Risk management for second‐hand clothing imports in least developed countries: Legislations and perception of public‐sector corruption

The second‐hand clothing imports are very popular in the least developed countries (LDCs). The social health risk (SHR) associated with second‐hand clothing products and the lack of relevant legislations in LDCs, however, bring substantial challenges. This article is therefore developed to explore the sterilization legislation design for second‐hand clothing supply chains in LDCs. To address LDCs’ different import requirements of fumigation, both the extended exporter responsibility (EER) legislation scheme and the extended importer responsibility (EIR) legislation scheme are considered. We also examine whether the perception of public‐sector corruption in LDCs may affect the performance of sterilization legislation schemes. We compare the performance of sterilization legislation schemes under different public‐sector corruption cases, different sterilization legislation structures, as well as market competition. Interestingly, our analyses show that the EER and EIR legislation schemes can achieve the same performance under a per unit SHR duty, no matter whether there is public‐sector corruption or not. However, these two legislation schemes perform differently under the lump‐sum SHR duty. Besides, with the presence of the public‐sector corruption perception, the prospect of financial benefits from bribing the regulatory agency can induce the firm to choose a higher optimal sterilization level when the bribe is sufficiently small. These implications complement the extant knowledge on risk management of second‐hand clothing in LDCs, and provide an important guidance regarding the design of sterilization legislations on second‐hand clothing imports.


2021
).The second-hand clothing imports, however, come with the social health risk (SHR) problems and can challenge public health risk management.As a typical example of LDCs, Ghana lists the second-hand clothing as one of the high-risk goods, which are defined as the products that have serious health, safety, or environmental influences on the public (The Ghana Standards Authority [GSA], 2021).The doctors in practice also emphasize that the public should pay close attention to the health risks associated with the second-hand clothing products, which are usually not properly cleaned and sterilized, and may induce scabies, lice, and ringworm (Akande, 2017).Companies such as Rentadella and Style Theory, for instance, are under the pressure induced by the increasing anxiety over health and hygiene of their second-hand clothing products (Robert, 2020).To address the SHR concerns, therefore, various LDCs (e.g., Ghana, Tanzania, Uganda, and Ethiopia) require the sterilization of the second-hand products at the time of import. 2  In the meantime, evidence suggests that a company may illegally bribe regulators in practice (Heitz et al., 2021).Typically, in contrast to the greater aversion to illegal behavior and closer monitoring of public officials' activities in wealthier countries, public-sector corruption affects poor countries substantially (Lee & Weng, 2013;Singh, 2017;Sudhir & Talukdar, 2015).According to the 2020 Corruption Perceptions Index (CPI) published by Transparency International in 2021, for instance, corruption is much more prevalent in the LDCs compared to developed economies (see Table 1). 3 This is also consistent with the data released by the Worldwide Governance Indicators 4 (by the World Bank).The high incidence of public-sector corruption can facilitate evasion of firms' corporate social responsibility (CSR, Julian & Ofori-dankwa, 2013).It can decrease social welfare and lead to lower growth and poverty traps of countries like LDCs (Birhanu et al., 2016;Capasso & Santoro, 2018).In particular, the global second-hand clothing economy is a rapidly expanding market with international networks of dealers, the governance of which is highly complex (Norris, 2015).Examining the impacts of the public-sector corruption perception on LDC markets is thus of great importance.
With the above observations, our study is propelled by two motivations.First, in contrast to the rich findings in the corruption literature on compensation corruption and taxation corruption (e.g., Ades & Di Tella, 1999;Dzhumashev, 2014;Célimène et al., 2016), few studies examine the impacts of the public-sector corruption perception on risk management of LDCs' second-hand clothing supply chain.This is, however, an urgent issue given the prevailing second-hand clothing imports in LDCs and the significance of health risk.Second, extant theories imply that there are two opposing predictions regarding the impacts of corruption (e.g., Acemoglu & Verdier, 2000;Célimène et al., 2016;Dzhumashev, 2014).Following this rationale, we address the high CPIs of the LDCs as observed from the practice and devote to exploring the impacts of the public-sector corruption perception.Accordingly, the analytical framework employed in this study (see Table 2) addresses the following research questions (RQs).
RQ 1: Comparing between the extended exporter responsibility (EER) legislation and the extended importer responsibility (EIR) legislation, which one is better for addressing the SHR problem in LDCs' second-hand clothing supply chain?
RQ 2: How does public-sector corruption impact the performance of the sterilization legislations in LDCs?
RQ 3: What are the impacts of the public-sector corruption perception on public health risk management?
We follow the Centers for Disease Control and Prevention (CDC) (US Department of Health & Human Services) 5 to define "sterilization" as a process that uses either physical or chemical methods to destroy microorganisms including large numbers of resistant bacterial spores in the product (i.e., the second-hand product in this article).We use the term "the regulatory agency" to represent the individual inspector or the related laboratory or any other regulators from the agency of government responsible for import inspection.Our article targets at exploring the impacts of the public-sector corruption perception caused by the regulatory agency.That is, the public information of a high CPI leads to the perception of weak government enforcement and a corruptible LDC market.Subsequently, the foreign exporter has the strategy of entering the LDC market by bribing the regulatory agency and therefore does not have to sterilize the secondhand product as reported. 6Following Dzhumashev (2014) and Capasso and Santoro (2018), we define public-sector corruption as an agreement through which the regulatory agency (2) The evidence may be either from the foreign exporter (e.g., Ghana) or the local importer (e.g., Uganda).

