 12-month period ending in the last month of the fiscal
year (QVolatility) to control for management pressure to report smooth earnings.
Lastly, in an effort to control for the potential that Big N clients have an incentive to choose
low risk clients, we include the variables used in the propensity score matching model
implemented by DeFond et al. (2016a) and Lawrence, Minutti-Meza and Zhang (2011). These
papers include five variables from the selection model in Chaney, Jeter, and Shivakumar (2004):
size, leverage, return-on-asset, asset turnover, and the percentage of assets that are current. As
such, we include AssetTurnover and Current to include the two variables not already in our model.
4.2.2 Determinants of the Propensity to Detect Misstatement Given a Violation of GAAP
Occurred: “P(Detection|Misstatement)”
We model the determinants of the propensity to detect fraud given a violation in GAAP
occurred as follows:
P(Detection|Misstatement) = 01 + 1Big4it + 2LogMVit + 3Litigationit + 4ActIssueit
+ 5RSSTit + 6ChgA/Rit + 7ChgINVit + 8%SoftAssetsit +9ChgSalesit + 10ChgROAit
+ 11AbChgEmpit +12OpLeaseit + 13RestateAnnouncedit + 14HighPEit
+ 15HighVolatilityit + 16LowReturn_Subit + 17HighVolatility_Subit +. (1b)
Our model generally follows Dechow et al. (2011) and is augmented by five additional
variables to control for detection probability. We include Litigation because litigation risk
increases monitoring associated with fraud detection (e.g., Jones and Weingram 1996; Wang
2013). We include the prediction variables used by Dechow et al. (2011) because the Division of
Enforcement uses a similar model to predict potential misstatements (Lewis 2012). They find
working capital accruals modified to include changes in long-term operating assets and long-term
operating liabilities (RSST), two accrual components, change in accounts receivable (ChgA/R) and
16
change in inventory (ChgINV), change in return-on-assets (ChgROA), and the presence of
operating leases (OpLease) to be positively associated with restatements. They also find the
percentage of soft assets on the balance sheet (%SoftAsset), change in cash sales (ChgSales), and
abnormal change in employees (AbChgEmp) to be negatively associated with restatements.
Next, we include the variables that are more likely to trigger a review by the SEC to attempt
to control for restatements detected by the SEC and not the auditors. SEC investigations begin
with a trigger event, which is generally a tip or complaint. The SEC's Division of Enforcement
receives tips from many sources, including auditors, investors, firms who have self-identified
noncompliance with securities laws, media attention, and through the SEC’s review of company
filings at the Office of Corporation Finance. Therefore, in addition to controlling for fraud
prediction variables identified by Dechow et al. (2011), we control for variables that predict the
probability of filing review by the Office of Corporation Finance. Section 408 of SOX identifies
6 criteria that the SEC should consider when selecting filings for review. These criteria are: (i)
issuers that have issued material restatements of financial results; (ii) issuers that experience
significant volatility in their stock price as compared to other issuers; (iii) issuers with the largest
market capitalization; (iv) emerging companies with disparities in price to earnings ratios; (v)
issuers whose operations significantly affect any material sector of the economy; and (vi) any other
factors that the Commission considers relevant. Per Criteria (i), the SEC will review the annual
filing of a company that announces a restatement during the fiscal year. For example, if in June
2015 a company announces it is restating fiscal years 2012 and 2013, its 2015 10-K filed in early
2016 will be selected for review by the SEC. This increases the likelihood that fiscal year 2015
will be restated as the filing is under greater scrutiny. Therefore, we include whether the firm
announced a 10-K restatement of a prior period during the fiscal year (Restate_Announced).
17
Consistent with the determinants of SEC review discussed in criteria (ii), (iii), and (iv), we control
for whether the firm is in the highest decile of volatility of stock returns (HighVolatility), the log
of market value (logMV), and whether the firm is in the highest decile of price-to-earnings ratio
during the fiscal year (HighPE), respectively. Given these factors are correlated with the
probability of filing review by the Office of Corporation Finance, we expect them to have positive
coefficients.
Lastly, we control for potential trigger events arising from sources other than the firm’s auditor,
litigation risk, and the SEC (both the Division of Enforcement and the Office of Corporation
Finance). We include two market-based ex-post detection factors that are likely correlated with
potential triggering events, but not with the firm’s ex ante likelihood of misstating earnings. The
first variable is whether the firm is the bottom decile of stock returns in t+1 (LowReturn_Sub). The
second variable is whether the firm is in the top decile of stock return volatility fiscal in year t+1
(HighVolatility_Sub). We expect both these variable to be positively associated with detection
probability because a large stock price decline or higher volatility is likely to trigger an
investigation.
4.3 Results
We report descriptive statistics in Table 2. Mean Restatement is 9.1% whereas median
Restatement is 0.0%. Mean Big4 is 71.7% and median Big4 is 100.0% suggesting that the majority
of firms in our sample are audited by Big 4 auditors. Mean IndustrySpecialist is 16.1% suggesting
that a small portion of firm-years are audited by the national-city leader based on aggregate audit
fees. Lastly, mean (median) OfficeSize is 57.796 (23.000).
Table 3 shows the Pearson correlations among the variables of interest. Similar to the
univariate results, we find a positive and significant correlation between Restatement and Big4,
18
IndustrySpecialist, and OfficeSize. As discussed earlier, the probability of misstatement and the
probability of detecting a misstatement are the result of two underlying processes with opposing
effects on the association between misstatements and audit quality. Therefore, the univariate
results and the correlations between Restatement and these three audit quality proxies should be
interpreted with caution.
Table 4 reports the results of estimating a probit regression that models the probability of
restatement using Big4 and all the control variables from model 1(a) and 1(b). The coefficient on
Big4 is positive and significant (coef. 0.383, p = 0.000). Without considering the two underlying
processes for probability of committing and detecting misstatements, this evidence could be
interpreted in multiple ways. In particular, one could conjecture from this result that that Big N
auditors provide lower quality audits because their clients are more likely to commit misstatements
that subsequently result in restated financial statements. Alternatively, one could also interpret this
result in a more traditional manner, as evidence that Big N auditors were superior in detecting
misstatements. Without separating these latent probabilities it is difficult to distinguish between
these alternatives.
