Supply chain stress tests for critical inputs : a proof-of-concept.
Date: 2024-09-05
Institutions: Directorate-General for Internal Market, Industry, Entrepreneurship and SMEs
Subjects: database, financial risk, financial stability, financial stress test, report, risk management, single market, supply chain, wind energy

 
 
 
 
 
 
 
The views expressed in this paper are solely those of the author  

and cannot be attributed to the European Commission 

EUROPEAN COMMISSION 

Directorate-General for Internal Market, Industry, Entrepreneurship and SMEs 
Directorate A – Strategy & Economic Analysis 
Unit A1 – Chief Economist Unit 

Contact: GROW-A1@ec.europa.eu 

European Commission 
B-1049 Brussels 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Supply chain stress tests for critical 
inputs: a proof-of-concept 

Single Market Economics Papers 

Beatrice Dumont  

Xosé-Luís Varela-Irimia 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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DOI: 10.2873/1355245 

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Supply Chain Stress Tests for Critical Inputs: 
A Proof-of-Concept 

Pr. Dr. Beatrice DUMONT (Sorbonne Paris University-CNRS & College of Europe & Climate 
Economics Chair & Visiting Research Fellow at DG GROW in 2022/23) 

Dr. Xosé-Luís VARELA-IRIMIA (Chief Economist Team, DG GROW)1 

We  acknowledge  support  from  DG  GROW.  This  economic  paper  was  prepared  under  the 
economic advisory programme of DG GROW of the European Commission. 

Abstract:  

This  article  aims  to  develop  a  ‘proof  of  concept’  for  testing  the  resilience  of  sectoral  supply  chain 

networks  at  firm  level  against  an  exogenous  shock  to  critical  inputs.  The  rationale  for  implementing 

supply chain resilience testing at the sector level is that outsourcing may be individually rational at the 

company level, but collectively suboptimal in terms of risk management at the supply chain level. The 

analysis  focuses  on  the  wind  power  sector  in  Europe  using  data  from  the  FactSet  Supply  Chain 

Relationships  database.  The  methodology  is  based  on  the  construction  of  a  matrix  of  resilience 

coefficients  linking  upstream  and  downstream  firms,  and  affecting  the  diffusion  of  shocks.  We 

implement  Monte  Carlo  simulations  and  examine  how  idiosyncratic  shocks  propagate  from  firms  to 

firms. Our findings show that supply chain stress tests can help identifying relatively weaker firms or 

more exposed sectors/countries and that the lack of critical inputs (downstream shock) can translate 

onto an upstream shock for suppliers of complementary inputs. At a more  detailed  level, our results 

show that the specificities of each firm network of suppliers-customers are a strong determinant of their 

resilience. 

1 The opinions expressed in this paper do not necessarily reflect the views of the European Commission. 

5  

 
 
 
 
 
 
 
 
 
 
 
1. Introduction 

The fragmentation of supply chains across countries is deemed to have brought cost-efficiency 

gains and facilitated technology diffusion2. However, this modular production structure3 is now 

being  called  into  question,  as  it  has  proved,  since  the  Covid  19  pandemic,  to  have  a  low 

resilience to shocks4, and possibly important negative spillover effects (Costinot & al., 2013)5. 

In fact, we have witnessed since the pandemic a series of exogenous shocks that have led to 

significant volatility in commodity markets (IMF, 2023), and massive supply chain disruptions 

(Bonneau & Nakaa, 2020). These shocks have revealed vulnerabilities in terms of sources of 

supply and have highlighted that security of supply is also a question of economic security. As 

stressed  by  OECD  Secretary  General Angel  Gurria  (2021)  “(...)  in  today’s  interconnected 

world,  shock  events  can  quickly  cascade  across  borders  and  economic  sectors,  and  have 

devastating effects on people’ lives, jobs, and opportunities, and on their trust in governments, 

institutions, and markets” 6. 

Under  these  circumstances,  the  question  arises  whether  policymakers  should  intervene. 

Indeed, the structure of global value chains is the outcome of decisions made by private firms 

based on both productivity and risk. It would thus be logical to consider that, after all, it is the 

responsibility of firms to ensure the resiliency of their supply chains, and that there is no need 

to 

implement  due  diligence 

laws.  However,  due 

to 

the  existence  of  market 

failures/externalities,  and  the  increase  in  the  number  of  cases  of  economic  coercions  in 

international trade, policy intervention may be necessary, in particular to monitor some supply 

chains deemed critical. 

First, outsourcing can be individually rational at the firm-level but collectively sub-optimal in 

terms  of  risk  management  at  the  supply-chain  level.  It  may  be  due  to  a  divergence  in 

public/private  risk  preferences,  and  more  precisely  a  potential  difference  of  incentives  to 

diversify/hedge against shocks between companies and governments. Risk externalities can 

thus  justify  public  intervention,  especially  in  a  context  of  a  supply-chain  network  where  the 

decision of each node neglects, or is unable to account for, the impact on the other nodes. 

2 See Amiti & Konings (2007); Grossman & Rossi-Hansberg (2008); Halpern & al. (2015); World Bank (2019). 
3 As opposed to a sequential production chain. 
4 Meier & Pinto (2020) show that US sectors with a large exposure to intermediates imports from China, contracted significantly 
more than other sectors and that they suffered from larger declines in production, employment, imports, and exports. 
5 Costinot et al. (2013) show that the microstructure of the value chain matters as it delivers distinct predictions about the impact 
of spillovers within value chains. 
6 Available at fostering economic resilience in a world of open and integrated markets: risks, vulnerabilities and areas for policy 
action (oecd.org) 

6  

 
 
 
 
 
 
Second, individual firms do not internalize the full risks of their actions. Not because they do 

not want it, but because companies are likely to face opacity about the identities of the firms 

involved in their supply chain beyond tier one. A consequence of this limited visibility is that 

firms cannot fully identify the risks of potential disruptions. To counterbalance this information 

asymmetry,  some 

large  companies  have  recently  adopted  contingency  plans  and 

implemented  their  own  stress  tests.7  However,  gathering  information  about  supply  chains 

involves  trade-offs  between  collecting  costs  and  data  quality,  and  often  concerns  tier-one 

suppliers only8. Moreover, such information is often considered as strategic, and therefore a 

trade  secret9.  As  a  result,  misjudgements  on  how  risky  a  supply  chain  is,  can  lead  to  a 

coordination  failure.  This  policy  problem  has  been  conceptualized  by  Baldwin  &  Freeman 

(2022) as a standard risk-reward trade-off10. Both firms and society would prefer less risk for 

any given level of reward, but the public cares relatively more about risk. In such a context, 

policy intervention could be justified if there is a Pigouvian wedge between private and social 

evaluations. 

Third, trade restrictions, especially those concerning critical raw materials have multiplied by 

five  since  2009,  and  10%  of  the  value  of  their  global  exports  faced  at  least  one  export 

restriction  measure11,  affecting  their  availability  (IMF,  2023;  OECD,  2023).  As  these  export 

controls  are  not targeted  at  a  specific  country,  but  are  instead  country-agnostic,  they  could 

potentially impact any EU’s manufacturers. These export restrictions should be a clarion call 

that over-dependence on China (or any other country) in any part of a value chain puts an 

economy at risk12. In this context, many countries are increasingly looking to “de-risk”—from 

their  dependencies  vis-à-vis  China  to  meet  their  supply  needs13.  But  contrary  to  its  major 

7 The telecoms group BT for instance has recently conducted stress tests on its supply chain to prepare for the disruption from a 
potential conflict between China and Taiwan. See Financial Times of April 16, 2023, BT hold China Taiwan war games to stress 
test supply chains. Available at https://www.ft.com/content/bb1f4951-eef5-4b3d-990a-f29d6fa28d54 
8 According to a study by the McKinsey Global Institute (2020, p. 44), beyond the first tier, which is easily identifiable, companies 
rely on a network of thousands of suppliers. This means that companies face opacity above the first tier and cannot fully identify 
the  risks  of  potential  disruptions.  Available  at  Risk-resilience-and-rebalancing-in-global-value-chains-full-report-vH.pdf 
(mckinsey.com) 
9 According  to  Marshall  et  alii,  (2016)  “External  pressure  [to  disclose  supply  chain  information]  has  come  from  government 
regulations, best practices of peers, and changing expectations from salient stakeholder groups such as NGOs”. (…)”. Recent 
examples  of  new  regulatory  pressure  in  the  United  States  include  the  2010  Dodd-Frank  Wall  Street  Reform  and  Consumer 
Protection Act and the California Transparency in Supply Chains Act 2010.  
10 This concept derives from portfolio theory (see Campbell et al., 2005).  
11 According to the OECD (2023, p.38), it even exceeded 30% for some critical minerals. Trade restrictions have been mainly 
imposed by China, Vietnam, Argentina, Russia, Kazakhstan, and Indonesia. In practice, these restrictions do not prevent exports 
altogether, but they require exporters to seek a license to ship these critical minerals. This means identifying importers and end 
users, and stipulating how these metals will be used. These restrictions cause delays, increase administrative costs, and the risk 
of rejection. It is also unclear how many licenses are issued. 
12 According to the newspaper Le Monde (July 1, 2024) in 1992, Deng Xiaoping (the leader of the People’s Republic of China) 
gave a speech that will go down in history: "The Middle East has oil, China has rare earths. Like oil for the Middle East, rare 
earths are of the utmost strategic importance for China. We must take advantage of this”. It is worth noting that since then, his 
successors have been inspired to cultivate this advantage. 
13 Since the rare earth export controls were enacted, Japan has shifted nearly 30% of its rare earths import mix from China to 
other countries, like Mongolia, Australia, and Vietnam, and invested in Australian producer Lynas, the world biggest producer of 
rare earth metals outside China. The United States also took steps to diversify, decreasing China’s share of its rare earth imports 
from about 100% in 2010 to 80% in 2020. However, such a move takes time to unfold given the costs involved in modifying supply 

7  

 
 
 
 
trading  partners,  the  European  Union  (EU)  did  not  take  major  steps  to  diversify  and  is  still 

relying on China for 98% of its rare earths in 2022 (IEA, 2023)14. The fear is that economic 

coercion through restrictions or boycotts on specific exports, like critical raw materials, could 

jeopardize the efforts of the EU to reach carbon neutrality and have adverse effects on growth. 

More generally, trade barriers linked to critical materials could split up nations into rival blocs 

and lead to a fragmentation of global trade (IMF, 2023)15. 

In such a context, policymakers have rediscovered the critical importance of having resilient 

supply  chains  and  have  brought  the  issues  of  open  strategic  autonomy  and  technological 

sovereignty to the fore16. This explains the increased temptation for policymakers to implement 

de-risking policies to enhance the resilience of supply chains. In practice, this translates into 

calls to adopt a “near-shoring”17 or “friend-shoring” agenda18. However, the efficiency of such 

de-risking  policies  is  not  proven.  Studies  show,  for  instance,  that  reshoring  increases 

aggregate  volatility  by  reducing  source  diversification  (D’Aguanno,  2021).  By  contrast, 

depending on the setting, policies that encourage diversification of foreign suppliers tend to 

lower  volatility  by  reducing  exposure  to  individual  economies  (Casselli,  2020,  Baldwin  & 

Freeman, 2021)19. Considering the European Union’s policy quadrilemma to simultaneously 

uphold  economic  security,  foster  sustainability,  maintain  the  competitiveness  and  a  relative 

autonomy20 of its industry, it is important to make sure that de-risking policies will not forego 

the benefits from trade specialisation and openness. In practice, this implies that de-risking 

policies should only be implementing to some specific supply chains deemed critical for the 

EU, namely when the incentives private actors are facing are sufficiently misaligned with the 

public interest to justify intervention. We should indeed not replace the risks related to supply 

chains by new policy hazards.  

chains. Moreover, China’s manufacturers have a competitive cost advantage that may keep international competitors out of the 
market until prices rise sufficiently. 
14 In April 2023, the European Union proposed a Critical Raw Material Act to make the EU more self-sufficient in the production 
of critical materials. The aim is to locate 10% of critical metal requirements and 40% of the processing industry within the EU. 
The project also includes an ambitious recycling target (to increase the share of recycled metals in supply to 15%) and a target 
for diversification of supply sources (to prevent any single country from holding more than 65% of the European market) by 2030. 
Available at European Critical Raw Materials Act (europa.eu) 
15 Depending on the scenario, the cost of this fragmentation could range from 0.2% to up 7% of global GDP (IMF, 2023). 
16  See  EU  Economic  Security  Strategy  Joint  Communication  (June  2023c).  This  strategy  proposes  to  carry  out  a  thorough 
assessment of risks to economic security in four areas. One of them encompass risks to the resilience of supply chains, including 
energy security. Available at An EU approach to enhance economic security (europa.eu) 
17 i.e., a relocation of some production geographically closer to the final production sites or country of sales. 
18 i.e., moving supply chains to jurisdictions that do not pose serious geopolitical risks. An ECB survey (2023a) of leading firms 
operating in the euro area shows that 42% of firms based in the EU plan to relocate their sourcing to “friendly” countries within 
the next 5 years in response to supply chain risks. This compares with only 11% in the 5 previous years. China is the country the 
most frequently mentioned in terms of perceived risks, either to the company’s own supply chain or that of its sector. 
19 This depends however on the variance/covariance of shocks across trade partners. 
20 Industrial autonomy can only be partial. It depends notably on the availability (and access to) of natural resources, but also of 
the existence of technological competences and skilled employees in the EU. 

8  

 
 
 
 
 
For  policymakers  to  make  informed  decisions  and  devise  the  most  appropriate  de-risking 

policies, it is thus important to develop new tools to assess risks to and from supply chain. In 

this  respect,  the  idea  to  implement  supply  chain  stress  tests  for  critical  inputs  is  gaining 

attention among policymakers. There are indeed similarities with the rationale for stress test 

in the banking sector where problems to a single bank may translate into aggregate shocks. 

Moreover,  stress  tests  have  proven  in  practice  to  be  an  important  monitoring  tool  in  the 

banking sector. They could potentially be adapted to supply chains to analyse risk factors and 

identify potential points of failures and/or choke points for inputs that are deemed critical. 

