Discussion Paper No. 134
The Non-monotonic Relationship Between ESG
Disclosure and Stock Price Crash Risk
Hui Zhou and Jun Nagayasu

December, 2022

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research

Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku

Sendai 980-8576, JAPANThe Non-monotonic Relationship Between ESG
Disclosure and Stock Price Crash Risk*
Hui Zhou Jun Nagayasu
December 2022

Abstract
We show a theoretical relationship between ESG disclosure and stock price crashrisk and provide statistical evidence to support their non-monotonic relation
using firm-level data from China. The weak relationship between these two
indicators reported in previous studies is attributable to the linearity assumption
used in the analysis.
JEL classification: M14, G32, H70
Keywords: Corporate environmental responsibility; Firm value; Centralization;
Local protectionism; Ownership type* This paper has been prepared for publication in the book “Topical Issues in Development Eco-nomics” edited by Desire Avom and Gilles Dufrenot (Cambridge Scholars Publishing) and was presented in the Fourth Conference on CSR, the Economy and Financial Markets (2021) and the Third
Fall Conference of the Nippon Finance Association (2021). We would like to acknowledge financial
support from the Tohoku Forum for Creativity via the thematic program “Environmental and Financial Risks” and thank Akira Hibiki, Giang Nguyen, Pakesh Pandey,Yuto Yoshinaga, and conference
participants for their constructive comments on the earlier version of the paper, “The Environmental,
Social, and Governance (ESG) and Stock Price Crash Risk: Evidence from China”.
 Tohoku University, Graduate Program in Economics and Management, Address: 27-1 Kawauchi,
Aoba-ku, Sendai, Miyagi 980-8576 JAPAN.Email: moyinghuifree@gmail.com, Tel: +81 22 795 6265,
Fax: +81 22 795 6270.
Tohoku University, Graduate School of Economics and Management, Address: 27-1 Kawauchi,
Aoba-ku, Sendai, Miyagi 980-8576 JAPAN. Email: jun.nagayasu.d8@tohoku.ac.jp, Tel: +81 22 795
6265, Fax: +81 22 795 6270.

1

1

Introduction

Environmental problems like environmental pollution, ecological imbalances, and resource depletion can severely hinder economic development and social progress. With
the growing public concern about intensifying environmental conservation to attainsustainable economic and social growth, sustainable development has gained more andmore attention nowadays (Caiado et al., 2017). For example, some measures have beentaken to alleviate environmental problems, such as the adoption of the 2015 Paris Climate Agreement, a legally binding international treaty on climate change, that aims
to limit the increase in global average temperature to 2 ◦ C. To achieve a win-win economic development and environmental protection situation, corporate sustainability isalso an essential part that should be seriously concerned (Lloret, 2016).
ESG1 is increasingly becoming a consensus in recent years (Qiu and Yin, 2019).
ESG is an extended notion of the green economy and responsible investment. It iscurrently an essential indicator for measuring enterprises’ sustainable development level(Qiu and Yin, 2019). People from all walks of life, especially investors and financial
practitioners, are growingly depending on ESG information and metrics to evaluate
long-term company value23 (Escrig-Olmedo et al., 2013). In the meantime, in response
to increasing stakeholder interest in ESG, many related agencies, e.g., Morgan Stanley
Capital International (MSCI), Thomson Reuters, and Bloomberg, started to report
ESG and associated data.
Stock price crash risk4 namely, extremely negative return outlier, is linked with
the negative skewness of individual stock return distribution (Kim et al., 2014). It
is the conditional skewness of return distribution.5 This is crucial for investors tomake investment judgments and conduct risk control (Chen et al., 2001). Crash risk isbased on the idea that corporate managers often tend to hide negative news within thecompany from the outside market, which accumulates negative news over time. Whenmanagers prevent bad information from flowing into the market, the distribution offirms’ stock returns will be an asymmetric shape (Hutton et al., 2009). If the collectionof bad news exceeds a certain level, it will be instantly exposed to the market, causing
1

ESG has three dimensions, namely: environmental (e.g., wastewater discharge and environmental penalties), social (e.g., charitable donations and employee benefits), and governance (e.g., board
composition and political relations) dimensions.
2
The Institute for Governance and Accountability (2017) reported that 82% of S&P 500 firms
published sustainability reports in 2017, compared to 53% of S&P 500 firms in 2012.
3
The SynTao Green Finance documented that about 1,021 (27%) A-share listed companies issued
ESG reports in 2020 in China, among them, 259 (86%) of the CSI 300 listed companies released
reports in 2020, indicating that the top listed companies already have a strong awareness of ESG
disclosure.
4
Stock price crash risk and crash risk are interchangeable.
5
Conditional skewness, defined as the third moment of the return distribution, is an essential
feature of the return distribution, along with the mean (first moment) and variance (second moment).

2

a sharp decrease in stock price.
The relationship between ESG disclosure and crash risk is now examined in many
developed countries. However, the empirical findings are mixed about whether ESG
disclosure affects crash risk positively or negatively (Murata and Hamori, 2021). Besides, this relationship in China is worth special attention for the following reasons.
First, China started ESG disclosure much later than developed countries and thus
lacks efficient data evidence.6 Second, the unique institutional background in China
may lead to a distorted relationship, which is common in other economic research.
Thus, although there is expected to be a significant link between ESG disclosure andcrash risk based on prior research, we should be cautious about investigating the specific relationship. There are two dominant factors overall. First, a higher ESG scoremeans a higher level of corporate information disclosure, less harmful news hoardingby managers and increased transparency of the firm’s financial reporting (Deng andCheng, 2019). However, higher ESG is more likely to be used as a tool by managers
to pursue their interests, thereby reducing credibility level and increasing crash risk
(Huang, 2021).
Kim et al. (2014) have examined the relationship between corporate social responsibility (CSR) and stock price crash risk. However, it is more beneficial to examine
the ESG information and crash risk because of the difference between ESG and CSR
reports.7 The difference between the two terms mainly contains three aspects. First,
the target audience is different. The target audience of the CSR report is very scattered, while the ESG report is very focused.8 Therefore, the ESG content usually hasa relatively more ”substantial” relationship with the company’s stock market performance. Second, the frame and content are different. CSR reports are generally notmandatory, while ESG reports typically have relatively detailed guidelines and requirements.9 This is reflected in the content, which requires coverage of certain content andeven quantitative disclosure. Third, the release and use are different. The CSR reportemphasizes dissemination and communication functions, and the release is flexible. At
6For example, the world’s first ESG Domini 400 Social Index, later renamed as MSCI KLD 400
Social Index, was released in the United States in 1990. However, Chinese firms issued the first ESG
report in 2006.
7
Previous studies like Kim et al. (2014) mainly concerned the relation between the social dimension
and firm-specific future stock crash risk. ESG is preferred to CSR, as it explicitly delineates its concerns(environmental, social, and governance).
8
The CSR report audience is nearly all stakeholders, including government regulatory agencies,
employees, partners, communities, and NGOs, and therefore the CSR’s content must meet the requirements of different sub-groups. The ESG report audience is mainly capital market participants,
especially institutional investors.
9Companies have more freedom in preparing CSR reports, as long as they follow the generalreporting framework, like the GRI standard, to expand the content, and it emphasizes the readability.
However, in addition to referring to the GRI standards and other frameworks, it is also necessary for
ESG reports to follow other specific requirements.

3the same time, the ESG report is mainly for investors and has strict release requirements.10 Some listed companies are beginning to realize the value of communicatingwith investors on ESG issues and use ESG reports as an important tool for investor
communication.
This paper explores the connection between ESG disclosure and firm-specific stock
price crash risk. Our methodology involves both analytical and reduced-form models. We first develop an analytical model based on two dominant factors and estimate
the non-monotonic relationship. We then empirically evaluate this relationship. The
dataset covers panel observations of Chinese A-share listed companies from 2006 to
2020. The key variable, the ESG score, is collected from Bloomberg Professional
Service, and others are collected from China Stock Market & Accounting Researchdatabase and Wind database. The findings hold after robustness checks, like addressing endogenous concerns.
This paper contributes to the existing literature in the following three aspects. First,
unlike existing research (e.g., Murata and Hamori, 2021), which provides only empiricalevidence, we develop an analytical model to reveal the hidden mechanism. Second, ouranalytical model includes dominant factors in two competing theories, demonstratingthat both theories work under different conditions. Our schema, therefore, can givea reasonable explanation of previously mixed findings. Third, our evidence from the
updated Chinese dataset is rare and complementary to existing empirical research,
primarily in developed countries. The analytical model reveals a non-monotonic (negative about the left-end boundary point but positive with regard to the right-end)
relationship between ESG disclosure and crash risk. Our empirical results also verify
this non-monotonic relationship using a Chinese dataset and support that the ESG
disclosure level acts as a ”market stabilizer” when the ESG score is low and acts as a”market destroyer” after the ESG score reaches a specific level. Therefore, the study
offers significant implications for the corporate manager, investor, policymaker, andregulator. Specifically, transparency and credibility of the financial report are two
positive factors that make ESG more valuable.
The rest of this paper is arranged as follows. We discuss the prior research in thenext section. Section 3 presents the literature evidence of non-monotonic. Section 4
is the analytical model, revealing the non-monotonic relation. Section 5 provides a
reduced-form analysis, verifying a non-monotonic relationship. Section 6 presents ourempirical results, and Section 7 concludes the paper.
10

CSR report pays special attention to the readability and dissemination of the report. There arevarious release forms, like the PDF version, H5 version, video version, etc. Some companies may
organize special conferences or combine them with corporate brand activities. However, The ESG
report must be released within the specified time, uploaded to the company’s official website, andsubmitted to the exchange.

