Fan Li et al., Statistical analysis of small business survival under the shock of multiple COVID-19 waves: A case study from Wuhan, China (2023)

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Article by Fan Li, Matteo Rubinato, Tao Zhou, Jiaye Li and Chen Chen in Frontiers in Environmental Science, published 20 February 2023, on small business survival in Wuhan, China after multiple COVID-19 waves. Data came from 382 small businesses in Wuhan's main urban area, surveyed in July 2020 and July 2022, and were analyzed with Bayesian methods. The authors find the difference in survival rates between businesses hit by no outbreak and those hit by one or several waves negligible. Owners with higher confidence in their abilities, or who accurately evaluated their strategies from the start, were more likely to keep their businesses open. Cutting staff, moving operations and promotion online, rent subsidies and tax reduction raised survival odds for businesses that went through at least one lockdown.

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“Fan Li et al., Statistical analysis of small business survival under the shock of multiple COVID-19 waves: A case study from Wuhan, China (2023).” Original at web.archive.org. Archived at Pandemic Darlings, https://pandemicdarlings.com/source-documents/fan-li-et-al-statistical-analysis-of-small-business-survival-under-the-ea263cb526/, SHA-256 f4bcd868540e01b7391054b327faa0a678ed705064734ce68f776245c3bc1ef6.

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TYPE Original Research
PUBLISHED 20 February 2023
DOI 10.3389/fenvs.2023.1092768

Statistical analysis of small
OPEN ACCESS business survival under the shock
EDITED BY
Hengyu Gu,
The Chinese University of Hong Kong,
of multiple COVID-19 waves: A
China

REVIEWED BY
case study from Wuhan, China
Bojan Obrenovic,
Zagreb School of Economics and
Management, Croatia
Fan Li 1,2, Matteo Rubinato 3*, Tao Zhou 4, Jiaye Li 1 and Chen Chen 2
Chao Zhang, 1
School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan, China,
Hebei University of Technology, China 2
Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies
*CORRESPONDENCE for Urban Lifeline Engineering, Dongguan University of Technology, Dongguan, China, 3Centre for
Matteo Rubinato, Agroecology, Water and Resilience, Coventry University, Coventry, United Kingdom, 4School of
ad2323@coventry.ac.uk Management Science and Real Estate, Chongqing University, Chongqing, China

SPECIALTY SECTION
This article was submitted to
Environmental Economics
and Management, The long-term viability of small businesses in the aftermath of multiple pandemics and
a section of the journal
Frontiers in Environmental Science consequent lockdowns has a crucial impact on the sustainable economic and social
development of any region across the world. Thus, in order to investigate what has
RECEIVED 08 November 2022
ACCEPTED 06 February 2023 been the major impact of COVID-19 pandemic within local small businesses and to
PUBLISHED 20 February 2023 identify which main factors helped small businesses to survive none as well as multiple
CITATION lockdowns, data were obtained from 382 small businesses in the main urban area of
Li F, Rubinato M, Zhou T, Li J and Chen C Wuhan, China, via two rounds of ﬁeld investigations and surveys in July 2020 and July
(2023), Statistical analysis of small
2022. This paper presents the results of the ﬁeld investigations and the surveys
business survival under the shock of
multiple COVID-19 waves: A case study completed and describes the Bayesian methods applied to quantitatively explore the
from Wuhan, China. impact of different variables on the probability of each business to remain active and
Front. Environ. Sci. 11:1092768.
open even after experiencing none or multiple lockdowns. Results obtained show that
doi: 10.3389/fenvs.2023.1092768
the difference between survival rates associated with businesses hit by no pandemic
COPYRIGHT
© 2023 Li, Rubinato, Zhou, Li and Chen.
outbreak with those hit by one or several waves is negligible. Furthermore, owners
This is an open-access article distributed who had higher conﬁdence in their abilities since the beginning or they implemented
under the terms of the Creative an accurate evaluation of their strategies to run their businesses since the start of the
Commons Attribution License (CC BY).
The use, distribution or reproduction in
pandemic, demonstrated to have a higher probability to keep their business alive with
other forums is permitted, provided the none as well as additional waves of the pandemic. Reduction of employees, transition
original author(s) and the copyright of operations and promotion activities online as well as rent subsidies and tax
owner(s) are credited and that the original
publication in this journal is cited, in
reduction were identiﬁed as crucial actions that enhanced the probability to
accordance with accepted academic maintain alive businesses that experienced at least one lockdown. Globally, there
practice. No use, distribution or was no clear policy approach at the start of the pandemic, however this study clearly
reproduction is permitted which does not
comply with these terms.
determines that in future governments should provide timely support to small
businesses in regions experiencing more severe impacts of the pandemic, and this
should consist of a mix of grants, loans, and temporary tax cuts since initial stages.

KEYWORDS

business, economy, COVID-19 pandemic, probability, bayesian method, Wuhan China

1 Introduction
COVID-19 pandemic has been one of the worldwide health emergencies with the fastest
transmission speed and the widest range of inﬂuence in the 21st century, which seriously
threatened the safety of people’s lives and hindered the sustainable development of mankind
(Raghavan and Demircioglu, 2021). As of July 2022, COVID-19 has infected more than ﬁve
hundred forty million people and killed more than six million people across two hundred

