North American Journal of Economics and Finance 74 (2024) 102238
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North American Journal of Economics and Finance
journal homepage: www.elsevier.com/locate/najef
Does liquidity connectedness affect stock price crash risk?
Evidence from China
Xin Yang a , Xuan Ao c , Jie Cao b, c, * , Chuangxia Huang c
a
b
c
School of Economics and Management, Changsha University of Science and Technology, Changsha, China
College of Management and Economics, Tianjin University, Tianjin, China
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China
A R T I C L E I N F O
A B S T R A C T
JEL:
G01
G10
Using a sample of CSI300 over the 2006–2021 period to establish liquidity spillover networks, we
find a significantly negative relationship between liquidity connectedness and stock price crash
risk. Further analysis shows that liquidity connectedness depresses stock price crash risk through
two potential channels: increased conditional conservatism and decreased stock price synchro­
nicity. Moreover, this effect is more prominent for firms with effective external monitoring, firms
with lower risk-taking, and state-owned enterprises (SOEs). Overall, our paper shows that
liquidity connectedness is an important factor influencing crash risk and provides useful guidance
for corporate management and investor decision-making.
Keywords:
Liquidity spillover network
Liquidity connectedness
Stock price crash risk
1. Introduction
The term “stock price crash” refers to a regular and significant decrease in the capital market value of a listed firm’s stock (Shi et al.,
2022). Since the 1920s, there have been numerous stock price collapses on the global stock market. This type of financial turbulence
has had a serious impact on investors’ wealth and the healthy development of the capital market (Franklin and Edwards, 1988), and
may even endanger the operation of the real economy and induce an economic crisis. This catastrophic phenomenon has garnered
attention from regulators, entrepreneurs, and academics alike, prompting their collaborative efforts to identify effective mechanisms
for mitigating the stock price crash risk (Zhang, Xie, and Xu, 2016).
In recent years, stock liquidity has been considered to affect capital market instability. Numerous studies show that there is a larger
stock price crash when there is greater liquidity, and they also identify two key causes for this effect (Chang, Chen, and Zolotoy, 2017).
First, the short-termism argument suggests that increased stock liquidity amplifies the pressure on firm managers to deliver short-term
results due to the influence of short-term investors, leading to the adoption of short-term strategies and resulting in adverse infor­
mation aggregation, ultimately culminating in heightened crash risk (Porter, 1992; Fang, Tian, and Tice, 2014). Second, the gover­
nance argument holds that the disclosure of negative information triggers a strong reaction from the market, which causes the stock
price to plummet (Edmans, 2009). These studies have typically regarded firms as independent entities (Shi et al., 2022). However,
there are strong ties between some firms in terms of economic conditions (Inekwe, 2020), so it is impossible to overlook the liquidity
connectedness between firms.
The connectedness phenomenon has been demonstrated to be beneficial given the stock market conditions, which indicates
* Corresponding author.
E-mail address: caojie_math@126.com (J. Cao).
https://doi.org/10.1016/j.najef.2024.102238
Received 13 March 2024; Received in revised form 10 June 2024; Accepted 1 July 2024
Available online 4 July 2024
1062-9408/© 2024 Published by Elsevier Inc.
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
liquidity waves can spread from a single firm to another via financial relations (Yang et al., 2024). Meanwhile, the correlation between
liquidity connectedness and the real economy has also received attention from researchers (Obstfeld, 1994; Devereux and Smith,
1994). The 2008 financial crisis placed a significant strain on European nations, and the spread of the crisis was indispensable to
changes in the dimension and direction of liquidity connectedness in European countries. Moreover, Smimou and Khallouli (2016)
reveal that a comprehensive grasp of different elements of individual financial channels, especially liquidity and liquidity connect­
edness, can aid in crafting suitable policies to mitigate or prevent crises. Thus, this article deviates from existing studies and focuses on
the connection between liquidity connectedness and stock price crash risk by constructing liquidity spillover networks (Wang et al.,
2021; Huang et al., 2023). At the same time, we conducted channel analysis and studied the heterogeneity of the impact of liquidity
connectedness on the stock price crash risk from three different perspectives: external monitoring, risk taking, and ownership type.
We contribute to the field in two primary respects. By examining the relationship between liquidity connectedness and stock price
crash risk, this paper expands the literature on stock price crash risk. Edmans (2009) suggests that the disclosure of negative news
would affect the shareholding situation, causing a strong reaction in the market. Chang, Chen, and Zolotoy (2017) present that
liquidity, as a governance mechanism, has an impact on management at the corporate level, which in turn affects stock price infor­
mation. Alp, Canbaloglu, and Gurgun (2022) show that there is a positive correlation between liquidity and stock price crash risk, but
this positive link is not driven by blockholder ownership. These studies show that liquidity can affect stock price information by
affecting enterprise management and information symmetry. In other words, there is a certain relationship between stock liquidity and
stock price crash risk. However, they ignore inter-firm connectedness when studying the stock price crash risk. Given the state of
financial markets, we demonstrate that liquidity connectedness is an important factor influencing crash risk.
Second, we explore the impact of liquidity connectedness on the Chinese market. Many works of literature have explored liquidity
connectedness in Europe (Smimou, Khallouli, 2016), the United States, and other regions (Inekwe, 2020), but there is little literature to
analyze the phenomenon of liquidity connectedness in China. Karolyi et al. (2012) and Huang (2020) demonstrate that among the 40
nations, the liquidity commonality of Chinese equities is the highest; that is, the liquidity connectedness of the Chinese market is
obvious and important. Therefore, this study investigates the liquidity connectedness of the Chinese market.
The remainder of this paper is structured as follows: Section 2 reviews the related literature. Section 3 describes the methodology,
key variables, and model design construction. Section 4 presents the data. Section 5 explains the features of the constructed liquidity
spillover network. Section 6 presents the empirical analysis, endogeneity concerns, and robustness tests. Meanwhile, this part outlines
the results of the channel analysis. Section 7 further studies and reveals the heterogeneity of the impact of liquidity connectedness on
stock price crash risk. Section 8 presents the conclusions.
