Stock price crash risk and auditor-client contracting

ABSTRACT

Using a large sample of Chinese-listed firms for the period of 2001–2014, we find that the auditors of clients with higher crash risk tend to charge higher fees, are more likely to issue modified audit opinions, and have a higher turnover tendency, which is consistent with the notion that a client’s exposure to higher crash risk imposes greater engagement risk on its auditor. Consistent with crash risk increasing auditor engagement risk, we find that crash risk is associated with a client’s poor accounting quality and high frequency of restatements, although auditors exert higher efforts when observing clients’ high crash risk. Taken altogether, our results suggest that a client’s crash risk serves as an informative signal for engagement risk, and that this factor plays a crucial role in shaping auditor-client contracting relationships.

KEYWORDS:

• Crash risk
• auditor-client contracting
• engagement risk

1. Introduction

The global financial crisis in 2008 and the recent stock market turmoil in China have caused huge losses of shareholder wealth and reduced investor confidence in the market. These market-wide stock price crashes have subsequently attracted considerable attention from academic researchers and security regulators, with respect to the causes or determinants of the likelihood that an individual firm will experience a large scale, abrupt decline in stock price or simply firm-level crash risk. At the firm level, stock price crashes are damaging to both the investors and firms involved.¹ Stock price crashes shake investor confidence in the firm’s management, depress demand for its securities, and reduce the liquidity of the stock concerned, thereby causing substantial losses in market value.

Regarding the internal forces that drive stock price crashes at the firm level, Jin and Myers (2006) develop a model in which agency conflicts between inside managers and outside investors incentivise managers to engage in bad news hoarding. According to the model of Jin and Myers (2006), however, managers can withhold bad news inside the firm only up to a certain threshold level. If the cost of bad news hoarding is less than the associated benefit, the managers tend to release the hidden bad news all at once, which leads to a stock price crash. In the model of Jin and Myers (2006), the managerial incentives for bad news hoarding are the key drivers that cause a firm’s stock price crash to occur.

Subsequent studies provide empirical evidence in support of the theory of Jin and Myers (2006) by documenting significant associations of crash risk with various firm-specific factors and/or manager-specific incentives that facilitate or constrain managerial bad news hoarding (e.g. Hutton, Marcus, & Tehranian, 2009; Kim, Li, Lu, & Yu, 2016; Kim, Li, & Zhang, 2011a, 2011b; Kim, Wang, & Zhang, 2016; Kim & Zhang, 2014, 2016; Robin & Zhang, 2015). All of these prior studies focus mainly on firm-specific determinants of crash risk from the perspective of outside investors. To date, however, prior research has paid little attention to the consequences or outcomes of high crash risk to outside investors in general, and to other (non-investor) stakeholders such as external auditors in particular. As a result, little is known about how outside stakeholders, or their contractual relationships with a firm, are influenced by high crash risk at the firm level.

To fill this gap, our study investigates the effects of crash risks on auditors and auditor-client contracting relationships. Auditors play an important role in monitoring the process of information production and dissemination by inside managers. Auditors search for information beyond a firm’s financial performance, and they respond to various risks identified during the audit engagement process. Therefore, observing the behaviour of auditors helps us to understand their risk assessment models. Specifically, we examine a question of whether auditors take into account their clients’ crash risk when assessing their audit engagement risks, and whether they perceive their engagement risk to be higher for their clients with greater exposure to crash risk. To this end, our analysis focuses on the effects of firm-level crash risk on various aspects of auditor-client contracting relationships, including audit pricing, audit opinion formation, and auditor turnover.

We posit that crash risk increases an auditor’s assessment of engagement risk. Crash risk affects engagement risk assessment because it increases audit risk. The term ‘audit risk’ refers to ‘the risk that an auditor may unknowingly fail to appropriately modify his or her opinion on financial statements that are materially misstated’ (DeFond, Lim, & Zang, 2016). According to Hogan and Wilkins (2008) and DeFond et al. (2016), the audit risk can be described by the product of the likelihood that the firm conducts a material error (‘inherent risk’), the likelihood that internal controls will not prevent or detect a material error (‘control risk’), and the likelihood that the auditor fails to detect that material error (‘detection risk’). High crash risk (or extremely negative tail risk) signals an increase in inherent risk, control risk and detection risk for the following reasons. First, bad news hoarding by managers is considered to be the most important firm-level factor that causes stock price crashes (e.g. Bleck & Liu, 2007; Jin & Myers, 2006). In terms of financial reporting, earnings management is often used to hinder the firm-specific information flow into the securities market (Hutton et al., 2009). For example, untimely loss recognition and aggressive tax avoidance are often used by managers to conceal bad news, and these activities increase inherent risk and are found to be positively associated with crash risk (Kim et al., 2011a; Kim & Zhang, 2016). In addition, aggressive financial reporting and lack of conservatism tend to increase the incidence of financial restatements (Ettredge, Huang, & Zhang, 2012). Second, several recent papers show that high crash risk is correlated with ineffective internal control (Kim, Yeung, & Zhou, 2019; Lobo, Wang, Yu, & Zhao, 2017), indicating that firms with high crash risk tend to have high control risk. In addition, higher crash risk signals higher detection risk. Information opacity has been shown to facilitate bad news accumulation before the resultant stock price crashes (DeFond, Hung, Li, & Li, 2015; Hong, Kim, & Welker, 2017; Hutton et al., 2009; Kim et al., 2016; Kim & Zhang, 2016). Meanwhile, information opacity increases the information asymmetry between auditors and management (Kim & Zhang, 2016), which makes it harder for auditors to detect hidden material errors. The above discussions, taken together, indicate that high crash risk engenders high audit risk by increasing all three components of audit engagement risk, that is, inherent risk, control risk and detection risk.

A client’s exposure to high crash risk may also increase an auditor’s assessment of engagement risk by raising both the auditor’s litigation risk and reputation risk, which are two important elements of auditor business risk (DeFond et al., 2016). To the extent that high crash risk increases the likelihood of poor earnings quality (and thus the likelihood of financial restatements in the future), which in turn increases the possibility of auditors being sued or investigated by regulators (Heninger, 2001). In addition, stock price crashes attract media attention. The dissemination of stock crash news hurts the auditor’s reputation in the long run, and further increases the likelihood of the auditor being subjected to regulatory enforcement measures (Carroll & McCombs, 2003; Dyck, Volchkova, & Zingales, 2008).

To analyse the effects of crash risk on auditors’ assessments of engagement risk, we examine auditors’ strategic responses to their clients’ exposure to high crash risk. Auditors have several strategic means of mitigating high expected engagement risks (DeFond et al., 2016; DeFond & Zhang, 2014). The first strategy is to increase audit quality through additional efforts (e.g. Davis, Ricchiute, & Trompeter, 1993; Kim, Liu, & Zheng, 2012; Simunic, 1980). Alternatively, auditors can pass the risk on to the clients by charging a risk premium (e.g. Bell, Landsman, & Shackelford, 2001). Both the increased effort and risk premium are reflected in the higher audit fees. The second strategy for auditors to reduce their engagement risk is to lower their threshold for issuing modified audit opinions. This strategy, in turn, lowers their litigation risk and reduces the likelihood of large financial settlements if they are named in lawsuits (Kaplan & Williams, 2013). Finally, auditors can completely avoid such risk by dropping risky clients (Kim & Park, 2014; Shu, 2000). Therefore, if high crash risk increases auditors’ assessments of engagement risk, we expect them to charge higher audit fees, issue more modified audit opinions, and resign more frequently.

Consistent with our expectation, we find that auditors tend to charge higher audit fees, are more likely to issue modified auditor opinions, and more likely to leave when clients are exposed to higher crash risk. Our results are robust to controlling for firm fixed-effect regressions and using the 2SLS regression. The results of path analyses show that inherent risk and auditor business risk are valid mechanisms through which crash risk affects auditor engagement risk.

Furthermore, we find that auditors’ responses to their clients’ exposure to high crash risk and their strategic choices vary with the characteristics of both the clients and auditors, such as state-owned enterprises, the existence of audit committees, size of audit firms and the marketisation of firms’ located provinces. Next, in additional tests, we provide evidence that firms exhibit poorer accounting quality and higher likelihood of financial report restatements during periods of higher crash risk, even auditors put more efforts when they face higher engagement risk signalled by high crash risk.

Our study contributes to the literature in the following ways. First, it adds to the crash risk literature. Although a growing body of prior research has explored the firm-specific determinants of crash risk, to our knowledge, few studies have investigated the consequences of a firm’s exposure to high crash risk. Even fewer studies have examined this issue from the perspective of outside stakeholders other than equity investors. Our paper is closely related to Hackenbrack, Jenkins, and Pevzner (2014). Their study uses changes in audit fee as a proxy for information opacity and show audit fee increases in advance of crash occurrences, a public realisation of ‘bad news’. The change in audit fee is not a direct consequence of crash but caused by some determinants of crash likelihood. Through an analysis of the relationship between auditor-client contracting and clients’ levels of crash risk, we find that auditors perceive higher engagement risk from clients with higher crash risk. In addition, our finding that auditors charge higher auditor fees to clients with higher crash risk represents a direct cost of crash risk to the client firms involved.