This article aims at developing a ‘proof-of-concept’ of such a tool in the form of a stress test of 

supply chains for critical inputs, with a special emphasis on the role of the network formed by 

firms. To do so, we use detailed data on firms direct and indirect suppliers and customers to 

reconstruct  a  value  chain.  As  supply  chains  differ  considerably  by  industry,  product 

characteristics, company’s strategies, distribution channels and so on, and given the proof-of-

concept nature of this paper, we focus on a single sector, that of the wind energy sector21, as 

it  is  supposed  to  form  the  backbone  of  EU  energy  security  in  the  short  term  and  carbon 

neutrality by 2050. From an empirical point of view, we opt for a single scenario, namely an 

export ban from China on processed critical raw materials. With China having a massive hold 

on the  worldwide supply chain of  critical raw materials 22, an export ban could potentially 

disrupt supply chains in several sectors, raise costs, and affect production, especially that of 

green technologies23. Such a scenario is an adverse but plausible one. It allows us to analyze 

the  resilience  (or  not)  of  firms  in  the  wind  energy  sector  to  withstand  such  a  shock  and  is 

justified  by  the  fact  that  in  recent  years,  export  controls  (trade)  restrictions24,  notably  by 

China25, have triggered a cycle of tit-for-tat retaliations, and have moved to the forefront of 

21 The EU faces foreign dependencies in the wind energy sector. See European Commission (2021 & 2023a, p.6) “(…) China 
dominates global supply chains, from mining and refinement to production, which are critical for the production of e-vehicles and 
wind turbines”. 
22 According to the last report of the IEA (2023) and that of the European Commission (2023), the critical metals refining 
and processing industry is largely located in China, and more generally concentrated in a small number of countries. 
China, for instance, produces 90 percent of the word’s gallium and 60 percent of germanium. Likewise, it is the world’s number 
one graphite producer and exporter and refines more than 90 percent of global graphite. 
23 According to some experts from the Stimson Center (2023), the effectiveness of the Chinese export bans of 2010 has been 
undermined by massive smuggling, which is supposed to have accounted for 40% of China’s rare earth exports. We assume 
here that the ban is strictly respected, and that smuggling is inexistent. See Why China’s Export Controls on Germanium and 
Gallium May Not Be Effective • Stimson Center 
24 It is noticeable that these measures depart from previous ones in the sense that they are undermining the legitimate objective 
of export controls — which are only intended to target dual-use items and technologies, i.e., goods that can be used for both 
military and civilian applications. 
25 In 2010, China enacted a series of export measures on pure rare earth, earth oxides, and rare earth salts to Japan, the United 
States, and the European Union. Those export controls took the form of a 40% lower quota (compared to 2009) for the export of 
rare earths. In addition, in 2011 China imposed a tariff of 15–20% on the export of rare earths and further reduced the quotas by 
32.5%.  Both  in  2010  and  2011,  China  also  raised  export  tax  rates  on  some  rare  earth  metals,  rare  earth  oxides,  rare  earth 
fluorides and rare earth carbonates. In 2012, as a reaction, Japan, the EU, and the U.S. filed a suit against China at the World 
Trade Organization (WTO) against these export restrictions. China lost the suit, and the WTO led countermeasures that eased 
prices and increased China’s export of rare earths. However, China adopted in return more stringent export licensing measures 
at  the  end  of  2014.  Most  recent  export  restrictions,  announced  in  July  2023  by  China’s  Ministry  of  Commerce,  include  eight 
gallium and six germanium products, two minerals essential for respectively the manufacture of photovoltaic cells and optical 
fibers but also bans on graphite commonly used in semi-conductors, electric vehicles, aerospace, chemical and steel industries. 

9  

 
 
 
 
trade policy. From a methodological point of view, we compare vulnerabilities at the level of 

firms, sectors and countries. We also compare these results across a range of hypotheses on 

sectoral  coverage  of  relevant  suppliers/customers,  the  degree  of  substitutability  within  and 

across sectors and the heterogeneity of resilience parameters drawn from probability density 

functions using Monte Carlo simulations. Our findings show that supply chain stress tests can 

help identifying relatively weaker firms or more exposed sectors/countries and that the lack of 

critical  inputs  (downstream  shock)  can  translate  onto  an  upstream  shock  for  suppliers  of 

complementary inputs. At a more detailed level, our results show that the specificities of each 

firm network of suppliers-customers are a strong determinant of their resilience. From a policy 

perspective,  this  means  that  microstructures  of  industrial  eco-systems  on  the  overall 

production  network  matter  and  that  it  is  therefore  important  to  promote  awareness  of  the 

importance  of  the  upper  (lower)  tiers  to  develop  more  effective  shields  against  shock 

propagation.  

This article contributes to the literature in two ways.  

First, it relates to a growing body of work that challenges the view of Lucas (1977) that micro-

economic shocks would average out and thus would have negligeable aggregate effects. More 

precisely,  these  papers  posit  that  micro  shocks  are  transmitted  in  the  economy  through 

industry  linkages  (Long  &  Plosser,  1997;  Carvalho,  2010; Acemoglu  et  al.,  2012  &  2016; 

Carvalho & Gabaix, 2013). Acemoglu et al. (2016) show, for instance, that depending on the 

setting, an industry-level shock could spread through a network of interconnections and play 

a  sizeable  role  in  macro-economic  fluctuations,  compared  to  what  is  typically  presumed  in 

macroeconomics26. Despite these findings, spillovers within networks of firms have received 

little attention in the empirical literature, as it is difficult to identify firm-specific shocks. In the 

same vein, while supplier-customer relationships are formed at the level of firms, most studies 

so far, are based on models that approximate the nature of these interactions at the industry 

level.  They  do  not  tackle  for  instance,  issues  such  as  firm-specific  relationships  and  the 

possibility of firm failures (Carvalho & Tahbaz-Salehi, 2019). Our paper tries therefore to fill a 

gap  in  the  literature  by  looking  at  how  idiosyncratic  shocks  propagate  from  firm  to  firm  in 

See  MOFCOM  Regular  Press  Conference  (July  6,  2023)  citing  national  security  reasons.  These  restrictions  took  effect  on 
December 1, 2023. In the same month, China also banned the export of technologies used in rare earth extraction and separation 
and in some rare earth magnets over national security. See Key Changes and Updates to Chinese Export Controls in 2023 | 
Insights | Mayer Brown. New Chinese regulations announced on July 1, 2024, and that will come into force on October, 2024, 
require  the  Chinese State  Council  to set  up  an  information system  for the traceability  of  rare  earth products.  Under this  new 
regulation, companies involved in the extraction, smelting and separation of rare earths, as well as the export of rare earth-based 
products, must set up a system to track product flows, record these flows "faithfully" and integrate them into a traceability system. 
Available at China's New Rare Earth Rules Seek Product Traceability Details (asiafinancial.com) 
26 As stressed  by  Horvath  (1998), the  empirical  evidence  on the  importance  of  sector linkages for  the  aggregation  of sector-
specific shocks is mixed and depends on the level of aggregation. As stressed by Baldwin & Freeman (2022), supply chains could 
also be a source of “shock diversification rather than magnification”. 

10  

 
 
 
 
production  networks  and  gradually  be  amplified,  in  the  particular  sector  of  wind  energy 

generation. 

Second, our paper departs from macro approaches traditionally used to assess the impact of 

exogenous shocks. Indeed, we use firm-level data to document firms’ input sourcing decisions 

and their location (upstream-downstream) in the supply chain. As stressed by Johnson (2018), 

one of the advantages of using firm-level data over macro data is that it allows us to model 

interactions between firms and their partners (both domestic and non-domestic), rather than 

inferring  them  by  combining  industry-level  information  with  trade  data.  Moreover,  another 

advantage  of  using  granular  data  on  supply  chain,  compared  to  aggregated  industry  level 

data,  is  that  it  captures  heterogeneity  in  supply  chains  linkages  across  firms  and  thus  the 

specific shape of the network. To do so, we use a commercial dataset FactSet Supply Chain 

Relationships, which collects information on supply chain relationships. We depart here from 

the methodology followed by the OECD (2023ab) that reconstructs production networks from 

firm-level value-added tax (VAT) transaction data, matching it with business registry data. Our 

choice to use commercial data, instead of administrative data, relies on the fact that, even if 

VAT data can shed light on intra-firm transactions and can be used to map firms’ linkages and 

interdependencies within supply chains, it covers just transactions with domestic partners. VAT 

data does not cover cross-border transactions, which can only be recovered aggregated at 

the country (destination or origin) by product level, using customs data that do not identify firm-

level  relationships.27  When  opting  for  this  commercial  dataset,  we  are  well  aware  that  it  is 

important to keep in mind the biases induced by the data collection process, which tends to 

overrepresent larger companies. However, we are comforted in our choice by the findings of 

a  recent  paper  from  Bacilieri  et  al.  (2023)  who  have  compared  some  standard  production 

network properties across several available (administrative vs. commercial) datasets28.  

27 Another drawback of using VAT data is that, in general, it does not report all sales and purchases of firms, due to reporting 
thresholds below which transactions are not reported. As a result, some edges can be lost, especially those where the typical 
transaction amount is low, but firms trade often enough to reach the threshold in the given reporting period. Moreover, some 
transactions reported by a customer and a supplier can display a different reported value or a negative value. This is not an 
anomaly in itself, as it corresponds to reimbursements or invoice modifications, but it complicates the network analysis. Last, VAT 
data exists in all OECD countries, except for the USA. 
28 Bacilieri et al. (2023) provide benchmark results from two administrative datasets (Ecuador and Hungary) and compare their 
network properties to those obtained with the commercial dataset FactSet(c). The authors show that administrative datasets with 
no  reporting thresholds  have  remarkably similar  quantitative  properties,  while  a  number  of  important properties  are  biased  in 
datasets with missing data. The authors exploit the change of VAT reporting thresholds in Hungary to show that as the threshold 
decreases  the  network  properties  of  the  Hungarian  network  resemble  more  closely  those  from  the  Ecuadorian  network  (in 
Ecuador there is no reporting threshold). However, the properties of the Hungarian network retrieved when reporting thresholds 
were in force tend to be similar of those from FactSet data. Given that the Hungarian VAT reporting thresholds were fairly small, 
it is likely that many connections captured by the missing links may not be relevant for the analysis of large industrial sectors, 
which would tend to be characterized by relatively large transactions. From this perspective, it is reassuring to see that the network 
properties stemming from FactSet data resemble those of a dataset where potentially less relevant transactions are dropped. 
Clearly, one should be cautious when analyzing individual firms’ supply networks using the FactSet Supply Chain Relationships 
data,  as  there  will  be  most  likely  missing  links.  Nevertheless,  the  fact  that  aggregate  network  properties  are  fairly  preserved 
provides some basis for the assumption that the absent links may be mostly randomly missing, which would be helpful in making 
inference from the dataset. 

11  

 
 
 
 
Against this backdrop, the reminder of the paper is organized as follows. Section 2 gives an 

overview of what stress tests are about. Section 3 turns to the choice of the wind energy sector, 

depicting  its  supply  chain,  as  well  as  the  challenges  it  is  facing.  Data  is  presented  in  

Section  4.  The  methodology  that  has  been  developed  regarding  stress  tests  is  detailed  in 

Section 5. The tests that have been conducted and the results are discussed in Section 6.  

Finally,  section  7  discusses  the  limits  of  this  proof-of-work  exercise  and  suggests  lines  for 

further improvement. 

2. Stress tests in a nutshell 

The problem of supply chain resilience is somehow akin to that faced by the banking sector. 

As stated by the adage “a chain is as strong as its weakest link”, supply chains, like banks are 

vulnerable  to  instability.  Supply  chains  are  subject  to  shocks29  that  can  be  multi-faceted 

(pandemics,  export  controls,  natural  disasters,  domestic  prioritization,  transport  bottleneck, 

labour shortages, lack of extra inventory or excess capacity, structural shifts such as the green 

& digital transition, cyberattacks, secondary impacts of sanctions…) [McKinsey, 2020]. 

In  the  banking  sector,  stress  tests  simulate  extreme  but  plausible  economic  and  financial 

conditions to measure the ability of banks to withstand such shocks. They have proven to be 

an essential (but not unique) tool to assess systemic risk of banking entities. One key element 

of stress tests in the banking sector is the drafting of different scenarios. “Baseline scenarios” 

are based on projections from national central banks while “adverse scenarios”30 reflect risk 

assessments  made  by  the  supervisor  and  assume  the  materialisation  of  severe  financial 

stability  risks31.  Results  of  these  stress  tests  help  to  gauge  the  solvency  of  EU  banks  and 

whether banks have enough capital to withstand an economic shock. However, stress tests 

are  also  not  a  monolithic  bloc.  In  practice,  European  banking  supervisors  conduct  several 

types  of  stress  tests32  depending  on  the  objective  of  banking  regulation.  For  instance,  the 

proximate objective of micro-prudential regulation is to limit distress of individual institutions, 

while macro-prudential regulation aims to ensure the stability of the banking & financial system 

29 Shocks have to be understood here as high impact/low frequency events. 
30 The convention used in the calibration of adverse scenarios is one of « no policy change ». This means that neither monetary 
policy  nor  fiscal  policy  reactions are  assumed  under  the  adverse scenario  over  and  above  what  is already  embedded  in  the 
baseline scenario. 
31 In the EU, this is done by the European Systemic Risk Board (ESRB). Risk assessments in the EU are made by the European 
Banking Authority (EBA). 
32 In the banking sector, different types of stress tests are implemented by different supervisors: (1) Annual stress tests: either 
(1.1)-EU-wide stress tests led by the European Banking Authority (EBA) based on capital requirements, complemented by ECB’s 
stress test under the Supervisory Review and Evaluation Process (SREP) or (1.2)-Thematic stress tests (climate & cybersecurity 
stress tests; sensitivity analysis of liquidity & interest rates risk) or (1.3)-Forward-looking vulnerability analyses (linked to Covid 
19 or the war in Ukraine to cite some examples). (2) Stress tests as part of comprehensive assessments and (3) Stress tests for 
macroprudential purposes (focusing on financial stability and system-wide effects rather than individual banks). See ECB (2023b). 
 Available at https://www.bankingsupervision.europa.eu/banking/tasks/stresstests/html/index.en.html 

12  

 
 
 
 
 
in its global dimension33. In both cases, instruments of regulation differ somehow. That being 

said, stress tests should not be considered as a panacea and should be complemented by 

other instruments34.  

To  draw  a  parallel  with  stress  tests  in  the  banking  sector,  it  is  possible  to  envision  a 

micro/macro monitoring of supply chains. In practice, this would mean implementing sectoral 

(macro) supply chain stress tests that could focus on system-wide risks and their aggregate 

impacts,  notably  disruptions  in  supply  chains  across  and  within  different  ecosystems.  This 

could also translate into the implementation of firm-level (micro) supply chain stress tests that 

could examine the impact of supply chains disruptions at the firm-level, and thus the risk of 

corporate bankruptcy for firms deemed as “strategic” for the autonomy of the EU. 