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2

Literature review

2.1

Environmental, social and governance

The ESG literature has mainly focused on the link between ESG and financial performance (Xie et al., 2019). Some academics examine whether the ESG score could beconsidered a probable essential element for successful investment (Richardson, 2009),
and whether investors are more willing to invest in companies with a more satisfactory
CSR profile, which might lead to more promising financial performances (De Bakker
et al., 2005). Regarding the relationship between ESG and firm performance, two
opposite views prevail. On the one hand, based on the Porter hypotheses (Porterand Linde, 1995), corporate social responsibility engagement, primarily environmental
responsibility engagement, can stimulate firm innovative behavior that generates additional gains to offset costs. Thus a suitable CSR approach may improve corporate
financial performance (CFP). Numerous empirical investigations find CSR is positively
related to CFP (Deng et al., 2013). On the other hand, CSR activities bring additionalcosts caused by inefficient resource allocation, which will make the firm less competitive in the free and competitive market (Sternberg, 1997). Much research uncoveredthat CSR is negatively correlated with a firm’s financial performance (Margolis andWalsh, 2003). Different from the positive or negative associations, some researchers
saw a neutral association between CSR and CFP (McWilliams and Siegel, 2001; Moore,
2001). Besides the relationship of ESG to FP, some studies suggest other factors thatcan strengthen or weaken this relationship, such as innovation, long-term orientation(Wang and Bansal, 2012), stakeholder relations, managerial action, financial Slack, andso on (Kim and Statman, 2012; Duque-Grisales and Aguilera-Caracuel, 2019).
The connection between ESG and the firm-level stock return has also been explored.
Belkaoui (1976) is one of the first scholars to study the linkage between corporate
exposure to environmental information and stock performance. His research uncoveredthat companies that reported environmental information underperformed others before
publishing it and surpassed them afterward. Klassen and McLaughlin (1996) propose
an analytical model that supports the notion that environmental performance awards
are associated with significantly positive returns, whereas environmental crises areheavily correlated with significant negative returns. Graham and Maher (2006) support
a negative association between environmental risk management and corporate bondratings or yields. More recently, Kim et al. (2014) investigate how CSR impacts stock
price crash risk and shows a negative influence of CSR on crash risk. Demers etal. (2020) investigate whether ESG scores could function as indicators of share priceresilience during the COVID-19 humanitarian crisis and documented that ESG scores

5

offer no such positive explanatory power for returns during COVID-19.

2.2

Stock price crash risk

There is a myriad of literature on stock price crash risk, and we can divide them into
five groups. The first group studies determinants of financial reporting and corporate
disclosures. Hutton et al. (2009) use the cumulative accrual to measure a firm’s earnings
management, and the findings demonstrate that companies with more opaque economic
information are prone to experience share price crashes. Chen et al. (2017) find thatcompanies with smoother earnings are more prone to share price crashes. DeFond et al.
(2015) investigate the effect of adopting different accounting standards on corporatecrash risks and discover that adopting International Financial Reporting Standards(IFRS) would reduce a company’s crash risk. Zhang et al. (2016) explore the impact
of corporate philanthropy (an important part of CSR) on the collapse risk of Chinesecompanies and verify that it decreases the collapse risk.
The second group of determinants is about managerial incentives and characteristics. Kim et al. (2011) study the impact of CFO equity incentives in compensationplans on businesses’ crash risk. Their results show that the higher the CFO option
portfolio value ratio, the greater the company’s crash risk. Park (2017) finds thatdifferences in the compensation of corporate employees could increase corporate real
revenue management (REM) behaviors, accordingly adding the risk of corporate stock
price plummeting.
The third group of determinants is related to the capital market. Chen et al.
(2001) believe that the trading volume of stocks mirrors the divergence of market
investors. Therefore, higher stock trade volume exhibits that some investors perceive
negative information inside the company. Callen and Fang (2015) demonstrate thatshort interest in a company’s stock is associated with its risk of a future crash. Ni and
Zhu (2016) state that the crash risks of stock prices in the market would increase whenshort-selling restrictions were removed.
The fourth group is about corporate governance. Andreou et al. (2016) show thatcompanies with a high percentage of independent directors and strict governance policies have a lower probability of collapse. Xu et al. (2014) point out that the perk
system of state-owned enterprises will encourage managers to conceal negative news
for their own benefit, leading to increased crash risks. Boubaker et al. (2014) find that
excessive control positively correlates with stock crashes.
The fifth group is regarding informal institutional mechanisms. Luo et al. (2016)
show that companies with political ties to government officers are less at risk of collapse.
Li and Chan (2016) discover that holding members of the Chinese Communist Party

6

(CPC) on the board reduces the collapse risk of the company. Li et al. (2017) explore
how social confidence and firms’ crash risk link, and the results show that companies
located in areas with high social confidence levels generally have lower crash risk.

3

Literature evidence of the non-monotonic relationship3.1

Benefits of ESG disclosure

There are two opposite views of the effect of ESG on firm-specific crash risk basedon earlier literature. Some researchers support a negative relationship since high ESG
disclosure helps to mitigate managers’ negative news hoarding activities and enhancetransparency in firms’ financial reports. For example, Gelb and Strawser (2001) uncover that companies that engage in more socially responsible activities tend to supply
better financial information disclosures. Because companies with high corporate social
responsibility usually have high ethical standards and better information transparency.
Eccles et al. (2014) discover that more long-term oriented, highly sustainable companies had better ESG measures and exposure patterns. Non-financial reports could be
employed to forecast the anticipated forthcoming economic performance of the company. Investing with consideration of ESG information can help investors bypass 90%
of bankruptcies (Lynch and Morgan, 2017). Wu and Hu (2019) reveal a lower crash risk
for such firms with high CSR scores. Other researchers, such as Cheng et al. (2014),
argue that companies with high ESG transparency have better operational reputations
and are more likely to acquire funds at lower costs.
Besides, the stakeholder perspective suggests that stakeholders and firms mutually
influence each other (Feng et al., 2021). Higher ESG disclosure helps firms enhancetheir reputation, which benefits the improvement and maintenance of the firm value.
For instance, the Legitimacy Theory view claims that a company’s ESG disclosure aims
to gain social legitimacy for the environmental or social influences of the company’s
operations (Lokuwaduge and Heenetigala, 2017). Amid the pressure of the public andstakeholders, ESG disclosure is a good management tool for maintaining a favorable
corporate reputation for the enterprise (Brammer and Pavelin, 2008). CSR, as anintangible asset, can strengthen the reputation of companies, improve performanceand safeguard the interests of shareholders in the long run (Dai et al., 2019).

7

3.2

Costs of ESG disclosure

By contrast, there is a concern about agency problems that managers may use ESG
opportunistically for personal gain. For example, Friedman (2007) argues that CSR
may be a kind of agency problem, as companies may employ CSR to conceal corporate
misconduct. Consistent with this notion, Petrovits (2006) and Prior et al. (2008) findthat CSR boosts a firm’s earnings management behaviors. If a firm uses ESG scoreas a mask to conceal poor information and shift shareholder inspection (Kim et al.,2014). To avoid reputation loss, managers are likely to use the ESG disclosure as a selfinterest tool to get promoted, which significantly undermines information transparency(Barnea and Rubin, 2010). Companies with poor performance or earnings management
and corruption are more likely to carry out charitable, public welfare, environmental
protection, and other social responsibility activities to avoid punishment and show agood image to external stakeholders (Barnea and Rubin, 2010).