Second, we contribute to the literature on the analysis of audit risk. Previous studies have shown that auditors use two types of information in their risk assessment models, that is: (i) information within the firm, such as clients’ conservatism (DeFond et al., 2016), internal control weakness (Hogan & Wilkins, 2008), or the managers’ ability and compensation (Billings, Gao, & Jia, 2014; Krishnan & Wang, 2015); and (ii) information outside the firm, such as short selling interests (Cassell, Drake, & Rasmussen, 2011). Our study documents another source, namely clients’ exposure to high crash risk, which is instructive for auditors in performing their engagement risk assessments. Hackenbrack et al. (2014) argue that auditors hold information about their clients’ idiosyncratic risk, which has the predictive power of future crash likelihood. Our paper is different from theirs. In the Hackenbrack et al. (2014) model, auditors do not get any new information from crashes as change in negotiated audit fee already determined before crash occurrences. The private information of auditors, measured by change in negotiated audit fee, comes from channels other than crash risk and turns out to be a determinant of future crash. However, we examine whether auditor get any new information about firms’ riskiness from observing high crash risk.²

Finally, our study also sheds light on auditor behaviour in China. Auditors play an even more crucial role in mitigating agency problems in emerging markets like China, where conventional corporate governance mechanisms typically do not function well (Choi & Wong, 2007; Fan & Wong, 2005). Therefore, it is important to better understand whether Chinese auditors care about signals that are informative to client risk and how they respond to them, which sheds light on important questions such as whether Chinese auditors’ behaviour is shaped by litigation risk and how their attitude towards clients’ risk influences reporting quality. Our study provides useful insights into how auditors respond to their clients’ exposure to high crash risk, and how the clients’ crash risk plays a role in shaping auditor-client contracting relationships in emerging economies like China.

The next section introduces the institutional background for Chinese auditors, discusses the related literature and develops our hypotheses. Section 3 discusses our sample and the construction of variables. Section 4 describes the model specifications and empirical results, and Section 5 presents the findings from additional tests of our analysis. Section 6 offers our conclusions.

2. Literature review and hypotheses development

2.1. Institutional background for Chinese auditors

Although China’s Law on Certified Public Accountants and the Company Law, released in 1993, clarified the legal consequences for firms and persons that were liable for financial fraud, the number of CPA firms brought to court for civil or criminal liability was negligible in the 1990s (Pistor & Xu, 2005). The law was ambiguous in auditor liability and explicitly forbade class action (Li & He, 2000). In general, the litigation risk of CPA firms was low in the 1990s. In the 2000s, in response to the break out of a series of accounting frauds, several litigation reforms were conducted to increase auditors’ responsibilities in auditing failures.³ The Chinese legal environment significantly changed and affected auditor behaviour. Chen, Sun, and Wu (2010) find that after 2001, the propensity to issue MAOs is positively associated with client importance, while it was negatively associated with client importance prior to 2001. The finding indicates a large institutional improvement after 2001.

During our sample period of 2001 to 2014, regulatory sanctions and legal lawsuits against firms misconducting accounting-related issues are quite common, while auditors bear the joint responsibilities. Chinese CPA firms operate in an environment with reasonable litigation exposure after 2001.

2.2. Crash risk and auditors’ engagement risk assessment

Stock price crashes cause huge losses in shareholder wealth, and do so in an abrupt manner. Cremers, Halling, and Weinbaum (2015) document a 3.5–5.1% drop in expected annual stock returns with a two-standard-deviation increase in jump factor loadings. Crash risk is fundamentally different from traditional risks in several aspects. First, while the traditional risk-return uncertainty is symmetric, in that it involves both losses and gains, crash risk is asymmetric. The asymmetric nature of crash risk refers to the likelihood of extreme losses or negative tail risk. Second, compared with the traditional business risks, the uniqueness of crash risk is its ‘extreme’, which happens occasionally but causes large-scale wealth destruction to investors. Hutton et al. (2009) and Kim et al. (2011a) argue that crash risk exposure reflects the extreme information asymmetry, and we expect its extreme could be informative for auditors’ risk assessment, in addition to fundamental and information risks. Controlling for other risk factors, previous literature still documents various influences of crash risk (e.g. An, Li, & Yu, 2015; Bollerslev & Todorov, 2011; Srivastav, Keasey, Mollah, & Vallascas, 2017). Furthermore, crash risk is captured by the third moment of return distribution, which is a higher moment of return volatility. The traditional volatility risk, which is based on the second moment of return distribution, reflects managerial risk preference, and investors can control this risk via their portfolio diversification strategies. However, unlike this traditional risk, crash risk (or extreme negative tail risk) is based on the third moment of return distribution, typically reflects managerial incentives for bad news hoarding rather than managerial risk preference, and thus it cannot be diversified away.

Both Bollerslev and Todorov (2011) and Conrad, Dittmar, and Ghysels (2013) find that investors require compensation for crash risk. Surprisingly, however, prior studies have given little consideration to questions concerning the aftermath or consequences of a firm’s exposure to high crash risk. As a result, little is known about how crash risk affects outside stakeholders, and particularly third parties other than the firm and its shareholders. To fill this void in previous research, our study explores how the crash risk of a client firm influences the behaviour of its auditors or the audit-client contracting relationships. Specifically, our analysis focuses on how a client firm’s exposure to high crash risk can change its auditor’s assessment of engagement risk. To this end, we first discuss crash risk, and then consider auditors’ engagement risk.

High crash risk can be driven by both market-wide and firm-specific factors. The identified market-wide factors include market bubbles (Blanchard & Watson, 1982), investor heterogeneity (Chen, Hong, & Stein, 2001; Hong & Stein, 1999) and short-sales constraints (Hong & Stein, 2003). Managerial incentives for bad news hoarding are considered the most important firm-specific factors that drive stock price crashes at the firm level (Bleck & Liu, 2007; Hutton et al., 2009; Jin & Myers, 2006). Thus, factors that incentivise managers to engage in bad news hoarding and other financial obfuscation via aggressive financial reporting in turn increase auditors’ engagement risk (e.g. Ahmed & Duellman, 2012; Cheng & Warfield, 2005; Kim et al., 2011a, 2011b, 2016).

Auditors’ engagement risk can be decomposed into (i) audit risk and (ii) auditor business risk. Audit risk is determined by ‘inherent risk’, ‘control risk’, and ‘detection risk’ (DeFond et al., 2016; Hogan & Wilkins, 2008). As discussed previously, high crash risk engenders high audit risk by increasing all three components of audit risk. Meanwhile, high crash risk also indicates higher litigation risk and reputation risk because of the poor earnings quality and high media attention accompany with high crash risk. The legal environment in China is not as sophisticated as that in the developed markets, but has been improving since the late 1990s. Chinese auditors have grown increasingly concerned about auditor litigation risk and the associated danger of reputation loss (Chen, Chen, Lobo, & Wang, 2011). Altogether, high crash risk leads auditors to adjust their engagement risk upward for clients with high crash risk.

2.3. Auditors’ strategic responses to crash risk

Drawing upon our discussions in the preceding section, we expect that a client’s exposure to high levels of crash risk increase the engagement risk assessed by auditors. We next develop our hypotheses about how Chinese auditors respond to high crash risk.

To mitigate the increased engagement risk, auditors have three strategic alternatives (DeFond et al., 2016). The first alternative is to charge higher audit fees. Several studies show that auditors charge higher fees to cover the additional efforts they exert to mitigate higher audit risks (Lobo & Zhao, 2013), and/or to compensate for higher risks that cannot be avoided through greater audit efforts (Bedard & Johnstone, 2004; Bell et al., 2001). To compensate for both additional effort and unavoidable risk, auditors may charge higher audit fees to clients that are exposed to higher crash risk. In the Chinese setting, both Firth, Mo, and Wong (2012) and He, Pan, and Tian (2017) find that auditors charge higher fees when their cap on the liability exposure of negligence is removed and thus facing higher litigation costs. Therefore, we propose and test the following hypothesis, stated in alternative form:

H1: All else being equal, auditors charge higher audit fees to client firms that have higher crash risk.

The second strategy of auditors is to reduce audit risk by lowering their threshold of issuing MAOs. Prior research documents that auditors increase their likelihood of issuing MAOs for clients that face high litigation risk (Kaplan & Williams, 2013) and for clients with large accruals (Francis & Krishnan, 1999). Blay, Geiger, and North (2011) argue that auditors use going-concern MAOs as a channel to communicate client risk to the capital market. Issuing going-concern opinions to financially distressed firms lowers the risk of alleged audit failure, auditor litigation, and litigation settlements (Carcello & Palmrose, 1994; Kaplan & Williams, 2013). For Chinese auditors, several studies (Chen et al., 2010; Firth et al., 2012; He et al., 2017) document that auditors lower their MAO issuance threshold when facing higher litigation risk. We therefore propose and test our second hypothesis as follows, stated in alternative form:

H2: All else being equal, auditors are more likely to issue modified audit opinions for their client firms that have higher crash risk.

Finally, if the increased audit efforts, risk premia, and/or lower threshold to issue MAOs cannot reduce the auditors’ engagement risk to a tolerable level, the auditors can choose to avoid that risk completely by dropping their high-risk clients. Prior research finds evidence that auditors are likely to resign from ongoing engagement with high-risk clients and less likely to accept risky clients (e.g. Bedard & Johnstone, 2004; Johnstone & Bedard, 2003; Kim & Park, 2014; Shu, 2000). Also, a bunch of studies (e.g. Hogan & Martin, 2009; Schroeder & Hogan, 2013) indicate auditors shed clients with increased risk, while facing increased supply shock or excess capacity, indicating auditors keep balancing client risk in their portfolio strategy. Hu, Cao, and Zheng (2012) find that auditor is more likely to resign financial restatement companies, suggesting that Chinese auditors also select the resignation strategy to manage risk. Based on the preceding discussion, we propose and test our third hypothesis as follows, stated in alternative form:

H3: All else being equal, auditor turnover rate is higher for clients that have crash risks above a tolerable level.