To our knowledge, except for some stress tests that have been undertaken in transportation 

services  (Adenso-Diaz  et  al.  2018)  and  in  the  South-Africa  lamb  chain (Jordaan  &  Kirsten, 

2019), there has been no application so far of stress tests on supply chains. Due to the scarcity 

of the literature on stress tests outside the banking sector, and thus the inability “to stand on 

the shoulders of giants”, the present work must be considered as a proof-of-concept exercise 

only, and thus as “exploratory”. At the present stage, it has no pretention to offer a ready-to-

use tool. Moreover, even if it is tempting here to draw parallels with stress tests in the banking 

sector, one needs to be cautious in undertaking such an exercise. Indeed, stress tests in the 

banking  sector  are  compulsory  and  imply  that  banks  comply  with  micro/macro  prudential 

regulation. In addition, stress tests in the banking sectors provide a uniform framework. This 

seems difficult to implement such uniform framework to supply chains, as stress tests depend 

crucially on the specific graph of the chain. 

Our aim here is to design a supply chain stress test to examine the ability of the wind energy 

supply  chain  to  bounce back  once  disrupted. It  is  indeed  important for  public  authorities to 

monitor the disruptions and points of failure in supply chains deemed critical, and above all to 

get information on the ability of EU firms to achieve homeostasis at different exposure levels 

if one wants to reduce EU strategic dependencies in the energy sector. To do so, the analysis 

is  conducted  under  an  adverse  but  plausible  hypothetical  scenario  designed  to  determine 

whether the supply chain in the wind energy sector can withstand a shock. This stress test 

also verifies if firms in the wind energy sector have access to a diversified pool of suppliers to 

33 Macro prudential supervision is analogous to the oversight of the forest, while micro prudential supervision is analogous to the 
oversight of individual trees. 
34 If we refer to one the most recent bankruptcy in the banking sector, that of Credit Suisse in 2023, it is worth noting that before 
being taken over by UBS, Crédit Suisse had a capital adequacy ratio of 14,1%, which enabled it, in theory, to absorb losses, and 
a liquidity ratio, which reflected its ability to self-finance in the short term, of 144%. By comparison, the French bank BNP Paribas' 
ratios were below 12.3% and 132% respectively. 

13  

 
 
 
 
 
 
survive  the  shock  formalised  in  the  scenario.  Due  to  the  proof-of-concept  nature  of  this 

exercise, we only test an export ban to the EU for Chinese companies selling processed critical 

raw  minerals. To  do  so,  we  retrieve  the  wind  energy  supply  chain  and  test  it  by  simulating 

disruptions  to  one  or  several  nodes.  This  disruption  consists  of  a  complete  break  of  the 

Chinese supplying links for processed critical raw minerals considered as “critical” inputs by 

the European Commission (2023a)35. 

3. Specificities of the wind energy sector 

Considering  the  nature  of  this  proof-of-concept  exercise  and  the  fact  that  supply  chains 

significantly differ from one sector to another, we restricted our analysis to the wind energy 

sector. Many factors have justified this choice. 

First (capacity expansion), in the framework of its Fit for 55 package36, the EU plans to boost 

the  share  of  renewable  energy  and  reduce  its  greenhouse  gas  emissions  by  at  least  55% 

(compared to 1990) by 2030. This EU target implies that the current share of renewable energy 

in the EU will almost double, bringing it to 42.5% of the total energy by 203037. Within renewal 

energies, onshore, but above all offshore wind energy, is expected to form the backbone of 

the  zero-carbon  electricity  supply  for  the  EU38.  According  to  the  EU  Reference  Scenario 

202039,  becoming  carbon-neutral  by  205040  requires  for  the  EU  a  huge  expansion  in  wind 

energy installed capacity (see Figure 1): from 204 GW in 2022 (188GW onshore and 16GW 

offshore representing 15.9% of EU’s electricity generation41) to more than 500 GW in 2030 

and 1300 in 2050 (European Commission, 2023b). But as stated by the European Commission 

(2023),  “a  record  16  GW  of  wind  power  installations  were  added  in  2022,  that  is  a  47% 

increase  compared  to  2021.  This  is  however  well  below  the  37  GW  per  year  required  to 

achieve the EU 2030 target for renewable energy” by 203042.  

35 See also Korniyeko et al. (2017). 
36 See https://www.consilium.europa.eu/en/policies/green-deal/fit-for-55-the-eu-plan-for-a-green-transition/ 
37 On 30 March 2023, the European Parliament and the Council reached a provisional agreement to raise the share of renewable 
energy in the EU’s overall energy consumption to 42.5% by 2030 with an additional 2.5% indicative top up that would allow to 
reach 45%.  
38 This prevalence is confirmed by data from the IEA’s World Energy Outlook (2022) which states that wind energy is supposed 
to be the leading source of electricity generation by 2027. 
39 Available at https://energy.ec.europa.eu/data-and-analysis/energy-modelling/eu-reference-scenario-2020_en 
40 Together with solar, wind power is considered as one of the energy sources that could help Europe break free from Russian 
fossil fuels, as it is expected to contribute much to capacity additions, in contrast with other renewable energy sources. 
41 Source: How is EU electricity produced and sold? - Consilium (europa.eu) 
42 See Press release from the European Commission (2023). Available at Immediate actions for the European wind power industry 
(europa.eu) 

14  

 
 
 
 
 
 
 
Figure 1: Electricity generation by source in the EU, 2019-2050 in the Sustainable 

Development Scenario 

Source: International Energy Agency, World Energy Outlook 2020, p.156. 

Scaling  up  wind  energies  to  meet  a  zero  net  pathway  will  require  massive  investments  in 

production capacities in a shorter investment cycle than previously foreseen43, and among the 

whole supply chain, from installation vessels to cranes, ports, grids and skilled workers. This 

is  an  ambitious  target,  especially  since  the  European  Green  Deal  assumes  an  energy 

transition “made in Europe”.44 However, data from GWEC (2022) show that wind energy is not 

growing nearly fast or widely enough to realize a secure and resilient energy transition. Indeed, 

the  EU  is  building  wind  farms  at  half  the  rate  it  should  be  to  meet  the  REPowerEU  Plan 

targets45, so there is a non-null probability that these high renewable targets will not translate 

into orders. Among the reasons often underlined to explain this slow pace, one finds permitting 

bottlenecks (Energy Monitor, 2023; European Commission, 2023)46, but also lawsuits against 

wind  projects  (MX  Underwriting  Europe,  2023)47.  Indeed,  approval  processes  are  complex 

and can take many years48.  

requirements  as 

43The EU energy security strategy REPower EU sets out a series of measures to reduce the EU’s dependence on Russian fossil 
fuels by accelerating the clean energy transition. Published on 18 May 2022. Available at REPowerEU: affordable, secure and 
sustainable energy for Europe (europa.eu) 
44 The European Commission Clean Tech Plan sets the bloc’s production capability to be able to meet at least 85 per cent of the 
EU’s 
target  of  net  zero  emissions  by  2050.  Available  at 
reach 
COM_2023_684_1_EN_ACT_part1_v11.pdf (europa.eu) 
45 Available at REPowerEU (europa.eu) 
46 There  is  five-times more wind capacity in permitting than under construction in the EU. Available  at  Could  too much  permitting 
reform hurt EU renewables? (energymonitor.ai) 
47 Available at Barriers-to-Wind.pdf (energymonitor.ai) 
48 As per the EU’s Renewable Energy directive, Member States are required to grant permits for new greenfield wind projects 
within two years, but this has not been the case with a procedure lasting up to five years in some Member States. 

the  EU 

tries 

its 

to 

15  

 
 
 
 
 
 
Second (rising costs), starting with the 2015 Paris Climate Agreement,49 wind energy prices 

have become cheaper at a much faster rate than anticipated (Wiser et al., 2021). This was 

achieved  through technological  advances  and  economies  of  scale50.  However, since  2020, 

rising commodity prices are reversing this long-term downward trend in the cost of renewables, 

making clean energy transitions more costly. In this respect, the price of some raw materials 

has  multiplied51,  driven  by  supply  chain  bottlenecks,  inflation  (Wind  Europe,  2022)  and 

competition for resources. Delays have for instance more than quadrupling the freight costs 

since 2020 (Reuters, 2022)52. Added to these pressures, the production of key raw materials, 

minerals, and components for which the EU is mainly dependent on imports, is concentrated 

in countries affected by conflicts and geopolitical tensions. This could become a crunch issue 

in  the  coming  years,  as  demand  for  certain  critical  minerals  is  expected  to  increase 

dramatically (IEA, 2023, p.65)53. Even if the rise in commodity prices is slowly reversing, prices 

remain volatile and regulatory uncertainty remain high54.  

Third (reduced revenues downstream), the wind industry started seeing a steep decline in 

prices and increased competition back in 2017 as some governments moved away from fixed, 

subsidized tariffs for power toward an auction-based system that favours the lowest bidders. 

For  instance,  offshore  wind  energy  auctions  in  Europe  have  witnessed  intense  competition 

resulting  in  subsidy-free  bids  across  major  countries  like  Germany  and The  Netherlands55. 

These zero-subsidy bids are gaining traction and have driven a race to the bottom with some 

countries allowing negative bidding where developers pay for the right to build a wind farm. 

As a result, firms in this sector are under enormous pressures on the cost side and on the 

price side. These pressures, in turn, drag back profitability downstream despite rising demand 

for renewable energy. 

Lastly  (profitability),  financial  reports  of  EU  wind  turbine  manufacturers  show  that  some 

equipment makers in the wind energy sector operate at a loss56. Siemens Gamesa for instance 

49 See https://unfccc.int/process-and-meetings/the-paris-agreement 
50 The overriding factor in cost reduction has been the increase in turbine size. 
51 According to Wind Europe, (2022) but also GWEC (2022 & 2023), wind turbine production costs have surged by 40% and much 
of this has been absorbed by suppliers as there was no indexation of contracts to rising prices. Soaring raw material costs have 
hurt the wind industry as turbines are 90% made of metals, like steel and aluminium. 
52 Reuters (May 5, 2022). Available at Focus: Wind turbine makers struggle to find pricing power | Reuters 
53 In the Announced Pledge Scenario (APS), projections of the IEA (2023) for future mineral demand (based on the latest policy 
and technology development) show that demand more than doubles by 2030 and is 3.5 times higher by 2050. In the Net Zero 
Emission (NZE) Scenario, an even faster deployment of clean energy technologies implies an increase in demand for critical 
minerals by three-and-a-half times in 2030 and 2050, compared with 2022. 
54 The European Commission implemented a price cap of €180 per MWh for wind and solar revenues plus additional national 
measures.  
55 To  ensure  the  viability  of  new  wind  offshore  projects, the  auction procedures  are  now shifting  to  multiple  criteria to  assess 
tenders. 
56 According to the CEO of Siemens Gamesa, Mr Jochen Eickhold (2022), “every time we sell a turbine, we lose 8 percent”. 

16  

 
 
 
 
 
reported an annual loss of 940 million euros in fiscal year 2022 and 4.6 billion euros in 202357. 

The renewable energy businesses of General Electric Vernova reported a loss of 1.44 billion 

dollars in 2023 versus 2 billion dollars in 202258. Beside the support from the Innovation Fund, 

wind turbine manufacturers also benefit from the Temporary Crisis and Transition Framework 

(TCTF) rules for State aid in support of wind manufacturing in the EU59. All these factors point 

to the fact that the wind energy sector does not have a sustainable configuration. According 

to the Bundesverband WindEnergie (2023), to be viable, the wind power price index would 

have to go up by approximatively 40 to 45%. Data from the wind industry also shows that wind 

turbine manufacturers are facing a scissor effect. On the one hand, they are engaged in a race 

to produce more powerful turbines, which means they have to invest heavily in research and 

development. On the other hand, rising production costs, quality issues60, and a shortage of 

raw  materials  have  a  negative  impact  on  their  profitability.  More  generally,  poor  financial 

performances  raise  issues  about  the  future  of  the  wind  industry61,  notably  about  turbine 

producers' ability to invest in new technologies. The fear here is to repeat the bitter experience 

of the EU solar panel industry62.  

These  considerations  apart,  it  is  of  utmost  importance  to  have  the  “right”  definition  of  the 

relevant wind power supply chain, “from cradle to grave”. From a theoretical point of view, a 

value chain refers to the full lifecycle of a product or process, i.e., the full range of activities 

which are required to bring a product or service from conception through the different stages 

of production, including material sourcing, consumption and final disposal/recycling after use. 

In practice, supply chains can be very complex with manifold links in multiple countries. We 

are more particularly interested here in the wind power global value chain, where a chain of 

activities is divided/fragmented among enterprises located in different countries. At this stage, 

the  available  data  did  not  allow  us  to  analyse  all  the  full  supply  chain.  For  instance,  the 

database  we  use  does  not  encompass  data  on  recycling.  However,  this  latter  being  quite 

marginal at the present time, it should not influence too much our results, notably because 

“approximately 75% of the total cost of energy for a wind energy project is related to upfront 

57  Available  at  https://www.siemensgamesa.com/-/media/siemensgamesa/downloads/en/investors-and-shareholders/periodic-
information/2022/q4/q4-activity-report-year-2022-siemens-gamesa.pdf  and  Siemens  Gamesa  suffers  €4.3bn  loss  -  reNews  - 
Renewable Energy News 
58 Source: GE Vernova's Renewable Energy reduces loss to USD 1.4bn in 2023 (renewablesnow.com). Enercon GmbH does not 
publish its financial results. It is said to have received in July 2022 about 500 million euros from the German government’s WSF 
economic  stabilization  fund  to  help  it  deal  with  the  impact  of  global  logistics  problems  arising  from  COVID-19.  See  Reuters 
https://www.reuters.com/article/germany-energy-enercon-state-idINL8N2YM45C 
59 The company Enercon GmbH has received in 2022 government support of 500 million euros via the Economic Stabilisation 
Fund. Available at Wind turbine maker Enercon to get $513 mln in German pandemic aid | Reuters 
60 See Press release by Reuters as of August 7, 2023. Available at What are the issues with Siemens Gamesa's wind turbines? 
| Reuters  
61 The Danish wind turbine manufacturer Vestas recorded losses of 1,572 million euros in 2022 but returned to profitability in 
2023, according to Vestas’ financial reports. Available at https://www.vestas.com/content/dam/vestas-
com/global/en/investor/reports-and-
presentations/financial/2023/2023%20Q1%20Investor%20Presentation.pdf.coredownload.inline.pdf and Vestas Annual Report 
2023 – A return to profitability 
62 According to data from GWEC Market Intelligence (2023), China had in 2022 a market share of about 60% in global turbine 
blad manufacturing, compared to 13% for Europe, 11% for India and 8% for the U.S. 

17  

 
 
 
costs  such  as  the  cost  of  the  wind  turbine,  foundations,  electrical  equipment  and  grid 

connection”63 (Wind Europe, 2019). 

4. Presentation of the data 

We use commercial data in order to map critical supply chains and perform a more thorough 

analysis  and  identification  of  potential  vulnerabilities.  More  precisely,  to  build  the  EU  wind 

supply chain, two types of data have been used. 