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countries. In addition to harming people’s lives and health, COVID-19 United States, Europe, Pakistan, and Vietnam, etc.; rare studies
has also posed a serious threat to the economic development of several have explored the situation and experience of China. In addition,
countries (Sarkodie and Owusu, 2021). According to Eurostat, Gross most of the abovementioned studies were carried after the ﬁrst wave
Domestic Product (GDP) in the Eurozone fell by 3.8 percent in the ﬁrst of the pandemic (late 2019) to observe the short-term survival and
quarter of 2020, the steepest decline since data were ﬁrst recorded in development of businesses during this initial timeframe, however,
1995 (Fernandes, 2020). The United States economy also experienced a survival and adaptation of a business after any crisis is a long process
sharp decline which shrank by 1.2 percent in the ﬁrst quarter of 2020 (Marshall and Schrank, 2014) and therefore results produced may
(Bai and Quayson, 2021). The COVID-19 pandemic has also severely have note been extremely accurate because a business’s short-term
damaged China’s economy, with the year-on-year GDP growth rate survival after the pandemic did not necessarily ensure its long-term
plummeting to 2.3 percent in 2020 (Zou and Huo, 2020). viability. Only an extremely limited number of studies investigated
Small businesses play an important role in the national economy the long-term survival of businesses that survived the pandemic.
and contribute more than 50 percent of GDP in China (Yuan, 2013). Moreover, existing studies mainly qualitatively summarizes the
Business is often affected immediately by sudden global events such as impact of the pandemic on businesses and their response
COVID-19 pandemic because spending is more likely to be shunned in measures to the pandemic through literature analysis,
times of high risk or uncertainty (Appel and Hardaker, 2021). questionnaire surveys and interviews (Shakil and Munim, 2020)
According to China’s National Bureau of Statistics, after the and to author’s knowledge there is a lack of research indicating, via
outbreak of the pandemic, the total consumption of social retail quantitative methods, if actions under-taken by businesses were
goods in China fell by 20.5 percent year-on-year in the ﬁrst quarter indeed effective for their medium and long-term sustained operation
of 2020. The proﬁts of small, medium and micro enterprises (MSME) in after the pandemic.
China fell by more than 30 percent year-on-year throughout 2020 Thus, important questions can arise: 1) What is the performance of
(Susanti, 2021). According to the Measures for the Division of Large, businesses that survived the ﬁrst wave of pandemic under the impact of
Medium, small and Micro Enterprises in Statistics (2017) issued by the subsequent waves of pandemic? 2) Can these initially surviving
National Bureau of Statistics of China, the business size of different businesses achieve sustained operation under the impact of the
sectors can be divided into large, medium, small and micro based on subsequent pandemic? 3) What factors will affect the sustained
their revenue and number of employees (Yang and Cai, 2016). For operation of these small businesses under the shock of pandemic? 4)
example, the business size for retail sector can be divided into four What measures can small business take to effectively increase the
categories: Large business (revenue ≥ $29.5 million, and probability of their sustained operation under the shock of
employees ≥300), medium business ($738.8 thousand ≤ revenue < pandemic? 5) What is China’s experience in promoting sustained
$29.5 million, and 50 ≤ employees <300), small business business operation after the pandemic? These are all crucial questions
($14.8 thousand ≤ revenue < $738.8 thousand, and 10 ≤ to be asked to address the issues that have been overlooked by previous
employees <50), micro business (revenue < $14.8thousand, and studies, therefore this study focused on small businesses in Wuhan,
employees <10). The small business in the current study refers to China, and carried out medium and long-term tracking for small
small and micro businesses, which are a vital component of MSMEs. businesses that survived the ﬁrst wave of the pandemic (that started
MSMEs accounts for more than 90 percent of the total number of at the end of 2019) in order to observe and evaluate their operating status
enterprises in China, contributing more than 50 percent of tax revenue 2 years later. The Bayesian model was adopted to identify key factors
and providing 80 percent of jobs in urban areas (Li and Huang, 2021). In affecting the sustained operation of small businesses after the ﬁrst wave
addition, MSMEs contribute nearly 70 percent of patented inventions of the pandemic (e.g., owner characteristics, business characteristics,
and more than 80 percent of new product development in China (Li and pandemic damage, response measures and external supports). The
Huang, 2021). MSMEs also play a signiﬁcant role in building urban conclusion of the current study has important signiﬁcance for
space and improving urban vitality and attractiveness (Kim and Yun, promoting the medium and long term sustained operation of small
2021). As an important component of MSMEs, the survival and businesses after the crisis induced by a global pandemic, and can help to
development of small businesses under the strike of any pandemic improve the ability of business operators and managers to cope with any
could closely affect many aspects of any region, such as economy, society, similar future crisis, with the intent to promote economic prosperity,
scientiﬁc and technological innovation, and urban vitality (Parker, 2006; social stability, and sustainable development.
Blanchard and Tolbert, 2012; Lee, 2018; Kalogiannidis, 2020; The paper is organized as follows: Section 2 presents an overview
Tuymuratovich, 2021; Vinberg and Danielsson, 2021). of factors inﬂuencing the short-term survival or long-term sustained
In the context of non-crisis, it is found that many factors may operation of small businesses after the pandemic; section 3 discusses
affect the value or performance of MSMEs, such as cash ﬂow (Deng the research methods and the process of data collection; section 4
and Zhao, 2022), production mode (Xu and Zhou, 2021) and incorporates the results and the key ﬁndings and ﬁnally, section 5
technological innovation (Ban and Liu, 2022). To date, previous combines the discussion of the ﬁndings and draws the conclusion.
studies have been conducted in the context of the COVID-19
pandemic focusing on the operating status of MSMEs, while
others have been completed to investigate the vulnerability of 2 Key factors affecting the survival of
businesses and the impact that the pandemic had on them small businesses
(Bartik and Bertrand, 2020; Hatab and Lagerkvist, 2020; Shakil
and Munim, 2020; Bai and Quayson, 2021; Huang and Liu, 2021; As previously mentioned, numerous studies have qualitatively
Khan and Niazi, 2021; Nguyen, 2021). The abovementioned studies summarized the damage of the pandemic to businesses or their
were conducted across a wide range of regions, including the response measures to the pandemic based what found in literature or