The validity of our hypotheses is subject to two conditions that (i) crash risk contains additional information for auditors; and (ii) auditors realise the usefulness of crash risk in risk assessments. Although previous literature shows that crash risk provides information beyond business risk and information risk to market participants and board of directors (Bollerslev & Todorov, 2011; Srivastav et al., 2017), it is still not clear whether it can provide auditors with additional information when auditors have an advantage to observe and consider many other risks in their risk assessment. Furthermore, even if crash risk, which is publicly observable in capital market, can provide new information, auditors may not realise it. In such cases, auditors will not respond to high crash risk. Therefore, whether auditors find crash risk, which is a proxy for extreme information asymmetry, to be informative for assessing their engagement risk, and use this information in their risk assessments is ultimately an empirical question. Our paper aims to answer the question by examining whether and how auditors respond to clients’ exposure to high crash risk.

3. Sample and variable construction

3.1. Sample

Our initial sample consists of all of the Chinese firms listed on the Shanghai and Shenzhen Stock Exchanges from 2001 to 2014 that are covered by the China Securities Markets and Accounting Research (CSMAR) database (from which we collect our data).⁴ Our sample period starts from 2001, when audit fees were first required to be disclosed and when all audit firms became financially independent from local government agencies (Chen et al., 2011). As we discussed in the institutional background, Chinese auditors’ litigation exposure improved after 2001. From the initial 25,951 observations, we delete 311 observations from the financial industry. We do so because the nature of business operations and thus the accounting numbers for firms in this industry differ from those in non-financial industries, and because the financial industry is subject to strict government regulations. After this, we exclude additional sets of observations that do not have sufficient data to calculate the variables included in each of our three models of auditing behaviour, and leave a sample of: (i) 17,965 observations for the audit fee model, (ii) 19,303 observations for the audit opinion model, and (iii) 16,962 observations for the auditor turnover model.⁵

3.2. Measuring firm-specific crash risk

The key variable of interest in this study is firm-specific crash risk, rather than market-wide crash risk. We construct two measures of firm crash risk following prior studies (Chen et al., 2001; Kim et al., 2011a, 2011b). The first measure is the negative conditional return skewness (NCSKEW), which is computed by taking the negative of the third moment of firm-specific weekly returns (after netting the market-wide component) for each sample year and dividing it by the standard deviation of firm-specific weekly returns raised to the third power. The firm-specific weekly return is defined as the natural logarithm of 1 plus the residual return from the expanded market model regression, including the lead and lag returns for the market index return.

Our second measure is the down-to-up volatility (DUVOL) measure of crash likelihood, which is computed as follows. For each firm over a fiscal year period, each week is classified as an ‘up’ (‘down’) week if the firm-specific weekly return is above (below) the annual mean. Then we calculate the standard deviation separately for the ‘up’ and ‘down’ subsamples. The DUVOL measure is the natural logarithm of the ratio of the standard deviation of the ‘down’ weeks to that of the ‘up’ weeks. Further details on the construction of these variables can be found in Hutton et al. (2009) and Kim et al. (2011a, 2011b).

4. Model specifications and empirical results

4.1. Crash risk and audit fees: test of H1

To test whether audit fees reflect crash risk (H1), we estimate the following regression model:

(1) $\begin{array}{rl}& LNFE{E}_{it}={\beta }_0+{\beta }_{1}CRAS{H}_{it-1}+{\beta }_{2}SIZ{E}_{it}+{\beta }_{3}AG{E}_{it}+{\beta }_{4}LE{V}_{it}+{\beta }_{5}QUIC{K}_{it}+{\beta }_{6}OC{F}_{it}+{\beta }_{7}RO{A}_{it}\\ & +{\beta }_{8}LOS{S}_{it}+{\beta }_{9}INV{R}_{it}+{\beta }_{10}ORE{C}_{it}+{\beta }_{11}M{B}_{it}+{\beta }_{12}GROWT{H}_{it}+{\beta }_{13}SEGMEN{T}_{it}\\ & +{\beta }_{14}ISSU{E}_{it}+{\beta }_{15}MERG{E}_{it}+{\beta }_{16}MA{O}_{it}+{\beta }_{17}BI{G}_{it}+{\beta }_{18}TENUR{E}_{it}+{\beta }_{19}LOCA{L}_{it}\\ & +{\beta }_{20}FOREIG{N}_{it}+{\beta }_{21}SO{E}_{it}+{\beta }_{22}RPTLOA{N}_{it}+{\beta }_{23}OWNE{R}_{it}\\ & +{\beta }_{24}MARKETINDE{X}_{it}+{\beta }_{25}LAGSDRE{T}_{it}+{\beta }_{26}LAGZSCOR{E}_{it}+{\beta }_{27}LAGI{C}_{it}\\ & +{\beta }_{28}LAGD{A}_{it}+{\beta }_{29}LAGRESTATE{A}_{it}+\sum Industry+\sum Year+{\epsilon }_{it}\end{array}$(1)

where LNFEE is the natural logarithm of total audit fees in the current year, and CRASH refers to our two crash measures (NCSKEW or DUVOL). In the preceding audit fee model, we use crash risk lagged by 1 year, and lagged CRASH refers to lagged NCSKEW or to lagged DUVOL, denoted by LAGNCSKEW or LAGDUVOL, respectively.⁶ All of the other variables except for CRASH and last five control variables are measured in the current year.

Following prior research (e.g. Hay, Knechel, & Wong, 2006; Kim et al., 2012), we control for firm characteristics, auditor attributes and market development, as these characteristics have been documented to have an effect on auditor fees. Table 1 provides detailed definitions of all of the variables. In all of the models, we winsorise all of the continuous variables at the top and bottom 1%. We report robust standard errors clustered by firm in all models, other than models including firm-fixed effects.

Table 1. Variable definitions.

Variables	Definitions
Dependent variables
LNFEE	Natural logarithm of total audit fees paid to the auditor in the current year.
MAO	1 if the audit opinion in the current year is a modified opinion, and 0 otherwise. Modified audit opinions include unqualified opinions with explanatory notes, qualified opinions, disclaimer opinions, and adverse opinions.
TURNOVER	1 if the company changes its audit firm in the current year, and 0 otherwise. Turnovers caused by CPA firms’ merger are not regarded as auditor turnover.
RESTATE	1 if the current-year annual report of the firm is subsequently restated, and 0 otherwise.
DA	Absolute value of performance-adjusted discretionary accruals based on modified-Jones model in the current year, as defined in Kothari et al. (2005).
AUDITLAG	Natural logarithm of days gap between financial report date and audit report date.
Test variables
NCSKEW	Negative skewness of firm-specific weekly returns in the current year, as defined by Kim et al. (2011a, 2011b).
DUVOL	Down-to-up volatility of firm-specific weekly returns in the current year, as defined by Kim et al. (2011a, 2011b).
Instrument variables
POSTSHO	1 if after the company stock is eligible for short selling, and 0 otherwise.
Mediator variables
SANCTION	1 if the company receives regulatory sanctions for accounting-related reporting issues in the current year, and 0 otherwise.
LAWSUIT	1 if the company and/or its auditor is sued within two years after receiving regulatory sanction for accounting-related reporting issues, and 0 otherwise.
Control variables
SIZE	Natural logarithm of total assets at the end of the current year.
AGE	Natural logarithm of 1 plus the number of years the company is listed on the stock exchange.
LEV	Total liabilities divided by total assets at the end of the current year.
QUICK	Current assets minus inventories divided by current liabilities at the end of the current year.
OCF	Operating cash flow divided by total assets at the end of the current year.
ROA	Net income before extraordinary items, scaled by the beginning balance of total assets.
LOSS	1 for firms reporting losses in the current year, and 0 otherwise.
INVR	Inventory divided by total assets at the end of the current year.
OREC	Accounts receivable divided by total assets at the end of the current year.
MB	Market-to-book ratio of common stockholders’ equity at the end of the current year.
GROWTH	Difference between current- and prior-year sales, divided by prior-year sales.
SEGMENT	Square root of the number of business segments.
ISSUE	1 if the company issues new shares in the current year, and 0 otherwise.
MERGE	1 if the company had a merger or acquisition in the current year, and 0 otherwise.
BIG	1 if the company is audited by a Top 8 CPA firm (as defined by total client assets over the sample period), and 0 otherwise.
TENURE	Number of years the company is audited by the same audit firm after its IPO.
LOCAL	1 if the registered province of the auditor is same as that of the company, and 0 otherwise.
FOREIGN	1 for firms issuing H-shares or B-shares, and 0 otherwise.
SOE	1 if the firm’s ultimate shareholder is a government entity, and 0 otherwise.
RPTLOAN	The amount of inter-corporate lending from the company to its controlling shareholder, divided by total assets at the end of the current year.
OWNER	Percentage of ownership held by the controlling shareholder.
MARKETINDEX	Decile ranking (0–9, divided by 9) of the marketisation index of Fan et al. (2010) for the province in which the firm is located. For years after 2009, we continue to use the index of year 2009, as the cross-province rankings change very little over time. Our definition is the same as Guan, Su, Wu, and Yang (2016).
EM	1 if an observation meets any of the following criteria: (1) firms with a small profit (0 < ROA ≤ 1%), (2) loss-making firms with a reported ROA that is lower than the median value of the non-positive ROAs of all of the listed firms and (3) firms with ROEs that are marginally above the CSRC’s rights offering requirements as specified for different periods (6-7% or 10-11% for 1999–2000, and 6-7% for a lower bottom-line ROE or recurring ROE after 2000), following footnote 12 of Chen et al. (2010).
SDRET	Standard deviation of weekly returns in the current year.
ZSCORE	Bankruptcy score in the current year, as defined in Altman (1968).
IC	Natural logarithm of the firm’s internal control index, as provided by DIB database.
RESTATEA	1 if the company announces the financial report restatement in the current year, and 0 otherwise.

For the lagged value of variable X, we use LAGX.