First, to identify a so-called “EU supply chain in the wind sector”, we have extracted from the 

WindPower©  database,  the  list  of  wind  turbine  manufacturers  which  have  both  their 

headquarters in the EU and equipped at least one wind farm in the EU territory over the period 

2017-2022. The WindPower© database provides detailed raw statistics on wind energy and its 

supporting  markets  from  a  variety  of  players  in  the  worldwide  industry  —  wind  farm 

developers, operators and owners, turbine manufacturers, to name only a few — and provides 

additional information about regions, countries, types and numbers of turbines, hub heights, 

installed capacities in MWs/GWs and commissioning dates64. Both large projects, but also the 

smaller, independent ones are listed in this database. 

The sample data contains 27 turbine manufacturers with their respective market shares based 

on installed capacities. Considering the nature of this proof-of-concept exercise, we have only 

analysed,  at  this  stage,  the  supply  chain  of  four  turbine  manufacturers,  which  altogether 

account for roughly 90% of the EU market65 (Wind Europe data, 2023). 

Additionally, we have collected data from the FactSet Supply Chain Relationships database©. 

The  structure  of  the  data  is  dyadic,  identifying  pairs  of  companies  involved  in  one  of  the 

different types of relation registered in the database (customer, supplier, competitor and up to 

13 types of partnerships). The database covers approximately 5500 entities in the EU since 

2011,  6500  in  North  America,  16500  in  Asia  and  about  3100  in  the  rest  of  the  world. 

Relationship information is sourced from public primary sources (such as annual reports or 

press releases) and reverse-linked to non-disclosing parties, i.e., if firm A reports that firm B is 

its customer then a supplier-customer relation between A and B is recorded even if B does not 

report A  as  being  its  supplier.  Relationship  statuses  are  updated  regularly,  allowing  for  a 

63 Available at Economics | WindEurope 
64 At this stage, only data on market shares have been used. 
65  Given the proof-of-concept nature of this paper, the identity of the chosen manufacturers is anonymized, such that they are 
referred to as companies A, B, C and D. 

18  

 
 
 
 
 
 
 
comprehensive  and  consistent  overview  of  the  relationship  graph  of  each  company  over 

time66. The database also reports relationship keywords to qualify more specifically the nature 

of the relationship, qualitative measures of the importance of the relationship, and revealed 

revenue dependencies (only for supplier-customer relationships). All this provides meaningful 

relationship-specific context. However, these extensions have not been used so far, mostly 

due to the large proportion of missing data. The database focuses primarily on public (listed) 

and  large  firms,  which  tend  to  be  relatively  more  represented  than  private  and  smaller 

companies. However, while the data coverage is geared towards large firms, many small and 

non-listed  firms  nevertheless  show  up  in  relationships  with  large  firms,  hence  the  overall 

network is much larger than the set of listed firms. Assuming that the publicly reported links 

are likely to be the most relevant ones for the companies concerned67, the database allows 

the  reconstruction  of  supply  chains  that,  despite  not  being  representative  for  the  whole 

economy  (or  a  whole  sector),  can  capture  the  most  relevant  players  and  their  major 

dependencies. Through network analysis it becomes then possible to identify weak links in 

these relationships. 

Our  sample  of  supply  chain  links  runs  from  January  2017  to  May  2023.  The  same  pair  of 

companies  can  appear  several  times  if  they  engage  on  different  types  of  relations  (e.g., 

partnerships and customer-supplier or if they have different relationships over time). However, 

for  the  purpose  of  this  exercise,  only  supplier-customer  relations  have  been  retained  and 

duplicates have been eliminated. Relationships have been pooled to provide a more stable 

picture of the EU wind supply chain from a mid- to long-term perspective. In the database, 

firms  are  allocated to  sectors  according to  a  FactSet(C)  proprietary  classification  (known  as 

RBICS). The RBICS classification can reach a level of disaggregation up to six digits, although 

in our supply chain data the maximum level of disaggregation is only two digits. Despite this 

apparent low level of disaggregation, the design of the RBICS classification does not make it 

unsuitable  for  sectorial  analysis68.  Additionally,  the  database  contains  a  mapping  of  the 

companies into the NACE rev.2 classification, reaching a level of disaggregation of up to four 

digits (although in this case the information is missing for some companies). In order to identify 

the firms constituting the wind supply chain, we have exploited the information in both sectorial 

classifications to filter out the companies not relevant, as explained below.  

For the purpose of this proof-of-concept exercise, we have only compiled at this stage a list of 

customers and suppliers of the four aforementioned European wind turbine manufacturers. 

66 It seems that FactSet(C) follows the policy of discontinuing a relationship in the dataset if after one year of the start date there 
is no factual evidence of its renewal or continuation. This is intended to not to inflate the database with ended relations which 
may have not been publicized as such. 
67 It seems safe to assume that if a company decides to report on a specific relationship, it is because it perceives that this can 
be valuable for itself, for example in terms of reputation or visibility. 
68 There are 37 different sectors at the two-digit level of disaggregation. 

19  

 
 
 
 
For the upstream, we have taken the respective suppliers and matched them with the whole 

list  of  company  links.  Then,  we  have  treated  the  suppliers  as  “customers”  to  recursively 

retrieve  the  suppliers  of  suppliers,  until  no  further  links  are  identified  in  the  data.  Figure  2 

illustrates  this  iterative  process. The  first  column  on  the  left  displays  the  customer-supplier 

links in the dataset. Let’s assume that we would like to retrieve the upstream supply chain of 

firm A (which would constitute tier 0)69. In tier -1 (second column in Figure 2), we first identify 

the direct suppliers of firm A in tier 0, namely firms E, D, C and H70. This becomes iteration 1 

in Figure 2. In tier -2 (iteration 2 in Figure 2), the suppliers of these direct suppliers are then 

identified. Note that firm H has no suppliers in the dataset so that it can be disregarded for the 

next  tiers.  The  process  is  repeated  until  some  stopping  rules,  further  discussed  infra,  are 

fulfilled. In the example of Figure 2, the process would stop at iteration 4 because from there 

on, the same set of supplier-customer links is identified in each subsequent iteration. Note that 

in iteration 4, the set of firms on the left is the same as the set of customers in the dataset and 

the set of their suppliers contains this same set of customer companies. This would lead to 

infinite iterations not adding any new information if the process would not be stopped. Hence 

the importance of introducing stopping rules. 

Figure 2: Iterative process to retrieve firms in the supply chain. 

Source: authors 

69 These  firms  may  not  be  starting  points  of  the  graph  representing  the  supply  chain.  In  our  application  case,  the  four  main 
European wind turbine manufacturers form the tier 0 and are neither starting points nor endpoints of the graph of the supply 
chain. 
70 We use the convention that tiers upstream tier 0 are numbered negatively while tiers downstream are numbered positively. 

20  

 
 
 
 
 
We repeated this procedure for the downstream firms, reversing the roles of “suppliers” and 

“customers”. To  avoid  links  artificially  duplicated, after the  iterative  process  we  only  keep  a 

unique  pair  of  companies  (“supplier-customer”)  allocated  to  the  lowest71  tier  in  which  they 

appear. 

A problem of circularity may appear if firm A supplies firm B which is a supplier of firm C, which 

in turn supplies firm A. In such a case, even if the resilience coefficients are greater than zero, 

the different rounds of shocks make them act in an infinite multiplicative form that converges 

to zero because these coefficients are less than one. Such a circularity thus leads to a total 

default of all firms involved in the circular loop. 

The iterative process to retrieve the supply chain would be almost endless without stopping 

rules to define when it can be considered that a firm is a starting point or an endpoint in a 

supply chain. Typically, in the sector studies, wind turbine manufacturers may have electricity 

producers  as  customers,  which  in  turn  have  many  firms  as  customers.  Conversely,  wind 

turbine manufacturers have these electricity companies as suppliers, as they need electricity 

for  the  functioning  of  their  plants.  We  are  not  necessarily  interested  in  including  these 

downstream  and  upstream  firms  in  the  analysis  of  the  wind  turbine  manufacturers  supply 

chain.  Therefore,  we  have  tried  various  filters  based  on  the  activity  sector  of  firms,  which 

restrict  the  supply  chain  to  firms  belonging  to  some  industrial  sectors  relevant  for  wind 

turbines: 

-  Filter 1: only relations where the supplier has as NACE division: 7, 8, 9, 20, 22, 23, 24, 

25, 26, 27, 28, 29, 30, 32, 33, 41, 42, 43, 49, 50, 51, 52, 62, 71, 72, 74 are kept. 

-  Filter 2: only relations where the supplier has as NACE division: 7, 8, 20, 22, 23, 24, 

25, 26, 27, 28, 32, 33, 62, 71, 72, 74 are kept. 

-  Filter 3: only relations where the supplier is in a "clearly" RBICS industrial sector are 

kept: "Aluminum", "Chemicals: Major Diversified", "Chemicals: Specialty", "Computer 

Communications", "Computer Processing Hardware", "Electrical Products", "Electronic 

Components", 

"Electronic  Equipment/Instruments", 

"Electronic  Production 

Equipment",  "Engineering  &  Construction",  "Industrial  Machinery",  "Industrial 

Specialties", 

"Metal  Fabrication", 

"Miscellaneous  Manufacturing", 

"Other 

Metals/Minerals", "Semiconductors", "Steel". 

-  Filter 4: filter 2 AND filter 3 simultaneously. 

Table 1 reports the counts of links and firms according to the different filters. The first two filters 

are based on NACE divisions to identify the activity of firms, with Filter 2 being more restrictive 

71 Lowest understood as closest to tier 0. 

21  

 
 
 
 
 
than Filter 1 (firms from the automobile industry -NACE division 29- for instance are excluded). 

Filter 3 makes use of the RBICS classification specific to the FactSet Supply Chain database 

instead of the NACE division code. Table 1 reveals that applying the RBICS classification is 

much more restrictive than applying the NACE division criteria, resulting in approximately a 

40% drop in the counts of links and firms. Filter 4 combines the two classifications and is thus 

the most restrictive of the four filters. 

Table 1: Counts of links and firms in the supply chain 

Filter 1 

Filter 2 

Filter 3 

Filter 4 

# of non-redundant upstream links 

# of non-redundant upstream firms 

# of non-redundant downstream links 

# of non-redundant downstream firms 

91763 

16070 

89096 

21540 

48308 

10845 

45788 

12843 

26603 

6771 

24298 

7618 

20425 

5411 

17975 

5656 

# of non-redundant firms in total 

29821 

18677 

11236 

8658 

Figure 3: Distribution of firms across the different tiers of the process. 

50000

45000

40000

35000

30000

25000

20000

15000

10000

5000

0

Filter 1

Filter 2

Filter 3

Filter 4

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Regardless  of  the  filter  used  to  retrieve  the  supply  chain,  Figure 3  highlights  that  most  of 

upstream and downstream firms are detected in our database between the third and fifth tiers. 

As regards headquarters by country (See Figure 4.a and 4.b), firms from China and the United 

States clearly dominate both upstream and downstream in the value chain, followed by firms 

from Asian  countries  (Japan,  South  Korea,  India,  Taiwan).  Most  of  the  companies  located 

upstream,  in  the  supply  chain  of  the  four  wind  turbine  manufacturers  studied,  are  located 

outside Europe. For those firms located within the EU, firms from Germany rank first, followed 

22  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
by  British  and  French  firms. The  upstream  and  downstream  parts  of  the  supply  chain  look 

rather symmetric in terms of firms’ location. It is also rather robust whatever the filter used to 

retrieve the supply chain, except for firms whose headquarters is located in Africa and South 

America as they are more numerous when applying Filter 1, i.e., the less restrictive filter. 

Figure 4.a: Count of upstream firms by country (Filter 4). 

Figure 4.b: Count of downstream firms by country (Filter 4). 

23  

 
 
 
 
 
 
 
Finally,  the  distribution  of  firms  among  the  different  RBICS  industrial  sectors  displayed  in 

Figure 5 indicates that firms from all these sectors belong to the supply chain, even if there is 

a  predominance  of  firms  from  the  “Industrial  Machinery”,  the  “Semiconductors”  and  the 

“Electrical Products” sectors both upstream and downstream. On Figure 5, sectors are ranked 

according to their  frequency  in the  upstream  part  of  the  supply  chain,  but  this  ranking  only 

marginally  changes  when  considering  the  downstream  part  of  the  supply  chain. At  a  first 

glance,  it may  be  surprising  that  the  downstream  part  of the  supply chain  involves  firms  in 

many different industrial sectors. A more thorough examination of the supply chain indicates 

that some customers of wind turbine manufacturers are conglomerates that not only buy wind 

turbines to exploit their own wind farms but also produce and sale equipment for other firms. 

Two examples are illustrative of this. 

The first is that of the company N,72 which is a direct customer (tier 1) of B and C because part 

of  its  activity  is  the  production  of  energy,  among  which  renewable  electricity.  Nevertheless, 

another  major  activity  of  N  is  also  the  production  of  aluminium  that  is  sold  to  many  other 

industrial firms that are therefore detected as indirect customers (tiers 2 or more) of B and C. 

The  second  example  is  that  of  X,  an  Asian  company  that  manufactures  and  markets 

connectors,  cable  assemblies,  and  power  packs,  which  are  used  in  computer  and 

communication industries. This company also has a cascade of subsidiaries, among which Y, 

which in turn, has as a subsidiary Z, acting as a renewable energy arm of X and investing in 

wind farms73. Both X and Z appear as direct customers (tier 1) of D in the database. X also 

appears as a supplier of other industrial firms, including Z. In that example, it is thus the nexus 

of  its  subsidiaries  that  makes  the  industrial  firm  X  appear  as  a  customer  of  D.  Its  own 

customers appear as indirect customers of D. 

Similar problems may arise in the upstream part of the supply chain, even if it is less surprising 

to  detect  firms  belonging  to  many  different  industrial  sectors  among  the  direct  and  indirect 

suppliers of wind turbine manufacturers. Let consider for instance the case of the Japanese 

firm J, which is detected as a direct supplier of D in the database. According to the database, 

J  has  more  than  a  hundred  of  direct  suppliers  in  15  different  RBICS  sectors,  including  the 

“Chemicals: Specialty” sector. The Asian firm K is for instance one of its suppliers and thus 

appears as an indirect supplier of D. It is nevertheless unclear to what extent D is dependent 

on K. 

72 Actual company names are replaced by letters to preserve anonymity. 

24  

 
 
 
 
 
 
 
Figure 5: Distribution of upstream and downstream firms according to the RBICS 

industrial sector (Filter 4). 