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gained by questionnaire surveys and interviews (Shakil and Munim, qualitatively highlighted the business operation problems during
2020; Saif and Ruan, 2021). Other studies have also quantitatively the pandemic crisis based on questionnaires, mainly including raw
identiﬁed the key factors affecting the survival of small business after material supply, customer loss, employee loss and cost increases
the ﬁrst wave of COVID-19 (Katare and Marshall, 2021). Overall, (Ratnasingam and Khoo, 2020; Grondys and Lusarczyk, 2021;
the following variables have been selected to be the most relevant Taneo and Noya, 2021). These operational problems can affect a
ones when assessing the performance of small businesses under the business to survive or recover from the pandemic (Carracedo and
impact of any pandemic. Puertas, 2021; Katare and Marshall, 2021). There is evidence that
longer is the duration of the closure and lower is the total amount of
income generated by the sale of goods or services related to the
2.1 Owner characteristics company’s primary operations, thus reducing the probability of a
business surviving a crisis (Webb and Tierney, 2002; Sydnor and
For owner characteristics this study includes gender, education, age, Niehm, 2017).
experience and expectation. To date, studies developed on the impact of
owner characteristics on small businesses’ survivals were conducted after
natural disasters and several were completed during the global COVID- 2.4 COVID-19 response measures
19 pandemic. Evidence indicated that small business survival or recovery
in the aftermath of a natural disaster were associated with owners’ For COVID-19 response measures, this includes employee
education, experience, and expectations (Asgary and Anjum, 2012; reduction, technological innovation, online transformation,
Khan and Sayem, 2013; Marshall and Niehm, 2015). Helgeson and pandemic prevention resource reserve, multi-point location and
Aminpour (2022) determined that female-owned businesses were more purchase of commercial insurance. Several studies have reported
likely to go bankrupt after the pandemic, while Katare and Marshall the online transformation (Raghavan and Demircioglu, 2021), the
(2021) reported that owners’ age and education could be the main drivers technological innovation (Ratnasingam and Khoo, 2020; Caballero-
to affect the performance of small businesses during the pandemic. In the Morales, 2021), the employee reduction (Siuta-Tokarska, 2021) and
context of COVID-19, there is evidence that owner’ enhancement of the pandemic prevention resource reserve applied by governments
employee empowerment can help motivate employees’ innovative work (Hatab and Lagerkvist, 2020) as response to the pandemic. However,
and organizational learning readiness, which has a direct impact on the only a limited number of studies have quantitatively examined the
sustainable economic performance of enterprises (Faulks and Song, impact of these measures on post-pandemic performance of small
2021). During the COVID-19 pandemic, entrepreneurial leadership businesses. For example, Katare and Marshall (2021) found that
had a signiﬁcant impact on employees’ perception of crisis and their increasing a business’s online social media presence can reduce
working status, which affected the sustainable economic performance of revenue loss and on the contrary, enhance the possibilities of
enterprises (Alsharif and Shu, 2021). Therefore, owner characteristics recovery after a pandemic. In addition, there is evidence that a
may have played a signiﬁcant role in the sustained operation of small business operating at multi-point locations can expect higher
business during the COVID-19 pandemic. probability of survival after such crisis (Sydnor and Niehm, 2017).

2.2 Business characteristics 2.5 Support from national and local
authorities
For business characteristics, this study includes business type, size,
primary market, and ﬁnancial condition. Gregurec and Tomičić Furjan Regarding support from governments or non-governmental
(2021) demonstrated that business type was associated with business organizations (NGO), this includes loans, rent subsidies, and
performance under the shock of pandemic. Many studies determined NGO assistance. Many countries have introduced policies to help
that small businesses were less likely to survive pandemic shocks than businesses cope with the pandemic, such as loans, rent subsidies, tax
large ones (Shaﬁ and Liu, 2020; Grondys and Lusarczyk, 2021; Yue and reduction and exemption (Bartik and Bertrand, 2020; Tetlow and
Korkmaz, 2021). Katare and Marshall (2021) found that business with Dalton, 2020; Vinberg and Danielsson, 2021). Katare and Marshall
smaller market coverage had higher probability of suffering ﬁnancial (2021) found that small businesses with access to a variety of these
problems, which reduced their likelihood of survival in a pandemic. The types of help can reduce their recover time from the pandemic.
variations of business characteristics imply different competitiveness Additionally, Lo (2009) suggested that government and non-
and access to pandemic relief resources implemented on purpose for government assistance have been extremely important for the
governments to support local and national businesses, and resilience of local and national businesses after the crisis.
unfortunately this usually leads to different survival outcomes
(Vinberg and Danielsson, 2021).
2.6 Summary of the key factors

2.3 Business operation Table 1 summarizes the factors that may affect business
performance under the shock of pandemic based on previous research.
For business operational problems due to COVID-19, this In general, the abovementioned studies explored a range of
includes closure duration, raw material supply, customer loss, factors that may inﬂuence the performance of business after the
employee loss and cost increases. Several studies have crisis. These factors provided an important reference for the current

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TABLE 1 Factors that may be related to sustained operation of a business after the pandemic.

Categories Factors References
Owner characteristics Gender Helgeson and Aminpour (2022)

Education Katare and Marshall (2021)

Age Katare and Marshall (2021)

Industry experience Asgary and Anjum (2012)

Owners’ expectations of business climate Khan and Sayem (2013)

Business characteristics Business type Gregurec and Tomičić Furjan (2021)

Business size Shaﬁ and Liu (2020)

Primary market Katare and Marshall (2021)

Owned or leased facility Wasileski and Rodríguez (2011)

Pre-pandemic ﬁnancial condition Li and Wang (2020)

COVID-19 induced business operational problems Closure duration Sydnor and Niehm (2017)

Raw material supply Taneo and Noya (2021)

Customer loss Ratnasingam and Khoo (2020)

Employee loss Grondys and Lusarczyk (2021)

Pandemic prevention costs increased Grondys and Lusarczyk (2021)

COVID-19 response measures Employee reduction Siuta-Tokarska (2021)

Technological innovation Ratnasingam and Khoo (2020)

Online transformation Raghavan and Demircioglu (2021)

Pandemic prevention resource reserve Hatab and Lagerkvist (2020)

Multi-point location Sydnor and Niehm (2017)

Supports from government and NGO Loans Vinberg and Danielsson (2021)

Rent subsidies Tetlow and Dalton (2020)

Tax reduction and exemption Tetlow and Dalton (2020)

NGO assistances Lo (2009)

work to construct a model to explore the sustained operation of measures to be promoted when small businesses are affected by a
businesses after multiple waves of COVID-19. However, most of the pandemic and require dissimilar operations in the medium and long
abovementioned studies focused on the performance of small term. Thus, one of the aims of this work is to elucidate the most
businesses after the ﬁrst wave of COVID-19, ignoring the important tasks that could secure the operation of local businesses during
sustained operation of businesses under the impact of subsequent the highly stress period imposed by a pandemic and consequently ensure
waves of COVID-19. In addition, most of existing studies regional economic prosperity and social stability. Therefore, this study
qualitatively analyzed or summarized the main measures of aims to provide further insights regarding 1) what was the operating
businesses response to the pandemic but lack further quantitative performance of initial surviving businesses under the impact of
testing of the effectiveness of these measures for the sustained subsequent waves of the pandemic and 2) what were the main
operation of the businesses during the COVID-19 pandemic. factors inﬂuencing the sustained operation of small businesses
Moreover, existing studies focus on the short-term performance experiencing lockdowns induced by multiple pandemic waves.
of business after the crisis, ignoring the medium - and long-term
perspective on sustained operation of business after the pandemic.
It is of foremost importance to explore the sustained operation of 3 Materials and methods
small businesses after multiple waves of the pandemic because such
understanding could help owners to carry out effective response 3.1 COVID-19 pandemic and the study area
measures to improve the probability of survival of their businesses
and mitigate the impact of multiple waves of the pandemic. Wuhan is the capital of Hubei Province and the main city of
Thus, this research could provide a reference and fundamental novel central China. The main city of Wuhan is composed of Wuchang,
knowledge that could be used by policy makers to develop more effective Hankou and Hanyang towns, including seven main urban areas:

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FIGURE 1
Study area and investigated streets distribution.