To address this issue, we separate the probability of committing and detecting a misstatement
by estimating a bivariate probit model with partial observability. The results are reported in Table
5. For the probability of misstatement (model 1a), we find that the coefficient on Big4 is
significantly negative (coef. = -0.485, p-value = 0.034). This result suggests that having a Big4
auditor lowers the probability of committing a misstatement. For the probability of detection given
misstatement (model 1b), we find that the coefficient on Big4 is significantly positive (coef. =
0.631, p-value = 0.000). This result suggests that having a Big 4 auditor increases the probability
of detecting a misstatement given a misstatement has occurred. Overall, the results suggest that
19
Big 4 auditors lower the probability of committing a misstatement but increase the probability of
detecting a misstatement given one has occurred.
Turning to the control variables in model 1a, we find that the coefficients on BM and Leverage
are positive and statistically significant consistent with predictions that these firms have increased
incentives to manage earnings. Two performance variables are significantly related to the
probability of misstatement: Loss and ROA. The coefficient on Loss is positive and significant
consistent with the prediction that financially distressed firms face greater pressure to misstate
earnings. However, the coefficient on ROA is positive and significant inconsistent with the
prediction that firms performing well have less incentive to engage in earnings management.
Consistent with the prediction that accounting complexity is positively related to the ability to
engage in earnings management, we find positive and significant coefficients on Segments and
ForeignOps. The decile rank of the volatility of the firm’s stock return (QVolatility) is positive
and significant consistent with management pressure to smooth earnings. Lastly, the coefficient
on AssetTurnover is positive and significant and the coefficient on Current is negative and
significant.
Our examination of the control variables in model 1b shows that the statistically significant
control variables are consistent with our predictions. The coefficient on Litigation is positive and
significant consistent with litigation risk increasing the probability of misstatement detection. We
find that the coefficients on OpLease, RestateAnnounced, and HighPE are positive and significant
consistent with these firm characteristics leading to greater scrutiny by the SEC which increases
the probability of detection. Also, we find that LowReturn_Sub is positive and significant
suggesting that a large stock price decrease in the subsequent year increases the probability of
detection by the SEC and/or other market participants.
20
4.4 Including only Big4 and 2nd Tier Auditors
In this section, we attempt to understand whether the results in our primary tests are robust to
comparing Big 4 auditors to their 2nd tier counterparts only (i.e. Crowe Horwarth LLP, BDO
USA LLP, Grant Thornton LLP, and McGladrey LLP) vs. a comparison sample including all
other auditors. In particular, we re-run model 1a and 1b on a sample that only includes only Big
4 and 2nd tier auditors. The reduced sample includes 29,564 firm-years and 3,096 restatement-
years. Table 6 Panel A reports the results of the traditional probit regression, where the
coefficient on Big4 is positive and significant (coef. 0.281, p = 0.000). Table 6 Panel B reports
the results of the bivariate probit regression. For the probability of misstatement (model 1a), we
find that the coefficient on Big4 is significantly negative (coef. = -0.869, p-value = 0.006). For
the probability of detection given misstatement (model 1b), we find that the coefficient on Big4
is significantly positive (coef. = 0.806, p-value = 0.000). Overall, the results suggest that Big4
auditors lower the probability of committing a misstatement, but increase the probability of
detecting a misstatement given one has occurred, even when compared to 2nd tier auditors.
4.5 Other Auditor Attributes
In this section, we control for and separately examine two additional audit quality proxies in
our probit and bivariate probit models. First, we include IndustrySpecialist, which is an indicator
variable equal to one for firms where their auditor is a national leader and a city leader, and zero
otherwise. IndustrySpecialist is equal to one for firms where their auditor is the number one auditor
in an industry in terms of aggregated audit fees in a specific fiscal year. City leader is equal to one
for firms where their auditor’ office is number one in terms of aggregated client fees in an industry
within that city (based on metropolitan statistical area, MSA) in a specific fiscal year. Second, we
21
include OfficeSize, a measure of practice office size based on number of clients per practice office,
based on MSA, in a specific fiscal year following Francis and Yu (2009).
Panel A of Table 7 reports the probit estimation results. When we include all three variables in
the probit regression, the coefficients on Big4 and IndustrySpecialist are positive and significant.
The coefficient on OfficeSize is not significant. Next, we separate the probability of committing
and detecting a misstatement by estimating a bivariate probit model with partial observability. The
results are reported in Table 7 Panel B. For the probability of misstatement (model 1a), we find
that the coefficient on Big4 is significantly negative (coef. = -0.387, p-value = 0.046). We find that
the coefficient on IndustrySpecialist is insignificant and the coefficient on OfficeSize is
significantly negative (coef. = -0.001, p-value = 0.004). This result suggests that having a Big4
auditor or an auditor with a large office lowers the probability of committing a misstatement. For
the probability of detection given misstatement (model 1b), we find that the coefficient on all three
audit quality proxies are significantly positive (Big4: coef. = 0.579, p-value = 0.000;
IndustrySpecialist: coef. = 0.078, p-value = 0.075; OfficeSize: coef. = 0.001, p-value = 0.004). This
result suggests that having a Big 4 auditor, industry specialist, or auditor with a large office
increases the probability of detecting a misstatement given a misstatement has occurred.5
5. Additional Analysis - Auditor Change Analysis and Restatement Duration
In this section, we revisit the notion that Big N auditors are more likely to detect restatements
by providing additional evidence on the length of time it takes to detect a misstatement after an
auditor switch (i.e. the time to detection). If higher quality auditors reduce the probability that a
5 As sensitivity analysis we include each alternative audit attribute in the bivariate probit regression individually and
the results are similar. IndustrySpecialist remains insignificant in the first stage (model 1a) and significantly positive
in the second stage (model 1b). OfficeSize remains significantly negative in the first stage (model 1a) and
significantly positive in the second stage (model 1b). Additionally, we estimated the bivariate probit regression on
OfficeSize individually for a sample that only included firms audited by the Big4, consistent with the sample
examined by Francis et al. (2013). Amongst this subset of firms, OfficeSize is significantly negative in the first stage
(model 1a) and significantly positive in the second stage (model 1b).