Model formulation:
The sterilization legislation can be applied either to the foreign exporter (the EER legislation) or the local importer (the EIR legislation).
Discussion 2: Public-sector corruption perception for passing the inspection and conformity assessment Practical support: At the points of entry in LDCs, inspection and conformity assessment will be conducted by local government agencies (e.g., the GSB, and the UNBS).These agencies collect additional fees from their services of quality assurance and testing activities.Dong et al. (2022) also highlighted that in practice, local government agencies in developing economies, such as the auditing bodies, usually operate under the jurisdiction of multiple government branches and these agencies may shirk their responsibilities (e.g., in maintaining food safety).
Model formulation: It is reasonable to explore the impacts of the public-sector corruption perception for passing the inspection and conformity assessment for the sterilization responsibility.

Extended models
Extension 1: Public-sector corruption perception for reducing the sterilization evasion risk receives a bribe from the private sector (i.e., denoted either by the foreign exporter or the local importer in this article) quate (Plambeck & Taylor, 2016).Our article targets at this consequence and studies the case when the government enforcement is weak and the foreign exporter is dishonest.
That is, our model can be the story of public-sector corruption after the responsibility violation has occurred.
in exchange for a favorable decision on the sterilization of the second-hand clothing imports. 7On this premise, we build a theoretical model to investigate the SHR of the secondhand clothing imports.We capture the real-world practices by rationalizing the foreign exporter's sterilization decision under different sterilization legislation schemes and different public-sector corruption cases.We also extend to explore different cost structures of sterilization legislation schemes, as well as market competition.Together with the considerations of the subsequent consumer surplus and social welfare, we examine how the sterilization legislation schemes may perform differently.The models are supported by the practice.Features of different models and relevant practical support are provided in Table 2.The analysis along these lines yields several important findings.For instance, it is interesting to note that under a per unit SHR duty, the EER and the EIR legislations can always achieve the same performance no matter whether publicsector corruption is present or not.While under a lump-sum SHR duty, the performances of these two legislations are different due to the SHR duty's scale effect.In addition, given the high sterilization cost, the prospect of financial benefits from bribing the regulatory agency can induce a higher optimal sterilization level of the second-hand product in the case of a sufficiently small bribe.These findings complement the knowledge on risk management of second-hand clothing in LDCs and the impacts of the public-sector corruption perception, and can serve as an important reference to the LDC governments regarding the design of sterilization legislation schemes on second-hand clothing imports.
The rest of this article is organized as follows.Section 2 provides a literature review covering the fields of corporate risk management, operations in LDCs, and developing economies, second-hand market, and public-sector corruption.Section 3 explains basic model formulation.The EER and the EIR legislations are introduced, the performances of which are further compared in Section 4. The impacts of the public-sector corruption perception are also discussed in Section 4. Afterward, extended exploration on different cost structures of the sterilization legislations and market competition is conducted in Section 5. Section 6 then concludes the article by highlighting the key findings and future research directions.

LITERATURE REVIEW
In the literature of operational risk management, popular areas include sustainable sourcing (e.g., supplier risks in Fang & Cho, 2020;Saunders et al., 2020;Liu et al., 2022;Lu & Tomlin, 2022), ecolabels and environmental certifications (e.g., label confusion risks in Harbaugh et al. (2011), credibility risk of firms' self-labeled environmental qualities in Murali et al. (2019)), and public health risk management (e.g., food safety risk in Veflen et al. (2020), Wang et al. (2020), andYin et al. (2021), and health externalities and we focus on the case when the agency is with a nonzero probability of taking the bribe.This captures the high CPIs of the LDCs as mentioned in Table 1.
policies in Alfaro et al. (2022)).This article focuses on the underexplored public health risk management of sterilizing the second-hand product import.There are also some prior studies covering corruption in global supply chains.However, both our analysis and results are fundamentally different from them.For instance, in contrast to the private sector's corruption risk explored in Fan et al. (2021a), our article addresses corporate risk management on the public-sector corruption perception in the LDC markets.Furthermore, the objective of Fan et al. (2021a) is to demonstrate the effectiveness of the optimal incentive-compatible mechanism.While our article is for discussing the performance of the sterilization legislation schemes on the second-hand product import.
Our article relates to the scant research stream on operations in LDCs and developing economies.The recent research in this emerging area covers the topics of agricultural operations and economics (e.g., de Zegher et al., 2019;Hu et al., 2019;Zhou et al., 2021;Xiao et al., 2020), retailing operations (e.g., Zhao et al., 2019;Zhang & Swaminathan, 2020), sourcing negotiations (e.g., Mu et al., 2022), and CSR (e.g., Dong et al., 2022).Similar to these studies, our article considers key operating characteristics of a fragmented market base in developing economies (e.g., small-scale firms with low bargaining power) and develop a noncooperative game based on a multistage supply chain.While unlike these studies, we examine the socially responsible operations in global supply chains.In this stream, Cho et al. (2019) also discuss socially responsible operations in developing economies.However, our article considers the SHR associated with the secondhand product import and the sterilization responsibility.In addition, Cho et al. (2019) do not consider the enforcement of government legislations and social welfare, which is the major focus of our article.These listed characteristics, to the best of our knowledge, have not appeared so far in models in LDCs and developing economies.
This article relates to the second-hand market, which has been studied extensively under the topics including extended producer responsibility (EPR) legislations (e.g., Atasu & Souza, 2013;Mazahir et al., 2019;Tian et al., 2019), market competition (e.g., Toyasaki et al., 2011;Chen & Chen, 2019), and inventory management under warranty service (e.g., Pinçe et al., 2016).Similar to these papers, this article also highlights the cost of the second-hand product and explores the second-hand market under the considerations of government intervention and social welfare.Innovatively, our article emphasizes consumers' sensitivity to both the retail price and the sterilization level of the second-hand product, and investigates government intervention in the form of sterilization legislation schemes.All of these appear novel in the second-hand market literature.
This article is also related to the public-sector corruption problem in operations.In the extant corruption models, the public sector basically interacts with the private sector in two broad fields: compensation corruption and taxation corruption.Examples include Ades and Di Tella (1999), Acemoglu and Verdier (2000), Fan, Chen, and Tang (2021b) them, this article investigates firms' CSR evasion.In addition, consumer surplus, which is ignored in these studies, is also emphasized in this article.Besides, there are some empirical works on public-sector corruption, including Montiel, Husted, and Christmann (2012), Bennett, Pierce, Snyder, andToffel (2013), andBirhanu, Gambardella, andValentini (2016).In addition, Jeong and Weiner (2012) and Lee and Weng (2013) both address the globalization trend (Yatsenko, Nitsenko, Mardani, & Tananaiko, 2018).Differently, this article addresses the impacts of the public-sector corruption perception on firms' sterilization actions over the second-hand clothing imports in LDCs.