Upstream

Downstream

0,18

0,16

0,14

0,12

0,1

0,08

0,06

0,04

0,02

0

5. Methodological aspects 

5.1.  Supply chains as graphs 

The starting point of the analysis is the graph formed by the supply chain where each firm 

(

) is a node and each supplier-customer link is an oriented edge of the graph. The 
𝐹𝐹𝑛𝑛
simple  graph  (compared  to  the  case  studied)  in  Figure 6  is  used  for  illustrative  purpose  all 
𝑛𝑛 ∈ {1, ⋯ , 𝑁𝑁}
along the text. The corresponding supply chain involves twelve firms (

). The labelling 

of firms is chosen so that it reflects their positioning within the supply chain, a low (resp. high) 

𝑁𝑁 = 12

value of the subscript 

 indicating that the firm is rather upstream (resp. downstream) in the 

supply chain. 

𝑛𝑛

25  

 
 
 
 
 
 
 
Figure 6: Graph of the illustrative supply chain 

The  above  graph  illustrates  the  business-as-usual  state  of  the  supply  chain,  where  the 

diversity of direct suppliers of each firm corresponds to its optimal individual sourcing strategy, 

without consideration of the consequences in terms of supply risk for downstream firms. Each 

firm 

 chooses its direct suppliers, which correspond to the sources of the edges that point to 

the node associated with the firm. Conversely, it has no control of its indirect suppliers, i.e., 

𝐹𝐹𝑛𝑛

the suppliers of its suppliers. As a result, when choosing its direct suppliers, a firm exerts an 

externality in the form of a supply risk transmission on downstream firms. 

The graph of supplier-customer links can be represented by a network square matrix 

 with 

 rows and columns corresponding to the different firms involved in the supply chain. Element 

Ω

 takes value 

 if and only if 

 supplies 

 (and thus there exists a 

 in row 

 and column 

𝑁𝑁
supplier-customer link of type 
𝜔𝜔𝑖𝑖 𝑗𝑗

𝑗𝑗

𝑖𝑖

 in the graph) and value 

𝐹𝐹𝑗𝑗

1

 otherwise. The network matrix 

𝐹𝐹𝑖𝑖

of our illustrative supply chain is given in Table 2. 

𝐹𝐹𝑗𝑗 → 𝐹𝐹𝑖𝑖

0

26  

 
 
 
 
 
 
 
Table 2: Network matrix of the illustrative example 

F1 

F2 

F3 

F4 

F5 

F6 

F7 

F8 

F9 

F10 

F11 

F12 

F1 

F2 

F3 

F4 

F5 

F6 

F7 

F8 

F9 

F10 

F11 

F12 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

1 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

Rows with only zeros signal firms that are starting points of the graph. Conversely, columns 

with  only  zeros  enable  to  identify  firms  that  are  endpoints  of  the  graph.  In  the  illustrative 

example, 

  and 

  are  starting  points  of  the  graph  and  correspond  to  firms  that  are 

uppermost in the supply chain. 
𝐹𝐹2

𝐹𝐹1,

𝐹𝐹4

 and 

 are endpoints of the graph and correspond to firms 

that are downmost in the supply chain. 

𝐹𝐹11

𝐹𝐹12

The construction of the network matrix requires information on supplying relationships among 

firms. As we do not have additional information on the share of purchases made by each firm 

from their different suppliers, a more sophisticated matrix accounting for these shares could 

not  be  constructed74.  Typically,  instead  of  having 

  in  row 

  and  column 

  if  and  only  if 

 from 

supplies 

, the element in row 

 could have reported the share of purchases of 
𝐹𝐹𝑗𝑗
1
 so that, except for firms that are starting points of the graph, the coefficients on each 
𝐹𝐹𝑖𝑖
row would sum to 
𝐹𝐹𝑖𝑖
𝐹𝐹𝑗𝑗

 and column 

. 

𝑗𝑗

𝑗𝑗

𝑖𝑖

𝑖𝑖

1

For the specific purpose of our stress test, a matrix 

 of random resilience coefficients, the 

exact  role  of  which  is  discussed  infra,  is  associated  to  the  network  matrix 

Θ

. A  non-zero 

resilience coefficient 

 is more specifically introduced for each link 

 in the graph. It 

Ω

measures the resilience of firm 

𝜃𝜃𝑖𝑖 𝑗𝑗

 to a shock on its supplier 

. Resilience coefficients range 

𝐹𝐹𝑗𝑗 → 𝐹𝐹𝑖𝑖

between 

 and 

. The higher the value, the less sensitive firm 

 is to a shock affecting its 

𝐹𝐹𝑖𝑖

𝐹𝐹𝑗𝑗

supplier 

. The resilience coefficients are key components of the measurement of stress along 
0
1
the supply chain. 
𝐹𝐹𝑗𝑗

𝐹𝐹𝑖𝑖

74 Such information was too sparse in the database to allow for the construction of this kind of alternative matrix. 

27  

 
 
 
 
 
 
 
 
 
 
5.2.  Measuring stress 

We define 

 as an aggregate measure of the degree of resilience of firm 

 at iteration 

 of 

the  stress  test.  This  measure  is  normalised  to 

𝑦𝑦𝑖𝑖 𝑡𝑡

  under  the  business-as-usual  state  of  the 

𝐹𝐹𝑖𝑖

𝑡𝑡

supply  chain,  which  serves  as  the  benchmark  for  the  stress  test. Therefore,  any  upstream 

1

disruption  in the  supply chain  implies  that 

  for 

. The  value  of 

reflects to  what  extent  the  access  of  firm 

following a disruption in the supply chain. Conversely, 

∀𝑖𝑖 ∈ {1, ⋯ , 𝑁𝑁}

  to  its  direct  and  indirect  suppliers  is  preserved 
𝑦𝑦𝑖𝑖 𝑡𝑡 ≤ 1
𝑦𝑦𝑖𝑖 𝑡𝑡
 must be thought of as the 
𝐹𝐹𝑖𝑖

𝑡𝑡 > 0

degree of “stress” incurred by a firm due to disruption in the supply chain. 

𝑠𝑠𝑖𝑖 𝑡𝑡 = 1 − 𝑦𝑦𝑖𝑖 𝑡𝑡

The stress test proceeds iteratively. The initial shock at iteration 

 is captured by setting 

 for 

 with 

 the subset of firms directly affected by the initial shock 

𝑡𝑡 = 0

and 
𝑦𝑦𝑖𝑖 0 < 1
disruption, from natural disasters to major strikes, trade litigation or geopolitical conflicts. The 

 for all the other firms. The initial shock may reflect any kind of macro or micro 
𝑖𝑖 ∈ Ψ,

Ψ ⊂ {1, ⋯ , 𝑁𝑁}

𝑦𝑦𝑖𝑖 0 = 1

first round of the stress test (

) consists in computing the impact on the aggregate measure 

of resilience of the customers of firms 

𝑡𝑡 = 1

. The second round (

) of the stress test looks 

at the consequences of changes in the degree of resilience of firms that are affected in the 

𝑖𝑖 ∈ Ψ
first round on the degree of resilience of their own customers and so on, iteratively. 

𝑡𝑡 = 2

Let’s assume for instance that in the supply chain illustrated in Figure 6, the initial shock affects 

firm 

  so  that 

.  The  first  round  of  the  stress  test  then  concerns  the  two  direct 

customers of 
𝐹𝐹4

, namely firms 
𝑦𝑦4 0 = 0.5

 and 

. The second round of the stress test then turns to the 

transmission of the impact affecting 

𝐹𝐹6

 and 
𝐹𝐹7

 on their own customers, which are firms 

 and 

𝐹𝐹4

. Note that firm 

 is affected through two channels, one as a customer of 

𝐹𝐹6

𝐹𝐹7

 and the other 
𝐹𝐹8

as  a  customer  of 
𝐹𝐹9
instance, in the illustrative example provided by Figure 7, firm 

𝐹𝐹6
 is a supplier of 

.  Note  also  that  loops  can  be  involved  in  the  iterative  stress  test.  For 

 which is a 

𝐹𝐹9
𝐹𝐹7

supplier  of 

,  which  in  turn  supplies 

  which  finally  supplies 
𝐹𝐹9

,  thus  closing  a  loop. The 
𝐹𝐹8,

iterative process may lead to either the total collapse of the supply chain at some iteration 

𝐹𝐹6,

𝐹𝐹9

𝐹𝐹3

(i.e.  

) or its convergence to a new degraded steady state, i.e., with some 
𝑇𝑇

firms having a non-null degree of resilience. 

𝑦𝑦𝑖𝑖 𝑇𝑇 = 0

∀𝑖𝑖 ∈ {1, ⋯ , 𝑁𝑁}

The iterative process heavily relies on the functional form linking the degrees of resilience at 

round 

+1  with  those  at  round 

.  We  propose  the following  functional  form,  inspired  by  the 

𝑡𝑡

𝑡𝑡

28  

 
 
 
 
 
 
 
 
 
Constant  Elasticity  of  Substitution  (CES)  functional  form  commonly  used  to  describe 

production function75: 

𝑦𝑦𝑖𝑖 𝑡𝑡 = 𝑦𝑦𝑖𝑖 𝑡𝑡−1 × �

1
⁄
−𝜎𝜎 𝜎𝜎−1

𝜔𝜔𝑖𝑖𝑗𝑗

�

 𝐶𝐶𝑖𝑖 𝑡𝑡

𝑁𝑁
𝑗𝑗=1

�∑

with 

𝑁𝑁
𝑖𝑖𝑖𝑖 ∑ 𝜔𝜔𝑖𝑖𝑗𝑗
𝑗𝑗=1
𝑁𝑁
𝑗𝑗=1

𝑖𝑖𝑖𝑖 ∑

𝜔𝜔𝑖𝑖𝑗𝑗

𝐶𝐶𝑖𝑖 𝑡𝑡 = �∑

𝑁𝑁
𝑗𝑗=1

𝜔𝜔𝑖𝑖𝑗𝑗�𝜃𝜃𝑖𝑖𝑗𝑗+ �1 − 𝜃𝜃𝑖𝑖𝑗𝑗� 𝑦𝑦𝑗𝑗 𝑡𝑡−1�

�

𝜎𝜎−1
𝜎𝜎

𝜎𝜎 𝜎𝜎−1

⁄

= 0

> 0

   ∀𝑡𝑡 > 0

(1.a) 

(1.b) 

The first row of (1.a) states that the resilience of firm 

 remains unchanged if the firm is a 

starting point of the graph. The second row of (1.a) recursively defines the degree of resilience 

𝐹𝐹𝑖𝑖

of firm 

 at iteration 

 of the stress test as a function of the degree of resilience of its suppliers 

at the previous iteration 

. The first component in this second row is a normalisation factor 

𝐹𝐹𝑖𝑖

𝑡𝑡

that  induces  that  the  degree  of  resilience  always  ranges  between 

𝑡𝑡 − 1

  and 

.  The  second 

component  denoted  by 

  and  defined  in  (1.b)  is  the  one  that  really  captures  the  stress 

0
  is  a  linear  combination  of 

1

  (i.e. 

contamination.  The  subcomponent 

𝐶𝐶𝑖𝑖 𝑡𝑡

insensitivity  to  a  stress on  direct  suppliers)  and the  degree  of  resilience of  suppliers  at the 
𝜃𝜃𝑖𝑖𝑗𝑗+ �1 − 𝜃𝜃𝑖𝑖𝑗𝑗� 𝑦𝑦𝑗𝑗 𝑡𝑡−1
previous  iteration  of  the  test,  with  respective  weights 

.  The  higher  the 

  and 

1

resilience parameter 

, the less sensitive is firm 

 to a stress affecting its suppliers. This 

�1 − 𝜃𝜃𝑖𝑖𝑗𝑗�

𝜃𝜃𝑖𝑖𝑗𝑗

subcomponent is embedded in a standard CES functional form to yield 

, except the factors 

𝜃𝜃𝑖𝑖𝑗𝑗

𝐹𝐹𝑖𝑖

 introduced in the summation to make firm 

 dependent to its direct suppliers only. 

𝐶𝐶𝑖𝑖 𝑡𝑡

𝜔𝜔𝑖𝑖𝑗𝑗

𝐹𝐹𝑖𝑖

75 Barrot & Savagnat (2016) and Boehm & alii. (2019), for instance, provide causal evidence that the scope for trade linkages to 
generate cross-country spillover depends on the elasticity of substitution with respect to downward inputs. They show that input 
linkages with strong complementarities are a key mechanism through which shocks are transmitted across borders. 

29  

 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 7: Influence of parameter 

𝝈𝝈

Parameter 

 in (1) captures to what extent there is substitutability or complementarity between 

direct  suppliers  of  a  firm  within  the  supply  chain.  Figure 7  illustrates  this  idea  for  a  firm 

𝜎𝜎

having two direct suppliers 

 and 

are 

 and 

. It is assumed that at iteration 

𝐹𝐹𝑘𝑘

𝐹𝐹𝑗𝑗

, in the simplified case where the resilience coefficients 
𝐹𝐹𝑖𝑖
 the two suppliers’ degrees of resilience 

are respectively 
𝜃𝜃𝑖𝑖𝑗𝑗 = 0

𝜃𝜃𝑖𝑖𝑘𝑘 = 0

 and 

 (black dot in Figure 7). If 

𝑡𝑡,

 goes to infinity, any alternative 

combination  of  the  degrees  of  resilience  of  its  direct  suppliers,  such  that  one  degree  is 

𝑦𝑦𝑗𝑗 𝑡𝑡 < 1

𝑦𝑦𝑘𝑘 𝑡𝑡 < 1
 whereas the other is increased by the same amount 

𝜎𝜎

decreased by an amount 

 let the 

new  degree  of  resilience  of  firm 

∆𝑦𝑦,

  unchanged.  Graphically,  this  case  corresponds  to  a 

∆𝑦𝑦,

displacement along the continuous line passing through point 

𝐹𝐹𝑖𝑖

 and having a slope 

equal to 

. It can be interpreted as a perfect substitutability case to the extent that a one-by-

�𝑦𝑦𝑗𝑗 𝑡𝑡 , 𝑦𝑦𝑘𝑘 𝑡𝑡�

one change in its direct suppliers’ degrees of resilience let the degree of resilience of the firm 

−1

unchanged. It is useful for comparison with other values of 

 to consider a variation 

 leading 

to a point on the bisector represented by an empty dot at the intersection between the line and 

𝜎𝜎

∆𝑦𝑦

the  bisector. At  the  opposite,  if 

  a  decrease  in  the  degree  of  resilience  of  one  of  its 

suppliers implies a decrease of its own degree of resilience for firm 

𝜎𝜎 = 0,

 even if the degrees of 

resilience of its other suppliers remain unchanged. It also means that any asymmetry between 

𝐹𝐹𝑖𝑖,

the degrees of resilience of its direct suppliers is worthless for firm 

 as it yields the same 

degree of resilience for the firm than if all its direct suppliers had a degree of resilience aligned 

𝐹𝐹𝑖𝑖

on the lowest one. As a result, all points lying on the dashed square passing through point 

30  

 
 
 
 
 
 
 and having their right angle on the bisector yield the same degree of resilience for 

. This case can thus be interpreted as a perfect complementarity case. As the dot at the 

firm 
�𝑦𝑦𝑗𝑗 𝑡𝑡 , 𝑦𝑦𝑘𝑘 𝑡𝑡�
right angle has a lower abscissa and ordinate, compared to the similar dot on the bisector in 

𝐹𝐹𝑖𝑖

the case where 

, it means that with 

 a stress on its direct suppliers has a more 

detrimental impact on the degree of resilience of firm 

. For 

 the set of points leading 

𝜎𝜎 → ∞

𝜎𝜎 = 0,

to  an  unchanged  degree  of  resilience for  firm 

compared  to  that  reached at  point 

  is  a 

𝐹𝐹𝑖𝑖

𝜎𝜎 ∈ ]0, ∞[,

decreasing and convex curve. In the specific case where 

𝐹𝐹𝑖𝑖, 

, the subcomponent 

 in (1.b) 
𝐹𝐹𝑖𝑖,

takes a Cobb-Douglass form, as illustrated by the fine doted curve in Figure 7. Note that the 

𝜎𝜎 = 1

𝐶𝐶𝑖𝑖 𝑡𝑡

associated dot at the crossing between the iso-resilience curve and the bisector lies between 

the two dots on the bisector associated to the previous cases 

 and 

 so that the 

degree of resilience for firm 

 is intermediate between that of these two cases. Finally, note 

𝜎𝜎 → ∞

𝜎𝜎 = 0,

that when resilience parameters 

𝐹𝐹𝑖𝑖

 and 

 are non-null and take different values, the slope 

of the isocurve of resilience on Figure 7 is no longer symmetric, with respect to the bisector, 

𝜃𝜃𝑖𝑖𝑗𝑗

𝜃𝜃𝑖𝑖𝑘𝑘

and  the  sensitivity  of  firm 

  with  respect  to  shocks  on  its  direct  suppliers  becomes 

asymmetric. 