22
misstatement occurs in the first place, and increase the probability that a misstatement will be
detected once it occurs, then it follows that a higher quality auditor should also detect a
misstatement more quickly.
To address this question, we focus on a sample of firms for which the auditor was different
between the misstatement period (i.e., when the misstatement was committed) and the
misstatement disclosure period (i.e., when the misstatement was detected). Panel B of Table 1
describes the auditor change sample. We begin with 3,802 restatements between 2003 and 2013
with non-missing control variables in Compustat, CRSP, or Audit Analytics. We exclude
restatements for which there are two or more different auditors during the misstatement period.
This results in 2,896 restatements. Next, we retain restatements for which the auditor during the
restatement period and auditor in the restatement disclosure period are different. This results in
309 restatements.
We classify these 309 restatements into four categories: (1) SwitchUp – firms that switched
from a non-Big 4 auditor to a Big 4 auditor (2) SwitchDown – firms that switched from a Big 4
auditor to a non-Big 4 auditor (3) LateralSwitchBig4 – firms that switched from one Big 4
auditor to another Big 4 auditor (4) LateralSwitchNonBig4 – firms that switched from one non-
Big 4 auditor to another non-Big 4 auditor. Then, we compare the duration of the restatement for
these four categories. We define Duration as the number of days between the disclosure date of a
restatement and the end date of the restatement.
Panel A of Table 8 reports the results of the univariate comparison of Duration across the
four categories. The first two rows compare LateralSwitchBig4 to SwitchDown. If Big 4 auditors
are more likely to detect a misstatement, we would expect LateralSwitchBig4 to have a shorter
duration compared to SwitchDown. Consistent with our prediction, we find Duration is
23
significantly longer for the SwitchDown sample: on average, it takes a non-Big 4 auditor almost
109 days longer than a Big 4 auditor to detect the restatement. Next, we compare the
LateralSwitchNonBig4 to the SwitchUp sample. If Big 4 auditors are more likely to detect a
misstatement, we would expect the SwitchUp sample to have a shorter duration compared to the
LateralSwitchNonBig4 sample. Although the SwitchUp sample has shorter duration, contrary to
expectations, it is not statistically significant. Since the SwitchUp sample only has 11
observations, the small sample size could explain the lack of significance.
We also conduct a multivariate analysis of duration on switch categories. We include three
switch categories: SwitchDown, SwitchUp, and LateralSwitchNonBig4. We also include five
control variables from Black et al. (2016) who examine restatement duration: LogMV, BM,
Leverage, %SoftAssets, and ROA. The results are reported in Panel B of Table 8. We find that the
coefficient on SwitchDown is positive and significant (coef. = 65.258, p-value = 0.051)
suggesting firms that switch from a Big 4 to a non-Big 4 have a longer restatement duration
compared to switchers that stay with a Big 4 auditor. We find the coefficient on SwitchUp is
negative and significant (coef. = -89.361, p-value = 0.073) suggesting firms that switch from a
non-Big 4 to a Big 4 have shorter restatement duration compared to switchers that stay with a
Big 4. Overall, this different methodology supports the evidence from our bivariate approach –
that Big4 auditors are more likely to detect misstatements.
6. Conclusion
Research examining the impact of oversight measures on accounting quality continues to grow.
Given the potential issues with accrual based measures of accounting quality, many studies now
rely on the existence of a restatement as an alternative measure of accounting quality. Despite the
intuitive appeal of restatements as a proxy for accounting quality, interpretations related to the
existence of restatements can be clouded by partial observability. In particular, many variables of
24
interest can have opposing effects on the probability of misstatement commission and the
probability of misstatement detection. As such, a traditional logistic model that is merely focused
on the existence of a restatement can lead to incorrect inferences.
We propose an econometric solution to resolve this partial observability issue by introducing
a bivariate probit model to separately examines the two underlying latent processes. Using the Big
N auditor setting to illustrate the importance of distinguishing these two latent processes, we find
that separately modeling these latent processes can have significant impacts on model
interpretations. In particular, we show that when using traditional logistic models Big N auditors
are more likely to be associated with a future restatement, which could imply that Big N auditors
have lower quality. However, when we employ our bivariate probit methodology that separates
the underlying latent processes, we find that the Big N clients are less likely to be associated with
misstatement commission. Perhaps more importantly, our evidence from the second model shows
that conditional on a misstatement occurring that there is an increase in the probability of a Big N
auditor detecting that misstatement. Combined, the evidence suggests that Big N auditors have
higher audit quality in the sense that they are more adept at both preventing misstatements in the
first place and catching them once they occur.
To provide further evidence supporting this notion that Big N auditors provide are more likely
to detect misstatements once they occur, we provide additional evidence on the length of time it
takes to detect a restatement after an auditor switch. In particular, we find that amongst firms with
Big N auditors during the restatement period, those misstatements where the Big N auditor
switched to another Big N auditor were detected on average over 100 days quicker (over 30%
faster) than cases where the Big N auditor switched to a non-Big N auditor. This evidence supports
25
the evidence from our bivariate probit model suggesting that Big N auditors provide higher quality
audits leading to superior accounting quality.
The combined evidence across the analyses in our study suggests that Big N auditors lead to
higher quality financial reporting. Although we think this is an important contribution to a large
literature debating the merits of Big N audit quality, we contend that the more important
contribution of this study is introducing a bivariate probit model to the restatement literature.
Specifically, the study highlights the importance of separating the underlying latent processes
when examining restatements. As such, we expect future researchers interested in the impacts of
other governance and oversight impacts on restatements will be able to implement similar models
to disentangle the probability of misstatement commission and the probability of misstatement
detection.
26
REFERENCES
Archambeault, D., T. Dezoort, D. Hermanson. 2008. Audit committee incentive compensation
and accounting restatements. Contemporary Accounting Research 25(N):965–992.
Bentley, K.A., T.C. Omer, and N.Y. Sharp. 2013. Business Strategy, Financial Reporting
Irregularities, and Audit Effort. Contemporary Accounting Research 30(2): 780-817.
