# Evaluating criticality of strategic metals: Are the Herfindahl–Hirschman Index and usual concentration thresholds still relevant?

Pauline Bucciarelli, Emmanuel Hache, Valérie Mignon

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Pauline Bucciarelli, Emmanuel Hache, Valérie Mignon. Evaluating criticality of strategic metals: Are the Herfindahl–Hirschman Index and usual concentration thresholds still relevant?. Energy Economics, 2025, 143, pp.108208. 10.1016/j.eneco.2025.108208. hal-04924186

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# Evaluating criticality of strategic metals: Are the Herfindahl-Hirschman Index and usual concentration thresholds still relevant?

Pauline Bucciarelli<sup>a,b,*</sup>, Emmanuel Hache<sup>a,b,c,●</sup>, Valérie Mignon<sup>b,d</sup>

## ARTICLE INFO

**JEL classification:**

Q02

Q34

C23

C24

**Keywords:**

Strategic metals

Criticality

Herfindahl-Hirschman index

Metal prices

Panel regression

## ABSTRACT

This paper aims to evaluate the criticality of strategic metals by (i) investigating the validity of the Herfindahl-Hirschman Index (HHI) for assessing the supply risk aspect of criticality and (ii) determining an appropriate threshold for using this indicator in the context of criticality studies. Relying on a large panel of 33 strategic metals over the 1995–2021 period, our findings show that the variation of HHI has more impact on metal prices at lower HHI levels and question the existence of a threshold that clearly distinguishes high-risk markets from less risky ones based on their concentration levels. Overall, we show that using the HHI as a supply risk indicator, especially in conjunction with a threshold, may result in underestimating risks in less concentrated markets.

## 1. Introduction

In recent decades, the increasing number of raw material criticality assessments reflects a growing focus on securing the supply of these resources, particularly for countries and companies heavily dependent on international commodity flows. Accurately assessing the criticality of minerals and metals has become essential in this context, especially as these raw materials have regained strategic importance since the late 2000s. This paper aims to address this challenge, which is far from straightforward. As noted by Graedel et al. (2015), defining criticality is a difficult task because “criticality depends not only on geological abundance, but on a host of other factors such as the potential for substitution, the degree to which ore deposits are geopolitically concentrated, the state of mining technology, the amount of regulatory oversight, geopolitical initiatives, governmental instability, and economic policy.”

The first decade of the 21st century witnessed remarkable economic growth and industrialization, mainly driven by emerging economies

such as China, which became a dominant force in the global marketplace. As China's demand for metals and minerals surged, global markets tightened, leading to historic price increases and heightened concerns over potential shortages and scarcity (Schmidt, 2019). The imposition of Chinese export restrictions on rare earth elements (REE) over the 2009–2011 period—especially in 2010¹—further exacerbated these fears, leading highly import-dependent industrialized countries to develop their criticality assessment methodology in order to secure their raw material supply chains (Frenzel et al., 2017). More recently, the COVID-19 pandemic and the war in Ukraine have had significant implications for global supply chains, including those related to metals and minerals.<fnref n="2" />

The pandemic's disruptive impact on production, transportation, and distribution of raw materials led to temporary shutdowns of mines and processing facilities (Gupta et al., 2020), highlighting vulnerabilities in global supply chains and tensions between economic powers (Jaravel and Méjean, 2021). These events have contributed to

<footnote><sup>a</sup> IFP Energies nouvelles, 1 et 4 avenue de Bois Préau, 92852 Rueil-Malmaison, France</footnote>

<footnote><sup>b</sup> Economix-CNRS, University of Paris Nanterre, France</footnote>

<footnote><sup>c</sup> The French Institute for International and Strategic Affairs (IRIS), France</footnote>

<footnote><sup>d</sup> CEPII, France</footnote>

<footnote>☆ This paper has been presented at the 3rd ARAE Annual Workshop 'Econometrics of the Energy Transition', Paris, December 8, 2023. We would like to thank Capucine Nobletz and all the participants for their constructive remarks and suggestions. We also thank two anonymous referees for their helpful remarks and suggestions.</footnote>