3.3

Reconciling the contradictory theoretical concepts

Two main competing perspectives about the relationship exist in the previous literature. One is the stakeholder perspective, which suggests that higher ESG disclosuremeans lower crash risk. Since a high ESG score reflects that the firm values long-term
performance and has a more transparent information disclosure system, it establishes
reputational capital and thus reduces crash risk. The other is the agency perspective,
which claims that higher ESG disclosure leads to higher crash risk. Because of theinterest conflict between shareholders and managers, the managers might construct anillusion of a high ESG level to obtain personal gain, which retains bad news in firms
and increases the crash risk.
Thus, the nature of the ESG-crash risk relationship may be more complex thana simple positive or negative one. There may be conflicts between the two, and therelationship assessment also depends on the level of the ESG disclosure. The law ofdiminishing marginal returns supports the theory of the ”too-much-of-a-good-thing”
effect, which can serve as an explanation of why beneficial expectations (ESG disclosure) might lead to negative outcomes (crash risk) when they are beyond a certain
level, where the costs exceed benefits. The ”too-much-of-a-good-thing” effect assumes
that the relationship between two objects has a specific maximum, after which an extra
rise introduces a decrease in the consequence, resulting in a non-monotonic link, likethe Environmental Kuznets Curve (Trumpp and Guenther, 2017; Aghion et al., 2019;
Andreoni and Levinson, 2001). Therefore, an inflection point of the ESG level appears
when the stock price crash risk reaches its minimum (the optimal level), and after that,
there is a positive link (Pierce and Aguinis, 2013). In a word, it is necessary to find a8

balance between the two extremes.
Therefore, we hypothesize that there is a non-monotonic relationship between the
ESG disclosure level and the stock price crash risk. When the ESG disclosure level islow, the increased ESG disclosure indicates a higher level of transparency and higher
stakeholder benefits, which leads to less bad news hoarding. As the ESG disclosurelevel rises to a certain level in China, ESG report is used more as a self-interest tool for
management, it may bring additional costs caused by agency problems and inefficient
resource allocation, which would put the firms in an unfavorable position and increase
the stock price crash risk.

4

Analytical model of the non-monotonic relationship

According to the above literature review, there are two competing perspectives on the
ESG-crash risk relationship. The stakeholder perspective suggests that high ESG companies are committed to long-term firm value and stakeholder trust building. Therefore, high ESG companies will provide more transparent information (in this case, high
ESG means high transparency and low crash risk). The other is the agency perspective, which means that when a company’s shareholders and managers have conflicting
interests, they will harm shareholders and maximize their own interests. Therefore,high ESG may be a tool for managers to seek their personal interests (high ESG means
low credibility and high crash risk). Since the relationship between ESG and crash risk
is affected by both channels, we show below that their relationship is characterized as
non-monotonic. A non-monotonic function is one that does not always increase or decrease. More specifically, a function is non-monotonic if its first derivative (which does
not have to be continuous) changes sign. That is, a non-monotonic function between yand x can be defined as y(x) where two different x1 and x2 in the domain of x follows
dy
dy
∗ dx
< 0.
dx1
2

4.1

Model setup

A company’s cash flow (Ct ) production process is as follows:C t = K 0 Xt

(1)where K0 is a constant, representing the initial investment, and Xt is the shocks
that affect the cash flow-generating process. Xt is the sum of three independent parts:

9Xt = ft + θ1,t + θ2,t(2)

Here ft captures a macroeconomic factor that affects all firms in the market and is
known by all people. θ1,t and θ2,t capture firm-specific factors. θ1,t is public information,such as annual financial reports, news, etc. θ2,t is information within the firm, such as
negative news hidden by managers. The managers inside the company observe both
θ1,t and θ2,t , but outsiders only know θ1,t . θ1,t and θ2,t are independent of each other.
For simplicity and rationality, we assume that ft , θ1,t and θ2,t are stationary AR(1)with the same AR(1) parameter φ (0 < φ < 1). We assume that the error terms, εt+1 ,
ξ1,t+1 , and ξ2,t+1 are all normally distributed with mean 0 and variance 1. That is:
ft+1 = f0 + φft + εt+1 ,
θ1,t+1 = θ1,0 + φθ1,t + ξ1,t+1 ,(3)

θ2,t+1 = θ2,0 + φθ2,t + ξ2,t+1 ,Thus, Xt is also stationary AR(1):
Xt+1 = X0 + φXt + λt+1(4)where X0 = f0 + θ1,0 + θ2,0 , and λt = εt + ξ1,t + ξ2,t .
Next, we define κ as the ratio of firm-specific to market variance:κ=Var (θ1,t + θ2,t )Var (ft )(5)

And we define a firm’s transparency as the ratio of the variance of θ1,t to the sumof the variances of θ1,t and θ2,t :η=Var (θ1,t )Var (θ1,t )=,Var (θ1,t + θ2,t )Var (θ1,t ) + Var (θ2,t )(6)

The second equation holds because θ1,t and θ2,t are independent of each other.

4.2

Transparency and crash risk are negatively related

Given the company’s current (t) stock price, the return for the next period (t + 1)
depends on two factors. One is market factor ε̃t+1 , captured by the market returnrm,t+1 ; and a firm-specific factor ξ˜t+1 . Thus, R2 of a firm, represented by the portionof variance explained by the market, is:R2 =Var (εt+1 )1=
Var (εt+1 ) + Var (ξt+1 )κη + 110(7)Here κ is the ratio of firm-specific to market variance, defined in Formula (2.5). ηis the firm’s transparency, defined in Formula (2.6). From the equation, we found that,when other things are equal, the less transparent the company is, the greater the R2 .
In other words, transparency is inversely proportional to R2 .
Next, we want to show that crash risk is proportional to R2 . Jin and Myers (2006)
state that stocks have higher R2 in less developed countries. Higher R2 means a higher
portion of variance explained by the market. In developing countries (with immature financial markets), such as China, where external regulation is weak, company
managers are more likely to steal company profits for their own benefit. We assume
managers can take away money, and the takeaways depend on market expectations. In
this case, if the macroeconomic environment improves year by year and the company’s
actual profit is 50, 100, and 200 for three consecutive years, the manager would steal
10, 50, and 125 in these three years, respectively. Ultimately, the amount of profit
that the company presents to the market is the actual profit minus stealing by managers, namely, 40, 50, and 75. However, in developed countries (with sound financial
markets), it is more difficult for companies to manipulate profits due to sound laws,
regulations, and supervision systems. Since crash risk means negative news hoarding
or potentially exposed takeaway, a high R2 implies a high level of bad news hoardingor high crash risk. In other words, R2 is proportional to crash risk, R2 ∝ crash risk.
Combining the above formula (7), we obtain the following formula:
Crash risk ∝1κη + 1(8)

Crash risk is inversely proportional to transparency.

4.3

Transparency and ESG score are positively related

Companies with high ESG scores disclose more ESG-relevant information to the market, which reflects high transparency. Therefore, we believe that ESG score and transparency are positively related. We assume that this positive relationship satisfies thefollowing, η(ESG = 0) > 0, η ′ > 0 and η ′′ < 0. This assumption is reasonable.
η(ESG = 0) > 0 is established because even if no ESG information is disclosed, thecompany still has positive transparency due to other disclosures, such as financial reports. η ′ > 0 is established because ESG disclosure is a form of information disclosure.
The higher the ESG score, the more information is revealed, thus higher transparency.
η ′′ < 0 is established because, intuitively, when the level of ESG disclosure is low, theincreased ESG disclosure at this time is important information, resulting in a rapid
increase in transparency. When the level of ESG disclosure is high, the increased ESG

11

disclosure at this time is trivial information and has little impact on the improvementof transparency.

4.4

Credibility and crash risk are negatively related

Managers have two options when negative θ2,t exists, namely bad news hoarding inside
the firm. One is to stay with the company and continue to hide bad news. Then
managers will need to pay a certain cost to cover up the bad news. The other is giving
up hiding bad news (like leaving the company and getting some money). For the first
option, managers need to pay a certain amount in the current year and future to coverup the bad news. We discount future money to the current period. According toMyers (2000), the following formula expresses managers’ total cost of sticking with thecompany to cover up bad news.
K0 θ2,t + P V {K0 E (θ2,t+1 | θ2,t ) , K0 E (θ2,t+2 | θ2,t ) , . . . ; r}
1 θ2,0φ
θ2,0= K0 θ2,t ++−+ θ2,tr1−φ 1+r−φ
1−φ

(9)

Here, P V stands for discounting future amounts to the current period. r is the riskfree rate. φ (0 < φ < 1) is the AR(1) parameter of θ2,0 . E (θ2,t+1 | θ2,t ) is the conditional
expectation of θ2,t+1 given θ2,t . K0 θ2,t means the cost in period t for managers to coverup bad news (θ2,t ). P V {K0 E (θ2,t+1 | θ2,t ) , K0 E (θ2,t+2 | θ2,t ) , . . . ; r} means discounted
future costs to period t (given θ2,t ).
Under the second option, managers give up hiding bad information, abandon thecompany, and get a one-time income. This income is related to the market’s valuationof the company. According to Myers (2000), the overall valuation of the company byexternal investors can be expressed as follows:
Manager’s stick cost=φ
K 0 X0
φ
1 K 0 X0
θ2,0−+
K0 ft + θ1,t +E (Kt | ft , θ1,t ) =r1−φ 1+r−φ1−φ 1+r−φ
1−φ
 


1 K 0 X0
θ2,0
K 0 X0φ=
K0 ft + θ1,t +−+r1−φ 1+r−φ
1−φ
1−φ
(10)
We assume that credibility will affect the lowering of the market’s valuation of thecompany and that managers get paid p(0 < p < 1) times the company’s overall valuation. Therefore, the amount that the manager can get at this time can be expressedas:12Manager’s gain=p ∗ ( credibility )
1 K 0 X0φ
K 0 X0+−+ K0 (ft + θ1,t + θ2,t )r1−φ 1+r−φ
1−φ

(11)

The indifference condition (both options11 are equivalent for managers) of managers
is:




1 θ2,0φθ2,0K0 θ2,t ++−+ θ2,tr1−φ 1+r−φ
1−φ



(12)
1 K 0 X0φ
K0 X 0+ p ∗ credibility+−+ K0 (ft + θ1,t + θ2,t )=0r1−φ 1+r−φ
1−φ
We can see that the higher credibility, the more managers can obtain from the firm,
and the less likely they will ditch the company (release bad news). Therefore, we provethat credibility is negatively related to crash risk.