Panel A of Table 2 reports the summary statistics of the variables used in Equation (1). Columns 1 and 2 in Panel B of Table 2 present the results of the ordinary least squares (OLS) regressions in Equation (1), with lagged NCSKEW and lagged DUVOL as the proxies for crash risk in the two columns, respectively. As shown in columns 1 and 2, we find that the coefficients on both measures of crash risk are positive and significant (0.007 with t = 2.004, and 0.011 with t = 2.594, respectively). In terms of economic magnitude, one standard deviation increase in crash risk measures increase audit fee by 0.7%-0.9%. These findings are consistent with H1, suggesting that higher crash risk is associated with higher audit fees in the following year.

Table 2. Analysis of crash risk and audit fees.

Panel A: Descriptive statistics
Variables	Mean	SD	P25	P50	P75	N
Dependent variables
LNFEE	13.287	0.687	12.899	13.218	13.592	17,965
Test variables
LAGNCSKEW	−0.191	0.968	−0.779	−0.185	0.423	17,965
LAGDUVOL	−0.127	0.790	−0.639	−0.149	0.384	17,965
Control variables
SIZE	21.686	1.230	20.849	21.568	22.376	17,965
AGE	2.249	0.492	1.792	2.303	2.639	17,965
LEV	0.511	0.231	0.353	0.508	0.648	17,965
QUICK	1.260	1.636	0.526	0.833	1.330	17,965
OCF	0.046	0.080	0.003	0.045	0.090	17,965
ROA	0.026	0.071	0.009	0.029	0.055	17,965
LOSS	0.128	0.334	0	0	0	17,965
INVR	0.169	0.155	0.065	0.130	0.218	17,965
OREC	0.109	0.103	0.027	0.080	0.160	17,965
MB	3.499	3.726	1.604	2.506	4.118	17,965
GROWTH	0.204	0.579	−0.031	0.116	0.289	17,965
SEGMENT	1.467	0.485	1	1.414	1.732	17,965
ISSUE	0.083	0.276	0	0	0	17,965
MERGE	0.679	0.467	0	1	1	17,965
MAO	0.072	0.259	0	0	0	17,965
BIG	0.283	0.451	0	0	1	17,965
TENURE	6.074	4.158	3	5	9	17,965
LOCAL	0.393	0.488	0	0	1	17,965
FOREIGN	0.102	0.303	0	0	0	17,965
SOE	0.606	0.489	0	1	1	17,965
RPTLOAN	0.003	0.017	0	0	0	17,965
OWNER	0.376	0.162	0.249	0.354	0.499	17,965
MARKETINDEX	0.455	0.301	0.222	0.444	0.667	17,965
LAGSDRET	0.124	0.051	0.088	0.112	0.148	17,965
LAGZSCORE	4.344	5.884	1.506	2.667	4.732	17,965
LAGIC	6.198	1.373	6.420	6.524	6.579	17,965
LAGDA	0.055	0.054	0.017	0.038	0.074	17,965
LAGRESTATEA	0.004	0.063	0	0	0	17,965
Panel B: OLS regression of audit fee model
	(1)	(2)	(3)	(4)
	OLS	OLS	OLS	OLS
Dependent variable	LNFEE	LNFEE	LNFEE	LNFEE
LAGNCSKEW	0.007**		0.006**
	(2.004)		(2.242)
LAGDUVOL		0.011***		0.008***
		(2.594)		(2.673)
SIZE	0.377***	0.377***	0.273***	0.273***
	(39.837)	(39.852)	(23.247)	(23.264)
AGE	−0.075***	−0.075***	−0.096**	−0.095**
	(−4.182)	(−4.179)	(−2.247)	(−2.239)
LEV	0.123***	0.123***	0.068**	0.067**
	(3.160)	(3.155)	(2.028)	(2.017)
QUICK	−0.023***	−0.024***	−0.012***	−0.012***
	(−4.802)	(−4.816)	(−2.885)	(−2.904)
OCF	0.084	0.084	0.036	0.036
	(1.473)	(1.468)	(1.044)	(1.041)
ROA	−0.139	−0.133	−0.041	−0.038
	(−1.293)	(−1.238)	(−0.604)	(−0.557)
LOSS	0.022	0.022	0.003	0.003
	(1.393)	(1.410)	(0.269)	(0.287)
INVR	−0.162***	−0.162***	−0.131***	−0.131***
	(−3.131)	(−3.131)	(−2.652)	(−2.654)
OREC	0.161**	0.161**	0.191***	0.190***
	(2.312)	(2.311)	(2.847)	(2.841)
MB	0.009***	0.009***	0.003***	0.003***
	(5.837)	(5.882)	(3.149)	(3.193)
GROWTH	−0.017***	−0.017***	−0.005	−0.005
	(−2.992)	(−2.976)	(−1.084)	(−1.076)
SEGMENT	0.063***	0.063***	0.032***	0.032***
	(4.108)	(4.108)	(2.839)	(2.844)
ISSUE	−0.000	0.000	−0.008	−0.008
	(−0.017)	(0.003)	(−0.999)	(−0.994)
MERGE	0.060***	0.060***	0.028***	0.028***
	(6.949)	(6.956)	(5.173)	(5.177)
MAO	0.103***	0.103***	0.032**	0.032**
	(5.047)	(5.051)	(2.399)	(2.411)
BIG	0.155***	0.155***	0.083***	0.083***
	(8.842)	(8.841)	(5.034)	(5.032)
TENURE	0.004**	0.004**	0.001	0.001
	(2.554)	(2.559)	(1.252)	(1.254)
LOCAL	0.065***	0.065***	0.014	0.014
	(3.906)	(3.903)	(0.899)	(0.904)
FOREIGN	0.400***	0.400***	0.297	0.297
	(8.795)	(8.797)	(0.992)	(0.994)
SOE	−0.087***	−0.087***	−0.028	−0.028
	(−5.210)	(−5.217)	(−1.164)	(−1.172)
RPTLOAN	0.235	0.232	0.105	0.102
	(0.931)	(0.920)	(0.558)	(0.544)
OWNER	−0.071	−0.071	0.012	0.012
	(−1.361)	(−1.360)	(0.178)	(0.179)
MARKETINDEX	0.187***	0.187***	0.280***	0.280***
	(6.063)	(6.063)	(3.810)	(3.814)
LAGSDRET	−0.072	−0.072	−0.042	−0.042
	(−0.744)	(−0.739)	(−0.652)	(−0.657)
LAGZSCORE	0.007***	0.007***	0.002*	0.002*
	(4.320)	(4.342)	(1.728)	(1.761)
LAGIC	0.003	0.003	−0.005*	−0.005*
	(0.611)	(0.616)	(−1.778)	(−1.767)
LAGDA	−0.182**	−0.179**	−0.132***	−0.131***
	(−2.463)	(−2.429)	(−2.728)	(−2.698)
LAGRESTATEA	0.057	0.056	0.078**	0.077**
	(1.269)	(1.255)	(2.328)	(2.315)
Intercept	4.850***	4.847***	7.066***	7.063***
	(24.501)	(24.482)	(28.623)	(28.616)
Year fixed effect	Yes	Yes	Yes	Yes
Industry fixed effect	Yes	Yes	No	No
Firm fixed effect	No	No	Yes	Yes
Adj. R^2	0.610	0.610	0.492	0.492
N	17,965	17,965	17,965	17,965

T-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test.

To alleviate concerns about the omitted variables, we re-estimate Equation (1) after including firm-fixed effects. The results of the firm fixed-effect regressions are reported in columns 3 and 4 in Panel B of Table 2. Overall, these regressions with firm-fixed effects are qualitatively similar to those reported in columns 1 and 2. These findings suggest that auditors assess a high engagement risk after observing clients’ exposure to high crash risk in the previous year. The coefficients on the control variables, whenever statistically significant, are consistent with our prior findings and with the results reported in prior studies.

4.2. Crash risk and modified audit opinions: test of H2

To test whether crash risk is positively associated with the likelihood of issuance of modified audit opinions (H2), we apply the following logit model:

(2) $\begin{array}{rl}& PROB\left(MA{O}_{it}=1\right)={\beta }_0+{\beta }_{1}CRAS{H}_{it}+{\beta }_{2}SIZ{E}_{it}+{\beta }_{3}AG{E}_{it}+{\beta }_{4}RO{A}_{it}+{\beta }_{5}LE{V}_{it}+{\beta }_{6}QUIC{K}_{it}\\ & +{\beta }_{7}INV{R}_{it}+{\beta }_{8}ORE{C}_{it}+{\beta }_{9}M{B}_{it}+{\beta }_{10}E{M}_{it}+{\beta }_{11}BI{G}_{it}+{\beta }_{12}TENUR{E}_{it}\\ & +{\beta }_{13}LOCA{L}_{it}+{\beta }_{14}FOREIG{N}_{it}+{\beta }_{15}SO{E}_{it}+{\beta }_{16}OWNE{R}_{it}\\ & +{\beta }_{17}MARKETINDE{X}_{it}+{\beta }_{18}LAGMA{O}_{it}+{\beta }_{19}SDRE{T}_{it}+{\beta }_{20}ZSCOR{E}_{it}\\ & +{\beta }_{21}I{C}_{it}+{\beta }_{22}D{A}_{it}+{\beta }_{23}RESTATE{A}_{it}+\sum Industry+\sum Year+{\epsilon }_{it}\end{array}$(2)

where PROB(MAO = 1) is the ex ante likelihood of auditors issuing modified opinions, which is ex post coded 1 if the auditor issues a modified audit opinion in the current year, and 0 otherwise. Modified audit opinions (MAO) include unqualified opinions with explanatory notes, qualified opinions, disclaimer opinions, and adverse opinions. We draw on recent studies (Chen et al., 2010; Firth et al., 2012; Wang, Wong, & Xia, 2008) to identify the control variables included in the audit opinion model in Equation (2). In addition, we include the audit opinion in the prior year (LAGMAO) to control for the persistence of audit opinions. Table 1 provides detailed definitions of all of the variables.