2. Literature review
First of all, we review the related literature on the stock price crash risk. The mechanism of the financial market indicates that the
source of crash risk is the leverage effect (Christie, 1982), the volatility feedback effect (Pindyck, 1984; Campbell and Hentschel,
1992), and the stochastic bubbles model (Li et al., 2017). If investors have different opinions and face short-sale restrictions, some
negative opinions can be missing from the stock price. So once hidden bad news builds up to a critical point, stock prices collapse. The
agency theory framework has another view of the sources of crash risk. In Jin and Myers’ (2006) model, managers hide bad news and
disclose good news because of conflicts of interest. When the volume reaches a certain point and managers give up, bad news specific to
the firm becomes public all at once, causing the stock to plummet. In recent years, there has been a growing body of empirical evidence
supporting this source of stock price crash risk (Kim, Li, and Zhang, 2011b; Xu et al., 2014; Chang, Chen, and Zolotoy, 2017). The
literature that examines the impact of stock liquidity on crash risk is a good example. Chauhan, Kumar, and Pathak (2017) show that
there is a larger stock price crash when there is greater liquidity because of the short-termism argument (Porter, 1992; Fang, Tian, and
Tice, 2014) and the governance argument (Edmans, 2009). Obviously, in the process of studying the factors influencing the stock price
crash risk, these documents treat stocks as independent individuals and do not consider the integrity of financial markets.
In fact, the complex interrelationships in the stock market can be effectively described by complex network theory (Huang et al.,
2016; Li, Wen, and Huang, 2023). Because firms have different degrees of shock diffusion intensity and liquidity connectivity, this
study expands the concept of connections to spillover networks and considers the liquidity connections between firms as edges (Gong
et al., 2023). On the basis of the Granger causality (Hiemstar and Jones, 1994) of CSI300 stock liquidity, liquidity spillover networks
are constructed quarterly from 2006 to 2021. Through the study of network topology indicators, it was found that liquidity connections
became stronger during crises, which can be convincingly explained by the herding effect (Yarovaya et al., 2022).
Furthermore, another question is how to properly measure liquidity connectedness for firms. Huang et al. (2021) demonstrate how
various traditional topological measures may effectively assess a node’s capacity for spreading. These indications, however, neglect the
features of the underlying diffusion dynamics, and the computation can get complex if the number of nodes is very high. Brin and Page
(1998) put forward the PageRank algorithm, widely used for identifying influential nodes in a Web network, to address these limi­
tations. Based on these theories, we decide to apply PageRank to measure liquidity connectedness. As expected, the empirical evidence
shows that liquidity connectedness has a significantly negative association with stock price crash risk. Specifically, centrally located
enterprises (i.e., liquidity connectedness recipients) receive more liquidity shocks and obtain lower liquidity (Inekwe, 2020), which
reduces stock price crash risk according to short-termism theory (Porter, 1992; Fang, Tian, and Tice, 2014) and governance theory
(Edmans, 2009).
In addition, connections between nodes in a liquidity spillover network can serve as a conduit for firms to obtain and exchange
information, which in turn affects the stock price crash risk. Therefore, the impact of liquidity spillovers on crash risk can be developed
through the following institutional channels: First, the C-score amplifies the impact of liquidity connectedness on stock price crash risk.
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North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
Centrally located firms have access to a greater amount of liquidity information and resources, which is beneficial for corporate
governance and operations (Kim, Li, and Zhang, 2011a). Indeed, executives often conceal negative information from investors for their
own benefit (Jin and Myers, 2006; Hutton, Marcus, and Tehranian, 2009), but central firms can enlarge conditional conservatism (Cscore) to reduce managers’ incentives to hide bad news, thereby reducing stock price crash risk (Kim and Zhang, 2016). Second, stock
price synchronicity can lessen the impact of liquidity connectedness on stock price crash risk. Centrally located firms are closely linked
to other firms that oversee corporate information disclosure, which is good for increasing information symmetry. The proportion of
firm-specific and market-level information included in stock prices increases with a decrease in common fluctuation (Boubaker,
Mansali, and Rjiba, 2014). This phenomenon reduces information asymmetry and, thus, lowers the likelihood of a stock price crash.
Finally, the corporate governance environment (Jensen and Meckling, 1976), managers risk-taking actions (Dye, 1988; Trueman
and Titman, 1988), and policy advantages (Piotroski et al., 2015) all affect the stock price crash risk, so the degree of impact of
liquidity connections on the crash risk can be distinct for different types of firms. We can analyze the heterogeneity of the influence of
liquidity connectedness on stock price crash risk from these three different perspectives. First, the impact of liquidity connectedness is
more prominent in firms with effective external monitoring. Xu et al. (2014) show that efficient external monitoring measures are able
to alleviate agency issues and construct a satisfactory corporate governance environment. Also, effective monitoring can curb
opportunistic conduct by managers and diminish the likelihood of future crashes (Li et al., 2017). Second, the impact of liquidity
connectedness is more prominent in firms with lower risk-taking. Outside investors or the board of directors are likely to take actions to
hide managers risk-taking actions once noticed, so managers tend to conceal excessive risk-taking actions to stabilize the stock price
(Dye, 1988; Trueman and Titman, 1988; Kim, Li, and Zhang, 2011b). Therefore, risk-taking has a strong impact on information
symmetry, which in turn affects the crash risk. Third, the impact of liquidity connectedness is more pronounced in state-owned en­
terprises (SOEs). Government interventions shield SOEs from resource competition in capital markets, so they pay less attention to
investor reactions and have less incentive to hoard bad news, which decreases crash risk (Zhang et al., 2010; Zhang, Xie, and Xu, 2016;
Wang et al., 2008).