4.5

Credibility and ESG score are negatively related

According to agency theory, when there is interest conflict between shareholders andmanagers, the managers might construct an illusion of a high ESG level to obtain
personal gain, which retains bad news in firms and increases the crash risk. Therefore,
there is a negative relationship between ESG scores and credibility. We assume that
this negative relationship satisfies the following, z2 (ESG = 0) = maximum > 0,z2′ < 0 and z2′′ < 0. This assumption is reasonable. z2 (ESG = 0) = maximum > 0
is established because when no ESG information is disclosed, the possibility of ESG
being used by managers as a tool for personal gain is 0, so the credibility is the highest.
z2′ < 0 is established because as ESG disclosure increases, ESG is more likely to be
used by managers as a tool for personal gain and thus lower credibility. z2′′ < 0 isestablished because, intuitively, when the level of ESG disclosure is low, the increased
ESG disclosure at this time is more likely to be true information, and the decreasein credibility is not obvious. When the level of ESG disclosure is high, managers arelikely to whitewash ESG performance to achieve personal goals or hide bad news, andcredibility declines faster as ESG increases.
11

Specifically, option one is that managers choose to pay a certain amount in the current year andin the future to cover up the bad news; option two is that managers give up hidden information,
abandon the company, and get a one-time income.

13

4.6

Formula simplification for crash risk function on transparency and credibility

According to proposition 4 in Jin and Myers (2006)12 , the return process of a firm’s
stock satisfies the following formula:˜(1 + r) ε̃t+1 + ξt+1
r̃i,t+1 = r +X0 (1 + r)/r + φ (ft + θ1,t )(13)

Where r̃i,t+1 is excess rate of return. r is the risk-free rate, From the above formula,
we can see that r̃ is inversely proportional to θ11 , namely:
1
θ1

r∝

(14)

We assume r− is the excess rate of return at times of stock crash. When the negative
news (θ2 ) is exposed to investors, the stock price will fall sharply (crash). Similar to
the above formula, we can infer that r− satisfies the following formula:r− ∝1
θ1 + θ2(15)

We calculate the crash risk as the proportion of the standard deviation of stock
returns on ”down” days to that on all days. And since Var(X) = E [X 2 ] − E[X]2 , weobtain the following formula for crash risk.
P 2Pr−var (r− )Crash risk = P 2 = Pr
var(r)(16)

Then we substitute formulas (2.14) and (2.15), and obtain:


1
var
T−
θ1 +θ2
 P
1
T var θ1

P
Crash risk =

(17)

P
Since
r− equals total days multiplied by the probability of negative returns,P
r equals total days. Meanwhile, according to the equation formula of the function
var(f (x)) = (f ′ (E(x)))2 Var(x), we transform the above formula into the following:
Crash risk ∝T · Pr− · var (θ1 + θ2 )1
= Pr− ·
T · var (θ1 )η(18)

Pr− represents the probability of occurrence of r− . It can be seen from the above
12

It is shown on page 268.

14

equation that when only considering transparency, the risk is inversely proportional totransparency. This is consistent with intuition.
We then simplify Pr− . The indifference condition for managers are:
1 θ2,0φθ2,0K0 θ2,t ++−+ θ2,tr1−φ 1+r−φ
1−φ



1 K 0 X0φ
K 0 X0+ p ∗ ( credibility )+−+ K0 (ft + θ1,t + θ2,t )=0r1−φ 1+r−φ
1−φ(19)
Because other factors are constants, we can simplify the two parts before and after
the plus sign into −β1 θ2 and z2 · β2 · (θ1 + θ2 ). Here, we describe the constant term
before θ2 as β1 . We add the ”negative sign” to indicate that this is the manager’s pay(cost). we describe the constant term before (θ1 + θ2 ) as β2 . We use z2 to represent
credibility for brevity.
Therefore, we get the following:
Pr− = Possibility of releasing bad news = P {−β1 θ + z2 β2 · (θ1 + θ2 ) < 0}

− β1 θ + z2 · β2 · (θ1 + θ2 )


β1 θ2
+ z2 β2= (θ1 + θ2 ) −θ1 + θ2θ1= (θ1 + θ2 ) −β1 1 −+ z2 β2θ1 + θ2

(20)

(21)

= (θ1 + θ2 ) [−β1 (1 − η) + z2 β2 ]∝ β1 η + β2 z2
Thus,1
Crash risk = P {η + z2 < 0}
η

(22)For η (transparency), when η is larger, η1 is smaller, p is smaller, and finally, thecrash risk becomes smaller. For z2 (credibility), when z2 is larger, the crash risk
becomes smaller. Therefore, for both transparency and credibility, the risk is inversely
proportional to them. This is also consistent with intuition.

4.7

The non-monotonic relation

Based on reasonable assumptions about the relationship of ESG to the two channels(transparency η and credibility z2 ) in subsections (2.4.3) and (2.4.5),13 and the simplified formula for crash risk function on transparency and credibility shown in equation
13

Specifically, for η, η ′ > 0 and η ′′ < 0; for z2 , z2′ < 0 and z2′′ < 0.

15

(22), we first illustrate the existence of a non-monotonic relationship by specifying thetrends of the two boundary points.
The trend of the left boundary point (when ESG is close to the minimum value,that is, the company does not disclose ESG information) is as follows: When ESG
increases, η increases substantially, and z2 decreases by a small amount (or almost
unchanged). It can be seen from equation (2.22) that a large increase in η causes alarge decrease in crash risk; a small reduction in z2 results in a tiny increase in crashrisk. Therefore, at the left boundary point, when ESG rises, the combined effect of ηand z2 causes a decrease in crash risk. This means that the relationship between ESG
dRisk
and crash risk is negative at the left boundary point, namely, dESG
< 0.
low
The trend of the right boundary point (when ESG is close to the maximum value,that is, the company almost fully discloses ESG information) is as follows: When
ESG increases, η increases by a small amount (or almost unchanged) and z2 decreases
substantially. It can be seen from equation (22) that the slight increase in η causes aslight decrease in crash risk; a large reduction in z2 results in a large increase in crashrisk. Therefore, at the right boundary point, when ESG rises, the combined effect of ηand z2 causes an increase in crash risk. This means that the relationship between ESG
dRisk
> 0.
and crash risk is positive at the right boundary point, namely, dESG
high

dRisk
So far, we have verified dESG
< 0 exists when ESG is small (close to the minimum
dRisk
value), dESGlow

> 0 exists when ESG is large (close to the maximum value). Therefore,

high

dRisk

dRisk
∗ dESG< 0, which shows that there is a non-monotonic relationship between
dESGlowhigh
ESG and crash risk.
Furthermore, we could select three ESG values to verify the possible non-monotonic
relationship between ESG and crash risk. When ESG takes values 1, 20, and 40, respectively (that is, ESG1 = 1, ESG2 = 20, and ESG3 = 40; ESG1 < ESG2 < ESG3 ),it is reasonable that η (transparency) takes the values of 5, 14, and 15, respectively.
And z2 (credibility) takes the values of 15, 14, and 5, respectively. Therefore, we getthree pairs of (transparency, and credibility), that is, (5,15), (14, 14), and (15, 5).
Substituting these three pairs of values into (2.22), we get the values of crash risk as1
1
1
1
P (20), 14
P (28), 15
P (20). The size relationship between them is 15 P (20) > 15
P (20) >51
P (28), namely Risk1 > Risk3 > Risk2 .
14

5

Research design

5.1

Data and sample

Our initial sample contains all firms listed on the A-shares (RMB ordinary stock) from
China Security Market from 2005 to 2020. Please note that the ESG scores and control
16

variables are gathered from 2005-2019, and crash risk data is calculated from 2006-2020.
Then, we impose the following requirements: (1) excluding enterprises in the financial
sector, (2) excluding enterprises with fewer than thirty trading weeks in one year,
and (3) excluding observations with missing data. Our sample finally includes 6777
observations with 1017 firms and ranges 16 years. We next winsorize all the continuous
variables at 1% and 99% percentages to ease the outliers’ influences. Data are collectedfrom China Stock Market & Accounting Research Database (CSMAR), Wind database,and Bloomberg Professional Service. The specific data sources for each variable areshown in Table 1.
[Table 1]