Wuchang District, Qingshan District, Hongshan District, Jianghan experienced a total of one, two or three lockdowns. The
District, Qiaokou District, Jiang’an District, and Hanyang District difference in the medium and long-term performance of
(Figure 1). Wuhan has a vast area and it is well known for its well- these businesses that have experienced different waves of
developed economy and large population. Unfortunately, such lockdown is therefore worthy of concern.
megacity is more prone than others to the accumulation,
breeding and wide spread of emergencies and their consequences.
Since December 2019, several cases of unexplained pneumonia 3.2 Data collection and methods applied
had been found in several hospitals in Wuhan, Hubei Province,
which lately had been conﬁrmed as acute respiratory infectious The current study focused on the operating status of businesses
diseases caused by the novel coronavirus infection (Dietz et al., that survived the ﬁrst wave of the pandemic after the second and
2020). The pandemic had developed rapidly in Wuhan, followed by third waves of lockdowns. Furthermore, it investigated the factors
associated conﬁrmed cases in many places in China (Di Renzo and linked with the sustained business operations and strategies. The
Gualtieri, 2020). Wuhan was placed on lockdown for 76 days from data was obtained via conducting two ﬁeld surveys and
January 23 to 8 April 2020, in response to the outbreak of the virus questionnaire surveys on business samples in Wuhan on 23 July
(Bo, 2020). During this period, many small, medium-sized and 2020 (three and a half months after the ﬁrst wave of lockdown was
micro enterprises suffered huge losses and experienced heavy blows lifted) and 23 July 2022 (2 years after the ﬁrst survey). The business
such as closures and work stoppages (Li, 2022). In order to support operating status were obtained through ﬁeld investigation. The data
these business, Wuhan’s government had issued a series of policies obtained from the questionnaire survey were used to identify the
to help small, medium and micro enterprises overcome difﬁculties, factors related to the sustained business operation in the context of
such as tax reduction, rent reduction and interest-free loans (Li, the pandemic. Field investigation and questionnaires were
2022). commonly used to obtain data related to business operating
Since the start of the pandemic, Wuhan has been reported to performance after a crisis. Many studies related to business post-
experience three waves by July 2022. Differently from the city- crisis recovery have documented business operating status through
wide lockdown adopted in the ﬁrst wave of the pandemic, the ﬁeld investigation and invited owners to participate in
latter two waves have seen the application of partial lockdown questionnaires to obtain data (Khan and Sayem, 2013; Li and
measures by the government. By July 2022, businesses that Hong, 2019; Li and Wang, 2020), which proves the usability and
survived the ﬁrst wave of the pandemic have therefore validity of such methods as ﬁeld investigation and questionnaires.

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TABLE 2 Business samples distribution. to observe the medium and long-term operating status of these three
hundred and 82 business samples.
Street name Total sample Valid sample
Minzu Road 27 25 3.2.2 Node variables
Minquan Road 23 22
One of the aims of the current study was to identify the key
variables inﬂuencing the operation of small businesses
Minyisi Road 31 29
experiencing lockdowns induced by multiple pandemic waves.
Beihu Road 13 13 The business operating status referred to the medium - and long-
term operating status of the businesses that survive in the short
Houhu Avenue 21 20
term under the impact of the pandemic. This can be classiﬁed
Jiefang Avenue 11 11 into two categories: 1) Continued operation of initially surviving
Chongren Road 23 19 businesses; or 2) initially surviving businesses closed by July
2022. The names, locations, and operating status of three
Youyi Road 17 17
hundred and eighty-two businesses were recorded in both ﬁeld
Jianghaner Road 18 17 surveys. If the same business in the same location was open for
both survey periods, it was marked as one; otherwise, it was
Wufu Road 17 15
marked as two. According to the indicators summarized in the
Sanyanqiao Road 23 19 literature review presented in Section 2.6, the variables involved
Zhongyi Road 12 8 in the ﬁeld investigation and their measurements are shown in
Table 3.
Youyinan Road 16 13
The ﬁrst component, owner characteristics, was measured by
Yingwu Avenue 25 19 selecting ﬁve variables. Gender was measured dichotomously.
Education, age, industry experience and owners’ expectations of
Hanyang Avenue 21 17
business climate were measured on ordinal scales. Combining the
Yulong Road 18 18 abovementioned ﬁve indicators, the comprehensive evaluation of
Heping Avenue 15 13 the owners to their business operation ability was divided into three
levels: Good, general, and poor.
Zhonghua Road 33 27
The second component, business characteristics, was measured
Zhangzhidong Road 26 23 by choosing ﬁve variables. Most of the small businesses along the
street in China’s urban built-up areas are engaged in retail, service or
Gongyesan Road 27 26
production (Liu and Li, 2022; Liu and Tong, 2022). Therefore,
Jianshesi Road 13 11 Business types are divided into three categories: Manufacturing,
Total 430 382 retail, service. Business size and pre-pandemic ﬁnancial condition
were measured on ordinal scales. Other variables were measured
dichotomously: Whether the business facility was owned or leased,
whether the business provided local or regional service. Combining
the abovementioned ﬁve indicators, the owners’ comprehensive
3.2.1 Sampling procedure evaluation to their businesses running status was divided into
To ensure the representativeness and unbiased sample selection, three levels: Well, general and poor.
the probabilistic proportional sampling (PPS) method was used for The third component, COVID-19 induced business
the initial sample selection. According to the probability sampling operational problems, was measured by picking ﬁve
proportional to the size of permanent resident population in the variables. Closure durations were measured on an ordinal
research area at the end of 2019, 21 blocks were randomly selected scale. The remaining four variables was measured using
from the main city of Wuhan, China. Thereafter, a street in each dichotomous variables: Whether the business suffered from
block was randomly selected and a questionnaire survey was raw material supply problems; whether the business suffered
conducted on all businesses along the street identiﬁed. The customer losses; whether the business suffered employee losses,
twenty-one streets selected in the current study are all located in whether the business experienced an increase in pandemic
areas with high population density to weaken the inﬂuence of prevention costs. Combining the abovementioned ﬁve
different human ﬂow caused by distinct locations on business indicators it was possible to determine whether each
performance. The sample distribution is shown in Table 2. A business had experienced any COVID-19 induced
total of 430 owners of businesses along the 21 selected streets operational problems.
participated in the survey. Excluding the business samples that The fourth component, COVID-19 response measures, was
did not experience the ﬁrst wave of pandemic lockdown and the measured using ﬁve dichotomous variables: Whether the business
samples with incomplete questionnaire data, a total of three hundred has taken measures of reducing the number of employees; whether
and 82 valid business samples were obtained. The ﬁrst survey was the business has taken measures of technological innovation;
conducted on 23 July 2020, with three hundred and 82 valid samples whether the business has adopted measures to transform the
from businesses that had survived the ﬁrst round of lockdown. Two approach into an online platform; whether the business has taken
years later, an additional round of ﬁeld investigation was carried out measures to reserve pandemic prevention resource; whether the