3. Methodology, key variables and model design
3.1. Stock liquidity measurement
Following Corwin and Schultz’s study, the liquidity metric CSHL demonstrates superior performance compared to various other
liquidity indicators, including the ROLL covariance estimator and Lesmond’s LOT estimator. Meanwhile, CSHL does not require an
iterative process or maximum likelihood estimation. It provides a closed diffusion solution, which makes it easy to use. Most
importantly, because CSHL is not computer-time-intensive, it is more suitable for extensive sample sizes and diverse markets with
different market structures (Corwin and Schultz, 2012). For these reasons, a bid-ask spread estimator (CSHL) that employs daily high
and low prices has been chosen as the means of gauging stock liquidity. It is defined as follows:
( αi − 1 )
2e
CSHL = max
,0 ,
(1)
1 + eα i
αi =
√̅̅̅̅̅̅̅ √̅̅̅̅ √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
2βi −
β
γi
√̅̅̅ i −
√̅̅̅,
3− 2 2
3− 2 2
(2)
1
∑
2
β = E(
[ln(h*t+j /l*t+j )] ),
(3)
j=0
2
γi = (max(h*t+1 , h*t ) − min(l*t+1 , l*t )) ,
(4)
where h*t and l*t represent the logarithmic highest price and the logarithmic lowest price, respectively. The higher the CSHL, the
lower the stock liquidity. For ease of interpretation, we multiply each CSHL by − 1 and define it as LIQ.
3.2. The liquidity spillover network construction
In this paper, we construct the liquidity spillover network based on the linear Granger causality test (Hiemstar and Jones, 1994;
Yang et al., 2023). The network can be expressed by an adjacency matrix:
⎛
⎞
0
caus1,2 ... caus1,k
⎜ caus2,1
0
... caus2,k ⎟
⎟,
Ccausality = (Ncausality , Dcausality ) = ⎜
(5)
⎝ ...
...
...
... ⎠
0
causk,1 causk,2 ...
where Ncausality indicates the vertex set, Dcausality indicates the edge set, and causi,j means whether stock i’s liquidity Granger causes stock
j’s liquidity significantly. Therefore, the Granger causality network is a directed and unweighted complex network (Gao et al., 2018).
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X. Yang et al.
{
causi,j =
1, stockiʹsliquidityGrangercausesstockjʹsliquiditysignificantly,
0, stockiʹsdoesnotGrangercausesstockjʹsliquiditysignificantly.
(6)
3.3. Key variables measurement
3.3.1. Dependent variable: Stock price crash risk
Prior to estimating the crash risk of stock prices, it is crucial to calculate firm-specific weekly returns, which are calculated as
follows (Chen, Hong, and Stein, 2001):
γj,τ = αj + β1j γ m,τ− 2 + β2j γm,τ− 1 + β3j γ m,τ + β4j γm,τ+1 + β5j γm,τ+2 + εj,τ ,
where γj,τ is the return on stock j in week τ and γ m,τ is the return on the CRSP value-weighted market index in week τ.
We further calculate the crash risk, which is based on negative conditional return skewness (NCSKEW) as:
∑
∑
3
2 3/2
NCSKEWi,t = − [n(n − 1)3/2
Wi,t
]/[(n − 1)(n − 2)(
Wi,t
) ],
(7)
(8)
)
(
where n is the number of weeks of firm i during quarter t. Wi,τ = ln 1 + εj,τ . A stock with a higher value for NCSKEW is more likely to
have a crash risk.
3.3.2. Independent variable: PageRank
PageRank is used as an index to measure node centrality, which can be described as a random walk on hyperlinked networks (Brin
and Page, 1998). Each node is assigned a score according to its relative importance. The probability that a node can leap to a random
node is given as a parameter γ. Therefore, the score PageRanki (t) for node i at time step t is defined as follows:
PageRanki (t) = γ + (1 − γ)
N
∑
aij
1
[ in (1 − δkin ,0 ) + δkin ,0 ]PageRankj (t − 1),
j
N j
ki
j=1
(9)
where kin
i is the in-degree of node j and N is the number of nodes in the network. aij = 1 if there is a link from i to j; otherwise, aij = 0.
δkin = 1 if kin
j = 0; otherwise, δkin = 0. Meanwhile, si (0) = 1 and the parameter γ is usually set to be 0.15. A node with a larger PageRank
j
j
has a higher centrality in the network.
3.4. Model specification
The model used to assess the impact of liquidity connectedness on stock price crash risk can be formulated as follows:
∑
∑
NCSKEWi,t = α + β1 PageRanki,t + γControlsi,t +
Year +
Industry+εi,t
(10)
∑
∑
where i indicates firm and t is year.
Year and
Industry refer to year and industry fixed effects, respectively. This model gathers
robust standard errors from the firm.
We select factors that have been demonstrated to have an impact on the stock price crash risk as control variables. In accordance
Table 1
Variable definitions.
Variable
Definition
NCSKEWi,t
Ratio of the third moment of firm-specific weekly returns for each quarter over the standard deviation of firm-specific weekly returns raised to the
third power, and then multiplied by − 1. Eqs. (7) − (8) show details.
Down-to-up volatility of firm specific weekly returns. Eq. (11) shows details.
A random walk on hyperlinked networks. Eq. (9) shows details.
DUVOLi,t
PageRanki,
t
ECi,t
CCi,t
BCi,t
Sizei,t
Levi,t
ROAi,t
Growthi,t
Agei,t
Sharei,t
C − scorei,t
SYNi,t
Z − Scorei,t
A common network centrality metric. Eqs. (14) − (15)
A network centrality metric. Eqs. (16)-(17) shows details.
A network centrality metric.. Eq. (18) shows details.
The log of the market value of equity.
Ratio of long-term debt over the book value of total assets.
Ratio of income before extraordinary items over the lagged total assets.
Asset growth rate.
Number of years since the firm was listed.
Shareholding proportion of the controlling shareholder.
The conservatism score calculated following Khan and Watts (2009).
Stock price synchronization, calculated following Jin and Myers (2006), reflects the correlation between individual stock fluctuations and overall
market fluctuations.
Z − Scorei,t = 0.3*Net Profiti,t / Total Assetsi,t + Salesi,t / Total Assetsi,t + 1.4*Retained Earningsi,t / Total Assetsi,t + 1.2*Working Capitali,t / Total
Assetsi,t + 0.6*Market Value of Equityi,t / Total Liabilitiesi,t.