5.2

Measurement of crash risk

Following the prior research, such as Kim et al. (2014) and Zhang et al. (2016), we use
two indexes to evaluate a firm’s crash risk: the first one is the negative coefficient ofskewness of a firm’s weekly stock returns (N CSKEWi,t ); the other is the crash likelihood estimation of the Down-to-Up Volatility (DU V OLi,t ) of a firm’s stock returns.
To calculate them, we need first calculate the firm’s weekly returns (Wi,t ), defined as
the natural logarithm of one plus the residual term, which is obtained from below themarket model regression:
Ri,t = αi + β1 Rm,t−2 + β2 Rm,t−1 + β3 Rm,t + β4 Rm,t+1 + β5 Rm,t+2 + εi,t(23)

where Ri,t is firm i’s stock return during week t. Rm,t−2 , Rm,t−1 , Rm,t , Rm,t+1 , andRm,t+2 are market returns of total value-weighted market index during weeks t − 2,t − 1, t − 1, t + 1, and t + 2, respectively. εi,t is the residual term.
Then, firm-specific weekly returns (Wi,t )14 are calculated below:
Wi,t = ln (1 + εi,t )(24)

Next, N CSKEWi,t , is computed via the third moment of firm i’s weekly stock
returns in year t, divided by the cubed standard deviation of a firm’s weekly returns,
then multiplied by a negative one. The calculation formula is explicitly shown as
follows:hi 
X3/2 
X
3/2
3
2
N CSKEWi,t = − n(n − 1)
Wi,t / (n − 1)(n − 2)
Wi,t
(25)
Here n represents the total number of trading weeks of firm i in year t. From the14

When εi,t is less than -1, Wi,t is a missing value. Here 36 observations were deleted.

17equation, we know that when N CSKEWi,t rises, the left skewness of the distributionof the excess returns will be more significant, which indicates a higher crash possibility.
Then, we evaluate DU V OLi,t , which is formed by taking the logarithm of the
proportion of the standard deviation of a firm’s weekly stock returns in ”up” weeks
to that in ”down” weeks. Up and down weeks are obtained by comparing returns inthat week with a firm’s average weekly returns for the year t. When the weekly stock
return is larger than the average value, this is an ”up” week; when the firm’s weekly
stock return is smaller than the average value, this is a ”down” week. The calculation
process is shown below:("
DU V OLi,t = log# "(nu − 1)

X
DOW N

2
Wi,t
/ (nd − 1)

#)
X

2
Wi,t

(26)

UP

Here nu (nd ) indicates the week’s number that firm i’ weekly stock returns arehigher (lower) than the average weekly stock returns during the year t. High DU V OLi,timplies high crash risk.

5.3

Environmental, Social and Governance information

We use ESG scores obtained from the Bloomberg Professional Services platform. Its
ESG information is primarily gathered from corporate sustainability reports, financial
reports, and firms’ news and announcements. The ESG disclosure score measures thetransparency of ESG information, and the scoring process takes into account disparities in importance and industry distinctions for each data point. Bloomberg’s ESG
data varies from 0.1 to 100, with the two extremes representing the minimum level of
disclosure and disclosure of all relevant information, respectively.

5.4

Empirical model

To investigate the relationship between firm ESG disclosure and stock price crash risk,
we construct the following regression model:
CrashRiskt+1 = β0 + β1 ESGt + β2 ESG2t + β3 Controlst + Industry + Year + εt (27)Here the dependent variable, CrashRiskt+1 , is derived from N cskew or Duvol. ESG
is the key independent variable. All independent variables are packaged in year t, witha one-year lag from the dependent variable. This permits us to check whether ESG
disclosure in year t can forecast the crash risk in year t + 1.
The control variables (Controls) are those factors that may affect future crash risk
based on previous literature (Kim et al., 2014). We first include the lagged variable18

of crash risk (N CSKEWi,t or DU V OLi,t ) for possible serial correlation. Then, we
include eight other control variables in the model. Chen et al. (2001) document that,besides trading volume, prior returns can also affect future crash risk because any
surging accumulated during past returns is usually followed by a plummet in price.
Therefore, we consider past returns (RET ), firm size (SIZE), and the market-to-bookratio (M B) as control variables. Since investor opinion heterogeneity has a link tothe stock price crash risk (Hong and Stein, 2003), the detrended stock trading volume(DT U RN ), an indicator of investors’ strategy set diverseness, is also added. Stockvolatility (Sigma) is included since volatile stocks are expected to undergo a future
price crash in a larger chance. Other firm-level variables, including the absolute valueof abnormal accruals (ABACC) used for measuring earnings management (Hutton
et al., 2009), financial leverage (LEV ), and profitability (ROA), are also included ascontrol variables. Table 1 shows the variable definitions.
Our empirical analysis regressed the firm-specific crash risk in year t+1 on ESG
and other control variables in year t. We considered industry and year-fixed effects(Industry and Y ear dummies) in our regression. Consistent with the prior literature,
we estimate the regression with the standard error modified by a two-dimensional cluster at both firm and year level (Petersen, 2009; Kim et al., 2014). In addition to thepanel data regressions, we also consider the endogenous issues which may confuse theaccurate relation between ESG and firm-specific crash risk. To lighten the endogenous concerns, we conduct the two-stage instrument variable method (2SLS) with theaverage ESG of remaining firms in the identical industry as the instrumental variable.

6

Empirical results

6.1

Descriptive statistics

Table 2 and Figure 1 show the yearly sample distribution. We can see that the sample
size increased rapidly from the year 2008. It may be due to the increased numberof companies that choose to publish ESG reports or the expanded coverage of theBloomberg database. The two gauges of crash risk (NCSKEW and DUVOL) show
relative stability across years, except for the highest crash risk in 2008.15 The years
2009 and 2016 have the lowest crash risk.16 The average ESG score keeps increasingover time, while the value is relatively small in the first three years. This means thelevel of ESG information disclosure by Chinese companies is increasing yearly.
15

The high value of crash risk in 2008 reflects the financial crisis.
The two years are right after the Chinese stock market crash, thus showing lower stock price crash
risk.
16

19

We can intuitively see the variations of ESG, NCSKEW, and DUVOL values over
the year in Figure 2. The blue line represents ESG values and shows an upward trend by
year. This means the firms in our sample are increasing ESG disclosure and investment,
and their ESG performance is improving yearly. The NCSKEW and DUVOL values
fluctuate over time. The low points in the years 2009 and 2016 were encountered rightafter the stock market crash in the last year, which released a lot of hidden bad news.
The values of two stock price crash risk measurements, NCSKEW and DUVOL in red
and green, are very close each year.
[Table 2][Figure 1 & 2]
Table 3 reports the descriptive statistics for the major variables used in our regression models. The average values of two crash risk evaluations N CSKEW and DU V OL
are -0.342 and -0.235, respectively. The mean ESG score is 21.881. The mean of thedetrended average monthly share turnover is 0.042. The mean and standard deviationof firm-specific weekly returns are 0.003 and 0.010, respectively. The firm in our sample
has an average book-to-market ratio of 2.133, an average leverage of 0.491, an average
return on assets of 0.046, and an average size of 23.095. The mean absolute valueof abnormal accruals is 0.053. These data are consistent with the previous literature(Kim et al., 2014).
[Table 3]
Table 4 presents the correlation matrix for the variables used in our main regression models. Pearson’s correlation determines the strength and direction of the linear
relationship between two variables. In Table 4, the correlation coefficient between
F N CSKEW and F DU V OL is 0.876 and statistically significant at the 1% level. It
means that the two measures for crash risk are highly significantly correlated with eachother and capture similar information, although their constructions are quite different.
The Pearson correlation coefficient of ESG and F N CSKEW (F DU V OL) is -0.003(-0.008).17 It shows that there is no linear relationship between ESG and crash risk
in bivariate analysis. Spearman’s rank-order correlation determines the strength anddirection of the monotonic relationship between two variables. The Spearman’s rankorder correlation coefficient between ESG and F N CSKEW (F DU V OL) is -0.005(-0.010), indicating a non-monotonic relationship between the two variables.
[Table 4]
Figure 3 intuitively shows the relation between ESG disclosure and firm-specificcrash risk. We use ”F NCSKEW” to represent a crash risk in the graph above and”F DUVOL” to represent a crash risk in the graph below. The red line in the graphs fits
the relationship between ESG and crash risk. We can see a non-monotonic relationship17

We put another measure of crash risk and the corresponding Pearson coefficient in parentheses.