MODEL SETTING
We have Supply Chain SH (with SH representing for secondhand) as shown in Figure 1, which consists of a local importer (I) in the LDC market and a foreign exporter (E).Capturing the fragmented market base in developing economies (de Zegher, Iancu, & Lee, 2019;Zhao, Lim, Guo, Ding, & Song, 2019), the local importer has a low bargaining power while the foreign exporter plays as the Stackelberg leader. 8The foreign exporter and the local importer maximize their own profits by controlling the values of w SH and p SH , respectively.Besides, given the SHR of the second-hand product (defined as the health risk), the foreign exporter sterilizes the secondhand product at the level s.Such a CSR-related decision is also addressed in the economics and social sciences literature, like the "cleanup" decision explored in Viscusi and Hamilton (1999).The sterilization cost follows . The quadratic cost structure is commonly used in the literature like Atasu and Souza (2013) and Xiao et al. (2020).
In line with Guan, Geng, and Gurnani (2021) and Shi, Tang, and Dong (2021), we consider a consumer market with size normalized to be 1.Each consumer buys at most one unit (Chen, Wang, Niu, & Chen, 2022;Hu, Wang, & Feng, 2020).Consumer heterogeneity in product valuations (i.e., the consumer's willingness to pay) is captured by taking v to be uniformly distributed over [0, 1] (Li et al., 2019;Niu & Zou, 2017;Pun et al., 2021).The utility a consumer generated from buying a second-hand product is The assumption of the consumer's sensitivity to the sterilization level of the second-hand product () is consistent with the literature which highlights that firms would risk losing consumers if the product quality is low on dimensions like health outcomes (Bennett et al., 2013;Gaynor, 2006).The hygiene risks are also reported as one of the key reasons behind the limited popularity of second-hand clothing in countries like Poland, Philippines, and Pakistan.9Accordingly, the demand of the second-hand product is q SH = 1 − (p SH − s).
Following the observed real-world practice, we assume the LDC government imposes a per unit SHR duty on the imported second-hand product either by the EER legislation or the EIR legislation.The per unit SHR duty is served as a penalty against the threats to consumer health by the second-hand product.Under the EER legislation, the foreign exporter has to pay an SHR duty t E to the LDC government; while under the EIR legislation, an SHR duty t I is charged on the local importer.Besides, we aim at exploring the industry-level performance of the sterilization legislation.Accordingly, we proxy the SHR duty faced by a firm by an average value experienced by all other firms in the same industry.The SHR duty therefore is assumed to be the same under the EER and EIR legislations, with t E = t I = t = a − s > 0 .
Social responsibility policies for firms are developed at the strategic level (Thekdi, 2016).The high CPI leads to the perception of weak government enforcement and a corruptible market.Subsequently, the foreign exporter (under the EER legislation) or the local importer (under the EIR legislation) has the strategy of bribing the regulatory agency for passing the inspection and conformity assessment.10As a result, the foreign exporter may reduce the actual sterilization level by  i s.The evasion rate  i is exogenously given and satisfies 0 ≤  i ≤ 1, where i = L, H stands for a low evasion rate and a high evasion rate, respectively.11That is, different from the sterilization level s as publicly reported, the real sterilization level is (1 −  i )s.Following the literature (e.g., Cho et al. 2019), we assume  L = 0, and  H = .As explained previously, our article targets at investigating the case after the responsibility violation has occurred (i.e., when the foreign exporter has reduced his sterilization level) in an environment with weak regulatory enforcement.Accordingly, we retain our main focus on the case of  H = .Following the corruption literature (e.g., Fan et al., 2021b), the bribe amount is known as an "open secret" in the market.The total bribe amount follows G () = (g + s)q SH + f , with g, , f > 0.12 Without loss of generality, we have  +  > , and p SH > c SH + a + g.Besides, consumers do not observe the firm's sterilization evasion behavior or the bribe transfer, because in most cases, no official record of these two actions exists. 13Similar to the literature on CSR (e.g., Murali et al., 2019), government intervention (e.g., Esenduran et al., 2017), and corruption (e.g., Fan et al., 2021b), we capture the practices by setting the government parameters (i.e., a, ) nonnegative and exogenously given.For ease of reference, we present all the notations and definitions in Table 3, and evidence support for key assumptions in Table 4.