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TABLE 3 Variables and their coding scheme.

Variables Coding scheme
Business operating status The operating states of initial surviving business in the subsequent pandemic. 1 = continued to be open, 2 = closed

Owner characteristics Self-evaluation of owner’s operating ability. 1 = Good, 2 = General, 3 = Poor

Gender 1 = Male, 2 = Female

Education 1 = primary school or below, 2 = junior middle school, 3 = high school/junior college, 4 = university degree or above

Age 1 = 20 or below, 2 = 21–35, 3 = 36–50, 4 = 51 and above

Industry experience 1 = less than 2 years’ experience, 2 = 2–5 years’ experience, 3 = more than 5 years’ experience

Owners’ expectations of business climate 1 = gotten worse, 2 = remained about the same, 3 = improved

Business characteristics Owners’ self-evaluation of their business. 1 = Well, 2 = General, 3 = Poor

Business types 1 = manufacturing, 2 = wholesale/retail, 3 = service

Business size 1 = 1 full-time employees, 2 = 2–4 full-time employees, 3 = 4 or more full-time employees

Primary market 1 = regional/national, 2 = local

Owned or leased facility 1 = owned facility, 2 = leased facility

Pre-pandemic ﬁnancial condition 1 = not doing well, 2 = general, 3 = good

COVID-19 induced business operation problems Whether the business has experienced COVID-19 induced operational problems. 1 = yes, 2 = no

Closure duration 1 = less than 3 months, 2 = 3–6 months, 3 = more than 6 months

Raw material supply 1 = yes, 2 = no

Customer loss 1 = yes, 2 = no

Employee loss 1 = yes, 2 = no

Pandemic prevention costs increased 1 = yes, 2 = no

COVID-19 response measures Whether the business has taken COVID-19 response measures. 1 = yes, 2 = no

Employee reduction 1 = yes, 2 = no

Technological innovation 1 = yes, 2 = no

Online transformation 1 = yes, 2 = no

Pandemic prevention resource reserve 1 = yes, 2 = no

Multi-point location 1 = yes, 2 = no

Supports from government and NGOs Whether the business has received supports from government or NGOs. 1 = yes, 2 = no

Loans 1 = yes, 2 = no

Rent subsidies or tax reduction 1 = yes, 2 = no

NGO assistances 1 = yes, 2 = no

business has taken measures to locate beneﬁts across multiple sites. 3.2.3 Statistical method
Combining the abovementioned ﬁve indicators it was possible to 3.2.3.1 Bayesian Network
determine whether the business has taken COVID-19 response The Bayesian Network, ﬁrst proposed by Pearl in 1988, is a
measures. model of uncertain knowledge representation and inference based
The ﬁfth component, which regards all the types of supports on probability theory and graph theory (Pearl, 1988). Bayesian
released by both government and NGO, was measured using three networks usually consist of a Directed Acyclic Graph (DAG) and
dichotomous variables: Whether the businesses applied for loans to Conditional Probability Table (CPT). The former is used to describe
support their operations; whether the businesses received rent the interdependence between variables, and the latter is used to
subsidies or tax reduction, whether the business received help reﬂect the strength of the causal relationship between nodes (Song
from NGOs. Combining the abovementioned three indicators it and Kou, 2021). Although regression methods, such as Logistic
was possible to determine whether the business has received regression and Probit regression, can also quantitatively identify the
supports from government or NGOs. factors affecting business sustained operation after the pandemic, it