The summary statistics are reported in Panel A of Table 3. For brevity, we only report summary statistics for variables not included in Equation (1). In Panel B of Table 3, columns 1 and 2 report the results of the logit regressions in Equation (2) without firm-fixed effects, using NCSKEW and DUVOL, respectively, as the test variables. As these two columns show, the estimated coefficients on NCSKEW and DUVOL are 0.140 and 0.218, respectively, and both coefficients are highly significant at less than the 1% level (t = 2.953 and 3.844, respectively). The marginal effect of NCSKEW and DUVOL on auditors’ MAO issuance probability is 0.5% and 0.7%, respectively (untabulated), suggesting one standard deviation increase from mean value of crash risk measures increase the MAO issuance probability by 0.5–0.6%. In columns 3 and 4, we further include firm-fixed effects to alleviate the concerns about correlated omitted variables. As shown in the last two columns, the results are qualitatively similar to those in the first two columns. In short, the results presented in Panel B of Table 3 are consistent with H2, and they indicate that auditors are more likely to issue modified audit opinions to mitigate the engagement risk assessed for clients with higher crash risk.

Table 3. Analysis of crash risk and audit opinion.

Panel A: Descriptive statistics
Variable	Mean	SD	P25	P50	P75	N
Dependent variables
MAO	0.075	0.263	0	0	0	19,303
Test variables
NCSKEW	−0.187	0.989	−0.785	−0.172	0.452	19,303
DUVOL	−0.117	0.811	−0.644	−0.129	0.415	19,303
Control variables
EM	0.201	0.401	0	0	0	19,303
LAGMAO	0.076	0.266	0	0	0	19,303
SDRET	0.126	0.053	0.089	0.113	0.151	19,303
ZSCORE	4.303	5.871	1.485	2.640	4.678	19,303
IC	6.188	1.391	6.416	6.523	6.579	19,303
DA	0.056	0.054	0.017	0.039	0.075	19,303
RESTATEA	0.004	0.066	0	0	0	19,303
Panel B: Logit regression of audit opinion model
	(1)	(2)	(3)	(4)
	Logit	Logit	Logit	Logit
Dependent variable	MAO	MAO	MAO	MAO
NCSKEW	0.140***		0.125***
	(2.953)		(2.606)
DUVOL		0.218***		0.192***
		(3.844)		(3.217)
SIZE	−0.183***	−0.181***	−0.498***	−0.500***
	(−3.735)	(−3.685)	(−5.072)	(−5.092)
AGE	0.319**	0.320**	−0.910*	−0.900*
	(2.488)	(2.491)	(−1.755)	(−1.734)
ROA	−9.530***	−9.440***	−8.805***	−8.710***
	(−19.222)	(−19.034)	(−14.915)	(−14.734)
LEV	2.292***	2.294***	2.960***	2.963***
	(10.363)	(10.387)	(9.060)	(9.062)
QUICK	0.028	0.026	0.038	0.037
	(0.692)	(0.644)	(0.718)	(0.695)
INVR	−2.081***	−2.072***	−2.488***	−2.471***
	(−5.042)	(−5.016)	(−4.993)	(−4.955)
OREC	1.152***	1.155***	1.618***	1.625***
	(2.674)	(2.676)	(2.758)	(2.766)
MB	0.002	0.003	−0.005	−0.005
	(0.186)	(0.333)	(−0.552)	(−0.480)
EM	0.225**	0.219**	0.232**	0.226**
	(2.276)	(2.218)	(2.085)	(2.025)
BIG	0.092	0.089	0.249	0.244
	(0.863)	(0.841)	(1.546)	(1.514)
TENURE	−0.014	−0.014	0.028*	0.028*
	(−1.203)	(−1.185)	(1.791)	(1.782)
LOCAL	−0.242**	−0.243**	−0.081	−0.083
	(−2.241)	(−2.245)	(−0.473)	(−0.485)
FOREIGN	−0.111	−0.112
	(−0.617)	(−0.623)
SOE	−0.265**	−0.265**	−0.004	−0.008
	(−2.535)	(−2.537)	(−0.019)	(−0.041)
OWNER	−0.918***	−0.918***	−1.296**	−1.305**
	(−2.813)	(−2.812)	(−1.983)	(−1.998)
MARKETINDEX	0.144	0.139	0.999	1.004
	(0.847)	(0.816)	(1.488)	(1.491)
LAGMAO	3.138***	3.143***	1.415***	1.420***
	(30.359)	(30.374)	(14.343)	(14.369)
SDRET	1.676	1.949*	3.202***	3.436***
	(1.565)	(1.805)	(2.824)	(3.017)
ZSCORE	0.028**	0.029**	0.011	0.012
	(2.336)	(2.389)	(0.793)	(0.834)
IC	−0.190***	−0.190***	−0.263***	−0.263***
	(−7.936)	(−7.911)	(−7.603)	(−7.590)
DA	−0.764	−0.750	−1.768**	−1.736**
	(−0.962)	(−0.942)	(−2.010)	(−1.969)
RESTATEA	1.205***	1.187***	0.844*	0.828*
	(2.846)	(2.804)	(1.922)	(1.891)
Intercept	1.152	1.052
	(1.091)	(0.995)
Year fixed effect	Yes	Yes	Yes	Yes
Industry fixed effect	Yes	Yes	No	No
Firm fixed effect	No	No	Yes	Yes
Pseudo R^2	0.514	0.515	0.425	0.425
N	19,303	19,303	5,885	5,885

Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test.

4.3. Crash risk and auditor turnover: test of H3

To test the association between crash risk and auditor turnover (H3), we follow prior research in selecting the determinants of auditors’ turnovers, and estimate the following logit regression:

(3) $\begin{array}{rl}& PROB\left(TURNOVE{R}_{it+1}=1\right)={\beta }_0+{\beta }_{1}CRAS{H}_{it}+{\beta }_{2}SIZ{E}_{it}+{\beta }_{3}AG{E}_{it}+{\beta }_{4}RO{A}_{it}+{\beta }_{5}LE{V}_{it}\\ & +{\beta }_{6}QUIC{K}_{it}+{\beta }_{7}M{B}_{it}+{\beta }_{8}MA{O}_{it}+{\beta }_{9}BI{G}_{it}+{\beta }_{10}TENUR{E}_{it}\\ & +{\beta }_{11}LOCA{L}_{it}+{\beta }_{12}FOREIG{N}_{it}+{\beta }_{13}SO{E}_{it}+{\beta }_{14}OWNE{R}_{it}\\ & +{\beta }_{15}MARKETINDE{X}_{it}+{\beta }_{16}SDRE{T}_{it}+{\beta }_{17}ZSCOR{E}_{it}+{\beta }_{18}I{C}_{it}\\ & +{\beta }_{19}D{A}_{it}+{\beta }_{20}RESTATE{A}_{it}+\sum Industry+\sum Year+{\epsilon }_{it}\end{array}$(3)

where PROB (TURNOVER = 1) is an ex ante likelihood of auditor turnover, and is ex post coded as 1 for firms whose auditors leave from ongoing audit engagement, and 0 otherwise.⁷ We include similar control variables to those in Equations (1) and (2). Please refer to Table 1 for detailed variable definitions. For brevity, we do not report summary statistics of these control variables.

Table 4. Analysis of crash risk and auditor turnover.

Panel A: Descriptive statistics
Variable	Mean	SD	P25	P50	P75	N
Dependent variables
TURNOVERt+1	0.108	0.311	0	0	0	16,962
Test variables
NCSKEW	−0.179	0.965	−0.766	−0.172	0.438	16,962
DUVOL	−0.116	0.794	−0.634	−0.133	0.401	16,962
Panel B: Logit regression of auditor turnover model
	(1)	(2)	(3)	(4)
	Logit	Logit	Logit	Logit
Dependent variable	TURNOVERt+1	TURNOVERt+1	TURNOVERt+1	TURNOVERt+1
NCSKEW	0.068**		0.072**
	(2.369)		(2.215)
DUVOL		0.088**		0.097**
		(2.487)		(2.452)
SIZE	0.010	0.010	−0.081	−0.084
	(0.361)	(0.367)	(−1.229)	(−1.265)
AGE	0.007	0.007	−0.713**	−0.718**
	(0.098)	(0.094)	(−2.194)	(−2.212)
ROA	−1.391***	−1.348***	−1.025	−0.958
	(−2.832)	(−2.732)	(−1.600)	(−1.490)
LEV	0.136	0.139	−0.041	−0.036
	(0.934)	(0.951)	(−0.177)	(−0.157)
QUICK	0.021	0.021	0.014	0.014
	(0.936)	(0.916)	(0.389)	(0.372)
MB	0.011*	0.012*	−0.001	−0.000
	(1.861)	(1.945)	(−0.113)	(−0.052)
MAO	0.704***	0.703***	0.735***	0.733***
	(7.480)	(7.461)	(6.155)	(6.131)
BIG	−0.345***	−0.345***	−0.505***	−0.505***
	(−4.908)	(−4.905)	(−5.216)	(−5.219)
TENURE	0.002	0.002	0.185***	0.185***
	(0.327)	(0.349)	(18.783)	(18.796)
LOCAL	−0.437***	−0.437***	−0.103	−0.103
	(−6.582)	(−6.583)	(−1.073)	(−1.070)
FOREIGN	0.094	0.093	0.728	0.755
	(1.044)	(1.031)	(0.673)	(0.701)
SOE	0.126**	0.126**	0.221	0.220
	(2.012)	(2.013)	(1.470)	(1.465)
OWNER	0.237	0.235	−0.490	−0.483
	(1.348)	(1.338)	(−1.226)	(−1.208)
MARKETINDEX	0.102	0.101	−1.328***	−1.325***
	(0.936)	(0.927)	(−2.990)	(−2.981)
SDRET	−0.101	−0.055	−0.572	−0.485
	(−0.155)	(−0.084)	(−0.753)	(−0.635)
ZSCORE	0.009	0.010	0.008	0.009
	(1.371)	(1.416)	(0.828)	(0.874)
IC	−0.032*	−0.032*	−0.061**	−0.061**
	(−1.724)	(−1.733)	(−2.118)	(−2.131)
DA	0.646	0.653	0.368	0.375
	(1.307)	(1.321)	(0.687)	(0.701)
RESTATEA	−0.210	−0.213	−0.438	−0.437
	(−0.525)	(−0.531)	(−0.941)	(−0.938)
Intercept	−2.571***	−2.581***
	(−4.303)	(−4.318)
Year fixed effect	Yes	Yes	Yes	Yes
Industry fixed effect	Yes	Yes	No	No
Firm fixed effect	No	No	Yes	Yes
Pseudo R^2	0.061	0.061	0.136	0.136
N	16,962	16,962	11,472	11,472

Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test.