<footnote>* Correspondence to: Economix-CNRS, University of Paris Nanterre, 200 avenue de la République, 92001 Nanterre cedex, France.
E-mail address: pauline.bucciarelli@parisnanterre.fr (P. Bucciarelli).</footnote>

<footnote n="1">¹ See Seaman (2019). The reader interested by the role of REE in the energy transition may refer to Depraiter and Goutte (2023).</footnote>

<footnote n="2">² For a historical review about the geopolitical supply risk of metals, see Habib et al. (2016).</footnote>
growing concerns about geographic fragmentation, prompting the In-
ternational Monetary Fund (IMF) to warn in 2023 that such fragmenta-
tion could reverse decades of globalization momentum (IMF, 2023). In
response, states are increasingly implementing economic policies aimed
at bolstering the resilience of their industrial sectors and safeguarding
economic sovereignty, often as a shield against potentially adversarial
economic partners. Metals have become central to these policies. Pro-
ducer countries have turned to protectionist measures such as export
embargoes, licensing restrictions, and quotas, while consumer countries
are prioritizing national development strategies and securing supply
chains to mitigate their exposure to geopolitical and economic risks.

In 2017, Donald Trump elevated the issue of critical metals to a
national priority, framing it as an extraordinary threat to the economy,
thereby reinvigorating U.S. policy on mining and strategic metals.
This trajectory was further reinforced under Joe Biden through the
enactment of the Inflation Reduction Act (IRA) in 2022. This legislation
includes provisions aimed at promoting domestic battery production,
potentially fostering the localization or reshoring of metallurgical ac-
tivities within the United States. It thus promotes the development
of more robust supply chains and domestic production of various
minerals. In particular, it introduces the New Advanced Manufacturing
Production Credit, a 10% tax credit granted to domestic producers of
specified critical minerals (IEA, 2023). The IRA also signals the prospect
of a more protectionist approach to international trade. This policy
shift represents a robust countermeasure to China's long-standing strat-
egy of securing critical minerals and metals, a policy Beijing has
systematically pursued for over two decades (Bonnet et al., 2022).

A few months later, the European Commission proposed the Critical Raw Materials Act (CRMA), a set of actions aimed to ensure “the EU’s access to a secure, diversified, affordable and sustainable supply of critical raw material” (European Commission, 2023). The European Commission has thus designated 34 materials as ‘critical’ and 17 as ‘strategic’, including cobalt, lithium, copper and nickel, with the latter two added to the list in 2023. To mitigate supply risks, it has established a maximum dependency threshold of 65% for imports from any single country and set ambitious domestic production goals: achieving 10% of national consumption through local production, 40% through metal refining, and 25% through recycling by 2030. This framework, supported by the industrial strategy outlined in the Net Zero Industry Act (NZIA), reflects a shift towards proactive intervention to address Europe’s growing concerns over mineral security.

Moreover, the ongoing global energy transition, aimed at reducing
greenhouse gas emissions, has significantly increased the demand for
specific metals and minerals.<fnref n="3" /> This transition heavily relies on low-
carbon technologies, which require both a higher metal content and
a greater diversity of materials compared to traditional systems (IEA,
2021). Batteries, for instance, rely on metals such as cobalt, copper,
lithium, manganese, and nickel, while permanent magnets, used in
electrified vehicle engines and certain offshore wind technologies, re-
quire REE. Electricity-generating technologies also depend on various
metals: aluminum, copper, and nickel for wind power systems; alu-
minum, silver, copper, and silicon for solar technologies; and hydrogen
low-carbon production technologies often involve nickel, iridium, pal-
ladium, and/or platinum. In its 2024 World Investment Report, the
International Energy Agency (IEA) projects that investments in clean
technologies and infrastructure will reach 2 trillion US dollars by
2024 (IEA, 2024). However, achieving a pathway consistent with lim-
iting global temperature increases to 1.5 °C above pre-industrial levels
by 2100 necessitates investments that are 2.5 times greater than current
levels. This growing demand is expected to further strain certain metal

markets, amplifying existing pressures in the years ahead. As a result,
the availability of metals and minerals has become a central concern
in the energy transition dynamic, with these resources potentially be-
coming limiting factors for achieving net-zero ambitions (Zhang et al.,
2022).