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North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
with previous studies (Kim, Li and Zhang, 2011a; Shi et al., 2022), the set of control variables includes firm size (Size), debt-asset ratio
(Lev), return on assets (ROA), asset growth (Growth), firm age (Age), shareholding proportion of the controlling shareholder (Share),
and stock price crash risk with a lag of one period used to control potential serial correlation. To categorize the industries of firms, we
utilize the WIND secondary industry standard for the year 2021. Furthermore, we incorporate industry-specific and annual dummy
variables as control variables in our analysis. Table 1 provides a detailed description of the definitions of each variable.
4. Data
4.1. Sample selection
This paper utilizes the daily closing prices of the CSI 300 Index between 2006 and 2021 to form the sample. The whole sample
period includes 3890 trading days. We obtain the data needed for research in the WIND database and the CSMAR database. According
to Hu et al. (2019), we improve the statistical reliability by following these steps: (1) Exclude stocks that have less than 80 % of the total
trading days. (2) Eliminate stocks that exhibit consecutive missing closing prices for more than 80 days. (3) Missing data is filled with
data from the previous period. Finally, 108 stocks in CSI300 are taken into account.
4.2. Descriptive statistics
Panel A in Table 2 presents the descriptive statistics of the indicators. The stock crash risk (NCSKEW) has a mean of 0.165, which
aligns with findings in the existing literature (Xu et al., 2013). With a standard deviation of 1.3754, the NCSKEW is quite different in
the selected sample. Therefore, the sample has the significance of further study. PageRank is a centrality-related metric that shows how
significant each single actor is inside a network. The mean and the standard deviation values for PageRank are 0.0093 and 0.0078,
respectively. These findings suggest that the firms hold distinct positions within the liquidity spillover network. Panel B in Table 2
indicates that there is no multi-collinearity in the regression model.
5. Illustration of liquidity spillover network
We establish 64 quarterly networks to analyze the change in liquidity connectedness from 2006 to 2021. We select four special
significance levels as thresholds: λ = 0.1, 0.05, 0.01, and 0.005, respectively (Huang et al., 2020). Table 3 indicates that as the
threshold λ decreases from 0.05 to 0.01, the average number of isolated nodes increases from 0.09 to 7.72. These results illustrate that
the connections to the liquidity spillover networks experienced severe impairment with λ = 0.01. At the same time, the liquidity
spillover networks exhibit a significant weakening of connections and a substantial loss of information. Thus, we choose 0.05 as the
threshold for the purpose of avoiding information redundancy.
Fig. 1 displays the liquidity spillover networks generated through the Granger causality test, spanning from 2006 to 2021. It is
worth mentioning that the stocks have been arranged in ascending order of market capitalization and partitioned into three categories,
each accounting for 30 %, 40 %, and 30 %, respectively. Light blue means ranking 1–32, dark blue means 33–76, and green means
77–108. In this paper, we only show some representative quarterly networks (2006Q1, 2007Q2, 2008Q1, 2009Q1, 2010Q3, 2013Q2,
2015Q3, 2018Q4, 2020Q1). From the results in Figure, there are significantly more network edges in times of crisis (2007Q2, 2013Q2,
2015Q3, 2018Q4, 2020Q1) than in normal times, which indicates that nodes are more closely connected.
Note that the network density can represent how close the stock points are to one another (Yu, Xie, and Jiang, 2018). As presented
Table 2
Descriptive statistics of variables.
Panel A
Variable
NCSKEWi,t
PageRanki,t
Sizei,t
Levi,t
ROAi,t
Growthi,t
Agei,t
Sharei,t
Panel B
Variable
PageRank
Size
Lev
ROA
Growth
Age
Share
A
B
C
D
E
F
G
N
Mean
Median
Std. Dev
25 %
75 %
6912
6912
6912
6912
6912
6912
6912
6912
0.165
0.0093
24.103
52.7513
4.4223
33.4213
15.4815
39.1148
0.104
0.0072
24.2336
52.7208
2.8261
13.6443
15
38.11
1.3754
0.0078
1.5019
21.3968
5.2992
269.8108
5.9811
16.7461
− 0.8757
0.0043
23.1119
37.0963
0.9576
5.6403
11
24.9315
1.1125
0.0117
25.0839
67.8907
6.4254
25.2152
20
52.13
A
B
C
D
E
F
G
1.0000
− 0.0164
0.0179
0.0150
− 0.0006
− 0.0066
− 0.0152
1.0000
0.2603
0.1150
0.0283
0.3204
0.0798
1.0000
− 0.4601
0.0473
0.0403
− 0.1665
1.0000
0.0057
− 0.0074
0.1327
1.0000
0.0291
0.0169
1.0000
0.0925
1.0000
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X. Yang et al.
Table 3
Statistic characteristics of the Granger causality networks.
p
0.1
0.05
0.01
0.005
NN
NNIN
MIIN
MAIN
AIN
MINE
MANE
ANE
108
108
108
108
0
3
64
64
0
0
1
3
0
4
27
51
0
0.09
7.72
18.55
1007
521
102
53
3281
2382
1102
765
1175.8
933.34
307.48
198.91
This table contains the special threshold(λ), number of nodes (NN) number of networks with isolated nodes (NNIN), minimum number of isolated
nodes (MIIN), maximum number of isolated nodes (MAIN), average number of isolated nodes (AIN), minimum number of edges (MINE), maximum
number of edges (MANE) and average number of edges (ANE).
Fig. 1. Liquidity spillover networks for different periods. This figure only shows some representative quarterly networks (2006Q1, 2007Q2,
2008Q1, 2009Q1, 2010Q3, 2013Q2, 2015Q3, 2018Q4, 2020Q1), there are significantly more network edges in times of crisis (2007Q2, 2013Q2,
2015Q3, 2018Q4, 2020Q1) than in normal times, which indicates that nodes are more closely connected.