In Table 4, Panel A reports the descriptive statistics for the variables used in Equation (3). The first two columns of Panel B report the logit regression results without firm-fixed effects, and the coefficients on NCSKEW and DUVOL are 0.068 and 0.088, respectively, with both coefficients significant at the 5% level. The marginal effect of NCSKEW and DUVOL on auditors’ turnover rate is 0.6% and 0.8%, respectively (untabulated), suggesting one standard deviation increase from mean value of crash risk measures increase the rate by around 0.6%. As shown in the last two columns, the results remain similar and become more significant after including firm-fixed effects. Collectively, the results in Table 4 show that auditors are more likely to resign from ongoing audit engagements when their clients are exposed to crash risks that are above a tolerable level.

4.4. Endogeneity tests

Our analysis thus far has focused on auditors’ responses to their clients’ exposure to crash risk. However, although we already control for various auditor attributes, firm characteristics and firm-fixed effects to alleviate the correlated omitted variable concern, crash risk may still likely to be affected by unobserved firm and auditor characteristics which may influence auditor-client contracting. Consistent with this argument, the Durbin-Wu-Hausman χ2 test reported in Table 5 rejects the null hypotheses that crash risk is exogenous to audit fees (columns 1 and 2), and auditor turnover (columns 5 and 6). To further address the problems of correlated omitted variables caused by unobserved and time-variant factors, we perform 2SLS regressions using an instrumental variable approach.

Table 5. Endogeneity test: 2SLS.

	(1)	(2)	(3)	(4)	(5)	(6)
Dependent variable	LNFEE	LNFEE	MAO	MAO	TURNOVERt+1	TURNOVERt+1
Second stage
PRE_LAGNCSKEW	0.655***
	(5.940)
PRE_LAGDUVOL		0.737***
		(6.191)
PRE_NCSKEW			0.789***		0.698***
			(3.532)		(2.968)
PRE_DUVOL				0.871***		0.746***
				(2.923)		(2.641)
Wald chi^2	7307.82	8022.83	4589.05	4052.20	1366.98	1135.65
N	17,965	17,965	19,303	19,303	16,962	16,962
First stage
LAGPOSTSHO	0.253***	0.227***
	(8.343)	(9.045)
POSTSHO			0.198***	0.197***	0.193***	0.192***
			(5.942)	(7.523)	(5.773)	(7.231)
Partial F of first stage	69.61	81.82	35.31	56.60	33.33	52.29
p-value for Durbin-Wu-Hausman χ2 test	0.000	0.000	0.120	0.138	0.049	0.052

T-statistics/Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test. The same set of control variables as those in Equations (1)–(3) and year and industry fixed effects are included.

We use the inclusion of the Chinese deregulation pilot programme on short-selling as the instrumental variable. The China Securities Regulatory Commission (CSRC) introduced the deregulation pilot programme of short selling in 2010. Stocks included in the programme are released from the short-selling prohibition while the rest stocks remain constrained. One-third of the listed stocks in China were gradually included in the pilot programme from 2010 to the present, creating both the time-series and cross-sectional variation in short-selling restrictions. Hong and Stein (2003) argue that removal of short sales constraints allows the unrevealed negative information to timely incorporated into stock price and thus reduces crash risk. Meanwhile, some others (e.g. Ausubel, 1990; Barlevy & Veronesi, 2003) argue that if uninformed investors interpret the falling stock price as a results of informed investors short selling on negative private news, they would rush to sell and thus leads to stock price crash. In such cases, removal of short selling constraints could lead to higher crash risk. The empirical study of Ni and Zhu (2016) shows that the second argument is more likely to be valid in China and results in a positive effect between short-selling restriction removal and crash risk. We expect the regulatory changes on short-selling constraints to be an exogenous shock on pilot firms’ crash risk. Meanwhile, we expect it to be unrelated to any potential-omitted variables such as uncontrolled business risk.

We construct a dummy variable (POSTSHO) which equals to one for firm-years included in the programme and thus allowed to be shorted, and zero otherwise. In the first stage, in addition to the instrument variable, we include the same set of control variables as those in the second stage. The results of IV regression are reported in Table 5. For brevity, we report only the coefficients on our variables of interest and omit those on the control variables. The results of first stage show that the instrument variable is significantly positively correlated with the crash risk measures, consistent with the findings of Ni and Zhu (2016). The partial F-stat. In first stage are larger than 10, which is the rule of thumb for checking for weak instrument, in all our models. Therefore, weak instrument is not a concern.⁸

In the second stage, we use the instrumented crash risk measures (PRE_NCSKEW and PRE_DUVOL) in lieu of the original crash risk measures and re-estimate Equations (1)–(3). All control variables in the first stage are included in the second stage. The results of the second stage show that all the coefficients on the predicted value of crash risk measures are significantly positive, consistent with the sign of the coefficients estimated by OLS. In short, the results shown in Table 5 buttress our earlier findings.

4.5. Path analysis

We perform a path analysis to test our maintained assumption that inherent risk and auditor business risk, two components of audit engagement risk, are valid paths through with crash risk affects auditor engagement risk. We use a structural equation model to decompose the correlation between crash risk and audit outcomes (i.e. audit fees, MAOs, and turnover) into two paths through mediating variables. Following DeFond et al. (2016), we expect auditor business risk to be an indirect path that is mitigated by litigation risk, through which crash risk affects audit outcomes. We construct two proxies for Chinese auditors’ litigation risk, i.e. regulatory sanction (SANCTION) and shareholder lawsuit (LAWSUIT). All variables are standardised with a mean of 0 and a standard deviation of 1, allowing comparison of the magnitudes of the coefficients. The results are reported in Table 6.

Table 6. Path analysis.

	(1)		(2)		(3)	(4)	(5)	(6)
Dependent variable	LNFEE		LNFEE		MAO	MAO	TURNOVERt+1	TURNOVERt+1
CRASH	LAGNCSKEW		LAGDUVOL		NCSKEW	DUVOL	NCSKEW	DUVOL
Panel A: Path analysis with regulatory sanction as mediator variable
Direct Path
p(CRASH, DepVar)	0.010**		0.013**		0.136***	0.175***	0.066**	0.070**
	(1.974)		(2.568)		(2.915)	(3.812)	(2.320)	(2.454)
Mediated Path for regulatory sanction
p(CRASH, SANCTION)	0.109***		0.110***		0.098***	0.104***	0.086**	0.091**
	(2.715)		(2.807)		(2.682)	(2.934)	(2.034)	(2.253)
p(SANCTION, DepVar)	0.077***		0.077***		0.358**	0.357**	0.316***	0.315***
	(3.415)		(3.414)		(2.435)	(2.420)	(2.788)	(2.785)
Total Mediated Path for regulatory sanction
p(CRASH, SANCTION)*p(SANCTION, DepVar)	0.008**		0.008**		0.035*	0.037*	0.027*	0.029
	(2.125)		(2.168)		(1.803)	(1.867)	(1.752)	(1.643)
N	17,965		17,965		19,303	19,303	16,962	16,962
Panel B: Path analysis with shareholder lawsuit as mediator variable
Direct Path
p(CRASH, DepVar)	0.010**	0.013***		0.137***		0.176***	0.067**	0.071**
	(1.984)	(2.582)		(2.937)		(3.839)	(2.351)	(2.489)
Mediated Path for shareholder lawsuit
p(CRASH, LAWSUIT)	0.113**	0.124***		0.076*		0.067	0.085	0.079
	(2.481)	(2.652)		(1.704)		(1.539)	(1.625)	(1.522)
p(LAWSUIT, DepVar)	0.128***	0.128***		0.419**		0.421**	0.083	0.084
	(3.441)	(3.443)		(2.465)		(2.476)	(0.580)	(0.586)
Total Mediated Path for shareholder lawsuit
p(CRASH, LAWSUIT)*p(LAWSUIT, DepVar)	0.014**	0.016**		0.032		0.028	0.007	0.007
	(2.013)	(2.101)		(1.402)		(1.307)	(0.546)	(0.547)
N	17,965	17,965		19,303		19,303	16,962	16,962

T-statistics/Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test. The same set of control variables as those in Equations (1)–(3) and year and industry fixed effects are included. All variables are all standardised with a mean of 0 and a standard deviation of 1, allowing comparison of the magnitudes of the coefficients. The significance of the indirect effect is estimated using the Sobel (1982) test statistics. The table reports the path coefficients of interest. We estimate the following model:

Mediator variables= α₀+ α₁CRASH+ε and Dependent variables= β₀+ β₁Mediator variables+β₂CRASH+Control Variables+ε.