20

in both pictures though it is not so obvious. The curve is an intuitive confirmation of
our hypothesis. In the next section, we explore the relationship statistically.
[Figure 3]

6.2

Effect of ESG on crash risk

Table 5 shows the regression results of the relationship between ESG and crash risk
with controlling other probable determining factors of crash risk. From the results inTable 5, we can see that the linear relationship in columns (1) and (2) (whether the
dependent variable shows as F NCSKEW or F DUVOL) is not significant, which means
the association between ESG and crash risk is not liner. This finding is inconsistent
with many studies that have verified a negative connection between ESG and crash risk
(Kim et al., 2014; Feng et al., 2021). It is also contradictory to Dai et al. (2019), which
proved an inverted U-shaped relationship between CSR and crash risk. The resultsin columns (3) and (4) in table 5 present that the coefficient of the ESG quadraticterm is significantly positive and the coefficient of ESG is significantly negative. Thismeans the link between ESG and predicted crash risk(in one year) (represented as
F NCSKEW and F DUVOL) is non-monotonic. Column (3) indicates that when ESG
increases, the crash risk in the next year first decreases and then increases afterward.
The critical point appears when the ESG score is about 20.91 (that is when the natural
logarithm of ESG score equals about 3.04). Column (4) also indicates the relationship,
which first goes down and then up. The critical point in column (2) appears when the
ESG score is about 20.70 (that is, when the natural logarithm of ESG score equals
about 3.03), which is very similar to column (1). Comparably, the mean and medianvalues of the ESG score are 21.88 and 21.07, respectively. Therefore, the critical pointis very close to the mean and median values.
As shown in previous studies, in developed countries, the negative relationshipshows that the higher the ESG level, the more transparent the company’s information,and the lower the risk of stock crashes. However, in developing countries, such as
China, ESG development is at an early stage, and the situation is different. Here, theESG disclosure and regulatory systems are immature. At the same time, due to thecountry’s emphasis on sustainable development, companies are likely to achieve theirpersonal goals by presenting high-level ESG information to the public. Therefore, thehigher ESG level here may not mean that the company’s information is transparent
and the available stakeholder advantages, but it hides serious agency problems, which
increases the risk of stock crashes. As to the control variables, M B and Ret are
significantly and positively correlated with crash risk, while Sigma is significantly andnegatively related to crash risk. The coefficients of the control variables are consistent21

with previous studies. (Kim et al., 2014; Dai et al., 2019).
However, the criterion of a significant quadratic term is weak. The problem arises
when the true relationship is convex but monotone over relevant data values. A
quadratic specification may then erroneously yield an extreme point.18 Lind and
Mehlum (2010) put forward ”utest” (a test in STATA) to provide the exact test of
the presence of a turning point on an interval. This test first calculates the locationof the extreme point according to the regression equation and then divides the whole
data into the data before and after the extreme point. After that, it checks whether
the first part of the data is monotonically downward and whether the latter part ismonotonically upward. The null hypothesis for this test is ”monotone or inverse Ushape”. After performing the utest, we obtain the values of the t-value and P-value,
1.56 and 0.0703, respectively. The null hypothesis is rejected at a 10% confidence level.
Overall, the results in table 5 present that the relationship between ESG and crash risk
is non-monotonic, which means an appropriate ESG disclosure, rather than a too-low
or too high-ESG score, is most beneficial to maintaining the stock price stable.
[Table 5]

6.3

Endogeneity

The preliminary result shows a non-monotonic link between ESG and one-year-ahead
firm-specific stock price crash risk. However, considering the potential endogeneity
problems is necessary. Endogeneity may arise due to unobservable firm-specific factors
which affect both ESG and crash risk at the same time. Our estimation model uses
the lagged ESG score to predict the following year’s crash risk. This could potentiallymitigate endogeneity concerns named reverse causality. The simultaneity concern remains since the ESG scores are very sticky over the sample years. Thus, we conduct
the instrumental variables method to estimate the model.
According to the prior research (e.g., (Kim et al., 2014)), we select the average
ESG score of the other firms in the same industry as the instrumental variable.19 This
instrumental variable satisfies both relevance and exogenous restrictions: first, theaverage ESG score of all other firms in the same industry is usually related to thisfirm’s ESG; on the other hand, the ESG of other firms cannot affect the crash risk ofthis firm. We have performed relevant tests to show that the instrumental variables
are appropriate. For the endogeneity test: The P values of the Durbin-Wu-Hausman
18

Specifically, given that the true relationship of the two variables is monotonically increasing (ormonotonically decreasing) when we add a quadratic term to the regression, this may generate an
unreal extreme point, presenting a falsely significant quadratic term.
19
The classification of the industries refers to the ”China 2012 Industry Classification Standard”
issued in 2012.

22

test were zero, rejecting the null hypothesis that lnESG and lnESG2 are exogenous
variables. For the weak instrumental variable test: The first-stage F values are around362 and 431, indicating that there are significant correlations between instrumental
variables and endogenous explanatory variables.20
The result of the instrumental variables method is shown in Table 6. For the firststage (Columns (1) and (2)), we consider two endogenous variables, namely, lnESG
and lnESG2 . For this reason, two IVs, IV− (lnESG) and IV− (lnESG2 ) are used. Here,IV− (lnESG) is the natural logarithm of the average ESG of all other firms in the same
industry. IV− (lnESG2 ) is the square of IV− (lnESG). For both lnESG equation and
lnESG2 equation, we have used both IV− (lnESG) and IV− (lnESG2 ). We control”Control” for both equations at the first stage. The control variables used in both
equations are the same and also the same as those used in the second stage. For thesecond stage (Columns (3) and (4)), we use two dependent variables, F NCSKEW
and F DUVOL, for robustness. The first stage results indicate that the instrumental
variable is significantly positively related to the lnESG and lnESG2 . The third andfourth columns are significant and consistent with the baseline findings. Therefore, thenon-monotonic relationship still holds after addressing the endogeneity concerns via
the instrumental variable method.
[Table 6]

6.4

Robustness test

Several robustness tests have been conducted to ensure the results’ reliability. First, we
use two indicators, N SKEW and DU V OL, to measure stock price crash risk, and wefind the results consistent between these two in all tables. Second, since ESG contains
social responsibility and environmental responsibility, the ESG engagement of dirty
industries21 will have a greater impact on their firm value. Therefore, we divided theresearch samples into dirty and clean industries to conduct regression. From Table
7, we can see that the quadratic relationship between ESG and crash risk exists indirty industries, but not in other industries. This suggests that ESG can significantly
impact company value in industries where ESG engagement is more important, likedirty industries. According to the 2012 version of the industry classification of listedcompanies, we classify B (mining industry), C (manufacturing industry), D (electricity,heat, gas, and water production and supply industry) as dirty industries, and otherindustries as clean industries.
[Table 7]
20
21

Both of the two F values have a P value of zero.
We refer to heavy-polluting industries as dirty industries.

23

We divided the samples into manufacturing (generally considered more pollutioncarrying) and non-manufacturing industries to conduct regression, respectively, andthe results are shown in Table 8. From Table 8, we can see that the quadratic relation
between ESG and crash risk exists in the manufacturing industry but not in otherindustries. This suggests that ESG can significantly impact company value in industries
where ESG engagement is more important, like manufacturing.
[Table 8]
Third, we divided the research samples into two parts, whether recent years or not(we took the recent five years as recent years) and presented the results in Table 9.
As ESG investment is increasingly valued in China, ESG engagement has likely had
a more significant impact on firm value in recent years than before. From the resultsin Table 9, we can see that the quadratic correlation between ESG and crash risk
exists only in the sample data after 2015, regardless of whether NSKEW or DUVOL
is taken as the dependent variable. This result shows that as the public attaches
more importance to ESG (environmental responsibility, social responsibility, corporate
governance) engagement in recent years, the company’s ESG performance significantly
impacts the firm value.
[Table 9]7Conclusion