𝐹𝐹𝑖𝑖,

5.3.  Nested model 

Equation (1) treats all suppliers on a similar basis, assuming that the degree of substitutability 

or complementarity between two suppliers is the same whether the two suppliers belong to 

the  same  sector  or  not.  Conditional  on  the  availability  of  information  on  the  main  sector  of 

activity of firms along a supply chain, it is worth introducing a nested version of (1) that allows 

us to have different degrees of substitutability or complementarity between firms. It is more 

specifically expected here that the degree of substitutability between suppliers within a same 

sector is higher than the degree of substitutability between suppliers from different sectors. 

We thus assume that the set of firms belonging to the supply chain at stake can be partitioned 

in 

 subsets 

 corresponding to activity sectors. Firms are gathered in these 

subsets according to their main activity. Let 
(𝑘𝑘𝑘𝑘{1, ⋯ , 𝐾𝐾})

Λ𝑘𝑘

𝐾𝐾

 denote the list of sectors in which firm 

 has 

at least one supplier. 

 stands for the cardinal of 

Φ𝑖𝑖

. The aggregate measure 

 of the degree 
𝐹𝐹𝑖𝑖

of resilience of firm 

 at iteration 
𝜑𝜑𝑖𝑖
𝐹𝐹𝑖𝑖

𝑡𝑡

 of the stress test is now defined by 

Φ𝑖𝑖

𝑦𝑦𝑖𝑖 𝑡𝑡

𝑦𝑦𝑖𝑖 𝑡𝑡 = 𝑦𝑦𝑖𝑖 𝑡𝑡−1 × �

−𝜎𝜎𝐵𝐵 𝜎𝜎𝐵𝐵−1
⁄

(𝜑𝜑𝑖𝑖)

𝑘𝑘𝑘𝑘Φ𝑖𝑖

�∑

𝑦𝑦𝑘𝑘 𝑖𝑖 𝑡𝑡

1

𝜎𝜎𝐵𝐵 𝜎𝜎𝐵𝐵−1

⁄

𝜎𝜎𝐵𝐵−1
𝜎𝜎𝐵𝐵

�

𝑖𝑖𝑖𝑖 𝜑𝜑𝑖𝑖 = 0

𝑖𝑖𝑖𝑖 𝜑𝜑𝑖𝑖 > 0

   ∀𝑡𝑡 > 0

(2.a) 

31  

 
 
 
 
 
 
 
 
 
 
with  

and 

𝑦𝑦𝑘𝑘 𝑖𝑖 𝑡𝑡 = �∑

𝑗𝑗𝑘𝑘Λ𝑘𝑘

𝜔𝜔𝑖𝑖𝑗𝑗

�

𝐶𝐶𝑘𝑘 𝑖𝑖 𝑡𝑡

−𝜎𝜎𝑊𝑊 𝜎𝜎𝑊𝑊−1
⁄

𝐶𝐶𝑘𝑘 𝑖𝑖 𝑡𝑡 = �∑

𝑗𝑗𝑘𝑘Λ𝑘𝑘

𝜔𝜔𝑖𝑖𝑗𝑗�𝜃𝜃𝑖𝑖𝑗𝑗+ �1 − 𝜃𝜃𝑖𝑖𝑗𝑗� 𝑦𝑦𝑗𝑗 𝑡𝑡−1�

𝜎𝜎𝑊𝑊−1
𝜎𝜎𝑊𝑊

𝜎𝜎𝑊𝑊 𝜎𝜎𝑊𝑊−1

⁄

�

(2.b) 

(2.c) 

Like in (1.a), the first row of (2.a) states that the resilience of firm 

 remains unchanged if the 

firm is a starting point of the graph. The second row of (2.a) defines the aggregate measure 

𝐹𝐹𝑖𝑖

of resilience of firm 

 as a CES function of sub-aggregate measures 

 of resilience of the 

firm, computed by sectors of activity of its suppliers. The first component in this second row 

𝑦𝑦𝑘𝑘 𝑖𝑖 𝑡𝑡

𝐹𝐹𝑖𝑖

aims at normalizing the maximum value of the measure of resilience to 1. In (2.a), parameter 

 captures the degree of substitutability or complementarity between sectors in which firm 

  of  resilience  of  the  firm  for  each 
has  suppliers.  In  turn,  the  sub-aggregate  measures 
𝜎𝜎𝐵𝐵
𝐹𝐹𝑖𝑖
supplying sector are defined in (2.b) in (2.c), in a similar way than the aggregate measure in 

𝑦𝑦𝑘𝑘 𝑖𝑖 𝑡𝑡

(1.a) and (1.b), except that the CES function is limited to suppliers within the sector 

. In (2.b) 

and  (2.c),  parameter 

  captures  the  degree  of  substitutability  or  complementarity  within 

𝑘𝑘

sectors in which firm 

 has suppliers. 
𝜎𝜎𝑊𝑊
𝐹𝐹𝑖𝑖

5.4.  Comments on calibration 

The  stress  test  detailed  in  the  previous  sections  involves  a  potentially  high  number  of 

parameters if, in addition to the elasticities of substitution 

 in the non-nested model, or 

 and 

 in the nested model, a different value of the resilience coefficient 

𝜎𝜎

 is allowed for each 

𝜎𝜎𝐵𝐵

link 
𝜎𝜎𝑊𝑊

 in the graph representing the supply chain. In the absence of case studies of firms 

𝜃𝜃𝑖𝑖𝑗𝑗

at the different links of the supply chain to infer the value of parameters, we have to rely on 

𝐹𝐹𝑗𝑗 → 𝐹𝐹𝑖𝑖

some a priori calibration and to implement a sensitivity analysis. 

The guideline for calibration is to select parameters’ values so that there is neither a too rapid 

collapse of the supply chain, nor a too high inertia, so that results of the stress test underscore 

heterogeneity across firms in terms of their resilience to stress. The underlying idea is thus to 

put the emphasis on the role of the specific network of suppliers and customers that features 

the supply chain under scrutiny. The stress test is iterated up to a number of iterations that 

32  

 
 
 
 
 
 
 
 
 
 
 
 
 
yields  no  additional  change  in  the  aggregate  measure  of  resilience  of  firms.  To  limit  the 

dependence of the results on specific values of the parameters, Monte Carlo simulations can 

be implemented. As they are potentially numerous, the case of resilience coefficients deserves 

some discussion. It is more specifically convenient to assume that 

 is a matrix of random 

resilience coefficients defined as follows: 

Θ

𝜃𝜃𝑖𝑖𝑗𝑗 = 0
�
𝜃𝜃𝑖𝑖𝑗𝑗 ∼ 𝐵𝐵𝐵𝐵𝑡𝑡𝐵𝐵(𝛼𝛼, 𝛽𝛽)

𝑖𝑖𝑖𝑖 𝜔𝜔𝑖𝑖𝑗𝑗 = 0
𝑖𝑖𝑖𝑖 𝜔𝜔𝑖𝑖𝑗𝑗 = 1

(3) 

Resilience coefficients are thus identically and independently drawn from a Beta distribution 

with two parameters 

 and 

. As a result, the calibration problem is reduced to the calibration 

of these two parameters. 

𝛼𝛼

𝛽𝛽

In the illustrative example introduced with Figure 7, the sensitivity analysis of the non-nested 

model reveals that unless 

 is sufficiently high, and the resilience coefficients 

 are drawn 

from a distribution with a sufficiently high mass on the right (i.e., close to 

𝜎𝜎

), the supply chain 

𝜃𝜃𝑖𝑖𝑗𝑗

rapidly  collapses. The  case  of  a  rapid  collapse  is  not  very  informative,  as  it  does  not  help 

1

identifying which firms are the most fragile along the chain and should therefore attract more 

attention. A  sufficiently  high  value  of 

  is  key  to  avoid  a  rapid  collapse  of  the  supply  chain 

because it guarantees that suppliers are sufficiently substitutable and that a shock affecting 

𝜎𝜎

one of them can be circumvented thanks to the other. Similarly, sufficiently high values of the 

resilience  coefficients  are  required  because,  as  suggested  by  equation  (1.b),  they  limit  the 

magnitude of shocks transmission from one iteration to the other. In the illustrative example 

developed  from  Figure 7, 

  and  a  beta  distribution  with  parameters 

  and 

reveals  to  be  a  good  compromise  as  it  limits  the  magnitude  of  shocks  transmission,  while 
𝛽𝛽 = 1
keeping a significant heterogeneity across the different links of the supply chain. An example 

𝛼𝛼 = 5

𝜎𝜎 = 2

of the matrix 

 of resilience coefficients drawn from this probability density function is reported 

in Table 3. It serves as a basis for the following elements of illustration.  

Θ

33  

 
 
 
 
 
 
 
 
 
 
Table 3: Example of a random draw of the matrix 

 of resilience coefficients 

F1 

F2 

F3 

F4 

F5 

F6 

F9 

F10 

F11 

F12 

F1 

F2 

F3 

F4 

F5 

F6 

F7 

F8 

F9 

F10 

F11 

F12 

0 

0 

0 

0 

0 

0 

0 

0 

0,987  0,617 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0,631 

0 

0 

0 

0 

0,754  0,903 

0 

0 

0 

0 

0,942 

0 

0,742 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0,851  0,943 

F7 
𝚯𝚯
0 

0 

0 

0 

0 

0 

0 

0 

F8 

0 

0 

0,797 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0,789 

0 

0 

0 

0 

0 

0,812  0,934 

0 

0 

0 

0 

0 

0 

0,748  0,656 

0,954  0,839  0,984 

0 

0,820 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

Table 4 displays the vector of aggregate measures of the degree of resilience of the 

 firms 

at iterations 

 (initial shock), 

, 

,  

, 

. As shown by the last column, 

𝑁𝑁

the aggregate measure of resilience falls to zero for almost all firms that are not starting points 

𝑡𝑡 = 0
of the value chain, except firm 

𝑡𝑡 = 10

𝑡𝑡 = 5
 which appears a little bit more resilient. More interestingly, 

𝑡𝑡 = 100

𝑡𝑡 = 20

the previous columns highlight that firm 

𝐹𝐹8

 is more at risk than the others. Of course, these 

results are contingent on the specific resilience coefficients reported in Table 3. To avoid this, 

𝐹𝐹7

we implement a Monte Carlo simulation approach, taking a large number of random draws of 

the  resilience  coefficients  in  order  to  construct  a  probability  distribution  of  the  aggregate 

measures of the degree of resilience of firms. 

34  

 
 
 
 
 
 
Table 4: Example of results at different iterations (minimum aggregate index of resilience 

in grey) 

F1 

F2 

F3 

F4 

F5 

F6 

F7 

F8 

F9 

F10 

F11 

F12 

iteration 0 

iteration 5 

iteration 10 

iteration 20 

iteration 100 

1 

1 

1 

0,5 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

0,998955 

0,979283 

0,747639 

2,48319*10^-7 

0,5 

1 

0,88368 

0,500677 

0,993306 

0,941326 

0,988679 

0,997415 

0,988817 

0,5 

1 

0,778018 

0,250677 

0,95209 

0,78684 

0,882192 

0,971964 

0,889503 

0,5 

1 

0,536165 

0,062839 

0,740214 

0,429889 

0,373787 

0,797842 

0,439319 

0,5 

1 

3,85067*10^-6 

9,79818*10^-7 

0,00339739 

1,44351E-05 

4,48036*10^-12 

0,00366014 

1,40967*10^-7 

The previous illustration is based on only one draw of the matrix 

 of resilience coefficients, 

and one value for parameter 

 of the CES function used to compute the aggregate resilience 

Θ

index of firms. To limit the dependence of the results on a specific draw of the matrix 

𝜎𝜎

specific choice of the CES parameter(s), Monte Carlo simulations are implemented. 

 and a 

Θ

The implementation of Monte Carlo simulation for the resilience coefficients is immediate given 

the way of generating them defined in equation (3). As regards the parameters of the CES 

function(s), we must define the probability distribution from which they can be drawn. Though 

any distribution defined over the set of positive or zero real numbers can be candidate, we 

retained the Gamma distribution due to its ability to integrate both an asymmetry and a mode 

that can be either positive or equal to zero. To implement the Monte Carlo simulations in the 

non-nested model, we draw several thousand values of 

 from a 

 distribution for each 

firm involved in the supply chain, in parallel to as many random draws of the matrix 

. The two 

𝜎𝜎

𝛤𝛤(𝑘𝑘 , 𝛿𝛿)

parameters  of  the 

  distribution  are  chosen  following  the  same  guidelines  as  those 

Θ

described above. More specifically, they are chosen so that the mass of values guarantees 

𝛤𝛤(𝑘𝑘 , 𝛿𝛿)

that  the  supply  chain  does  not  collapse  too  rapidly  and  that,  conversely,  a  sufficiently  high 

degree of discrimination in terms of the final resilience of firms at the steady state of the stress 

test is obtained. 