3.1
The EER legislation (Model E) We consider a two-stage Stackelberg gaming model, which is commonly adopted in the literature (e.g., see Ma et al., 2018;Wang et al., 2019).Following the practices (e.g., Baden & Barber, 2005), we have the sequence of events as follows.In the first stage, the foreign exporter as the Stackelberg leader simultaneously determines the wholesale price w SH and the sterilization level s of the second-hand product exported to the LDC market.In the second stage, the local importer follows by taking the foreign exporter's decisions into considerations and choosing the unit retail price p SH for the second-hand product.All supply chain members are profitmaximizing (Feng, Govindan, & Li, 2017;Perera, Dawande, Janakiraman, & Mookerjee, 2020) and have the same assess to the market information (Niu, Dai, & Li, 2022).Accordingly, we have the objectives and social welfare function under the EER legislation as: 1. Local importer : max 2. Foreign exporter : max 3. Social welfare: Following Zhang and Zhang (2018) and Guan et al. (2020), the social welfare is defined as the sum of supply chain members' expected profits (denoted by Π I and Π E ) and the consumer surplus (denoted by CS) net the expected government social health expenditure of the secondhand product (denoted by H SH (s)): (3) The LDC government's expected social health expenditure .14 Ω denotes the initial healthcare system cost without any sterilization legislation.l is the healthcare system's cost coefficient with respect to the sterilization level of the second-hand product.Health concerns and the social health expenditure have been emphasized in The proportional rate of the bribe to the market demand The minimum bribe amount the firm needs to pay for participating in the bribing game Ω The initial healthcare system cost without any sterilization legislation l The healthcare system's cost coefficient with respect to the sterilization level of the second-hand product The chance that the evasion on product sterilization will be identified by the inspection and conformity assessment activities

𝛾
The extra penalty for the identified evasion of product sterilization The chance of being bribed

𝜑
The coefficient of the SHR duty's scale (economies/diseconomies) effect

𝜉
The extra third-party certification fee

𝛿
The consumers' willingness to pay for the third-party certification The foreign exporter's profit The LDC government's social health expenditure

CS
The consumer surplus

SW G
The social welfare Abbreviations: LDC, least developed country; SHR, social health risk.

TA B L E 4
Evidence support for key assumptions.

Key assumptions Evidence support
1.The foreign exporter is responsible for the sterilization.
LDCs like Ghana, Tanzania, and Uganda (see more details in Tables B1a and B1b in Online Supplementary Appendix B) require all second-hand clothing to be cleaned and fumigated by the foreign exporter before import.
2. The LDC government imposes either the EER or the EIR legislation.
Evidence of conformity for fumigation standards (i.e., the statutory sterilization responsibility) is required in LDCs, which can either be provided by the foreign exporter or the local importer (see Table 2). 1 3. The government parameters (i.e., a, ϕ) are nonnegative and exogenously given.
(1) Given the complexity of the global market, the LDC government can never maximize its social welfare when imposing their legislations.Especially, for the East African Community (EAC) members like Burundi, Rwanda, Tanzania, Uganda, and South Sudan, the governments have limited flexibility in setting their legislations for second-hand clothing product imports.As reported by the US Trade Data, for example, Burundi, Tanzania, and Uganda all charge a same value of import tariff on the worn textile products (The International Trade Administration, 2021). 2 (2) The extant literature (e.g., Acemoglu & Verdier, 2000) highlights that in the presence of corruption, it is much harder to achieve "optimal" government intervention.
economics and social sciences literature, such as Viscusi and Hamilton (1999).This also addresses the highlights in Taylor and Xiao (2019), which indicates that the expensive drugs to treat diseases can lead to a heavy burden on the developing economies' public health systems.The consumer surplus CS

The EIR legislation (Model I)
Following the same logic, we have the objectives and social welfare function under the EIR legislation as: 1. Localimporter : max 2. Foreignexporter : max (5)

Social welfare:
The LDC government's social welfare function SW G is the same as in Model E.