Panel A reports the results using regulatory sanction as the mediator variable. The direct path coefficients between crash risk measures and audit outcomes (p(CRASH, DepVar)) are all significantly positive at 5% level or higher, consistent with higher inherent risk signalled by higher crash risk. The path coefficients between crash risk and regulatory sanction are all significantly positive (p(CRASH, SANCTION)), consistent with higher crash risk leading to more regulatory sanctions. The total mediated path for litigation risk (p(CRASH, SANCTION)*p(SANCTION, DepVar)) is significantly positive at 5% level. Thus, both inherent risk (direct path) and auditor business risk (indirect path mediated by litigation risk) are valid paths through which crash risk affect auditor-client contracting. In panel B, we use shareholder lawsuit (LAWSUIT) as the mediator variable, and find similar results as Panel A. These results show that crash risk encourages auditors to take strategies to protect themselves from business risk through litigation risk. Meanwhile, crash risk also directly influences inherent risk and change auditor behaviour. In summary, crash risk affects audit behaviour through both inherent risk and auditor business risk.

4.6. Cross-sectional tests

We now examine how the effects of crash risk vary across the different characteristics of clients and auditors. To this end, we partition the full sample into two subsamples, based on four characteristics: (i) state-owned versus non-state-owned firms, (ii) firms with audit committees versus those without them, (iii) firms with Big 8 audit firms versus those with smaller audit firms, and (iv) high versus low provincial marketisation. We then re-estimate Equations (1)–(3) for each subsample. The results are reported in Table 7.

Table 7. Cross-sectional test.

Panel A: The association between crash risk and audit fees: Cross-sectional test
	State Ownership		Audit Committee		Auditor Size		Institutional Development
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Non-SOE	SOE	No	Yes	Non-Big	Big	Low	High
Dependent variable	LNFEE	LNFEE	LNFEE	LNFEE	LNFEE	LNFEE	LNFEE	LNFEE
LAGNCSKEW	0.005	0.007	0.000	0.007*	−0.001	0.012	0.003	0.011**
	(1.092)	(1.428)	(0.056)	(1.767)	(−0.176)	(1.443)	(0.604)	(2.172)
Adj. R^2	0.558	0.639	0.418	0.622	0.534	0.649	0.635	0.587
N	7,077	10,888	3,452	14,513	12,873	5,092	9,803	8,162
χ2 test	0.08		0.65		2.15		1.53
p-value	0.388		0.210		0.071		0.108
Panel B: The association between crash risk and audit opinions: Cross-sectional test
	State Ownership		Audit Committee		Auditor Size		Institutional Development
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Non-SOE	SOE	No	Yes	Non-Big	Big	Low	High
Dependent variable	MAO	MAO	MAO	MAO	MAO	MAO	MAO	MAO
NCSKEW	0.076	0.191***	0.018	0.214***	0.120**	0.221**	0.145**	0.122
	(1.067)	(3.129)	(0.252)	(3.671)	(2.298)	(2.092)	(2.441)	(1.584)
Pseudo R^2	0.554	0.485	0.460	0.537	0.512	0.537	0.523	0.517
N	7,555	11,698	3,682	15,545	13,868	5,344	10,545	8,664
χ2 test	1.52		4.34		0.77		0.06
p-value	0.109		0.019		0.191		0.401
Panel c: The association between crash risk and audit turnover: Cross-sectional test
	State Ownership		Audit Committee		Auditor Size		Institutional Development
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Non-SOE	SOE	No	Yes	Non-Big	Big	Low	High
Dependent variable	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1	TURNOVER t+1
NCSKEW	0.089*	0.049	0.048	0.075**	0.063*	0.108*	0.059	0.059
	(1.718)	(1.390)	(0.782)	(2.305)	(1.886)	(1.751)	(1.620)	(1.200)
Pseudo R^2	0.096	0.055	0.066	0.069	0.078	0.071	0.061	0.077
N	6,208	10,706	3,675	13,220	12,499	4,415	9,258	7,656
χ2 test	0.41		2.08		0.41		0.00
p-value	0.260		0.074		0.262		0.496

T-statistics/Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test. The same set of control variables as those in Equations (1)–(3) and year and industry fixed effects are included. χ² test is for subsample coefficient difference of LAGNCSKEW and NCSKEW. p-value for χ² test is one-tailed.

4.6.1. Client characteristics

First, we investigate whether the auditors of state-owned enterprises (SOEs) are more likely to respond to their clients’ levels of exposure to crash risk. SOEs have greater access to capital via national banks and government sources. In addition, they are likely to be supported by the government, which provides greater financial insurance to outside shareholders. Therefore, both the SOEs and their outsider shareholders have less demand for high-quality auditing than non-SOEs and their shareholders (Wang et al., 2008). In this audit environment, receiving modified audit opinions (MAOs) may be less costly for SOEs. We can therefore conjecture that the auditors of SEOs are more likely to issue MAOs as their preferred strategy to mitigate their engagement risk (as perceived from crash risk), rather than to charge higher audit fees or to resign from an ongoing audit engagement.

In Table 7, Panels AtoC report the subsample results of the regressions in Equations (1)–(3), where audit fees (LNFEE), the likelihood of modified audit opinion issuance (MAO) and the rate of auditor turnover (TURNOVER), respectively, are used as the dependent variables. For brevity, we report only the coefficients on LAGNCSKEW (Panel A) and NCSKEW (Panels B and C) throughout Table 7. The results from using the other crash risk measure, DUVOL, are qualitatively the same as the results from using NCSKEW. In all three of the panels, columns 1 and 2 report the results of regressions for the subsamples of non-SOE firms and SOE firms, respectively. In each panel, the last row reports the p-value for testing the differences in the LAGNCSKEW or NCSKEW coefficients between the two subsamples. As shown in columns 1 and 2 of Panel B, we find that the coefficient on NCSKEW is significantly positive and of a larger magnitude for the SOE subsample (column 2) than for the non-SOE subsample (column1). In columns 1 and 2 of Panel C, the coefficient on NCSKEW is only significant in column 1. The aforementioned findings, taken altogether, suggest that the auditors of SOEs are more likely to issue MAOs and less likely to turnover than the auditors of non-SOEs.

The second client characteristic we consider is whether the client firms have audit committees. Carcello and Neal (2000) show that auditors are more likely to issue going-concern opinions for firms in financial distress if those firms have independent audit committees, as audit committee members are concerned about the monetary and reputational losses that may result from lawsuits or SEC sanctions (Abbott & Parker, 2000). Furthermore, auditors are shielded by audit committees after the going-concern opinions are issued (Carcello & Neal, 2003). Therefore, when the auditors charge higher audit fees or issue MAOs more frequently as strategies for mitigating the engagement risk (associated with the clients’ exposure to high crash risk), we expect these auditors to face less resistance from clients that have independent audit committees.

In Panels A to C, columns 3 and 4 report the results of the regressions for the audit fee model in Equation (1), the auditor opinion model in Equation (2), and the auditor turnover model in Equation (3), respectively. We find that compared with firms without audit committees (column 3), auditors of firms with audit committees (column 4) are more sensitive to crash risk in that they tend to charge higher audit fees (Panel A), issue MAOs more frequently (Panel B), and more likely to resign (Panel C). The last rows of Panels A to C show the differences between the coefficients are significant in Panel B and C, but insignificant in Panel A.

4.6.2. Auditor characteristics

Next, we consider the influence of auditor size, namely Big 8 versus non-Big 8 auditors, on auditors’ sensitivity to crash risk. Prior research shows that large auditors have stronger incentives for delivering higher audit quality than small auditors do, as the reputation costs increase with audit firm size and the ‘deep pockets’ of larger auditors make them attractive targets for litigation. In addition, large auditors have more extensive client pools, and are thus less likely to sacrifice independence for the sake of retaining their existing clients. Therefore, we expect big auditors to be more sensitive to high levels of engagement risk arising from higher crash risk. In Panel A to C of Table 7, columns 5 and 6 report the results of regressions of audit fees, audit opinion issuance and auditor turnover likelihood on crash risk for the two subsamples of client firms, respectively.

Consistent with our expectation, we find that the coefficients for LAGNCSKEW are of larger magnitude for big auditors in Panels A to C. This finding suggests that big audit firms are more sensitive to crash risk. The differences between coefficients are significant in Panel A but insignificant in Panels B and C.

4.6.3. Institutional development

Finally, we examine whether the extent of institutional development in the province or region matters in shaping the auditor-client contracting relationship. To this end, we partition the sample based on the degree of marketisation in the province or region where the client firm is located. Several studies (e.g. Chen et al., 2010) show that the institutional environment affects auditors’ trade-offs between audit quality and the client’s economic importance. Within China, there is a significant variation in institutional development across provinces or regions. Auditors whose clients are located in the more institutionally developed provinces face higher litigation risks. Therefore, we expect that auditors doing business in those more developed markets are more responsive to the engagement risk associated with crash risk. We measure the degrees of institutional development by using each province’s marketisation index, which is available from Fan, Wang, and Zhu (2010). In Panel A of Table 7, the last two columns report the results of regressions of audit fees on lagged crash risk, i.e. LAGNCSKEW. Consistent with our expectation, we find that auditors’ fees significantly increase in response to their clients’ exposure to crash risk when the client firms are located in more developed markets or provinces. Audit fees are insensitive to crash risk for client firms located in less developed markets or provinces. In Panels B and C, we find no evidence of significant differences between auditor behaviour across subgroups.