The  case  of  the  nested  model  deserves  more  attention.  Indeed,  it  is  expected  that  the 

parameter 

, capturing the degree of substitutability or complementarity between sectors, is 

𝜎𝜎𝐵𝐵

35  

 
 
  
 
 
 
 
lower than the parameter 

 capturing the degree of substitutability or complementarity within 

sectors. Therefore, the Monte Carlo simulation proceeds in two steps. In a first step, a different 

value of 

𝜎𝜎𝑊𝑊
 is drawn from a 

 distribution for each firm. In a second step, a 

distribution is used to generate values of 

. Nevertheless, we impose the condition that 

𝜎𝜎𝑊𝑊

𝛤𝛤(𝑘𝑘𝑊𝑊 , 𝛿𝛿𝑊𝑊)

 by drawing the value of 

 from the truncated version of the 

𝜎𝜎𝐵𝐵

𝛤𝛤(𝑘𝑘𝐵𝐵 , 𝛿𝛿𝐵𝐵)
 where, for each 
𝜎𝜎𝐵𝐵 ≤

firm, truncation occurs on the right of the value 
𝜎𝜎𝑊𝑊

𝜎𝜎𝑊𝑊

 drawn in the first step for the firm. 

𝛤𝛤(𝑘𝑘𝐵𝐵 , 𝛿𝛿𝐵𝐵)

𝜎𝜎𝑊𝑊

6. Results 

6.1.  Stress definition and implementation 

The first step of the stress test consists in identifying which group of firms is affected by the 

initial shock (a Chinese ban on processed critical raw materials) within the supply chain, and 

what is the magnitude of this initial shock, given that these inputs are an important, and so far 

difficult to substitute, component to produce wind turbines. 

To do this, we have identified Chinese firms involved in the extraction and processing of rare 

earths materials. We have then introduced a shock on these Chinese firms that corresponds 

to a total drop in their accessibility (i.e., we set their initial aggregate index of resilience in the 

supply chain of A, B, C and D to 0). These firms have been identified by searching for the 

keywords “rare” or “earth” in the name of upstream firms, in addition to the country code being 

“CN”. The keyword “rare” is systematically associated with “earth” or “-earths”, whereas there 

is  one  firm  name  where  the  keyword  “earth”  is  not  associated  with  “rare”,  namely  the  firm 

Earth-Panda  Advanced  Magnetic  Material.  Nevertheless,  this  firm  produces  permanent 

magnet  products  based on  rare  earth.  We  also  checked  on  the  web  if  other  Chinese  firms 

were referred to when searching for Chinese firms specialised in rare earths materials, but we 

were not able to identify additional firms by doing so. The name and FactSet ID of the firms 

that  we  have  selected  for  the  initial  shock  with  the  sectoral  Filter  4  in  order  to  retrieve  the 

supply chain are reported in Table 5. The tiers at which the firms appear in the supply chain 

are also reported. The Chinese firms involved in the extraction and/or processing of rare earth 

materials spread all along the upstream part of the supply chain, from tiers close to the wind 

turbine manufacturers (tiers -2 or -3) to tiers much further upstream (up to tiers -5 and -6). 

36  

 
 
 
 
 
 
Table 5: FactSet ID and name of Chinese firms identified as extracting or processing 

rare earths 

FactSet ID 

Name of the company 

0JXTP0-E 

JL MAG Rare-Earth Co., Ltd. 

062XTP-E 

China Northern Rare Earth (Group) High-Tech Co., Ltd. 

0JQKNN-E 

China Rare Earth Co. Ltd. 

0FYW7V-E 

Earth-Panda Advanced Magnetic Material Co., Ltd. 

0DK62Z-E 

Fujian Changting Golden Dragon Rare-Earth Co., Ltd. 

062NW3-E 

China Rare Earth Resources & Technology Co., Ltd. 

0CP0KG-E 

Gansu Rare Earth New Material Co. Ltd. 

08M0W5-E 

Ganzhou Chenguang Rare Earths New Material Co., Ltd. 

0DJM1Q-E 

Baotou Xinyuan Rare Earth Hi-Tech & New Material Co. Ltd. 

Tier 

-3; -4; -5 

-2; -3; -4 

-2 

-2; -3; -4 

-3 

-4; -6 

-4 

-5 

-3 

The  next  step  of  the  stress  test  consists  in  implementing  the  iterative  formula  (1)  or  (2), 

depending on whether the non-nested version, or the nested version of the model, is applied. 

Thereafter, we focus on results obtained with the nested version of the model applied to the 

supply  chain  as  retrieved  from  using  Filter  4,  and  with  Monte  Carlo  simulations  for  all 

parameters. Corresponding results obtained with the non-nested version of the model, Monte 

Carlo  simulations  for  the  resilience  coefficients  only  (CES  parameters  are  set  equal  to 

expected values of the Gamma distribution), and filters 1 to 4 are reported in the appendix. 

The parameter values used in this application for the distribution 

 of the CES function 

between sectors are chosen such that 

values used for the distribution 

that 

 and 

the Appendix, we used 

𝐸𝐸[𝜎𝜎𝑊𝑊] = 0,2

2
𝑉𝑉[𝜎𝜎𝑊𝑊] = 0.1

 and 

𝐸𝐸[𝜎𝜎𝐵𝐵] = 0,05

𝛤𝛤(𝑘𝑘𝐵𝐵 , 𝛿𝛿𝐵𝐵)
2
 of the CES function within sectors are chosen, such 
𝑉𝑉[𝜎𝜎𝐵𝐵] = 0.05
. For the non-nested model, whose results are displayed in 

𝛤𝛤(𝑘𝑘𝑊𝑊 , 𝛿𝛿𝑊𝑊)
. As regards the beta distribution of resilience coefficients, we 

. In parallel, parameter 

choose 

 and 

, which yields an expected value of 

 and a standard deviation 

𝜎𝜎 = 0,1
 for the distribution of these coefficients. 

𝛼𝛼 = 1 2⁄

𝛽𝛽 = 3 2⁄

of 

1 4⁄

1 4⁄

Our Monte Carlo method relies on 2000 random draws of both the resilience matrix and the 

CES  parameters.  In  each  random  draw,  different  values  of  the  resilience  matrix  and  CES 

parameters  are  drawn  for  each  firm.  For  each  draw,  we  iterated  the  computation  of  the 

resilience index eighty-five times to browse the network of firms forming the supply chain, and 

then stopped. The stopping rule reveals to be largely sufficient to make the stress test reach 

a steady state for the four wind turbine manufacturers, as shown by Figure 8 (see Appendix A 

37  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
for  the  non-nested  model,  where  fifty  draws  were  enough  to  reach  convergence).  Figure 8 

displays the dynamics of the average aggregate index of resilience across the different Monte 

Carlo simulations for each of the four wind turbine manufacturers. It highlights that, whatever 

the firm under consideration, the resilience index drops rapidly during the first iterations of the 

test, and then stabilises. The steady state seems to be almost reached after twenty iterations, 

but the index still changes marginally, up to seventy-five iterations. As a result, an upper bound 

of  eighty-five  iterations  has  been  chosen  to  make  sure  that  no  changes  occur  for  ten 

successive  iterations. A  similar  pattern  is  observed  with  the  non-nested  model,  except  that 

convergence is reached earlier (see Appendix A). On average, the resilience aggregate index 

is close to 0.388 for A, 0.346 for B, 0.21 for C and 0.311 for D. The shock considered is thus 

rather drastic for the four firms, as they can keep at most a little bit more than one third of their 

initial capacity and one fifth at worst. Nevertheless, the figures obtained with the nested model 

and with sector filter 4 are significantly higher than those obtained with the non-nested model 

and reported in Appendix A: It seems that the non-nested model (with 

) exacerbates 

the consequences of the shock. Of course, comparing the nested and the non-nested model 

𝜎𝜎 = 0,1

is  not  obvious  as  their  specification  is  different,  and  their  number  of  parameters  differs. 

However, it clearly appears that using sector filter 4 reduces the impact of the initial shock, 

whereas sector filter 1 maximises its impact (Cf. Appendix A). 

38  

 
 
 
 
 
Figure 8: Convergence of the stress test to a steady state with the nested model 

A 

B 

resilence

0.388925

0.388920

0.388915

0.388910

0.388905

resilence

0.34622

0.34621

0.34620

0.34619

0

20

40

60

80

iteration

0

20

40

60

80

iteration

C 

D 

resilence

0.210080

0.210075

0.210070

0.210065

0.210060

resilence

0.311706

0.311704

0.311702

0

20

40

60

80

iteration

20

40

60

80

iteration

6.2.  Results  at  the  aggregate  level  for  the  nested  model, 

upstream the supply chain 

The  magnitude  of  the  stress  impact  on  wind  turbine  manufacturers  depends  on  the 

transmission of the stress shock in the upstream layers of the value chain. Figure 9 displays 

the distribution of the resilience index within each layer in the “violin” form for each layer in 

abscissa, with the width of the violin indicating the density of the value of the index reported 

in ordinate. Figure 9 highlights that, whatever the upstream layer considered, the distribution 

of the resilience index is much more asymmetric compared to its distribution for the four wind 

turbine  manufacturers  in  layer  0.  To  draw  Figure  9,  2000  random  draws  of  the  resilience 

parameter of all firms have been generated. Then, results for firms within a same layer have 

been selected to produce Figure 9. This Figure captures both the heterogeneity across firms 

within each layer and the uncertainty surrounding the parameter values. However, it does not 

distinguish intra-firm variance and inter-firm variance of the resilience index. Results show that 

almost all firms in the upstream layers remain unaffected by the initial shock. By contrast, a 

39  

 
 
 
 
 
 
 
 
few  of  them  are  highly  impacted  and,  to  a  similar  magnitude,  compared  to  the  four  firms 

gathered in layer 0. Such a high asymmetry in the distribution of the resilience index for the 

upstream  firms  is  consistent  with  the  high  diversity  of  firms  in  these  layers.  Moreover,  as 

already outlined, a significant number of firms involved in the supply chain are conglomerates. 

These companies are in fact involved in many other supply chains that do not necessarily rely 

on processed critical raw materials, whereas the four firms in layer 0 are pure players in the 

wind turbine industry. 

Figure 9: Distribution chart of the resilience index in upstream layers 

Table 6: Upstream NACE sectors ranked in increasing number of firms 

NACE 24 
NACE 20 
NACE 27 
NACE 28 
NACE 26 
NACE 72 
NACE 33 
NACE 74 
NACE 62 
NACE 32 
NACE 8  
NACE 23 
NACE 22 
NACE 7  
NACE 71 
NACE 25 
NACE 71 
NACE 25 

Manufacture of basic metals 
Manufacture of chemicals and chemical products 
Manufacture of electrical equipment 
Manufacture of machinery and equipment n.e.c. 
Manufacture of computer, electronic and optical products 
Scientific research and development  
Repair and installation of machinery and equipment 
Other professional, scientific and technical activities 
Computer programming, consultancy and related activities 
Other manufacturing 
Other mining and quarrying 
Manufacture of other non-metallic mineral products 
Manufacture of rubber and plastic products 
Mining of metal ores 
Architectural and engineering activities; technical testing and analysis 
Manufacture of fabricated metal products, except machinery and equipment 
Architectural and engineering activities; technical testing and analysis 
Manufacture of fabricated metal products, except machinery and equipment 

40  

 
 
 
 
 
 
 
Figure 10: Comparison between NACE sectors in the upstream layers 

Results are more contrasted when gathering upstream firms according to their main NACE 

sector of activity rather than their layer (Figure 10). The detailed labels of NACE sectors are 

reported in Table 6. The continuous line (in blue) in the radar graph (10) indicates the average 

resilience  index  obtained  for  all  firms  within  the  sector  and  all  random  draws  of  the  Monte 

Carlo  simulations.  The  two  thin  dashed  lines  indicate  the  first  and  last  quartiles.  Like  in 

Figure 9, the underlying distribution of the resilience index in Figure 10 captures both firms’ 

heterogeneity within a NACE sector and uncertainty surrounding the values of the  different 

parameters. The NACE 72 sector “Scientific research and development” and NACE 33 sector 

“Repair and installation of machinery and equipment” have none of their firms affected by the 

initial shock on processed critical earth materials. At the opposite, the NACE 62 “Computer 

programming,  consultancy  and  related  activities”  sector  is  the  most  affected  one,  with  an 

average index of resilience below 0.7 and a first quartile below 0.4, meaning that a quarter of 

the firms in this sector have a resilience index below 0.4. Other sectors exhibit an average 

index of resilience close to 0.8 but still differ in terms of the dispersion of the index with some 

having a relatively large gap between their first and last quartiles (NACE 7 “Mining of metal 

ores”;  NACE  20  “Manufacture  of  chemicals  and  chemical  products”  and  NACE  27 

“Manufacture of electrical equipment”) and other having a narrow gap between these quartiles 

(NACE 32 “Other manufacturing”; NACE 22 “Manufacture of rubber and plastic products” and 

NACE 23 “Manufacture of other non-metallic mineral products”). 

41  

 
 
 
 
 
Figures  11  complements  Figures  10  by  comparing  EU  versus  non-EU  firms  from  NACE 

sectors in the upstream layers. It shows that for those sectors in which the EU has upstream 

firms, the resilience of these firms does not strongly depart from that of non-EU firms. 

Figure 11: Comparison between EU versus non EU firms from NACE sectors in the 

upstream layers 

First quartile out of EU
Mean out of EU
Last quartile out of EU
First quartile EU
Mean EU
Last quartile EU

At  this  stage,  it  is  worth  recalling  that  EU  countries  generally  differ  in  terms  of  sectoral 

specialization,  but  also  in  terms  of  sourcing  of  inputs  for  a  same  sector. As  a  result,  it  is 

expected  that countries are  differently  impacted by  a  same  initial  shock upstream  a supply 

chain. Figure 12 illustrates this differentiated impact with a focus on the specific case of EU 

member states. It reveals that the least resilient EU member state is Ireland with a resilience 

index close to 0.5, and to lesser extent Austria, Greece and Estonia, whereas countries like 

the  Czech  Republic,  Hungary,  Italy,  Poland  and Sweden  are the most resilient  ones  with  a 

resilience index above 0.9. Countries known for their large development of wind power, both 

in terms of cumulated capacity of commissioned wind farms and installed base of domestic 

wind turbine manufacturers, namely Germany, Denmark and Spain, are in a medium position 

with an average index of resilience between 0.8 and 0.9. Looking ahead, this means that from 

a policy point of view, a uniform de-risking strategy at the EU level could be beneficial for some 

EU countries but detrimental for others. 