Equilibrium decisions
Using backward induction, it can be found that under the 15 we have the respective equilibrium results of Models E and I as Table 5, where The profit allocation between two firms in a supply chain is determined by the agreed price that the downstream firm pays to the upstream firm (Zhong, Zhou, & Leng, 2021).It is surprising to notice that although the EER and the EIR legislations can lead to different profit allocations between the firms, the market demand, consumer surplus as well as social welfare are always the same.That is, in response to different sterilization legislations, the foreign exporter as the Stackelberg leader changes the profit allocations between the firms 15 The condition addresses the fact that the cost of sterilization can be high relative to the price of the second-hand product.This is in line with the practice observed by Katende-Magezi (2017) through the interviews with major importers of the second-hand clothing in LDCs like Ghana, Tanzania, and Uganda.
by adjusting the wholesale price while without influencing the overall equilibrium decisions of the sterilization level and the retail price of the second-hand product.
Lemma 1.For the influences of the EER and the EIR legislations (j ∈ ME, MI): (a) (i) (ii) When  <  + , , otherwise As can be seen from Lemma 1, a higher fixed SHR duty and a lower sterilization-level-based SHR duty reduction can both lower the sterilization level of the second-hand product, profits of the foreign exporter and the local importer, as well as the consumer surplus.In particular, when the foreign exporter's cost coefficient of sterilization is sufficiently large (i.e., k > (+−) (1−) 2 ), a high fixed SHR duty can only do more harm than good to consumers, since in addition to a low sterilization level, the consumers will also bear a subsequently high retail price of the second-hand product.For this case, the LDC government should set a high sterilization-level-based SHR duty reduction (i.e.,  > 3 + ) 16 instead, which can contribute to a low retail price of the second-hand product (i.e., a higher affordability to the low-income consumers) but a high sterilization level.
Theorem 1.To stimulate a high sterilization level and achieve a high consumer surplus level, the LDC government can use a sterilization legislation (either EER or EIR) that consists of a low fixed SHR duty but a high sterilization-level-based SHR duty reduction.
Lemma 2. For the influences of the EER legislation and the EIR legislation (j ∈ ME, MI): (a) When Ω < Lemma 2 complements Proposition 1 and Lemma 1.In particular, Lemma 2 shows the dominant advantage of the sterilization legislation structure proposed in Theorem 1 in achieving a high social welfare level under the condition of a sufficiently large initial healthcare system cost.17In addition, Theorem 1 also holds when the LDC government's initial 16 Notice that when  > 3 + , (+−) . As a result, when k > (+−) and  > 3 + , Optimal wholesale price Market demand Expected profit of foreign exporter ; Expected profit of local importer Consumer surplus ; Overall social welfare healthcare system cost is low but the healthcare system's cost coefficient (with respect to the second-hand product's steril- ). 18

Discussions: Public-sector corruption perception
To analyze the impacts of the public-sector corruption perception, we first explore the equilibrium decisions under the case without public-sector corruption and the foreign exporter has to strictly sterilize the second-hand product as reported (i.e.,  L = 0).Following the same logic, under the condi- , we have the equilibrium results in Table 6.tem cost.Together with the challenges induced by epidemic outbreaks and pandemics like the COVID-19, it is true that the initial healthcare system cost associated with the second-hand product can be high in practice. 18As a remark, given that k > always hold.
Accordingly, we have Propositions 2 and 3, with observations and implications summarized in Table B3 in Online Supplementary Appendix B. Besides, although the comparisons in Proposition 3 are based on the bribe format of G () = (g + s)q SH + f (for the case with public-sector corruption), similar results can be found in other bribe formats as shown in Online Appendix C1. Proposition Proposition 3 explains the drivers of public-sector corruption and identifies the conditions under which the Expected profit of foreign exporter Expected profit of local importer Consumer surplus ; Overall social welfare . public-sector corruption perception reduces the social health responsibility effort.Sterilization, as mentioned by Oxfam International, can lead to a high cost for the second-hand product. 19With such a high sterilization cost, there is a strong motivation for the foreign exporter to reduce his sterilization level.The prospect of financial benefits from bribing the regulatory agency therefore creates an incentive for the foreign exporter to join the corruption.Besides, it is believed that the presence of the public-sector corruption perception promotes violation instead of responsibility.Interestingly, Proposition 3 indicates that if the expected bribe is sufficiently small (i.e., g < min( ), and , the public-sector corruption perception will still contribute to a higher optimal sterilization level of the imported second-hand product (sterilization responsibility).As a consequence, the increased sterilization level brings more consumer surplus and more social welfare. 20 19 By selling donated second-hand clothes, Oxfam International raised £76m during the year of 2019/2020 to support people in need.Interested readers can also refer to https://www.oxfam.org.uk/about-us/faq/common-faq/ for more information (Accessed August 2021). 20This article examines the sterilization legislation design.We hence consider direct stakeholders including the local importer in the LDC market, the foreign exporter, consumers, and the government.However, we do not mean that the public-sector corruption would benefit the whole society.Regarding the impacts of public-sector corruption on other stakeholders or components different from economic efficiency of the private sector, we leave it for further research.