Sustainable development is becoming more and more important nowadays. As an important part of the economy and society, to improve their competitiveness in the fierce
market and achieve sustainable development while pursuing profit, enterprises must
actively conduct their ESG engagement. As China has focused more on sustainable
development at all levels of the country in recent decades, it is of great significance for
Chinese-listed enterprises to fulfill their ESG.
This paper examines the effect of ESG disclosure on firm-specific stock price crashrisk. This is a meaningful problem as a business invest a lot in ESG event and wish toearn some benefits from ESG engagement. Previously, there are two mainstream rival
claims on this relationship. On the one hand, ESG disclosure equals a high degreeof transparency in financial reporting, which is found significantly reduce crash riskby previous studies in financial transparency (e.g. Lowenstein, 1996). Thus, ESG is
expected to reduce the stock price crash risk (e.g., negatively related). On the other
hand, ESG disclosure is also viewed as an expectation management tool (moral hazard
problem), a sign of hypocrisy of managers who may hide bad news and even grasp
benefits for their private interest. In this case, ESG may increase the stock price crashrisk (e.g., positively related). Each theory received empirical support from previous
24research, leading to a controversial pending problem.
This paper tries to solve the problem quantitatively. We first develop an analyticalmodel to cover dominant variables in both theories and establish an important resultthat the relationship overall is non-monotonic. Specifically, a low ESG level should
decrease crash risk, while a high ESG level does the contrary. This insight is very
useful and solid, yet insufficient to give a specific function form. Therefore, we further use reduced-form analysis to derive a non-monotonic curve. Using the Chinese
A-share listed firms during the year 2006-2020 as a sample, we find that there is a nonmonotonic relationship between ESG and crash risk, and the relationship holds after
controlling other impacting factors. In addition, our results remain robust after considering potential endogenous problems using the IV method. This finding means thatthe discretional exposure of ESG information has a complicated connection with firmspecific stock price crash risk. Specifically, as the firm discloses more ESG information,
its stock price crash risk first decreases and increases afterward.
Our study adds to the growing ESG literature in two senses. First, this paper
expands the scope of ESG research as we introduce an analytical model instead ofpure empirical evidence. This offers us more insight into the mechanism and can bringabout counterfactual knowledge. Second, our empirical finding of the non-monotonic
curve is novel and robust. This finding coincides with our analytical result using datafrom Chinese listed companies. There are some implications for the manager, investor,
policymaker, and other relevant agents. For the manager, it is important to conduct
ESG engagement at an appropriate level since it can not only help enhance the firm’s
reputation but also help keep the stock price stable. For the investor, it is possible tochoose firms with appropriate ESG to score rather than too low or too high to invest,
to reduce the potential damage that may cause by the stock price crash to personal
interests. For the policymaker, making regulations encouraging companies with low
ESG scores to disclose more ESG information can help reduce the volatility in thestock market.
This study still has some limitations. First, the ESG score in this study was measured by the evaluation index of the third-party rating agency. Albeit it seems appropriate and is generally accepted by academics, the index still has some deficiency inreflecting the actual ESG performance of listed firms in China. Since the ESG scoreis attained based on the ESG information disclosed by the firms, the rating agencies
have not evaluated the actual ESG performance of the listed firms. The advanced
measurement method is necessary to be carried out for more credible results. Second,
the sample only contains the listed firm disclosing the ESG information. It is not ahigh percentage compared to all the listed firms; thus, the evaluation index can not
fully reflect the ESG performance of all Chinese listed firms. More firms with ESG
25

disclosure will help ease this problem in the future.

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30

Table 1: Variable definition
Variables Definition
Crash risk variables
NCSKEW The negative coefficient of skewness.
See Eq. (25) for details.
DUVOL
The down-to-up volatility. See Eq. (26)for details.
Key independent variables
ESG
ESG scoreFirm-level control variables
SIZE
measured as the natural log of a firm’s
total assets
ROA
measured as the income before extraordinary items divided by total assetsMBmeasured as the ratio of the firm’s market value to the book value
LEV
measured as the total liability scaled bytotal assets
Sigma
the standard deviation firm-specificweekly return over the fiscal yearRetthe average firm-specific weekly return
over the fiscal year
DTURN
the detrended stock trading volume,
calculated as the average monthly shareturnover for the current fiscal year minus the average monthly share turnoverfor the previous fiscal year
ABACC
The absolute value of discretionary
accruals, where discretionary accruals
are estimated from the modified Jonesmodel (Dechow et al., 1995).

31

SourceCalculated by the authors
Calculated by the authors

Bloomberg
CSMAR
CSMAR
CSMAR
CSMAR
Calculated by the authors
Wind
Wind

Calculated by the authors

Table 2: Sample distribution
Year
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Total

Frequency
4
12
28
216
277
297
429
585
642
638
710
671
728
794
746
6777

Percent
0.06
0.18
0.41
3.19
4.09
4.38
6.33
8.63
9.47
9.41
10.48
9.9
10.74
11.72
11.01
100

ESG
12.29314.91015.50719.41320.65221.27521.82620.76620.88521.11321.58422.28022.82623.36323.54221.881

NCSKEW
0.175-0.438-0.222-0.039-0.498-0.138-0.229-0.243-0.420-0.426-0.282-0.542-0.190-0.108-0.437-0.309DUVOL
0.111-0.316-0.116-0.019-0.370-0.122-0.156-0.152-0.270-0.288-0.207-0.382-0.123-0.092-0.299-0.214

Note: This table shows the sample size and mean values of ESG and crash risk
measures by year. The sample includes 6777 firm-year observations from 2005
to 2019.

Table 3: Descriptive statistics
VarNameF NCSKEWF DUVOLESG
NCSKEW
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
ABACC

Obs
6777
6777
6777
6777
6777
6777
6777
6777
6777
6777
6777
6777

Mean
-0.342-0.23521.881-0.3090.491
23.095
0.042
2.133
0.046
0.003
0.059
0.053

SD
0.725
0.481
5.284
0.721
0.197
1.266
0.138
1.608
0.065
0.010
0.024
0.052

Min
-5.170-2.0469.091-5.1700.008
19.541-0.7460.692-0.902-0.0380.015
0.000Median-0.296-0.23521.074-0.271
0.502
23.018
0.000
1.631
0.039
0.002
0.054
0.037

Max
3.736
2.239
61.722
3.736
1.698
28.3410.770
30.674
0.590
0.075
0.232
0.470

Note: This table reports the descriptive statistics of all variables. The data ranges
from 2005 to 2019 for ESG and control variables and from 2006 to 2020 for crash risks.

32

33

F NCSKEW
10.876***-0.0030.072***
0.064***-0.066***-0.059***0.005
0.151***
0.117***
0.068***-0.067***0.016

1-0.0080.070***
0.060***-0.076***-0.082***0.009
0.148***
0.111***
0.058***-0.077***0.014

F DUVOL1
0.001-0.0070.089***
0.364***-0.048***-0.145***-0.007-0.042***-0.135***-0.073***ESG

10.878***-0.080***-0.074***0.038***
0.095***
0.109***-0.168***-0.088***0.025**NCSKEW1-0.089***-0.097***0.035***
0.085***
0.100***-0.186***-0.086***
0.012

DUVOL

1
0.493***-0.032***-0.450***-0.474***-0.024**0.039***
0.053***

LEV

1-0.059***-0.445***-0.106***-0.089***-0.219***-0.063***SIZE

10.044***
0.058***
0.018
0.003
-0.014DTURN

10.436***
0.375***
0.264***
0.084***

MB

1
0.117***-0.100***
0.012

ROA

1
0.394***
0.003

Ret

1
0.095***

Sigma

1

ABACC

Note: This table reports the correlation coefficients of each variable in our main regression. All correlation coefficients are below 0.8 (except the correlation coefficients of similar measures),indicating no significant multi-collinearity problem exists. * denotes p < 0.1, ** p < 0.05, and *** p < 0.01.

F NCSKEWF DUVOLESG
NCSKEW
DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
ABACC

Table 4: Pearson correlation matrix

Table 5: Regression analysis on the effect of ESG on crash risk

lnESG

(1)
F NCSKEW
0.024(0.86)(2)F DUVOL
0.019(0.80)

lnESG2
NCSKEW

0.059*(1.93)

DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
AbsDA
Constant
IndustryYearNadj. R2F

0.018(0.25)
0.007(0.26)-0.025(-0.36)
0.052***(6.01)
0.164(0.73)
9.733***(3.70)-0.714(-0.82)-0.018(-0.16)-0.352(-0.58)
Yes
Yes
6777
0.091
2659.527

0.046**(2.66)
0.012(0.24)-0.005(-0.29)-0.005(-0.13)0.033***(5.09)
0.072(0.44)
6.448***(3.40)-0.847*(-1.81)-0.019(-0.20)0.081(0.18)
Yes
Yes
6777
0.090
3145.522(3)F NCSKEW-0.845**(-2.27)0.139**(2.47)
0.059*(1.93)

0.018(0.25)
0.006(0.24)-0.027(-0.39)0.051***(5.98)
0.163(0.73)
9.720***(3.70)-0.722(-0.83)-0.022(-0.19)0.974(1.61)
Yes
Yes
6777
0.091
106.443(4)F DUVOL-0.632*(-1.98)0.104*(2.11)

0.046**(2.63)
0.012(0.24)-0.006(-0.32)-0.006(-0.16)
0.033***(5.06)
0.071(0.43)
6.438***(3.39)-0.853*(-1.81)-0.022(-0.24)
1.075*(1.98)
Yes
Yes
6777
0.090
157.664

Note: This table reports regression results of the impact of ESG scores on the probability of firm-level stock crash risk. The sample covers 6777 firm-year panel observations
from 2006 to 2019. Notice that the two-tailed t-values, based on standard errors
modified by a two-dimensional cluster at the firm and year levels, are disclosed inparentheses. * denotes p < 0.1, ** denotes p < 0.05, and *** denotes p < 0.01.