5. Further analysis

5.1. Auditor over-conservatism

According to Geiger, Raghunandan, and Rama (2005), auditors make Type I errors (i.e. issuance of going-concern opinions in the absence of bankruptcy within the subsequent year) about 90% of the time. This finding suggests that auditors may possibly overestimate engagement risk indicated by crash risk, although crash risk does not involve new information about engagement risk beyond what is already known to the auditors. To examine whether auditors respond over-conservatively to crash risk, we test for the association between accounting quality and crash risk. To this end, we use two measures of accounting quality. First, we measure accounting quality by using the absolute value of performance-adjusted discretionary accruals, as defined in Kothari, Leone, and Wasley (2005). Our second measure of accounting quality is the ex post restatement indicator, which equals 1 if the annual report of the firm is subsequently restated. We regress these two measures of accounting quality on our crash risk measures and report the results in Table 8.

Table 8. Additional test: Analysis of crash risk and accounting information quality.

	(1)	(2)	(3)	(4)
	OLS	OLS	Logit	Logit
Dependent variable	DA	DA	RESTATE	RESTATE
NCSKEW	0.001**		0.058**
	(2.050)		(2.497)
DUVOL		0.001*		0.063**
		(1.934)		(2.189)
Control Variables	Yes	Yes	Yes	Yes
Year fixed effect	Yes	Yes	Yes	Yes
Industry fixed effect	Yes	Yes	Yes	Yes
Adj. R^2/Pseudo R^2	0.103	0.102	0.090	0.090
N	19,303	19,303	22,434	22,434

T-statistics/Z-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test. The control variables include SIZE, LEV, INVR, OREC, QUICK, OCF, ROA, LOSS, ISSUE, MERGE, MB, GROWTH, FOREIGN, SOE, OWNER, AGE, BIG, LOCAL, MARKETINDEX, MAO, and RPTLOAN.

As shown in Table 8, we find that the coefficients on our crash risk measures, NCSKEW and DUVOL, are positive and significant across all of the columns. The significantly positive associations between accounting quality and crash risk lend support to the view that firms tend to exhibit poor accounting quality (with a high likelihood of future restatements) in periods exposed to high levels of crash risk. These results are also consistent with the insight of DeFond et al. (2016), who points out that accounting conservatism predicts future restatements, which affects auditors’ decisions. Our results indicate high crash risk is a signal for deteriorating accounting quality in the future, which provides rationality for auditors’ behaviour.

5.2. Auditor efforts

As previously discussed, when facing high engagement risk, auditors may exert more efforts and charge risk premiums, both of which are reflected in higher audit fees. However, the auditor responses of making additional effort versus charging a risk premium have differing implications for audit quality. As DeFond and Zhang (2014) point out, it is important to disentangle whether the increased audit fees are due to increased auditor efforts (and consistent with audit quality) or to premiums for increased audit risk (in which case the expense is a deadweight loss for society as a whole). To shed light on the implications of higher audit fees, we further examine how auditor efforts change when auditors observe high crash risk during the year. Following previous studies (e.g. Ashton, Graul, & Newton, 1989; Bamber, Bamber, & Schoderbek, 1993; Knechel & Payne, 2001), we use auditor reporting lag (i.e. the natural logarithm of the number of days between a firm’s fiscal year end and the auditor’s report signing date) as a proxy for auditor efforts. We then regress two measures for crash risk (NCSKEW and DUVOL) on auditor reporting lag, and include the same set of control variables as those used in Equation (1).⁹ Results reported in Table 9 show a significant positive relation between audit report lag and crash risk, with or without firm-fixed effects included. The results indicate that auditors exert more audit efforts for firms with higher crash risk.

Table 9. Additional test: Analysis of crash risk and audit effort.

	(1)	(2)	(3)	(4)
	OLS	OLS	OLS	OLS
Dependent variable	AUDITLAG	AUDITLAG	AUDITLAG	AUDITLAG
NCSKEW	0.006**		0.005*
	(2.249)		(1.870)
DUVOL		0.015***		0.011***
		(4.550)		(3.535)
Control Variables	Yes	Yes	Yes	Yes
Year fixed effect	Yes	Yes	Yes	Yes
Industry fixed effect	Yes	Yes	No	No
Firm fixed effect	No	No	Yes	Yes
Adj. R^2	0.110	0.111	0.108	0.109
N	17,964	17,964	17,964	17,964

T-statistics based on robust standard errors that are clustered by firm are displayed in parentheses. ***, ** and * represent 1%, 5% and 10% significance levels, respectively, based on a two-tailed test. The same set of control variables as those in Equation (1) are included.

Together with the results on auditor efforts, the evidence indicates that more audit efforts are exerted but cannot fully neutralise the negative effect on financial reporting quality brought by the ‘extreme’ information asymmetry (proxy by high crash risk). In such situation, the higher audit fee documented is to cover both higher audit costs and higher audit risk premium.

6. Conclusion

This study investigates how auditors revise their engagement risks when their clients are exposed to high levels of crash risk. Specifically, we predict and find that auditors charge higher audit fees, issue MAOs more frequently, and are more likely to leave when their clients experience higher crash risk. To address concerns about the problem of correlated omitted variables, we adopt the 2SLS regression approach with an instrumental variable, which helps us to establish the casual effect of crash risk on changes in auditor-client contracting. In addition, we use path analysis to provide evidence for the mechanisms how crash risk affects audits behaviour.

To our knowledge, our study is the first to examine the consequences of crash risk for a third party outside the firm, rather than the determinants of crash risk or its consequences on equity holders. Our study provides the first empirical evidence that extreme negative tail risk or crash risk affects auditors’ assessments of engagement risk. In addition, by demonstrating the changes in auditor-client contracting relationships subsequent to the clients’ exposures to high crash risk, we document another set of costs to firms caused by high crash risk, that is, higher audit fees, greater frequency of MAOs and higher auditor turnover rate.

Research has shown how auditors consider information from various channels in their risk assessments (e.g. Billings et al., 2014; Cassell et al., 2011; DeFond et al., 2016; Hogan & Wilkins, 2008; Krishnan & Wang, 2015). This study documents another channel of information, i.e. clients’ crash risk, and provides useful insights into the economic consequences of crash risk for non-equity stakeholders.

Acknowledgments

We appreciate the insightful comments and suggestions of two anonymous referees. We acknowledge financial support from the National Natural Science Foundation of China (71602037 and 71872048).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China; [71602037]; [71872048].

Notes

¹ According to our sample, the average immediate loss in market value caused by one crash event at the firm level is about 13%. This figure represents the average weekly return for weeks with returns falling 3.2 standard deviations below the mean firm return during the fiscal year.

² Our study does not contradict to Hackenbrack et al. (2014) in the sense that auditors can still get new information from crash risk even if they already hold some information that can predict crash risk. As long as auditors do not realise all determinants of crash risk in advance, they still can extract new information from crash occurrences.

³ Specifically, in 2001, the Supreme Court issued a Notice to accept civil lawsuits against false statements in the security market. In 2002, the Chinese Supreme Court enacted the Act about the Acceptance of Tort Cases Caused by Fraudulent Financial Reporting in Security Market, which clarified the legal proceedings for investors seeking to claim civil compensation for financial fraud from liable firms and individuals, including individual auditors. In 2005, the amended Act of Security passed, which further defined the joint responsibility and the legal consequences for negligent auditors in cases of financial fraud. Furthermore, in 2012, all Chinese audit firms are required to transform from a limited liability company (LLC) structure to a limited liability partnership (LLP) structure, which removed the cap on the liability exposure of negligent auditors (He et al., 2017).

⁴ To avoid any potential influences of confounding events including financial crisis, split-share reform and new accounting standard, we conduct a robustness test by dropping year 2007 and 2008 from the sample. Our results (untabulated) remain similar.

⁵ In an untabulated test, we also estimate Models 1, 2, and 3 on a common sample of company-year observations for which data is available to calculate all necessary regression variables. All our results survive using the common sample.

⁶ We lag crash risk by one year relative to audit fees, as audit fees are largely determined at the beginning of the fiscal year. Thus, we expect that any increase in audit fees will be better reflected in the following year. Audit opinions are viewed as a timelier reflection of auditor risk assessment than audit fees. We therefore use contemporaneous crash risk in our audit opinion model.

⁷ We still can hardly tell resignation from dismissal. To get a better proxy for auditor resignation, we employ a stricter definition of auditor turnover. As Lennox (2000) points out, firms are more likely to engage in opinion shopping after getting MAOs. Thus, auditors’ turnovers without MAO issuance in the previous year are more likely to be auditor resignation rather than dismissal. According to this, we construct a stricter definition for auditor turnover, i.e. auditor turnovers without MAO issuance in the previous year, which is more likely to imply auditor resignation. The untabulated results are similar to those of Table 4. Another concern is regular auditor rotations. Our results are similar if we code compulsory regular auditor rotation as 0 for TURNOVER.

⁸ To mitigate the concern of the violation of exclusive restriction of the IV, we adopted the method presented by Conley, Hansen, and Rossi (2012), who relaxed the exclusion restriction and developed consistent estimation when only plausibly exogenous IV is used. As long as the impact bound of Chinese deregulation programme on audit fee is within (−0.025, 0.119), which is the mean±3 standard deviations of the impact of U.S. SHO programme on audit fee estimated by Hope, Hu, and Zhao (2017), we are able to document a significantly positive correlation between crash risk and audit fee.

⁹ Different from audit fee model, we measure audit effort conducted for the annual report of the same fiscal year during which we measure crash risk. It is reasonable to use one-year-ahead audit fee because audit fee is usually decided at the beginning of the fiscal year. However, audit effort is decided after the fiscal year end. Therefore, it’s more reasonable to use the audit report lag for same fiscal year of crash risk.