Separating the Probability of Committing and Detecting

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Preliminary Draft: Please do not cite or quote without authors’ permission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.

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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).

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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).

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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

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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

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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

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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

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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

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“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

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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

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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

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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.

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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.

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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)”

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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

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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

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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).

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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

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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


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)


ChgSales 0.017 (0.315)

ChgROA 0.012 (0.910)

AbChgEmp 0.005 (0.929)

OpLease 0.183 *** (<.0001)


HighPE 0.171 *** (<.0001)


LowReturn_Sub 0.031 (0.421)


Year Fixed Effects


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.)


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)


HighPE + 0.157 *** (0.001)

HighVolatility + 0.054 *** (0.288)

LowReturn_Sub + 0.070 * (0.098)


Year Fixed Effects

No. of Firm-Years (Restatements)


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


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)


ChgSales 0.009 (0.480)

ChgROA 0.014 (0.881)

AbChgEmp -0.013 (0.795)

OpLease 0.194 *** (<.0001)


HighPE 0.156 *** (<.0001)


LowReturn_Sub 0.062 * (0.082)


Year Fixed Effects



Panel A: Probit estimation of restatement on Big4 and other auditor

attributes

P(Restatement)

Yes

36,306 (3,319)

7

Table 7 (cont.)


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)


HighPE + 0.145 *** (0.000)

HighVolatility + 0.051 (0.302)

LowReturn_Sub + 0.085 ** (0.045)


Year Fixed Effects




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


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

Documents

Separating the Probability of Committing and Detecting