Public-sector corruption for reducing the sterilization evasion risk
Public-sector corruption can happen for reducing the evasion risk and expenditure (Célimène, Dufrénot, Mophou, & N'Guérékata, 2016).In the LDC market, firms are required to renew their import licenses and product registration periodically.As mentioned in Trade Policy Review of Uganda, for example, importers' import licenses are valid for 6 months and product registration is valid for 1 year.The sterilization evasion record can challenge the firms' credibility and affect the possibility of renewal.This brings the firms the motivation of corruption.We next examine the case when the firms face a corruptible regulatory agency to whom they propose bribes for reducing the sterilization evasion risk (Case P, with P denotes for penalty of the sterilization evasion) and maintaining their market permit.Relevant notations are summarized in Table 3. Governmental policies are long-term decisions in practice.Changes in the policies therefore are rare.Accordingly, making changes in the level of the inspection and conformity assessment or in the sterilization evasion penalty is also difficult.To address this fact, h p and  are both set as exogenous.The expected sterilization evasion expenditure follows Ĝ with 0 ≤ h p < 1 and 0 ≤ h b ≤ 1 .Such a structure can be supported by prior literature like Célimène et al. (2016), Singh (2017), and Capasso and Santoro (2018).The objective functions of the local importer and foreign exporter under Model E are: The objective functions of the local importer and foreign exporter under Model I are: , we have the equilibrium results in Results in Table 7 show the same equilibrium decisions for Models E and I.This verifies the robustness of Proposition 1 under the case of public-sector corruption perception for reducing the sterilization evasion risk.While surprisingly, Lemma 3 reveals that any increase in the chance of being identified (regarding sterilization evasion) can lead to a decrease in the optimal sterilization level and consumer surplus.The strategic rationale is the following.If the chance of being identified is small, the expected expense of sterilization evasion is low.In this case, the foreign exporter will be induced to select a high sterilization level which can contribute to a large demand.As a result, the consumers can still be benefited despite of their sterilization evasion behavior, which partially reduces the actual sterilization level.When the chance of being identified increases, however, the firm becomes less likely to do sterilization evasion as it implies that the expected expense of sterilization evasion now is high.This forces the firm to select a relatively low sterilization level.Consequently, consumers suffer.In particular, if the sterilization evasion penalty is sufficiently large (i.e.,  > γp ), a higher possibility of identifying the sterilization evasion behavior reduces social welfare.Lemma 4 presents the impacts of the public-sector corruption perception regarding the chance of bribing the regulatory agency for reducing the sterilization evasion risk.As known by the extant literature (e.g., Acemoglu & Verdier, 2000), when the fines are large, there is usually more room for public-sector corruption.The firm-level survey data in Amin and Soh (2021) also reports that firms in practice experience a significantly higher level of corruption when the regulatory burden is heavier.Interestingly, Lemma 4 reveals that a higher chance to bribe the regulatory agency cannot lead to a higher optimal sterilization level.Instead, it reduces the optimal sterilization level and consumer surplus.This proves the importance of corruption management regarding the chance to bribe the regulatory agency.Together with the findings in Lemma 3, Lemma 4 provides an important guideline for how to improve the optimal sterilization level and consumer surplus.To be specific, the LDC government is advised to give a higher priority to reduce the chance of bribing the regulatory agency compared to increase the chance of identifying the sterilization evasion.

An alternative cost structure of the sterilization legislations
In practice, the LDC government may charge the SHR duty by other cost structures.For instance, LDC governments like Tanzania and Uganda are known to charge the tariff duty on the second-hand product import by a lump-sum fee rather than by per unit product. 21In this section therefore, we explore the case of a lump-sum SHR duty (i.e., Case L).In Case L, the SHR duty follows the general lump-sum structure of tE = tI = ms − ns 2 , with m > 0, and n > 0. 22 Define the coefficient of the SHR duty's scale (economies/diseconomies) effect as  = 2n m .We assume that  is low enough to ensure a nonnegative SHR duty (i.e., s < 2  always holds).Besides, the quadratic term captures the characteristics of the SHR duty which can either be decreasing in s (scale economies when s 21 See https://www.theeastafrican.co.ke/business/East-African-states-defend-tariff-onused-clothes/2560-4016600-15n85y/index.html(accessed April 2020).The SHR duty helps shift the social health expenditure burden induced by the SHR of second-hand clothing products back to the firms who are responsible for.Similar social responsibility costs can also be found in practice.One typical example is carbon pricing, different forms of which have been widely applied by various governments as an instrument to manage firms' social responsibility. 22Here, by letting m=0 and n=ξ/2, the SHR duty captures the widely applied lump-sum structure of t = F − s 2 2 .In addition, interested readers can refer to Online Appendix C2 for Case L without public-sector corruption, which shows similar equilibrium results.

Model E
Model I Optimal sterilization level Expected profit of foreign exporter Consumer surplus ; Overall social welfare is higher than ) or increasing in s (scale diseconomies when s is lower than ).This allows us to generate different circumstances of the SHR duty and capture the fact that scale economies and diseconomies can both happen in practice.This ensures the comprehensiveness of our article.The popularity of such a cost structure can also be supported by literature like Souza (2013) and Guo et al. (2019).The objective functions of the local importer and the foreign exporter under Model E thus become: The objective functions of the local importer and foreign exporter under Model I are updated as max 2 ), we have the equilibrium results in Table 8.Accordingly, we have Propositions 4, 5, and 6, with observations listed in Table B5 in Online Supplementary Appendix B.
Interestingly, Proposition 4 shows that the SHR duty's scale effect (i.e., ) plays an important role in determining which sterilization legislation (the EER legislation or the EIR legislation) is better for addressing the second-hand clothing' SHR problem.For example, when the SHR duty's coefficient Optimal wholesale price Expected profit of foreign exporter ; Expected profit of local importer Overall social welfare of scale effect is sufficiently high (i.e.,  > ), the threshold value on achieving economies of scale (i.e., 1 ) becomes lower.Above this threshold value of , as economies of scale increase, the marginal SHR duty of providing a higher sterilization level decreases.As a result, the cost efficiency brought by an increased sterilization level provides the foreign exporter an incentive to enhance the sterilization level further.The EER legislation can hence bring a higher sterilization level and more consumer surplus than the EIR legislation.In contrast, when the SHR duty's coefficient of scale effect is sufficiently low (i.e.,  < ), the threshold value on achieving economies of scale (i.e., 1  ) becomes higher.The benefit from the scale effect can then be limited to the foreign exporter when compared with the significant cost increase in sterilization and the SHR duty.As a result, compared with the EER legislation, the EIR legislation can show a superior performance in stimulating a higher sterilization level and more consumer surplus.Proposition 5. (a) . Proposition 5 complements Proposition 3 by revealing the influences of the public-sector corruption perception under a lump-sum SHR duty.In the case with a lump-sum SHR duty, if the minimum bribe is high (i.e., f > max(f L E , f L I )), the foreign exporter can achieve more profits under the EIR legislation while the local importer can have more profits under the EER legislation.In fact, by checking the equilibrium results in the case with a per unit SHR duty, it can be found that the results hold in both cases.Proposition 6 complements Proposition 4 by showing how the SHR duty's scale effect (i.e., ) influences the performance of sterilization legislations from the perspective of social welfare.We find that when the healthcare system TA B L E 9 Supply chain features with market competition