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is difﬁcult to reﬂect the complex structural relationships among each on target variables by changing input variables and observing the change
variable. Comparatively, the Bayesian Network has more advantages amplitude of variable response probability, which can be expressed by the
in the visualization of multivariate knowledge diagram (Wang and percentage of the variance reduction (VR). The larger the VR value is, the
Amriljaharadak, 2020). greater is the inﬂuence of input variables on target variables. The
The Bayesian network structure is used to describe the diagnostic analysis was implemented to set a speciﬁc state on the
interaction between variable nodes. A and B are linked by target variable, and then observe the probability change amplitude of
directed arcs if there is a relevance between node A and node B. the inﬂuence factor to evaluate its impact. The greater is the change of the
The directed arc points from A to B represents that A is the parent of probability value, the greater is the effect of the inﬂuence factor on the
B and B is the child of A. If a variable has no parent node, the target variable. The calculation formula of the variance reduction (VR) is
conditional probability of this variable is the prior probability. The shown in Eq. 3.
conditional probability table is the parameters of the Bayesian
network, which reﬂects the strength of the causal relationship VVR V(Q) − V(Q|F)
between nodes (Zheng and Chen, 2020). Bayesian networks rely 2 2
PqXq − PqXq − P qf Xq − P qf Xq
on the Bayes rule formula (Eq. 1) to infer the inﬂuence of q q q q
explanatory variables on relevant results.
(3)
P(A|B) P(BA)P(B) (1)
Where, VVR is variance reduction percentage; V is the variance; Q
Where, P (A |B) is the probability of event A under the condition of represents the target node; F indicates other nodes; Symbols q and f
event B has occurred; P(BA) is the probability that event A and event represent the state of Q and F, respectively; Xq is the true value
B occur together; P(B) is the prior probability of event B. The corresponding to state Q.
structure of the Bayesian network can be expressed by using Eq. 2.
S (V, L) (2)
4 Results
Where, S represents the structure of Bayesian network; V is the
nodal variable set, V = {V1, V2, V3,...,Vn}; L is a directed edge and 4.1 Statistical analysis of target node
L = ViVj (Vi, Vj∈V). variables
3.2.3.2 Network structure construction and parameter The target node variable of the current study is the business
learning operating status. Figure 3 shows the operating status of businesses
The construction of the Bayesian network includes model experiencing different waves of lockdown when the two surveys
structure construction and node parameter learning. Although were conducted. Among the businesses that survived in the ﬁrst
the traditional three-stage analysis, SGS and other machine wave of the pandemic, zero experienced two additional rounds of
learning algorithms can obtain the statistical relationship between lockdown, ninety experienced one additional round of lockdown,
the variables, they cannot reﬂect the real causal relationship between and two hundred ninety did not experience additional lockdown in
them. To date there are many relevant existing previous studies the following 2 years. Focusing on the rate of businesses that did not
which used the Bayesian network to discuss the inﬂuencing factors close, there was slight difference between small business
of dependent variables or the causal relationship between variables experiencing one round of lockdowns and those experiencing
(Chen and Lv, 2022; Johnson and Lulla, 2022; Xie and Xie, 2022), two rounds of lockdowns, 66.9 percent for those that experienced
demonstrating the usability and validity of using this model to one lockdown and 64.1 percent for those that experienced two
explore the factors inﬂuencing sustained business operations. lockdowns, respectively.
Accordingly, the current study referred to the existing studies on
post-pandemic business recovery or sustained operation (Xiao and
Su, 2020; Katare and Marshall, 2021; Raghavan and Demircioglu, 4.2 Model construction results
2021; Taneo and Noya, 2021) and constructed a Bayesian network
structure model based on the causal relationship between variables The sample data were divided into two groups (those that
discussed in the previous studies, as shown in Figure 2. experienced one wave and those that experienced two waves of
Node parameter learning refers to ﬁnding the conditional the pandemic) to show the Bayesian network after implementing the
probability distribution among node parameters based on sample parameter learning within Netica software, as shown in Figures 4, 5,
data after the determination of the network structure model. This respectively. About 57.5 percent of the small businesses that survived
study used the maximum likelihood method for the parameter the ﬁrst wave of the pandemic achieved sustained operation after
learning, which was obtained by MATLAB BNT toolbox 2 years later. In terms of the owner characteristics, 41.1 percent of
programming. owners rated their ability to run small businesses as good, while only
21.6 percent of owners considered their ability to run small
3.2.3.3 Sensitivity analysis and diagnostic analysis businesses as poor. 36.9 percent of the owners rated their
The sensitivity analysis and the diagnostic analysis were used to businesses as operating well. 82.8 percent of small businesses
measure the relationship between node variables in the Bayesian network experienced COVID-19 induced operation problems after the
model developed. The sensitivity analysis adopts the forward reasoning ﬁrst wave of pandemic. About two-thirds of the small businesses
ability of the Bayesian network to evaluate the inﬂuence of input variables have taken certain COVID-19 response measures, and about a third

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FIGURE 2
The structure diagram of the Bayesian network implemented.

FIGURE 3
Survival rate of business experiencing one and two rounds of lockdowns since the ﬁrst wave of the global COVID-19 pandemic, respectively.

have received help from government or NGOs after the ﬁrst wave of businesses took COVID-19 response measures (63 percent), while
the pandemic. a larger proportion of small businesses received help from
As shown in Figure 5, about 52.4 percent of the small businesses government or NGOs (52.1 percent).
that survived the ﬁrst wave of the pandemic achieved sustained
operation after one additional wave of the pandemic. 33.4 percent of
owners rated their ability to run small businesses as good, while only 4.3 Sensitivity analysis results
29.5 percent of the owners rated their businesses as operating well.
Compared with small businesses that experienced only one wave of With the target variable “business operating state” as the analysis
COVID-19, small businesses that experienced two waves of COVID- variable, Netica software was used to conduct the sensitivity analysis
19 had a smaller proportion (69.9 percent) of operation problems on other variables to explore the inﬂuence of each variable on the
caused by the pandemic, and a smaller proportion of small target variable. The effects that 27 driving factors had on the target

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FIGURE 4
Bayesian network results for businesses that experienced one wave of pandemic.

FIGURE 5
Bayesian network results for businesses that experienced two waves of pandemics.

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TABLE 4 Sensitivity analysis results of the target variables (%).

Node variables Business operating states

Experienced one wave of pandemic Experienced two waves of pandemic
Owner characteristics 1.46 0.45

Gender 0.06 0.00

Education 0.14 0.00

Age 0.20 0.01

Industry experience 0.12 0.16

Owners’ expectations of business climate 0.03 0.00

Business characteristics 2.47 0.45

Business types 0.14 0.01

Business size 0.35 0.00

Primary market 0.06 0.02

Owned or leased facility 0.07 0.01

Pre-pandemic ﬁnancial condition 0.18 0.00

COVID-19 induced business operation problems 0.13 0.02

Closure duration 0.01 0.00

Raw material supply 0.04 0.01

Customer loss 0.03 0.00

Employee loss 0.13 0.01

Pandemic prevention costs increased 0.05 0.00

COVID-19 response measures 1.71 0.02

Employee reduction 0.83 0.01

Technological innovation 0.46 0.00

Online transformation 0.86 0.01

Pandemic prevention resource reserve 0.76 0.00

Multi-point location 0.06 0.01

Supports from government and NGOs 1.01 0.54

Loans 0.71 0.17

Rent subsidies or tax reduction 0.85 0.20

NGO assistances 0.75 0.01

variables are shown in Table 4. For small businesses that experienced reduction had a signiﬁcant impact on sustained business
one wave of the pandemic, in the middle layer node variables, operations, with variance reduction ratios of 0.86, 0.85, and 0.83,
business characteristics have a signiﬁcant impact on business respectively.
sustained operation after the pandemic, with the percentage of For small businesses that have experienced two waves of the
variance reduction as high as 2.47 percent. COVID-19 respond pandemic, in the middle layer node variables, owner characteristics,
measures, owner characteristics and supports from government and business characteristics, supports from government and NGOs have
NGOs also had an important impact on sustained business a strong inﬂuence on sustained business operation, with variance
operation, and the variance reduction ratios were 1.71, 1.46 and reduction ratios of 0.45, 0.45, and 0.54, respectively. COVID-19
1.01, respectively. The impact of COVID-19 induced by business induced business operation problems and COVID-19 response
operation problems on the target variable is small, and the variance measures had minor impact on sustained business operations. In
reduction ratio is only 0.13. In the input layer node variables, online the input layer node variables, rent subsidies or tax reduction, loans,
transformation, rent equipment or tax reduction and employee and industry experience had a signiﬁcant impact on sustained

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TABLE 5 Diagnostic analysis results (%).