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North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
in Fig. 2, the network density fluctuated dramatically (from 2007Q1 to 2009Q1) when the subprime mortgage crisis occurred in
2007–2009. Afterwards, the Chinese stock market returned to a relatively stable period from 2010 to 2012. With the serious money
shortage in the Chinese market in 2013, the network density attained its peak value in 2013Q2. In 2015, it can be seen that the network
density accessed a turbulent period (from 2014Q4 to 2016Q1) because of a stock market crash and reached the highest value (0.206 in
2015Q3) during all the sample periods. When trade disputes between China and the US occurred in 2018, the network density rose to
0.125 (2018Q1). Since then, sharp fluctuations in the network density can be discovered in 2020 due to COVID-19. Thus, we find out
that the liquidity interconnections have been strengthened during crises, which is consistent with that of other related studies (Si et al.,
2021), and the herding effect has convincingly explained the results (Yarovaya et al., 2022). In other words, crises can be identified
based on network density.
6. The impact of liquidity connectedness on stock price crash risk
6.1. Baseline results
This section analyzes the relationship between liquidity connectedness and stock price crash risk. From Panel B in Table 2, we
conclude that there is no multi-collinearity in this model.
Table 4 presents the findings. In particular, the initial column showcases the model that does not contain control variables. The
second column shows the model with PageRank and control variables. The results reveal that the PageRank has a significantly negative
association with stock price crash risk. In fact, centrally located enterprises (i.e., liquidity connectedness recipients) that receive more
liquidity shocks obtain lower liquidity (Inekwe, 2020). According to short-termism theory and governance theory, firms with less
liquidity accumulate less negative news and limit the strong market reaction, so the crash risk is smaller (Chang, Chen and Zolotoy,
2017).
6.2. Robustness tests
6.2.1. Endogeneity concerns
We employ instrumental variables in order to reduce the possible impact of endogeneity on our research. According to the previous
studies of Faccio et al. (2011) and Hao and Xiong (2021), this paper chooses average PageRank in the same industry, PageRankInd, and
average PageRank in the same region, PageRankArea, as the instrumental variables of PageRank. Normally, the significance of a firm
within the same industry and region as a recipient within the network is linked to the target enterprise, but it does not directly impact
crash risk. As a result, the instrumental variables meet the prerequisites of relative exogeneity and economic significance.
Fig. 2. Network density over time. This figure shows the network density of the liquidity spillover network for each quarter from 2006 to 2021. The
network density fluctuated dramatically (from 2007Q1 to 2009Q1) when the subprime mortgage crisis occurred in 2007–2009. With the serious
money shortage in the Chinese market in 2013, the network density attained the peak value in 2013Q2. Because of the stock market crash, network
density reached the highest value in 2015Q3. When trade disputes between China and the US occurred in 2018, the network density rised to 0.125
(2018Q1). Sharp fluctuations of the network density can be discovered in 2020 due to the COVID-19.
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X. Yang et al.
Table 4
The impact of liquidity connectedness on stock price crash risk.
Variable
NCSKEWi,t
NCSKEWi,t
PageRanki,t
− 6.3180***
(− 2.0133)
− 6.4045***
(2.0438)
− 0.0738***
(0.0112)
0.0509*
(0.0292)
− 0.0010
(0.0016)
− 0.0088*
(0.0048)
− 7.58e-06
(2.5e-05)
0.0027
(0.0141)
− 0.0010
(0.0019)
− 0.9215
(0.7132)
Yes
Yes
0.0980
6804
NCSKEWi,t− 1
Sizei,t
Levi,t
ROAi,t
Growthi,t
Agei,t
Sharei,t
con_s
− 0.0059
(− 0.1575)
Yes
Yes
0.0910
6912
Year fixed effect
Industry fixed effect
adj-R2
N
This table indicates the effects of the liquidity connectedness on stock price crash risk. The stan­
dard deviation are reported in parentheses. ***, **, * indicate statistical significance at the 1%,
5%, 10%.
Taking into account the likelihood of a two-way causal relationship, we introduce the current stock price crash risk into the initial
regression. In the second regression stage, we add the previous crash risk to avoid its impact on the current (Shi et al., 2022). From
Table 5, it can be seen that the endogenous problem is solved.
Meanwhile, we also apply a PSM sample to deal with the problem. When the liquidity shock is greater than the sample median, we
Table 5
Results of the instrumental variable analysis.
Variable
PageRanki,t
PageRanki,t
PageRankInd
PageRankArea
NCSKEWi,t
NCSKEWi,t− 1
Sizei,t
Levi,t
ROAi,t
Growthi,t
Agei,t
Sharei,t
con_s
Year fixed effect
Firm fixed effect
Hansen J
P
0.1555***
(− 0.0563)
− 0.3974***
(− 0.1105)
− 0.0002***
(− 7.03e-05)
0.0002
(− 0.0002)
1.61e-05
(− 9.83e-06)
1.11e-05
(− 3.37e-05)
− 4.20E-08
(− 1.99e-07)
− 5.96e-05
(− 0.0001)
− 1.34e-05
(− 1.02e-05)
0.0065*
(− 0.0039)
Yes
Yes
NCSKEWi,t
− 780.2720***
(− 54.6773)
− 0.0595***
(− 0.0105)
0.2248***
(− 0.0277)
0.0119***
(− 0.0017)
0.0015
(− 0.0044)
− 4.58e-05
(− 3.04e-05)
− 0.0402***
(− 0.0124)
− 0.0115***
(− 0.0020)
2.4272***
(− 0.6563)
Yes
Yes
0.0590
0.8075
This table presents the results of the instrumental variables analysis. Column1 shows the first
regression stage, and Column2 shows the second regression stage. The standard deviation are
reported in parentheses. ***, **, * indicate statistical significance at the 1%, 5%, 10%.
8
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
define High Liquidity Connectedness as 1; otherwise, it is zero. Panel A of Table 6 shows the regression results of the High Liquidity
Connectedness dummy on the firm-level control variables, and then we use the estimated coefficients to compute the propensity score
for each observation in our sample. Panel B of Table 6 reports the OLS estimation result of the relationship between liquidity
connectedness and stock price crash risk using the matched sample. The coefficient of High Liquidity Connectedness is − 0.1278 with a
significance level of 1 %, which indicates the results are unchanged.
6.2.2. Other robustness tests
In order to ensure baseline findings are robust to substitutable metrics for crash risk, network centrality, and stock liquidity, we
perform robustness tests.