Supply chains Features and practical meanings
Supply Chain H (1) A supply chain with high sterilization credibility (i.e., the evasion rate  L = 0).
(2) The foreign exporter in Supply Chain H enters the LDC market by providing the external fumigation certificate, which can show the reliable sterilization level without any chance of bribing the regulatory agency.
(3) Reliable sources of the products play an important role in the second-hand market (Guo, Zhang, Zhang, Liu, & Zhou, 2020).With an extra third-party certification, the consumers' willingness to pay can be enhanced by v, where 0 <  < 1.This is in line with the literature such as Gaynor (2006) and Bennett et al. (2013), which highlight that under competition, firms risk losing consumers when the product's health quality is low.Accordingly, the utility of a consumer generated from buying a second-hand product from Supply Chain H is expressed by U H SH = (1 + )v − (p SH − s).(4) One typical example of such third parties is IDFL, which is a global leader committed to guaranteeing the quality of textiles products and provides audits as well as certifications services including sterilization.
(2) The foreign exporter in Supply Chain L enters the LDC market by claiming the approval-based duty, under which the foreign exporter can have an unreliable sterilization level (i.e., lower than the published sterilization level) by bribing the regulatory agency.
(3) The utility of a consumer generated from buying a second-hand product from Supply Chain L is U L SH = v − (p SH − s).
cost associated with the second-hand product is sufficiently large (i.e., Ω > max( ), the EIR legislation can bring more social welfare.

Market competition and public-sector corruption perception
Keen market competition may encourage firms to engage in unethical activities, especially when the product is socially costly while the government is unable to adequately monitor and enforce relevant regulations (Ades & Di Tella, 1999;Blundell, Griffith, & Van Reenen, 1999;Bennett et al., 2013).We next extend to a competitive market scenario.Without loss of generality, we consider two competing supply chains, H and L, with asymmetric sterilization credibility as explained in Table 9.Similar asymmetric supply reliability structures can also be found in literature such as Li et al. (2017).The sequence of events is shown as Table 10.Using and k > k.
As found in Jildeh et al. (2021), there is currently no standard sterilization procedure in the market and products can differ in their sterilization processes and techniques in terms of factors such as choice of the sterilizing agent and operational conditions.Interestingly, Proposition 7 reveals that consumers' extra willingness to pay for the third-party certification and a low third-party certification fee (i.e.,  < − P Y ) do not necessarily guarantee a higher sterilization level than the second-hand product sold under the approval-based sterilization duty.In the meantime, a high third-party certification fee (i.e.,  > − P Y ) may still stimulate a higher sterilization level than the approval-based sterilization duty.As an example of the situation when the third-party certification fee is high (i.e.,  > − P Y ), if the foreign exporter in Supply Chain L follows a relatively high noncompliance degree (i.e., (1 − ) ), the foreign exporter in Supply Chain H will also vote for a higher sterilization level even under a sufficiently large sterilization cost coefficient (i.e., k > k). 25 As shown in the numerical results in Online Supplementary Appendix D, 26 when the extra third-party certification continues to increase the consumer acceptance level of the second-hand product, the foreign exporter in Supply Chain H can achieve a profit increase while the foreign exporter in Supply Chain L will suffer a profit decrease.Accordingly, even under a high third-party certification fee and a high sterilization cost coefficient, the foreign exporter in Supply Chain H may still increase the sterilization level.