Chaney, P., D. Jeter, and L. Shivakumar. 2003. Self-Selection of Auditors and Audit Pricing in
Private Firms. The Accounting Review 79(1): 51-72.
Carcello, J.V., T.L. Neal, Z.-V. Palmrose, and S. Scholz. 2011. CEO Involvement in Selecting
Board Members, Audit Committee Effectiveness, and Restatements. Contemporary
Accounting Research 28(2): 396-N30.
Chin, C.L. and H.Y. Chi. 2009. Reducing restatements with increased industry expertise.
Contemporary Accounting Research 26(3): 729-765.
Choi, J.H., C. Kim, J.B. Kim, and Y. Zang. 2010. Audit office size, audit quality, and audit
pricing. Auditing: A Journal of practice and Theory 29(1):.73-97.
DeAngelo, L. 1981. Auditor size and Audit Quality. Journal of Accounting and Economics
3(3):183-199.
Dechow, P.M., W. Ge, C.R. Larson, and R.G. Sloan. 2011. Predicting Material Accounting
Misstatements. Contemporary Accounting Research 28(1): 17-82.
DeFond, M. and J. Jiambalvo. 1991. Incidence and Circumstances of Accounting Errors. The
Accounting Review 66(3): 6N3-655.
DeFond, M., D.H. Erkens, J. Zhang. 2016. Do Client Characteristics Really Drive the Big N
Audit Quality Effect? New Evidence from Propensity Score Matching. Management Science,
Articles in Advance, 1–2N.
DeFond, M.L., C.Y. Lin, and Y. Zang. 2016. Client Conservatism and Auditor-Client
Contracting. The Accounting Review 91(1): 69-98.
Dyck, A., A. Morse, and L. Zingales. 2013. How Pervasive is Corporate Fraud? University of
Chicago Working Paper.
Eshelman, J.D. and P. Guo. 201N. Do Big N Auditors Provide Higher Audit Quality after
Controlling for the Endogenous Choice of Auditor? Auditing: A Journal of Practice and
Theory 33(N): 197-219.
Ferguson, A., J. Francis, and D. Stokes. 2003. The Effects of Firm-Wide and Office-Level
Industry Expertise on Audit Pricing. The Accounting Review 78(2): 429-448.
Francis, J., K. Reichelt, and D. Wang. 2005. The Pricing of National and City-Specific
Reputations for Industry Expertise in the U.S. Audit Market. The Accounting Review 80(1):
113-136.
27
Francis J., P. Michas, M. Yu. 2013. Office size of Big N auditors and client restatements.
Contemporary Accounting Research 30(4): 1626–1661.
Francis, J. and M. Yu. 2009. Big 4 Office Size and Audit Quality. The Accounting Review 84(5):
1521-1552.
Hennes, K. A. Leone, and B. Miller. 2018. The Importance of Distinguishing Errors from
Irregularities in Restatement Research: The Case of Restatements and CEO/CFO Turnover.
The Accounting Review 83 (6): 1487-1519.
Hennes, K. A. Leone, and B. Miller. 2014. Determinants and Market Consequences of Auditor
Dismissals after Accounting Restatements. The Accounting Review 89 (3): 1051-1082.
Hribar, P. and D.W. Collins. 2002. Errors in Estimating Accruals: Implications for Empirical
Research. Journal of Accounting Research, 40(1): 105-134.
Jones, C., and S. Weingram. 1996. The Determinants of 10b-5 Litigation Risk. Stanford Law
School Working Paper.
LaFond, R., and S. Roychowdhury, S. (2008). Managerial Ownership and Accounting
Conservatism. Journal of Accounting Research, 46(1), 101-135.
Lawrence, A., M. Minutti-Meza, P. Zhang. 2011. Can Big N versus non-Big N differences in
audit-quality proxies be attributed to client characteristics? The Accounting Review
86(1):259–286.
Lewis, C. M. 2012. Risk Modeling at the SEC: The Accounting Quality Model. Speech given to
Financial Executives International Committee on Finance and Information Technology.
Lobo, G.J. and Y. Zhao. 2013. Relation between Audit Effort and Financial Report
Misstatements: Evidence from Quarterly and Annual Restatements. The Accounting Review
88(N): 1385-1N12.
Newton, N.J., D. Wang, and M.S. Wilkins. 2013. Does a Lack of Choice Lead to Lower Quality?
Evidence from Auditor Competition and Client Restatements. Auditing: A Journal of
Practice and Theory 32(3): 31-67.
Owhoso, V.E., W.F. Messier Jr, and J.G. Lynch Jr. 2002. Error detection by industry‐specialized
teams during sequential audit review. Journal of Accounting Research 40(3), 883-900.
Palmrose, Z-V. 1986. Audit Fees and Auditor Size: Further Evidence. Journal of Accounting
Research 24(1): 97-110.
Poirier, D. 1980. Partial Observability in Bivariate Probit Models. Journal of Econometrics
12(2): 209-217.
Romanus, R.N., J. J. Maher, and D.M. Fleming. 2008. Auditor Industry Specialization, Auditor
Changes, and Accounting Restatements. Accounting Horizons 22(4): 389-413.
Schroeder, M. 2001. SEC List of Accounting-Fraud Probes Grows. Wall Street Journal (July 6):
C1, C16.
28
Simon, D.R. and J.R. Francis. 1988. The Effects of Auditor Change on Audit Fees: Tests of Price
Cutting and Price Recovery. The Accounting Review 63(2): 255-269.
Subramanyam, K.R. 1996. The pricing of discretionary accruals. Journal of Accounting and
Economics 22 (1): 249-281.
Wang, T.Y. 2013. Corporate Securities Fraud: Insights from a New Empirical Framework.
Journal of Law, Economics, and Organization 29 (3): 535-68.
Wang, T. Y., A. Winton, and X. Yu, 2010. Corporate Fraud and Business Conditions: Evidence
from IPOs. Journal of Finance 65(6), 2255-2292.