Node variables Levels of variables Change of the probability

Experienced one wave of lockdown Experienced two waves of lockdowns
Owner characteristics Good +6.50 +3.30

General −2.10 +0.30

Poor −4.40 −1.00

Industry experience Less than 2 years’ experience — −1.00

2–5 years’ experience — −0.10

More than 5 years’ experience — +1.10

Business characteristics Well +8.60 +2.90

General −6.30 +0.20

Poor −2.40 −3.10

COVID-19 response measures Yes +12.10 —

No −12.10 —

Employee reduction Yes +3.00 —

No −3.00 —

Online transformation Yes +3.80 —

No −3.80 —

Supports from government and NGOs Yes +3.90 +3.10

No −3.90 −3.10

Loans Yes — +1.10

No — −1.10

Rent subsidies or tax reduction Yes +2.00 +1.90

No −2.00 −1.90

business operations, with variance reduction ratios of 0.2, 0.17, and owners had a higher evaluation of their own business operation
0.16, respectively. ability, the business had a higher probability to stay alive after two
waves of the pandemic. Pandemic response measures and access to
government or NGO assistances can help improve the alive
4.4 Diagnostic analysis results probability of businesses that have experienced two lockdowns.
The probabilities of employee reduction, online transformation
The owner characteristics, business characteristics and other and rent equipment or tax reduction increased by 3 percent,
inﬂuential factors were selected for the diagnostic analysis. The 3.8 percent, and 2 percent, respectively. They are effective
quantitative causal relationship between the inﬂuencing factors and pandemic response and assistance measures to improve the
the target variables was obtained by backward inference using the probability of business alive.
Bayesian network model. The value of the business operation status For businesses that experienced two lockdowns, when their
was set to level1, which assumed that all small businesses that probability to stay alive increased from 52.4 percent to
survived the ﬁrst wave of the pandemic at the end of 2019 were 100 percent, the probability of owners’ evaluation of their
going to still be alive by July 2022 after an additional lockdown and business operation ability as good increased by 3.3 percent, and
observe the change in the probability of impact factors. The results the probability of owners’ evaluation of their business running as
are shown in Table 5. well increased by 2.9 percent. Moreover, the rich experience of the
Table 5 shows that for the case in which the probability of a owners could improve the probability to keep the business alive.
business being alive after one wave of lockdown increased from Receiving supports from the government or NGOs could help
57.5 percent to 100 percent, the probability of owners’ evaluation of improve the probability to keep the business alive. Rent
their business operation ability as good increased by 6.5 percent, and equipment or tax reductions and loans rose 1.9 percent and
the probability of owners’ evaluation of their business running as 1.1 percent, respectively, indicating that they are the most
well increased by 8.6 percent. This outcome indicates that when the effective equipment to boost business alive.

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5 Discussion pandemic: More in detail, reduction of employees, online
transformation and rent subsidies or tax reduction were
Many previous studies have demonstrated that the pandemic identiﬁed as the more beneﬁcial support to local businesses and
has had an obvious repercussion on businesses survival (Xiao and other studies have come to similar ﬁndings. For example, Asgary and
Su, 2020; Carracedo and Puertas, 2021; Grondys and Lusarczyk, Anjum (2012) found that rent subsidies or tax reduction could help
2021). Thus, it was expected that the higher the number of lockdown boost business recovery in the context of disasters. Exposure on
waves, the lower would have been their survival rate. However, the online social media could increase product sales during a pandemic
current study found out only a small reduction in the survival rate and thus improve businesses’ survival (Katare and Marshall, 2021).
for businesses that experienced two waves of lockdowns compared Furthermore, employees’ reduction and rent subsidies could reduce
with those that only experienced one wave. These results may be the cost of running businesses and increase the probability of their
because areas that did not experience lockdowns consequent to the survival (Xiao and Su, 2020).
third wave of the pandemic, suffered as much from reduced For businesses that have experienced two waves of the
consumer demand as areas that did. pandemic, the respond measures had negligible impact on their
For the situation where the owners had a higher evaluation of probability to survive, while the support from government or NGOs
their own abilities in managing their businesses, a higher probability had a signiﬁcant effect on this probability. This may be induced by
to survive the pandemics was recorded, and this applies both for the fact that the businesses suffered from aggravated loss after
businesses that have experienced one and two waves of the experiencing multiple waves of the pandemic, and the resources
pandemics. This may be induced by the fact that owners who available to them were limited (Grondys and Lusarczyk, 2021; Taneo
have a high evaluation of themselves and their businesses have a and Noya, 2021; Vinberg and Danielsson, 2021). Therefore, the
more positive attitude towards business operations to be response measures taken by businesses could no longer effectively
implemented after each wave, and they will spare no effort to use improve their probability to survive. In this case, government’s
various resources to promote more sustainable operation of their support, such as rent subsidies or tax reduction and the interest-free
businesses (Khan and Sayem, 2013). Therefore, their business has a loans, could have helped businesses in time and increase their
higher probability to survival after multiple waves of the pandemic. chances of survival.
In addition, the current study found that experienced owners can The ﬁndings of the current study have important signiﬁcance for
help improve the probability of survival after experiencing two improving the probability of small business to avoid closure after a
waves of pandemic. Several studies in the context of disasters pandemic. However, this study has also some limitations. Firstly, the
also found that valuable owners’ experience helps them make current study only focuses on the operation state of the original surviving
correct decisions and undertake efﬁcient response measures, and business after 2 years and ignore the business operation process in the
they have a higher probability to keep functioning after the crisis long term after the pandemic involving several years. This is another type
(Marshall and Niehm, 2015; Orhan, 2016; Li and Hong, 2019). of study that would require future research to explore the process of
The COVID-19 pandemic caused problems to the normal operation businesses’ survival in crisis based on multi-time and longitudinal
procedures however it had small impact on the probability of businesses’ observations covering several years. Secondly, the current study uses
survival, and this statement is valid for both businesses that experienced dichotomous variables to measure COVID-19 induced operation
one as well as those that experienced two waves of the pandemic. Many problems, response measures and government’s support, which lacks
studies have found that the damage caused by natural disasters or risk measures that are more detailed. Future research could therefore further
accidents will adversely affect the survival of small businesses after these focus, for example, on the impact of the degree of operational problems,
external shocks (Sydnor and Niehm, 2017; Brown and Seville, 2019; the degree of pandemic response measures implemented, and the degree
Carracedo and Puertas, 2021). However, the current study found little of access to government supports on post-pandemic business survival.
correlation between COVID-19 induced operation problems and the Finally, although the current study has concerned the inﬂuence of many
survival probability of a business after the pandemic. This may be because factors on the operating status of businesses, including further extensive
the ﬁrst wave of pandemic swept Wuhan at the end of 2019. During the factors in the discussion could obtain even more signiﬁcant ﬁndings. For
lockdown, except for a few small businesses that ensured people’s example, location was suggested to be a key factor affecting business
livelihood and normal operation during the pandemic thanks to performance, both in crisis and non-crisis contexts (Lesage and Pace,
prevention measures adopted, the rest of the businesses were required 2011; Craioveanu and Terrell, 2016; Li and Zhou, 2019). Considering
to close, and thus, most of them suffered from indirect and not planned location factors and using spatial regression models to do some spatial
operational problems caused by the pandemic. Furthermore, the analysis of business post-epidemic performance will provide more
operational problems caused by the ﬁrst wave of the pandemic in late abundant ﬁndings for related research topics.
2019 may have affected the survival of some businesses, but this study
focused on the sustained operation of those that survived the ﬁrst wave of
the pandemic and were affected by subsequent waves of the pandemic. 6 Conclusion
Therefore, business operational problems caused by the ﬁrst wave of the
pandemic could have affect the survival of businesses in the short term but The long-term viability of small businesses that survived in the short
had trivial effect on the sustained operation for those that initially survived term after the pandemic started were ignored in the previous studies
the pandemic. conducted to date. However, the long-term operating approach of small
Implementing measures to reduce the impacts and receiving businesses that survived the pandemic has a critical impact on any regional
supports from government or NGOs could improve the probability economic growth, social stability, and sustainable development. Thus, the
of survival for all businesses that had experienced one wave of the current study took Wuhan as an example, focused on the rate of businesses