Main conclusions
To address the associated public health risk challenges, this article is developed to explore the sterilization legislations on SHR of the second-hand clothing supply chains in LDCs.
Based on the comparisons on different sterilization legislation designs and the explorations on different public-sector corruption perceptions, important observations have been found which are listed as follows: 1. Design of the sterilization legislations: Risk management is largely missing in the development and implementation of CSR policies (Thekdi, 2016).This article serves as a guideline that considers risk associated with CSR policy implementation and compliance.First of all, it is interesting to note that under a per unit SHR duty, the EER and the EIR legislations can always achieve the same performance no matter whether there is public-sector corruption perception or not.In particular, in response to different sterilization legislations, the foreign exporter can flexibly change the profit allocations by adjusting the wholesale price, without influencing the equilibrium decisions of the sterilization level and 25 This finding can also be interpreted as follows: In a competitive market, the foreign exporter in Supply Chain H will always vote for a higher sterilization level even under a sufficiently large sterilization cost coefficient (i.e., k > k) and a high third-party certification fee (i.e.,  > − P Y ), as long as the third-party certification fee is not extremely high (i.e., − . 26 The numerical setting is based on the practice, including the interviews conducted by Katende-Magezi (2017) on the second-hand clothing markets in LDCs and the survey reported in Amin and Soh (2021) on the public-sector corruption.Details are provided in Online Supplementary Appendix D.
the retail price of the second-hand product.While under a lump-sum SHR duty, the performances of these two legislations are different due to the scale (economies/diseconomies) effect.Second, to address the SHR associated with the second-hand product but in the meantime to avoid challenging the export market, the LDC government can impose the EIR sterilization by a per unit SHR duty that comprises a low fixed SHR duty together with a high sterilization-level-based SHR duty reduction.Alternatively, the LDC government can set a lump-sum SHR duty either by the EIR sterilization with a small-scale effect of the SHR duty or by the EER sterilization with a large-scale effect of the SHR duty.
2. Public-sector corruption perception: Firms precisely control process parameters to achieve the required sterilization conditions of the products.In the prior risk analysis literature, Braud et al. (2000) highlight that a risk-based design takes into consideration possible factors in the sterilization process that could result in variation in the final sterilization value.We quantify how the public-sector corruption perception can affect the overall risk of the second-hand product.Given the high sterilization cost of the second-hand product, the prospect of financial benefits from bribing the regulatory agency creates an incentive for the firms to commit corruption.In the case of bribing for passing the inspection and conformity assessment, for instance, the prospect of financial benefits from bribing the regulatory agency can induce a higher optimal sterilization level of the imported second-hand product when the bribe is sufficiently small.The social responsibility efforts such as sterilization are expensive in practice.This explains the drivers of having public-sector corruption.
3. Enforcement of the sterilization legislations: In the case of bribing for reducing the sterilization evasion risk, any increase in the chance of being identified (regarding the sterilization evasion behavior) can lead to the decrease in the optimal sterilization level and consumer surplus.In the meantime, a higher chance to bribe the regulatory agency can also reduce the optimal sterilization level and consumer surplus.Accordingly, to improve the optimal sterilization level of the imported second-hand product and consumer surplus, the LDC government is advised to give a higher priority to reduce the "chance of bribing the regulatory agency" rather than to increase the "chance of identifying the sterilization evasion."This also addresses the operational challenge that the secondhand clothing trade in LDCs is mainly managed by the SMEs (Gui et al., 2019;Guo et al., 2021), which requires substantial governance efforts to increase the "chance of identifying the sterilization evasion." 4. Market competition: As found in Choi and Jeon (2020), "public on their own" often does not have the ability to acquire adequate information about risks while companies inherently seek to maximize their benefits in a loose governmental regulation framework.In a competitive LDC market, when the extra third-party certification continues to increase the consumer acceptance level of the second-hand product, the foreign exporter with high sterilization credibility can achieve a profit increase while the foreign exporter with low sterilization credibility may suffer a profit drop.Accordingly, the foreign exporter with high sterilization credibility has the incentive to increase the sterilization level under competition, even if the third-party certification fee and the subsequent sterilization cost are both high.

Future research directions
Several extensions can be investigated in the future.First, we examine the story of the second-hand clothing trade in LDCs with symmetric information.In practice, the foreign exporter and the local importer may not always share all the related information.It therefore can be interesting to examine the design of sterilization legislations and the impacts of publicsector corruption perception in an information asymmetric situation.One potential research area is the impact of asymmetric information relating to the sterilization level of the second-hand product as well as the potential risk (Ullah, Ayat, He, Huang, & Jiang, 2022).This extension may lead to interesting signaling games in product sourcing and risk-averse consumer behavior problems that deserve further investigation.It is also meaningful to develop a guide to explain how the best practice cost structure of sterilization legislations can be established to optimize a second-hand clothing product's supply chain with asymmetric information.For example, the SHR duty could be a tool for the LDC government to assess the public health risk and perhaps help reveal some private information in the system.The LDC government may also use it as a tool to evaluate their healthcare investments by including the cost of SHR in economic analyses or to find some of the solutions to alleviate challenges that have been faced.Second, we restrict our attention to the second-hand clothing imports while new products in the market (either domestically produced or imported) are not considered.In the future, we may explore the competitive threats from the new products in the LDC market and explore how public-sector corruption perception on the sterilization evasion behavior can impact the society.Third, more studies could be done in the area of LDC governments' endogenous responsibility as well as auditing and monitoring.These measures help the LDC governments better manage the SHR of the second-hand clothing imports and overcome the challenges associated with the public-sector corruption perception.Comparisons on the performances of internal auditing with public scrutiny and their respective impacts on foreign exporter actions related to behaving responsibly, for example, could be a fruitful direction for future work.

A C K N O W L E D G M E N T S
We sincerely thank the editor and reviewers for their kind and helpful comments, which led to important improvement of this article.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflicts of interest.

Models Practical support from LDCs (More details are available in Tables B1a and B1b in Online Supplementary Appendix B)
Features of different models and practical supports TA B L E 2

Different from F I G U R E 1
, Dzhumashev (2014), and Célimène et al. (2016).The supply chain structure under the basic model.EER, extended exporter responsibility; EIR, extended importer responsibility; LDC, least developed country; SHR, social health risk.

TA B L E 3 Notations and definitions w SH The wholesale price of the second-hand product paid by the local importer to the exporter
The foreign exporter's cost coefficient of sterilization (i.e., the sterilization effort cost factor).
All abbreviations are available in Table A1 in Online Supplementary Appendix A. Observations and implications from Proposition 1 and Lemma 1 are listed in Table B2 in Online Supplementary Appendix B.

Table 7
, where τ = h p h b  , ĝ = h p h b g .Observations from Lemmas 3 and 4 are listed in TableB4in Online Supplementary Appendix B.Lemma 3.For the influences of the inspection and conformity assessment (j ∈ ME, MI): (a)

The foreign exporters (E H , E L ) The local importers (I H , I L )
Decision variables in the competition game backward induction, it can be found that under the conditions of k > k (i.e., k is sufficiently big), we have Proposition 7.24Proposition 7. (a) s H−ME *