APPENDIX A - Prior Literature Relevant to the Big N/ Restatement Relationship
Paper Primary Research Question of Interest Sample Big N/Restatement Association Table(s)
Defond and
Jiambalvo (1991)
What are the driving factors (particularly the
economic or managerial incentives) behind
overstatement errors?
sample of 41
overstatements in
earnings for 1976-1987
negative and insignificant 5
Archambeault,
Dezoort, and
Hermanson (2008)
What is the relation between audit committee
incentive-based compensation and
restatements?
sample of 153
restatements occurring
between 1999-2002
positive and insignificant 3
Carcello, Neal,
Palmrose, and Scholz
(2011)
What is the impact of certain corporate
governance characteristics (CEO involvement,
audit committee characteristics) on
restatements?
1999-2001 or 2001-2003 negative and insignificant or positive and
insignificant, depending on the
specification
2, 3, and
6
Lobo and Zhao
(2013)
What is the relation between auditor effort and
restatements?
2000-2009 (using both
quarterly and annual
restatements)
negative and significant, negative and
insignificant, or positive and insignificant
relation depending on the specification
5, Panels
A-C
Newton, Wang, and
Wilkins (2013)
What is the relation between auditor
competition in a metropolitan area and the
probability of restatement?
2000-2009 negative and insignificant or positive and
insignificant, depending on the
specification
4, 6, 7,
and 8
Bentley, Omer, and
Sharp (2013)
Do companies following different business
strategies experience different rates of
restatement?
1998-2009 positive and insignificant relation 4
Francis, Michas, and
Yu (2013)
Does the relative office size of Big 4 auditors
impact the quality of the audits received by
their clients, as measured by restatements?
2003-2008 only Big 4 offices from the upper quartile
of office size have a negative and
significant association with restatements
8, Panel
B
Defond, Lim, and
Zang (2016)
Do auditors value conservatism in audit
clients (using income decreasing restatements
as a proxy for audit clients reporting
improperly in a non-conservative manner in
the past)?
2000-2010 (income
decreasing restatements
only)
positive and insignificant, or positive and
highly significant
6, Panel
B
Eshelman and Guo
(2014)
Is there an association between Big N and
Restatements, after controlling for self-
selection of Big N auditor?
2000-2009 negative & significant, negative &
insignificant, depending on specification &
PSM
5 and 7
Defond, Erkens,
Zhang (2016)
Is there an association between Big N auditors
and various audit quality metrics, including
restatements?
2004-2013 evidence for a Big N effect is weak and
highly dependent on research design
choices
3,4, and
5
APPENDIX B - Variable Definitions
Misstatement = an indicator variable equal to one for firms that issued a restatement, and
zero otherwise (Audit Analytics).
Big4 = an indicator variable equal to one for firms audited by a Big 4 audit firm
(Deloitte, Ernst & Young, KPMG, or PricewaterhouseCoopers), and zero
otherwise (Audit Analytics).
IndustrySpecialist = an indicator variable equal to one for firms where their auditor is a
National Leader and a City Leader, and zero otherwise. National Leader
is equal to one for firms where their auditor is the number one auditor in
an industry in terms of aggregated audit fees in a specific fiscal year.
City Leader is equal to one for firms where their auditor’ office is
number one in terms of aggregated client fees in an industry within that
city (based on MSA) in a specific fiscal year.
OfficeSize = measure of practice office size based on number of clients of a practice
office (based on MSA) in a specific fiscal year.
Control variables in the first stage bivariate probit:
Actissue = an indicator variable equal to one if sale of common or preferred stock
(SSTK) or long-term debt issuance (DLTIS) are nonzero, and zero
otherwise (Compustat).
AssetTurnover = sales (REVT) divided by lagged total assets (AT) (Compustat).
BM = book value (SEQ) divided by market value (PRCC_F*CSHO)
(Compustat).
Current = current assets (ACT) divided by total assets (AT) (Compustat).
ForeignOps = an indicator variable equal to one if the firm has foreign operations, zero
otherwise (Compustat).
Leverage = Long-term debt (DLC+DLTT) divided by average total assets (AT)
(Compustat).
Litigation
= an indicator variable equal to one if the firm operates in a high-litigation
industry, and zero otherwise (high-litigation industries are industries with
SIC (SICH) codes of 2833-2836, 3570-3577, 3600-3674, 5200-5961, and
7370-7370) (Compustat).
LogMV = the natural logarithm of the market value of equity (CSHO*PRCC_F) in
millions (Compustat).
Loss = an indicator variable equal to one if earnings before extraordinary items
(IB) is negative, and zero otherwise (Compustat).
Merger = an indicator variable equal to one if pre-tax acquisitions or mergers
(AQP) are nonzero, and zero otherwise (Compustat).
QReturn = decile rank of the firm’s stock return (CRSP).
QVolatility
= decile rank of the firm’s monthly stock return volatility. Return volatility
is calculated over the 12-month period ending in the last month of the
fiscal year (CRSP).
ROA = earnings before extraordinary items (IB) divided by total assets (AT)
(Compustat).
Segments = the number of business segments (Compustat Segment File).
1
Additional control variables in the second stage bivariate probit:
RSST = working capital accruals following Richardson et al. 2005. ((ΔWC +
ΔNCO + ΔFIN)/average AT; WC = (current assets - cash and short-term
investments) – (current liabilities - debt in current liabilities); NCO =
(total assets – current assets – investments and advances) – (total
liabilities – current liabilities – long-term debt); FIN = (short-term
investments + long-term investments) – (long-term debt + debt in current
liabilities + preferred stock)
ChgA/R = change in accounts receivable divided by average total assets (ΔRECT /
Average AT) (Compustat).
ChgINV = change in inventory divided by average total assets (ΔINVT / Average
AT) (Compustat).
%SoftAssets = total assets minus property, plant and equipment minus cash and cash
equivalents divided by total assets ((AT-PPENT-CHE)/AT) (Compustat).
ChgSales = percentage change in cash sales (REVT-ΔRECT) (Compustat).
ChgROA = change in earnings before extraordinary (IB) items divided by total assets
(AT) (Compustat).
AbChgEmp = percentage change in the number of employees (EMP) minus percentage
change in assets (AT) (Compustat).
OpLease = an indicator variable equal to one if noncancelable operating lease
obligations (MRC1-MRC5) are nonzero, and zero otherwise
(Compustat).