34

Table 6: Regression analysis to address endogeneity concerns

Dep. Var.
IV− (lnESG)
IV− (lnESG2 )(1)First1lnESG
0.164***(4.04)-0.044(-0.17)(2)
First2lnESG2-6.497***(-3.72)2.032***(7.24)(lnESG) HAT(lnESG2 ) HAT
NCSKEW(3)
Second1
F NCSKEW(4)
Second2
F DUVOL-6.305*(-1.69)1.050*(1.74)
0.056***(4.39)-4.551*(-1.79)0.750*(1.83)

DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
AbsDA
Constant
IndustryYear
N
F-0.095***(-2.99)0.061***(9.71)-0.030(-1.26)-0.007**(-2.77)-0.068(-1.35)1.632***(4.45)-0.479***(-2.98)-0.067(-1.51)0.404(1.35)
Yes
Yes
6777
362

-0.597***(-3.11)0.388***(8.97)-0.178(-1.22)-0.043**(-2.68)-0.420(-1.36)10.309***(4.49)-2.949**(-2.91)-0.396(-1.46)
2.252(1.11)
Yes
Yes
6777
431

0.043
(0.65)-0.014(-0.89)-0.029(-0.45)0.051***(5.92)
0.161(0.81)
9.152***(5.85)-0.679(-1.06)-0.031(-0.18)9.371(1.64)
Yes
Yes
6777

0.043***(3.34)
0.025(0.55)-0.018(-1.64)-0.009(-0.21)0.032***(5.47)
0.070(0.51)
6.113***(5.72)-0.838*(-1.92)-0.031(-0.27)7.089*(1.82)
Yes
Yes
6777

Note: This table shows the regression result after dealing with endogeneity issues on theeffect of ESG scores on crash risk. Columns (1) and (2) present the first-stage resultsof the instrumental variable method, and columns (3) and (4) report the second-stage
results of the instrumental variable method. The two-tailed t values, based on standard
errors modified by a two-dimensional cluster at the firm and year levels, are disclosed inparentheses.. * denotes p < 0.1, ** denotes p < 0.05, and *** denotes p < 0.01.

35

Table 7: Regression analysis: dirty vs clean industries

lnESG
lnESG2
NCSKEW(1)(2)
F NCSKEW
clean
dirty
-1.075-0.732(-1.12)(-1.72)0.166
0.123*(1.07)(1.93)
0.081*
0.047(1.84)(1.70)

DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
AbsDA
Constant
IndustryYearNadj. R2
F

0.295**(2.95)-0.006(-0.23)0.070(1.35)
0.069***(3.50)
0.289(1.07)
10.826**(2.97)-0.418(-0.27)-0.127(-0.57)1.259(1.19)
Yes
Yes
1980
0.093
510.366-0.073(-0.76)0.011(0.37)-0.067(-0.68)0.046***(6.67)
0.135(0.57)
9.288***(3.40)-0.992(-0.97)0.006(0.04)
0.647(1.08)
Yes
Yes
4797
0.096
317.316(3)
F DUVOL
clean-0.320(-0.51)0.049(0.46)(4)dirty-0.694*(-1.99)0.115**(2.17)

0.051(1.38)
0.213***(2.98)-0.017(-1.01)
0.039(0.95)
0.042***(3.24)
0.305(1.02)
7.268***(3.60)-0.762(-0.74)-0.046(-0.22)0.578(0.89)
Yes
Yes
1980
0.090
2111.252

0.042**(2.49)-0.053(-0.95)-0.001(-0.07)-0.024(-0.50)0.030***(5.63)
0.003(0.01)
6.094**(2.96)-0.986**(-2.68)-0.021(-0.17)1.006(1.40)
Yes
Yes
4797
0.097
1078.668

Note: This table shows the regression result of the effect of ESG on
crash risk in dirty and clean industries. Columns (1) and (2) present theresults of the dependent variable F NCSKEW, and columns (3) and (4)report the results of the dependent variable F DUVOL. The two-tailed tvalues, based on standard errors modified by a two-dimensional cluster
at the firm and year levels, are disclosed in parentheses. * denotes p <0.1, ** denotes p < 0.05, and *** denotes p < 0.01.

36

Table 8: Regression analysis: manufacture vs other industries

lnESG
lnESG2
NCSKEW(1)(2)
F NCSKEW
othersmanufacture-0.718-0.909*(-0.81)(-1.81)0.118
0.148*(0.80)(1.99)
0.064
0.055*(1.49)(2.12)

DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
AbsDA
Constant
IndustryYearNadj. R2F

0.161**(2.19)
0.003(0.11)-0.016(-0.17)0.078***(3.78)
0.095(0.37)
11.128***(3.35)-1.464(-1.58)-0.032(-0.13)0.962(0.85)
Yes
Yes
2698
0.083
666.117-0.059(-0.52)0.009(0.31)-0.034(-0.42)0.042***(7.04)
0.202(0.84)
9.011***(3.69)-0.315(-0.22)-0.017(-0.10)0.596(0.57)
Yes
Yes
4079
0.102
2226.738(3)
F DUVOLothers-0.394(-0.52)0.067(0.52)(4)
manufacture-0.782*(-1.83)0.127*(1.95)

0.045(1.38)
0.110**(2.21)-0.008(-0.41)-0.023(-0.31)
0.046***(3.56)
0.113(0.51)
6.839***(3.46)-1.329*(-2.02)0.016(0.08)
0.766(0.81)
Yes
Yes
2698
0.078
694.626

0.046**(2.75)-0.037(-0.62)-0.005(-0.26)0.002(0.05)
0.028***(5.44)
0.054(0.30)
6.238***(3.39)-0.614(-1.01)-0.041(-0.39)1.095(1.27)
Yes
Yes
4079
0.106
1125.902

Note: This table shows the regression result of the effect of ESG scores on crashrisk in different industries (manufacture or not). Columns (1) and (2) present theresults of the dependent variable F NCSKEW, and columns (3) and (4) report
the results of the dependent variable F DUVOL. The two-tailed t values, based onstandard errors modified by a two-dimensional cluster at the firm and year levels,
are disclosed in parentheses. * denotes p < 0.1, ** denotes p < 0.05, and ***denotes p < 0.01.

37

Table 9: Regression analysis: recent vs previous years

lnESG
lnESG2
NCSKEW(1)(2)
F NCSKEW
previous
recent0.204-1.072*(0.23)(-2.16)-0.0290.163*(-0.19)(2.23)
0.063**
0.039(2.79)(0.88)

DUVOL
LEV
SIZE
DTURN
MB
ROA
Ret
Sigma
AbsDA
Constant
IndustryYearNadj. R2F

0.061(0.71)-0.036(-1.21)-0.075(-0.74)0.044**(2.91)
0.705***(4.61)
8.486*(1.85)
0.310(0.25)-0.100(-0.88)0.359(0.35)
Yes
Yes
3128
0.114
789.283-0.014(-0.13)0.061***(5.99)
0.032(0.38)
0.062***(19.34)-0.172*(-2.63)9.644**(3.71)-0.869(-0.66)0.009(0.05)
0.739(1.97)
Yes
Yes
3649
0.101
43.355(3)F DUVOLprevious
0.264(0.31)-0.039(-0.26)(4)
recent-0.924***(-7.32)0.143***(6.81)

0.049*(2.19)
0.003(0.05)-0.030(-1.32)-0.008(-0.14)0.029**(2.78)
0.441**(2.81)
5.581(1.66)
0.012(0.02)-0.054(-0.57)0.286(0.30)
Yes
Yes
3128
0.112
2014.699

0.028(1.71)
0.028(0.41)
0.026*(2.42)-0.008(-0.10)0.040***(39.72)-0.189*(-2.67)
6.946**(4.05)-1.119(-1.64)-0.016(-0.09)1.432***(6.50)
Yes
Yes
3649
0.100
54.619Note: This table shows the regression result of the effect of ESG scoreson crash risk in different years (recent years from 2015-2019 or not).
Columns (1) and (2) present the results of the dependent variable
F NCSKEW, and columns (3) and (4) report the results of the dependent
variable F DUVOL. The two-tailed t values, based on standard errors
modified by a two-dimensional cluster at the firm and year levels, aredisclosed in parentheses. * denotes p < 0.1, ** denotes p < 0.05, and ***denotes p < 0.01.

38

800
600
Frequency
400
200
0
2005

2010

year

2015

2020

Figure 1: The number of firms with ESG disclosure in each year

Figure 2: The values of ESG, NCSKEW, and DUVOL over the year

39

2
1
0
-1
-2
-3
2.5

3

ln_esg4

Fitted values

-2

-1

0

1

2

F_NCSKEW

3.5

2.5

3

ln_esg

F_DUVOL

3.5

4

Fitted values

Figure 3: The relationship between ESG disclosure and crash risk

40