Firstly, this paper uses DUVOLi,t as a substitutable parameter to calculate crash risk, which indicates the down-to-up volatility of
firm-specific weekly returns. The parameter DUVOLi,t is computed as follows (Chen, Hong, and Stein, 2001):
∑
∑
DUVOLi,t = ln([(nu − 1) Wd2 ]/[(nd − 1) Wu2 ])
(11)
down
up
specifically, the number of up and down weeks for each firm in quarter t are denoted by nu and nd , respectively. “Down weeks” in­
dicates the weekly return Wi,t value is lower than its quarterly average, and “up weeks” means the Wi,t value of this week is higher than
quarterly average. The likelihood of a stock price collapse increases with increasing DUVOLi,t The results of changing the alternative
parameter to measure crash risk are shown in Column 1 of Table 7. The negative correlation between liquidity connectedness and stock
price crash risk (β = − 3.3804) has a significance level of 10 %.
Secondly, this section applies different liquidity indices to construct the liquidity spillover networks. According to Roll et al. (2010)
and Chen et al. (2015), bid-ask spreads can be used to measure stock liquidity:
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
SROLL = 2 max(− cov(Δpt , Δpt− 1 ), 0)
(12)
specifically, pt represents the trading price of the stock at the moment t. The price first-order difference is Δpt = pt − pt− 1 . The larger the
SROLL, the less stock liquidity. Also, we define ROLL as SROLL multiplied by − 1.
In accordance with Amihud (2002) and Lee et al. (2014), we find the indicator Amihud can be applied to compute liquidity, which
is defined below:
Amihudi,d = − log[1 + (|Ri,d |/(Pi,d *Voli,d ))]*106
(13)
Table 6
Liquidity connectedness on stock price crash risk: propensity score matching.
Panel A: First-stage propensity score matching
NCSKEWt− 1
Sizet
LEVt
ROAt
Growtht
Aget
Sharet
con_s
Year fixed effect
Firm fixed effect
Pseudo R2
N
Panel B: Liquidity connectedness and stock price crash risk
High Liquidity Connectedness
Controls
N
adj-R2
High liquidity connectedness
− 0.0187*
(− 0.0113)
− 0.0038
(− 0.0121)
− 0.0020**
(− 0.0009)
0.0017
(− 0.0034)
9.08E-06
(− 0.0001)
0.0016
(− 0.0028)
− 0.0021**
(− 0.0010)
− 0.0976
(− 0.2622)
Yes
Yes
0.0017
6804
NCSKEWt
− 0.1278***
(0.0358)
Yes
6804
0.0980
This table displays the results of endogeneity concerns with PSM approach. Panel A
presents the first-stage Probit model estimation results. Panel B shows the regression
results with the PSM sample.
9
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
Table 7
Results of other robustness tests.
Variable
PageRankt
ECt
(1)
(2)
(3)
(4)
(5)
(6)
DUVOLt
NCSKEWt
NCSKEWt
NCSKEWt
NCSKEWt
NCSKEWt
− 3.3821*
(− 2.0039)
− 5.0778**
(− 2.3094)
− 6.1572***
(− 2.1257)
CCt
− 0.6048**
(0.2542)
BCt
NCSKEWt− 1
DUVOLt− 1
Sizet
Levt
ROAt
Growtht
Aget
Sharet
con_s
Year fixed effect
Industry fixed effect
adj-R2
N
0.1459***
(− 0.0129)
0.0729**
(− 0.0336)
− 0.0011
(− 0.0018)
− 0.0098**
(− 0.0049)
2.43e-05
(− 3.91e-05)
− 0.0214
(− 0.0145)
− 0.0001
(− 0.0024)
− 1.0674
(− 0.7903)
Yes
Yes
0.0920
6804
− 0.5278***
(0.1999)
− 0.0731***
(− 0.0113)
− 0.0731***
(− 0.0113)
− 0.0735***
(0.0112)
− 0.0730**
(0.0112)
− 2.3501***
(0.8872)
− 0.0735***
(0.0112)
0.0506*
(− 0.0292)
− 0.0010
(− 0.0016)
− 0.0089*
(− 0.0048)
− 3.79E-06
(− 2.47e-05)
0.0028
(− 0.0141)
− 0.0010
(− 0.0019)
− 0.9270
(− 0.7163)
Yes
Yes
0.0970
6804
0.0502*
(− 0.0292)
− 0.0011
(− 0.0016)
− 0.0090*
(− 0.0048)
− 2.84E-06
(− 2.48e-05)
0.0029
(− 0.0141)
− 0.0010
(− 0.0019)
− 0.9062
(− 0.7162)
Yes
Yes
0.0980
6804
0.0511*
(0.0292)
− 0.0010
(0.0016)
− 0.0089*
(0.0048)
− 8.55e-06
(2.54e-05)
0.0029
(0.0141)
− 0.0010
(0.0019)
− 0.9361
(0.7150)
Yes
Yes
0.0970
6804
0.0515**
(0.0291)
− 0.0011
(0.0016)
− 0.0089*
(0.0048)
− 8.45e-06
(2.53e-05)
0.0016
(0.0141)
(0.0019)
− 0.7590
− 0.7590
(0.7152)
Yes
Yes
0.0970
6804
0.0483*
(0.0291)
− 0.0010
(0.0016)
− 0.0088**
(0.0048)
− 7.80e-06
(2.48e-05)
0.0035
(0.0141)
− 0.0009
(0.0019)
− 0.9006
(0.7150)
Yes
Yes
0.0970
6804
This table presents the results of alternative parameter to measure crash risk, stock liquidity and network centrality. The standard deviation are
reported in parentheses. ***, **, * indicate statistical significance at the 1%, 5%, 10%.
where Ri,d is the daily return, Voli,d is the trading volume of stock i at day d, and Pi,d is the adjusted closing price. The outcomes of
applying the alternative stock liquidity parameters to establish liquidity spillover networks are shown in Column 2 and Column 3 of
Table 7. As we can see, there is a negative association between ROLL and stock price crash risk (β = − 5.0693) with a significance level
of 5 %, and Amihud and stock price crash risk (β = − 6.1484) have a negative correlation with a significance level of 1 %.