RestateAnnounced = an indicator variable equal to one for firms that announced a restatement
of a previous period, and zero otherwise (Audit Analytics).
HighPE = an indicator variable equal to one if the firm is in the highest decile rank
of price to earnings ratio (PRCC_F/EPSFX), and zero otherwise
(Compustat).
HighVolatility = an indicator variable equal to one if the firm is in the highest decile rank
stock return volatility, and zero otherwise (CRSP).
LowReturn_Sub = an indicator variable equal to one if the firm is in the lowest decile rank
stock return in t+1, and zero otherwise (CRSP).
HighVolatility_Sub = an indicator variable equal to one if the firm is in the highest decile rank
stock return volatility in t+1, and zero otherwise (CRSP).
Additional control variables in the auditor change analysis:
Duration = number of days between the disclosure date of a restatement and the end
date of the restatement (Audit Analytics).
SwitchUp = an indicator variable equal to one for firms that switched from a nonBig
4 auditor to a Big 4 auditor, zero otherwise (Audit Analytics)
SwitchDown = an indicator variable equal to one for firms that switched from a Big 4
auditor to a nonBig 4 auditor, zero otherwise (Audit Analytics)
LateralSwitchBig4 = an indicator variable equal to one for firms that switched from a Big 4
auditor to a Big 4 auditor, zero otherwise (Audit Analytics)
LateralSwitchNonBig4 = an indicator variable equal to one for firms that switched from a nonBig
4 auditor to a nonBig 4 auditor, zero otherwise (Audit Analytics)
Table 1
Panel A: Main Sample
Compustat firm-years between 2003 through 2013
84,793
Less firm-years without an audit opinion in Audit Analytics
63,340
Less firm-years with a restatement in which the auditor during the restatement period and auditor during the
announcement period are different
61,172
Less firm-years with missing control variables in Compustat, CRSP, or Audit Analytics
36,306
Number of firm-year restatements
3,319
Number of restatements
1,924
Panel B: Auditor Change Sample
Number of restatements between 2003 through 2013 with audit opinion in Audit Analytics and non-missing control
variables in Compustat, CRSP, or Audit Analytics
3,802
Less restatements for which there are multiple auditors during the restatement period
2,896
Restatements for which there is a different auditor for the restatement period and disclosure date
309
Table 2
Mean Median Std.Dev. 25% 75% Min Max
Restatement 0.091 0.000 0.288 0.000 0.000 0.000 1.000
Big4 0.717 1.000 0.450 0.000 1.000 0.000 1.000
LogMV 6.160 6.110 2.008 4.699 7.519 1.975 11.160
Litigation 0.223 0.000 0.416 0.000 0.000 0.000 1.000
ActIssue 0.912 1.000 0.283 1.000 1.000 0.000 1.000
BM 0.642 0.509 0.585 0.293 0.809 -0.367 3.625
Leverage 0.202 0.149 0.209 0.019 0.311 0.000 0.952
ROA -0.009 0.025 0.180 -0.010 0.071 -0.906 0.297
Loss 0.280 0.000 0.449 0.000 1.000 0.000 1.000
Merger 0.022 0.000 0.146 0.000 0.000 0.000 1.000
Segments 2.080 1.000 1.571 1.000 3.000 1.000 7.000
ForeignOps 0.312 0.000 0.464 0.000 1.000 0.000 1.000
QReturn 4.500 5.000 2.872 2.000 7.000 0.000 9.000
QVolatility 4.500 5.000 2.872 2.000 7.000 0.000 9.000
AssetTurnover 0.895 0.733 0.782 0.296 1.265 0.009 3.796
Current 0.405 0.414 0.296 0.124 0.645 0.000 0.971
RSST -0.026 0.001 0.293 -0.116 0.094 -1.187 0.892
ChgA/R 0.016 0.007 0.057 -0.006 0.033 -0.151 0.259
ChgINV 0.006 0.000 0.034 -0.001 0.010 -0.119 0.153
%SoftAssets 0.598 0.630 0.268 0.392 0.831 0.037 0.980
ChgSales 0.073 0.078 0.922 -0.034 0.209 -5.239 4.261
ChgROA 0.000 0.000 0.121 -0.023 0.023 -0.474 0.503
AbChgEmp -0.026 -0.030 0.209 -0.107 0.050 -0.842 0.755
OpLease 0.811 1.000 0.392 1.000 1.000 0.000 1.000
RestateAnnounced 0.079 0.000 0.269 0.000 0.000 0.000 1.000
HighPE 0.100 0.000 0.300 0.000 0.000 0.000 1.000
HighVolatility 0.100 0.000 0.300 0.000 0.000 0.000 1.000
LowReturn_Sub 0.100 0.000 0.300 0.000 0.000 0.000 1.000
HighVolatility_Sub 0.100 0.000 0.300 0.000 0.000 0.000 1.000
IndustrySpecialist 0.161 0.000 0.368 0.000 0.000 0.000 1.000
OfficeSize 57.796 23.000 79.541 10.000 70.000 1.000 502.000
Descriptive statistics
1
Table 3
Restatement Big4Industry
Specialist
Big4 0.109***
Industry Specialist 0.048*** 0.275***
OfficeSize 0.048*** 0.337*** 0.129**
The sample consists of 36,606 firm-years between 2004 and 2014
(3,319 restatement firm-years). */**/*** represent statistical
significance at 10%/5%/1% levels (two-tailed). All continuous
variables are winsorized at the 1% and 99% percentiles. See
Appendix B for variable definitions.