Figure 13  complements  Figure 12  by  positioning  four  EU  member  states  with  significantly 

different  average resilience  index,  namely Germany  (DE),  Denmark  (DK),  Poland  (PL)  and 

42  

 
 
 
 
 
 
Ireland  (IE),  in  terms  of  their  average  resilience  index  disaggregated  at  the  sectoral  level. 

Relatively smaller countries like Ireland and Denmark have firms in a smaller set of sectors 

and thus, more heavily depend on the resilience of these few sectors. It is also likely that within 

these few sectors, results for smaller countries depend on fewer firms. Consistently with that 

remark, Ireland has firms in only three sectors upstream and exhibits a low average index of 

resilience in two of these sectors, compared to the three other countries. Nevertheless, in the 

third  sector  (NACE  71  “Architectural  and  engineering  activities;  technical  testing  and 

analysis”), Ireland outperforms Germany and Poland, probably because, even if it only has 

few firms in that sector, these firms are particularly resilient compared to those of Germany 

and Poland. Interestingly, Figure 13 shows that Poland is the only member state, among the 

four considered, that has firms in the NACE sector 7 “Mining of metal ores”. However, Polish 

companies in that sector have a low average resilience index. 

Figure 12: Average index of resilience of their upstream firms for EU Member States 

(those not coloured have no firms upstream the supply chain) 

43  

 
 
 
 
 
 
 
Figure 13: Comparison between NACE sectors and EU Member States 

Our  stress  test  allows  us  to  provide  a  more  in-depth  explanation  of  heterogeneity  across 

countries within a same sector. An illustrative example is given by Figure 14 in the case of the 

NACE  27  sector  “Manufacture  of  electrical  equipment”.  Figure 14  displays  the  cumulative 

density function of the resilience index for upstream firms in the NACE 27 sector and located 

in  each  of  the  four  countries  also  analyzed  in  Figure 13.  Our  results  show  that  only  5%  of 

Polish firms have a resilience index less than approximately 0.5, whereas this index is about 

55% in Ireland and 40% in Denmark. Overall, our results show a strict dominance of Ireland 

(the least resilient Member State) compared to other MS. 

Figure 14: Comparison within NACE 27 sector and EU Member States 

(Cumulative Density Functions of the resilience index of firms) 

44  

 
 
 
 
 
 
 
 
 
6.3.  Results at the firm level for wind turbine manufacturers 

So far, results from the stress test have been presented at a more-or-less granular level, from 

the layer level to the inter-sectoral and national level, and then the intra-sectoral and national 

level. Our stress test is also able to generate heterogeneous results at the firm level, even 

when comparing firms within a same sector and/or a same country. Thereafter, we illustrate 

this capacity by focusing on the comparison between the four wind turbine manufacturers, the 

supply chain of which we have retrieved. For that purpose, we first display in Figure 15 the 

partial density functions and the cumulative density functions of the index of resilience of the 

four wind turbine manufacturers. The partial density functions reveal that the distribution of the 

aggregate resilience is unimodal with a higher mode for A compared to B, which in turn has a 

higher  mode,  compared  to  D. The  company  C  is  the  one  exhibiting  the  lowest  mode. This 

ranking  corresponds  to  an  overall  switch  of  the  distribution  to  the  left  when  the  mode 

decreases. This is confirmed by the comparison between the cumulative density functions with 

a striking dominance of the distributions from D to A. Our stress test thus shows that A is the 

wind turbine manufacturer that is the most resilient to a shock on Chinese rare earth extraction 

and processing, followed by B, then D. The company C appears to be significantly less resilient 

to such a shock. Again, this ranking is robust to a switch to the non-nested model and whatever 

the  choice  of the filter  to  retrieve  the  supply chain  (See Appendix  B). This  is  an  interesting 

result as we showed earlier that Germany fared better than Denmark in NACE 27. However, 

this ordering in terms of nationality does not hold when we consider the results for the four 

wind turbine manufacturers.76 It turns out that the firm-level perspective suggests a different 

picture than the aggregated one. 

76 Further details on the relation between the two orderings are omitted in order to preserve anonymity. 

45  

 
 
 
 
 
Figure 15: Comparison of the distribution of the aggregate index of resilience at the 

final iteration of the stress test for the four wind turbine manufacturers 

Partial density function 

density

3.0

2.5

2.0

1.5

1.0

0.5

density

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

resilience

Cumulative density function 

0.2

0.4

0.6

0.8

1.0

resilience

46  

 
 
 
 
 
 
 
 
 
 
 
Figure 16: Distribution of the aggregate index of resilience at different iterations of the 

stress test 

density

2.0

1.5

1.0

0.5

density

3.0

2.5

2.0

1.5

1.0

0.5

A 

B 

density

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

C 

D 

density

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

As the parameters used for the four firms are drawn from the same distributions to process 

the Monte Carlo simulations, the difference in the shape of the partial and cumulative density 

functions  can  only  been  explained  by  differences  in  the  networks  of  suppliers.  This  is 

confirmed  by  Figure 16 where  the  shape  of  the partial  density  of the resilience  index  for  C 

does not vary much from iteration 10 of the stress test onwards, suggesting that key suppliers 

of that firm are affected by the shock and “contaminate” C as soon as the tenth iteration. By 

contrast, A and B, and to a lesser extent D, have the partial density function of their resilience 

47  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
index still significantly displaced between the tenth and twentieth iteration, while being more 

concentrated on the right. These three firms are thus less affected by the shock and when 

affected, it is due to firms that are on some layers much more upstream. These observations 

are robust to a switch from the nested model to the non-nested model and, to whatever is the 

choice of the filter to retrieve the supply chain (see Appendix C). 

7. Conclusive remarks 

Issues of supply chain disruptions are bound to be with us for a while. Beyond micro shocks, 

these  disruptions  can  have  detrimental  macro-economic  effects.  This  leads  to  question 

whether policymakers should intervene, and whether they should be instrumental in ensuring 

supply chain resiliency. However, at this stage little is known in the economic literature about 

what resilience means at a country or global level. The same holds for the desirability of having 

public  policies  to  promote  resilience.  That  is  why  it  is  important  to  deepen  our  analysis  of 

critical supply chains by applying stress tests and assessing their level of riskiness.  

This article has tried to address this issue and thus to fill a gap in the literature by developing 

a supply chain stress test for critical inputs. To develop this proof-of-concept exercise, we have 

used  firm-level  data  to  document  firms’  input  sourcing  decisions  and  their  location 

(upstream/downstream) in the supply chain.  

Our findings show that supply chain stress tests can help identifying relatively weaker firms or 

more exposed sectors/countries. Our results show that the lack of critical inputs (downstream 

shock) can translate onto an upstream shock for suppliers of complementary inputs. At a more 

detailed level, our results also show that the specificities of each firm network of suppliers-

customers are a strong determinant of their resilience. In terms of policy recommendations, 

our results stress the importance to go beyond country/regional aggregation and monitor trade 

between firms. Indeed, microstructures of industrial eco-systems, (i.e. the position of individual 

firms), on the overall production network, matter. It is thus important to track risks over time to 

ensure resilience and to promote awareness of the importance of the upper (lower) tiers to 

develop more effective shields against shock propagation.  

In this respect, the idea of having supply chain monitoring tools seems to be gaining ground. 

The International Monetary Fund (IMF), for example, is now seeking to measure the economic 

impact of extreme weather events on shipping, and to assess how disasters affect trade and 

supply  chains77. Together  with  stress  tests,  these  types  of  instruments  analyze  how  global 

77 See IMF and University of Oxford Launch “PortWatch” Platform to Monitor and Simulate Trade Disruptions 

48  

 
 
 
 
 
 
supply  chains  are  exposed  to  present  and  future  disruptions.  These  new  tools,  still 

experimental,  offer  cutting  edge  analytical  tools  to  produce  actionable  insights  for 

policymakers, but also private actors to respond to disruptions quickly and more efficiently, so 

as  ultimately  to  increase  resiliency.  Considering  the  diversification  and  magnification  of 

shocks, the development of such tools should be further encouraged, as they can underpin 

the design of better-informed policies. 

That being said, stress tests should not be considered as a “regulatory talisman” and are best 

used in combination with other tools, as they are sensitive to methodological choices. Validity 

of  the  results  is  indeed  affected  by  several  factors,  such  as  data  granularity  and  quality, 

severity  or  scope  of  the  different  scenarios  studied  and  model  risks.  Results  are  also 

conditional  on  assumptions  in  the  methodology,  notably  with  regards  to  the  stopping  rules. 

These limits are not specific to our study. In the banking sector, where stress tests are well 

established, some scholars, like Tarullo (2020), argue that regulators seem to have forsaken 

the original purpose of stress tests namely, to ensure the resiliency of the banking system, 

and that they tend to shift towards little more than a predictable compliance exercise. Others, 

like  Shahhosseini 

(2014)78,  consider 

that  stress 

tests  have  negative  unintended 

consequences and should therefore be complemented by other instruments.  

To  avoid  the  above-mentioned  pitfalls,  future  research  should  focus  on  the  nature  of  the 

shocks. One of the issues is how do we think the unthinkable, and having done so, how to act 

on it? Following the input from Simchi-Levi & Simchi-Levi (2020), further research could also 

try to quantify under different scenarios “the time to recover”, i.e., the time it would make for a 

particular node in a supply chain to be restored to full functionality after a shock. In the same 

way, it could be interesting to analyse the “time to survive”, i.e., the maximum duration that a 

supply chain can match supply with demand after a shock79. More generally, data availability 

limits the applicability of the obtained results. First, in presenting our results, we are mindful 

that our analysis has some limitations, as we treat on equal feet all suppliers within a same 

sector (we have relations of type 0-1), which is obviously not the case. In a complementary 

work, we aim at adding data on shares of revenues to put weight on relationships. In the same 

vein, having a resilience matrix based, at least partially, on expert knowledge could improve 

the representativeness of the exercise. However, obtaining such expert knowledge may be 

78  According  to  Shahhosseini  (2014),  “There  is  a  negative  causal  impact  of  capital  adequacy  requirements  on  managerial 
decisions in the U.S. banking system. Stress-tested banks reduce net loan charge-offs and keep problematic loans on their books 
to a greater extent than banks in a non-tested group to meet the capital ratio requirements. Managers increase the level of non-
performing loans in the aftermath of stress tests announcement. Stress-tested banks with greater exposure to the housing market 
change the classification of loan losses to a greater extent than other banks”. 
79 The underlying idea is that if the “time to recover” is greater than the “time to survive”, the supply chain will not be able to match 
supply with demand. 

49  

 
 
 
 
 
challenging and not necessarily easily replicable across sectors. Second, at this stage we did 

not consider competition between companies that would result in a dynamic restructuring of 

the network at stake. Future work aims therefore at creating/deleting/replacing a link to see 

how it modifies resilience. The underlying idea is to examine to what extent a supply chain 

could be made more resilient by not making it less efficient, and more precisely how proactively 

mitigate  risks  rather  than  react  to  disruptions  after  the  fact.  Lastly,  data  could  be 

complemented  by  patent  data  to  control  for  technological  dependencies  and/or  potential 

technological disruptions that could substitute to a critical input.  In considering future research 

directions, we are cognisant of this, and our future research will focus on incorporating and 

analysing these further elements. 

50  

 
 
 
 
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54  

 
 
 
 
Appendix A: convergence of the stress test with the non-nested model 

Figure A1: Convergence of the stress test to a steady state with the non-nested model 

(Filter 1) 

A 

C 

B 

D 

55  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A2: Convergence of the stress test to a steady state with the non-nested model 

(Filter 2) 

A 

C 

B 

D 

56  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A3: Convergence of the stress test to a steady state with the non-nested model 

(Filter 3) 

A 

C 

B 

D 

57  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A4: Convergence of the stress test to a steady state with the non-nested model 

(Filter 4) 

A 

C 

B 

D 

58  

 
 
 
 
 
 
 
 
 
 
 
 
 
Appendix B: comparison of the aggregate index of resilience with the non-nested model 

Figure B1: Comparison of the distribution of the aggregate index of resilience at the 

final iteration of the stress test for the four wind turbine manufacturers (non-nested 

model, Filter 1) 

Partial density function 

density
8

6

4

2

density

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

resilience

Cumulative density function 

0.2

0.4

0.6

0.8

1.0

resilience

59  

 
 
 
 
 
 
 
 
 
 
Figure B2: Comparison of the distribution of the aggregate index of resilience at the 

final iteration of the stress test for the four wind turbine manufacturers (non-nested 

model, Filter 2) 

Partial density function 

density

5

4

3

2

1

density

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

resilience

Cumulative density function 

0.2

0.4

0.6

0.8

1.0

resilience

60  

 
 
 
 
 
 
 
 
 
 
Figure B3: Comparison of the distribution of the aggregate index of resilience at the 

final iteration of the stress test for the four wind turbine manufacturers (non-nested 

model, Filter 3) 

Partial density function 

density

4

3

2

1

density

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

resilience

Cumulative density function 

0.2

0.4

0.6

0.8

1.0

resilience

61  

 
 
 
 
 
 
 
 
 
 
 
Figure B4: Comparison of the distribution of the aggregate index of resilience at the 

final iteration of the stress test for the four wind turbine manufacturers (non-nested 

model, Filter 4) 

Partial density function 

density
4

3

2

1

density

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

resilience

Cumulative density function 

0.2

0.4

0.6

0.8

1.0

resilience

62  

 
 
 
 
 
 
 
 
 
 
Appendix C: distribution of the aggregate index of resilience with the non-nested model 

Figure C1: Distribution of the aggregate index of resilience at different iterations of 

the stress test (non-nested model, Filter 1) 

density

6

5

4

3

2

1

density
6

5

4

3

2

1

A 

B 

density

5

4

3

2

1

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

C 

D 

density
8

6

4

2

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

63  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C2: Distribution of the aggregate index of resilience at different iterations of 

the stress test (non-nested model, Filter 2) 

density
3.5

3.0

2.5

2.0

1.5

1.0

0.5

density
5

4

3

2

1

A 

B 

density

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

C 

D 

density

5

4

3

2

1

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

64  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C3: Distribution of the aggregate index of resilience at different iterations of 

the stress test (non-nested model, Filter 3) 

density

3.0

2.5

2.0

1.5

1.0

0.5

density

4

3

2

1

A 

B 

density

3.0

2.5

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

C 

D 

density

4

3

2

1

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

65  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C4: Distribution of the aggregate index of resilience at different iterations of 

the stress test (non-nested model, Filter 4) 

density

2.0

1.5

1.0

0.5

density
4

3

2

1

A 

B 

density

2.5

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

C 

D 

density

3.0

2.5

2.0

1.5

1.0

0.5

0.2

0.4

0.6

0.8

1.0

resilience

0.2

0.4

0.6

0.8

1.0

resilience

66  

 
 
 
 
 
 
 
 
 
 
 
 
 
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DOI: 10.2873/1355245 
ISBN: 978-92-68-20580-8