Thirdly, we also replace different network centrality metrics to avoid accidents caused by the selected topology metric for
regression results. This section selects other centrality metrics, including eigenvector centrality (EC), closeness centrality (CC), and
betweenness centrality (BC). EC is defined as follows:
Ax = λx
N
∑
λxi =
j=1
(14)
aij × xj
(15)
where A is the adjacency matrix for this graph. aij = 1 if vertices i and j are connected by an edge; otherwise aij = 0. λ is the largest
eigenvalue of A, and N is the number of vertices.
di =
N
1 ∑
dij
N − 1 j=1
CCi =
(16)
1
di
(17)
where the average distance between node i and the remaining points is given as di .
BCi =
∑ ni
1
st
(N − 1)(N − 2)/2 s∕=i∕
g
=t st
(18)
where nist indicates the number of shortest paths through point i and gst for the number of shortest paths connecting s and t.
10
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
Columns 4 to 6 in Table 7 show the results of EC, CC, and BC, respectively. For each test, the coefficients for centrality metrics are
negative and significant (the β of EC is − 0.6048 with a significance level of 5 %, the β of CC is − 0.5278 with a significance level of 1 %
and the β of BC is − 2.3501 with a significance level of 1 %), indicating that our outcomes are robust to substitutable network centrality
metrics.
6.3. Potential channel
6.3.1. Conditional conservatism
Centrally located firms have access to a greater amount of liquidity information and resources, which is beneficial for corporate
governance and operations (Shi et al., 2022). Indeed, executives often conceal negative information from investors for their own
benefit (Hutton, Marcus, and Tehranian, 2009), but central firms can enlarge conditional conservatism (C-score) to reduce managers’
incentives to hide bad news, thereby reducing stock price crash risk (Kim and Zhang, 2016).
We are concerned about the interaction effects between liquidity connectedness and C-score (Khan and Watts, 2009). To solve this
problem, we add the interaction variable of C-score and PageRank (PageRank * CSCOREt). From Column 1 in Table 8, the coefficient of
PageRank * CSCOREt is positive with a significant level of 5 % which indicates that the C-score amplifies the impact of liquidity
connectedness on stock price crash risk.
6.3.2. Stock price synchronicity
Centrally located firms are closely linked to other firms that oversee corporate information disclosure, which is good for increasing
information symmetry. The proportion of firm-specific and market-level information included in stock prices increases with a decrease
in common fluctuation (Boubaker, Mansali, and Rjiba, 2014). This phenomenon reduces information asymmetry and, thus, lowers the
likelihood of a stock price crash.
This part researches the interaction effects between liquidity connectedness and stock price synchronicity (Jin and Myers, 2006).
To solve this problem, we introduce the interaction variable of stock price synchronicity and PageRank (Pagerank * SYNt). From
Column 2 in Table 8, the coefficient of Pagerank * SYNt is negative with a significant level of 10 %. The results indicate that stock price
synchronicity can lessen the impact of liquidity connectedness on stock price crash risk.
Table 8
Results of mechanism analysis.
Variable
NCSKEWt
NCSKEWt
PageRankt
− 6.1363***
(− 2.0400)
− 9.8135***
(− 2.5886)
− 0.0136
(− 0.0299)
− 4.8547*
(− 2.6979)
SYNt
PageRank * SYNt
C-scoret
PageRank * CSCOREt
NCSKEWt− 1
Sizet
Levt
ROAt
Growtht
Aget
Sharet
con_s
Year fixed effect
Industry fixed effect
adj-R2
N
− 0.0009
(− 0.0006)
0.0769**
(− 0.0006)
− 0.0740***
(− 0.0112)
0.0509*
(− 0.0292)
− 0.0010
(− 0.0017)
− 0.0087*
(− 0.0049)
− 7.57E-06
(− 2.48e-05)
0.0028
(− 0.0141)
− 0.0010
(− 0.0019)
− 0.9218
(− 0.7124)
Yes
Yes
0.0980
6804
− 0.0736***
(− 0.0111)
0.0581*
(− 0.0307)
− 0.0009
(− 0.0017)
− 0.0082*
(− 0.0048)
− 1.41e-05
(− 2.46e-05)
0.0040
(− 0.0148)
− 0.0013
(− 0.0020)
− 1.1752
(− 0.7402)
Yes
Yes
0.1010
6804
This table presents the results of heterogeneity analysis. Column1 shows the results for the external
monitoring. Column2 shows the results for the Z-Score. The standard deviation are reported in
parentheses. ***, **, * indicate statistical significance at the 1%, 5%, 10%.
11
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
7. Further analyses
7.1. The effect of external monitoring
Li et al. (2017) and Jensen and Meckling (1976) have investigated that monitoring has a strong impact on stock price crash risk.
Particularly, effective monitoring can curb opportunistic conduct by managers and diminish the likelihood of future crashes. Efficient
external monitoring measures are able to alleviate agency issues and construct a satisfactory corporate governance environment (Xu
et al., 2014). Therefore, this section examines heterogeneity from the perspective of the external environment.
Previous studies (Hartzell and Starks, 2003) show that high institution ownership represents effective external monitoring. Thus,
the swatch is classified according to the ratio of outstanding shares that institutional owners of a firm own. Firms with institutional
shareholdings above the median of the overall sample are classified as effective external monitoring groups, and others are classified as
ineffective external monitoring groups. Column 1 of Table 9 reports that the PageRank coefficient is negative and significant at the 1 %
level, and the result in Column 2 of 9 is not significant. In fact, efficient external monitoring deters managers’ negative news hoarding
conduct and improves information symmetry, which reduces the chance of stock price crash risk.
7.2. The effect of risk-taking
In accordance with the previous studies (Dye, 1988; Trueman and Titman, 1988; Kim, Li, and Zhang, 2011b; Li et al., 2017), outside
investors or the board of directors are likely to take actions to hide managers risk-taking actions once noticed, so managers tend to
conceal excessive risk-taking actions to stabilize the stock price. Therefore, risk-taking has a strong impact on information symmetry,
which in turn affects the crash risk. To reinforce our understanding, this section explores heterogeneity from the perspective of risktaking.