Pearson correlation matrix
2
Table 4
Coeff. p-value
Constant -1.894 *** (<.0001)
Big4 0.383 *** (<.0001)
LogMV -0.017 (0.156)
Litigation 0.089 *** (0.000)
ActIssue 0.053 (0.166)
BM 0.097 *** (<.0001)
Leverage 0.258 *** (<.0001)
ROA 0.285 *** (0.001)
Loss 0.123 *** (<.0001)
Merger -0.011 (0.865)
Segments 0.016 *** (0.009)
ForeignOps 0.046 ** (0.047)
QReturn 0.002 (0.708)
QVolatility 0.034 *** (<.0001)
AssetTurnover 0.027 * (0.083)
Current -0.148 *** (0.004)
RSST 0.006 (0.859)
ChgA/R 0.028 (0.883)
ChgINV -0.205 (0.490)
%SoftAssets 0.065 (0.122)
ChgSales 0.008 (0.493)
ChgROA 0.014 (0.877)
AbChgEmp -0.013 (0.792)
OpLease 0.190 *** (<.0001)
RestateAnnounced 0.286 *** (<.0001)
HighPE 0.153 *** (<.0001)
HighVolatility -0.049 (0.299)
LowReturn_Sub 0.062 * (0.083)
HighVolatility_Sub -0.058 (0.213)
Year Fixed Effects
No. of Firm-Years (Misstatements)
Log liklihood
The sample consists of 36,606 firm-years between 2003 and 2013 (3,319
misstatement firm-years). */**/*** represent statistical significance at 10%/5%/1%
levels (two-tailed). All continuous variables are winsorized at the 1% and 99%
percentiles. See Appendix B for variable definitions.
-10582
Probit estimation of restatement on Big4
P(Restatement)
Yes
36,306 (3,319)
3
Table 5
Pred. Coeff. p-value Pred. Coeff. p-value
Constant ? -2.307 *** (0.004) ? -0.467 (0.136)
Big4 – -0.485 ** (0.034) + 0.631 *** (0.000)
LogMV ? 0.367 *** (0.000) ? -0.163 *** (0.000)
Litigation – -0.140 (0.164) + 0.155 *** (0.002)
ActIssue + -0.097 (0.527) + 0.090 (0.298)
BM + 0.220 *** (0.000)
Leverage + 0.531 *** (0.001)
ROA – 0.469 *** (0.009)
Loss + 0.258 *** (0.001)
Merger + -0.024 (0.883)
Segments + 0.065 *** (0.003)
ForeignOps + 0.162 ** (0.019)
QReturn – 0.009 (0.433)
QVolatility + 0.059 *** (0.002)
AssetTurnover ? 0.101 ** (0.014)
Current ? -0.372 *** (0.007)
RSST + -0.012 (0.752)
ChgA/R + -0.140 (0.526)
ChgINV + -0.400 (0.246)
%SoftAssets – 0.046 (0.311)
ChgSales – 0.004 (0.777)
ChgROA + 0.015 (0.885)
AbChgEmp – -0.021 (0.712)
OpLease + 0.189 *** (0.000)
RestateAnnounced + 0.301 *** (0.000)
HighPE + 0.140 *** (0.001)
HighVolatility + 0.052 (0.282)
LowReturn_Sub + 0.081 ** (0.030)
HighVolatility_Sub + 0.055 (0.280)
Year Fixed Effects
No. of Firm-Years (Misstatements)
Wald Chi-Square (df)
Log liklihood -10517
The sample consists of 36,606 firm-years between 2003 and 2013 (3,319 misstatement firm-years). */**/***
represent statistical significance at 10%/5%/1% levels (two-tailed). All continuous variables are winsorized at the
1% and 99% percentiles. See Appendix B for variable definitions.
Bivariate probit model with partial observability
P(Misstatement) P(Detection|Misstatement)
Yes
36,306 (3,319)
989 (52)
4
Table 6
Coeff. p-value
Constant -1.755 *** (<.0001)
Big4 0.281 *** (<.0001)
LogMV -0.035 *** (0.005)
Litigation 0.107 *** (<.0001)
ActIssue 0.066 (0.123)
BM 0.151 *** (<.0001)
Leverage 0.287 *** (<.0001)
ROA 0.363 *** (0.001)
Loss 0.128 *** (0.000)
Merger -0.059 (0.397)
Segments 0.013 ** (0.037)
ForeignOps 0.048 ** (0.043)
QReturn 0.008 (0.130)
QVolatility 0.036 *** (<.0001)
AssetTurnover 0.020 (0.225)
Current -0.135 ** (0.015)
RSST 0.029 (0.449)
ChgA/R -0.102 (0.652)
ChgINV 0.051 (0.875)
%SoftAssets 0.085 (0.054)
ChgSales 0.017 (0.315)
ChgROA 0.012 (0.910)
AbChgEmp 0.005 (0.929)
OpLease 0.183 *** (<.0001)
RestateAnnounced 0.295 *** (<.0001)
HighPE 0.171 *** (<.0001)
HighVolatility -0.057 (0.255)
LowReturn_Sub 0.031 (0.421)
HighVolatility_Sub -0.015 (0.759)
Year Fixed Effects
No. of Firm-Years (Misstatements)
Log liklihood
Panel A: Probit estimation of restatement on Big4 for a sample of Big
4 and 2nd tier auditors only
P(Restatement)
Yes
-9583
29,564 (3,096)
5
Table 6 (cont.)
Pred. Coeff. p-value Pred. Coeff. p-value
Constant ? -2.000 *** (0.002) ? -0.172 (0.702)
Big4 – -0.869 *** (0.006) + 0.806 *** (0.000)
LogMV ? 0.329 *** (0.000) ? -0.209 *** (0.000)
Litigation – -0.046 (0.636) + 0.145 ** (0.011)
ActIssue + -0.041 (0.791) + 0.090 (0.393)
BM + 0.265 *** (0.000)
Leverage + 0.453 *** (0.002)
ROA – 0.496 ** (0.014)
Loss + 0.215 *** (0.005)
Merger + -0.133 (0.351)
Segments + 0.043 ** (0.031)
ForeignOps + 0.126 ** (0.046)
QReturn – 0.022 * (0.056)
QVolatility + 0.057 *** (0.007)
AssetTurnover ? 0.064 * (0.079)
Current ? -0.266 ** (0.039)
RSST + 0.010 (0.814)
ChgA/R + -0.283 (0.300)
ChgINV + -0.124 (0.744)
%SoftAssets – 0.067 (0.187)
ChgSales – 0.017 (0.319)
ChgROA + 0.021 (0.865)
AbChgEmp – -0.008 (0.898)
OpLease + 0.182 *** (0.000)
RestateAnnounced + 0.330 *** (0.000)
HighPE + 0.157 *** (0.001)
HighVolatility + 0.054 *** (0.288)
LowReturn_Sub + 0.070 * (0.098)
HighVolatility_Sub + 0.065 (0.223)
Year Fixed Effects
No. of Firm-Years (Restatements)
Wald Chi-Square (df)
Log liklihood -9513
The sample consists of 29,564 firm-years between 2003 and 2013 (3,096 misstatement firm-years). 2nd Tier
auditors include Crowe Horwarth LLP, BDO USA LLP, Grant Thornton LLP, and McGladrey LLP. */**/***
represent statistical significance at 10%/5%/1% levels (two-tailed). All continuous variables are winsorized at
the 1% and 99% percentiles. See Appendix B for variable definitions.