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that survived the ﬁrst wave of COVID-19 at the end of 2019 and were also from more expert people as well as boost the opportunities of
affected by subsequent pandemic waves. The Bayesian model was used to survival during challenging times.
quantitativelyexaminetheimpactofdifferentvariablesontheprobabilityof
businesses that survived the pandemic. The main ﬁndings of this study can The government should provide timely supports to small
be summarized as follows: businesses experiencing the pandemic, such as tax reduction, rent
subsidies and interest-free loans. In addition, policies implemented
(1) There was minor difference between the initial surviving businesses should give priority to small businesses in regions experiencing
that did not experience additional pandemic lockdown and those more severe impacts of the pandemic.
that survived and had to go through one lockdown.
(2) Businesses managed by owners who had a high evaluation of
their abilities, or a good assessment of their running operations, Data availability statement
had a high probability of achieving sustained operation after one
or two lockdowns. The authors will provide data available on request.
(3) Operational problems induced by COVID-19 had minor impact
on the long-term operating status of initial survival businesses.
(4) Employee reduction and online transformation have been identiﬁed Author contributions
as effective respond measures to the pandemic and rent subsidies or
tax reduction have been seen to be effective government supports, FL, MR, TZ, JL, and CC methodology; FL, MR, TZ, JL, and CC
which helped businesses and their probability to remain alive. formal analysis; FL, MR, TZ, JL, and CC investigation; FL, MR, TZ,
(5) Government supports, especially rent subsidies or tax reduction JL, and CC resources; FL, MR, TZ, JL, and CC data curation; FL, MR,
and loans, were essential to improve the alive probability of TZ, JL, and CC writing—original draft preparation; FL, MR, TZ, JL,
businesses that experienced two waves of lockdowns. and CC writing—review and editing; FL, MR, TZ, JL, and CC
visualization; FL, supervision; FL, project administration; FL,
The Chinese experience provided in the current study may have funding acquisition. All authors have read and agreed to the
important signiﬁcance and could be used as a reference to ensure a published version of the manuscript.
higher chance of achieving sustained operation after multiple waves of
pandemic lockdowns for small businesses in other countries. Moreover, the
abovementioned ﬁndings provide important implications. For business Funding
owners, they should actively learn and understand the knowledge related to
post-crisis business operation, integrate their usual experience with the This research work is supported by the GuangDong Basic and
special background of the pandemic, and sum up the post-epidemic Applied Basic Research Foundation (No. 2022A1515110339, No.
operation methods applicable to their businesses. Based on the operating 2021A1515110768) and National Natural Science Foundation of
experience, business owners should maintain a high conﬁdence in their China (No. 52109079).
abilityandthewaytheyruntheirbusiness,andtheyshouldactivelycontinue
to take measures to cope with the pandemic. For example, the adoption of
advanced technology could play a critical role for business survival during Conﬂict of interest
the COVID-19 crises especially with small businesses. For businesses
suffering from multiple waves of COVID-19 lockdown, owners should The authors declare that the research was conducted in the
payattentiontoactivelyseekexternalhelps,especiallysupportpoliciesissued absence of any commercial or ﬁnancial relationships that could be
by the government, in addition to taking respond measures by themselves. construed as a potential conﬂict of interest.
The pandemic has affected many businesses in China and across
the world and it is crucial to learn the following lessons:
Publisher’s note
- monitor both future exogenous events and political changes.
- Be aware of the global economy, identifying sources that could All claims expressed in this article are solely those of the authors
supply similar materials with lower prices to mitigate the and do not necessarily represent those of their afﬁliated organizations,
increase of costs from other countries. or those of the publisher, the editors and the reviewers. Any product
- Join forces, because small businesses could stipulate and join that may be evaluated in this article, or claim that may be made by its
associations (national and international) to gain knowledge manufacturer, is not guaranteed or endorsed by the publisher.

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