The managers’ incentives to hide risk-taking activities can be measured by the modified Z-SCORE (Li et al., 2020), because a
smaller Z-SCORE can draw investors’ attention to managers’ anomalous risk-taking actions (Li et al., 2017). Firms that fall into the
high-risk category are those whose z-score is below the median (Li et al., 2017). At the same time, Columns 3 and 4 of 9 reveal the
outcomes of the low-risk group and the high-risk group, respectively. According to the findings, managers are less inclined to conceal
negative news when the z-score is higher. This leads to a decrease in the likelihood of a stock price meltdown because there is more
information available.
7.3. The effect of state-owned enterprises (SOEs)
Piotroski et al. (2015) suggest that firms’ crash risk may be affected by their ownership type. State-owned enterprises are controlled
by the central government, reducing the likelihood of stock price crashes through policy regulation (Zhang et al., 2010, 2014). In
situations where SOEs find themselves facing economic challenges, the government provides them with bailouts (Wang et al., 2008).
Therefore, the ownership type is applied to explore heterogeneity in this part.
Columns 5 and 6 of 9 show the outcomes of the SOEs group and the non-SOEs group, respectively. Column 5 reports the PageRank
coefficient is negative and significant at the 1 % level, and the finding in column 6 is not significant. The reason for the result is that the
government protects SOEs from competing for basic resources in the capital markets, so SOEs pay less attention to investor reactions
and have less incentive to hoard negative news (Zhang, Xie, and Xu, 2016), decreasing the likelihood of stock price crashes (Inekwe,
2020).
8. Conclusion
This paper introduces liquidity spillover networks to research the impact of a firm’s liquidity connectedness on its stock price crash
risk with a sample of CSI300 over the 2006–2021 period. The conclusions are as follows: (a) Liquidity connectedness is substantially
inversely correlated with stock price crash risk. (b) Conditional conservatism amplifies the negative impact of liquidity connectedness
on stock price crash risk, while stock price synchronicity lessens it. (c) Firms with effective monitoring, firms with lower risk-taking,
and state-owned enterprises (SOEs) all show a stronger negative correlation between liquidity connectedness and stock price crash
risk.
Given that liquidity connectedness can influence stock price crash risk, we propose some recommendations to improve market
stability. First, firms ought to enhance their liquidity associations with others. Firms cannot isolate themselves in the market, and
common changes in liquidity favor market risk sharing. Second, investors should be inclined to choose firms with high liquidity
connectedness. Investors need to look not only at a firm’s financial information but also at its position in the market, making better
decisions based on the results of the research.
CRediT authorship contribution statement
Xin Yang: Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. Xuan Ao: Writing –
original draft, Visualization, Software, Investigation, Data curation. Jie Cao: Writing – review & editing, Conceptualization.
Chuangxia Huang: Methodology, Conceptualization.
12
North American Journal of Economics and Finance 74 (2024) 102238
X. Yang et al.
Table 9
Results of the heterogeneity analysis.
External monitoring
Variable
PageRankt
NCSKEWt− 1
Sizet
Levt
ROAt
Growtht
Aget
Sharet
con_s
Year fixed effect
Industry fixed effect
adj-R2
N
Risk-taking
The ownership type
Effective monitoring
Invalid monitoring
Low-risk
High-risk
SOEs
Non-SOEs
(1)
NCSKEWt
− 10.6038***
(2.8327)
− 0.0726***
(0.0174)
0.0076
(0.0473)
− 0.0030
(0.0027)
− 0.0053
(0.0066)
3.28e-05
(3.72e-05)
− 0.0053
(0.0173)
− 0.0011
(0.0032)
0.3401
(1.2814)
Yes
Yes
0.0690
3528
(2)
NCSKEWt
− 3.4859
(2.7714)
− 0.0721***
(0.0155)
0.1070***
(0.0386)
− 0.0002
(0.0022)
− 0.0110
(0.0070)
− 4.99E-05
(3.52e-05)
0.0068
(0.0219)
0.0006
(0.0023)
1.54e-05
(0.0022)
Yes
Yes
0.1410
3276
(3)
NCSKEWt
− 10.4202**
(4.2587)
− 0.0711***
(0.0238)
0.2241***
(0.0473)
0.0021
(0.0037)
− 0.0080
(0.0057)
0.0004
(0.0001)
− 0.0409
(0.0323)
− 0.0018
(0.0046)
− 4.5990
(1.2407)
Yes
Yes
0.1270
1638
(4)
NCSKEWt
− 4.4486*
(2.3342)
− 0.0770***
(0.0123)
0.0143
(0.0307)
− 0.0017
(0.0017)
− 0.0189**
(0.0073)
− 2.64e-05
(2.23e-05)
0.0121
(0.0147)
− 0.0002
(0.0020)
− 0.1058
(0.7753)
Yes
Yes
0.098
5166
(5)
NCSKEWt
− 7.3422***
(2.4886)
− 0.0651***
(0.0133)
0.0262
(0.0338)
− 0.0002
(0.0018)
− 0.0102
(0.0056)
− 1.11e-05
(1.56e-05)
0.0075
(0.0145)
− 0.0032
(0.0020)
− 0.2468
(0.8486)
Yes
Yes
0.0700
4851
(6)
NCSKEWt
− 3.2591
(3.3859)
− 0.0820***
(0.0170)
0.1834***
(0.0541)
− 0.0019
(0.0036)
− 0.0111
(0.0076)
− 6.72e-05
(0.0003)
− 0.0290
(0.0328)
0.0038
(0.0033)
− 3.7505***
(1.1762)
Yes
Yes
0.1860
1953
This table presents the results of alternative parameter to measure crash risk, stock liquidity and network centrality. The standard deviation are
reported in parentheses. ***, **, * indicate statistical significance at the 1%, 5%, 10%.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
This paper is supported by the National Natural Science Foundation of China (No. 72101035), the Excellent Youth Foundation of
the Educational Committee of Hunan Provincial (No. 21B0339), the Hunan Provincial Natural Science Foundation of China (No.
2024JJ6075), and the Science and Technology Innovation Program of Hunan Province (No. 2023RC1060).
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