Panel B: Bivariate probit model with partial observability for a sample of Big4 and 2nd tier auditors only
P(Misstatement) P(Detection|Misstatement)
Yes
29,564 (3,096)
1002 (52)
6
Table 7
Coeff. p-value
Constant -1.886 *** (<.0001)
Big4 0.367 *** (<.0001)
IndustrySpecialist 0.081 *** (0.001)
OfficeSize 0.000 (0.674)
LogMV -0.019 (0.107)
Litigation 0.090 *** (0.000)
ActIssue 0.052 (0.168)
BM 0.095 *** (<.0001)
Leverage 0.256 *** (<.0001)
ROA 0.293 *** (0.001)
Loss 0.124 *** (<.0001)
Merger -0.008 (0.902)
Segments 0.016 *** (0.010)
ForeignOps 0.045 * (0.050)
QReturn 0.002 (0.714)
QVolatility 0.034 *** (<.0001)
AssetTurnover 0.025 (0.110)
Current -0.147 *** (0.004)
RSST 0.007 (0.842)
ChgA/R 0.038 (0.844)
ChgINV -0.209 (0.480)
%SoftAssets 0.063 (0.135)
ChgSales 0.009 (0.480)
ChgROA 0.014 (0.881)
AbChgEmp -0.013 (0.795)
OpLease 0.194 *** (<.0001)
RestateAnnounced 0.283 *** (<.0001)
HighPE 0.156 *** (<.0001)
HighVolatility -0.051 (0.280)
LowReturn_Sub 0.062 * (0.082)
HighVolatility_Sub -0.059 (0.203)
Year Fixed Effects
No. of Firm-Years (Misstatements)
Log liklihood -10576
Panel A: Probit estimation of restatement on Big4 and other auditor
attributes
P(Restatement)
Yes
36,306 (3,319)
7
Table 7 (cont.)
Pred. Coeff. p-value Pred. Coeff. p-value
Constant ? -2.463 *** (0.001) ? -0.407 (0.201)
Big4 – -0.387 ** (0.046) + 0.579 *** (0.000)
IndustrySpecialist – 0.069 (0.530) + 0.078 * (0.075)
OfficeSize – -0.001 *** (0.004) + 0.001 *** (0.004)
LogMV ? 0.377 *** (0.000) ? -0.176 *** (0.000)
Litigation – -0.191 * (0.057) + 0.186 *** (0.000)
ActIssue + -0.070 (0.639) + 0.079 (0.366)
BM + 0.219 *** (0.000)
Leverage + 0.494 *** (0.001)
ROA – 0.431 ** (0.014)
Loss + 0.253 *** (0.001)
Merger + -0.019 (0.904)
Segments + 0.064 *** (0.003)
ForeignOps + 0.154 ** (0.019)
QReturn – 0.007 (0.486)
QVolatility + 0.055 *** (0.002)
AssetTurnover ? 0.097 ** (0.013)
Current ? -0.339 *** (0.008)
RSST + -0.012 (0.764)
ChgA/R + -0.123 (0.580)
ChgINV + -0.408 (0.241)
%SoftAssets – 0.029 (0.533)
ChgSales – 0.004 (0.760)
ChgROA + 0.017 (0.871)
AbChgEmp – -0.026 (0.660)
OpLease + 0.190 *** (0.000)
RestateAnnounced + 0.301 *** (0.000)
HighPE + 0.145 *** (0.000)
HighVolatility + 0.051 (0.302)
LowReturn_Sub + 0.085 ** (0.045)
HighVolatility_Sub + 0.053 (0.297)
Year Fixed Effects
No. of Firm-Years (Misstatements)
Wald Chi-Square (df)
Log liklihood -10504
The sample consists of 36,606 firm-years between 2003 and 2013 (3,319 misstatement firm-years). */**/***
represent statistical significance at 10%/5%/1% levels (two-tailed). All continuous variables are winsorized at
the 1% and 99% percentiles. See Appendix B for variable definitions.
Panel B: Bivariate probit model with partial observability on Big 4 and other auditor attributes
P(Misstatement) P(Detection|Misstatement)
Yes
36,306 (3,319)
905 (56)
8
Table 8
N Mean Median
LateralSwitchBig4 96 310.04 242.50
SwitchDown 34 419.21 429.50
p-value for test of difference 0.02 0.01
LateralSwitchNonBig4 168 345.55 296.50
SwitchUp 11 261.91 223.00
p-value for test of difference 0.25 0.25
Duration
Panel A: Univariate comparison of duration on auditor switch categories
Coeff. p-value
Constant 363.971 *** (<.0001)
SwitchDown 65.258 * (0.051)
SwitchUp -89.361 * (0.073)
LateralSwitchNonBig4 -31.708 (0.129)
LogMV -17.573 ** (0.015)
BM -0.323 (0.382)
Leverage 0.766 (0.417)
%SoftAssets 28.186 (0.406)
ROA 0.194 (0.591)
p-value of F-test:
(SwitchUp = LateralSwitchNonBig4 )
Year Fixed Effects
No. of Firms
R2
The sample consists of 309 firm-years between 2003 and 2013 with a
restatement that switched auditors between the end of the restatement and the
disclosure date of the restatement. */**/*** represent statistical significance at
10%/5%/1% levels (two-tailed). p-values are in parentheses. All continuous
variables are winsorized at the 1% and 99% percentiles. See Appendix B for
variable definitions.
Panel B: OLS regression of duration on auditor switch categories
Duration
0.42
309
0.12
Yes