Within this context, adequately assessing the criticality of minerals
and metals is crucial. Originally developed by states to ensure their
military-strategic positions and later to sustain economic growth and
contemporary lifestyles, criticality studies are now conducted by a
multitude of actors at different scales (state, industry, company or
even technology scale) (Schrijvers et al., 2020). As a result, multiple
criticality assessment methodologies have been developed to identify
materials of concern and assist decision-making processes, drawing on
the pioneering work of the National Research Council (2008) and the
European Commission (2010). Two key aspects are commonly used
as criteria to identify critical raw materials: (i) their economic and/or
strategic importance, and (ii) the likelihood of supply disruptions, often
referred to as ‘supply risk’ (Frenzel et al., 2017).<fnref n="4" /> However, the mea-
surement of these criteria varies from one study to another, from the
selection of the indicators used to the way they are aggregated (Gleich
et al., 2013).

The absence of a standardized theoretical framework for criti-
cality measurement coupled with the proliferation of such studies,
has led to the emergence of a distinct field in the scientific litera-
ture reviewing the various criticality assessment methods and their
relevance (Erdmann and Graedel, 2011; Achzet and Helbig, 2013;
Glöser et al., 2015; Frenzel et al., 2017; Hatayama and Tahara, 2018;
Schrijvers et al., 2020). It is commonly observed that certain indicators
lack sufficient relevance. Therefore, experts and researchers recom-
mend identifying best practices (Schrijvers et al., 2020), primarily
through acquiring more robust empirical evidence on widely used
indicators (Helbig et al., 2021).

One of the most commonly used indicators for assessing the supply risk of a material is the country's production concentration. Helbig et al. (2021) conduct a thorough review of different indicators employed to measure supply risk and find that country's production concentration appears in about 75% of the 88 assessment analyses presented in their paper and has been in use since 1977. The rationale behind using such an indicator is that as the production of a given raw material becomes more concentrated in a few countries, the likelihood of supply disruptions increases due to various factors, including economic, political, or environmental considerations (Frenzel et al., 2017). Moreover, “in the context of global studies, “production” is used as a proxy for “supply”” (Brown, 2018). Therefore, world production by country is used to evaluate supply diversity (Thomas et al., 2022), which is known in the literature as a significant factor in supply resilience and, consequently, supply risk (Sprecher et al., 2015; Sato et al., 2017).<fnref n="5" /> The Herfindahl–Hirschman Index (HHI) (Herfindahl, 1950; Hirschman, 1945) is the dominant measure for assessing this indicator (Helbig et al., 2021; Brown, 2018). The HHI is a widely recognized measure of market concentration. It was initially developed in the field of industrial organization to assess market structure and quantify market power and has since been extensively used, particularly in the field of competition law. The HHI is calculated by summing the squares

<footnote n="4">⁴ A third component, the environmental implications, is also considered in some methodologies (Graedel et al., 2012).</footnote>

<footnote n="5">⁵ In recent years, the study of network resilience has become a significant subfield in network science (Liu et al., 2022), referring to the ability to withstand and rapidly recover from environmental changes or disruptions. An essential component of resilience, as highlighted by recent research, is redundancy, denoting the use of multiple pathways, functions, or components within a system (Kharrazi et al., 2020). In the context of trade systems, redundancy refers to the diversity of supply, which involves having multiple suppliers for a specific product, as emphasized by Sprecher et al. (2015) and Kharrazi et al. (2020).</footnote>

<footnote n="3">³ For a recent overview of the main challenges faced by countries regard-
ing economic development and climate sustainability, see Goutte and Sanin
(2024).</footnote>
of individual firms’ market shares, thereby assigning greater weight to larger market shares.<fnref n="6" /> As a result, the HHI approaches zero when a market consists of numerous firms of relatively equal size, while reaching its maximum value of 10,000 points when a single firm dominates the market.

In the metal and mineral production sector, various HHIs are available to evaluate concentration. The HHI can be assessed at different scales, either based on the national production of countries (referred to as country HHI) or by focusing on the production of specific firms. Moreover, the HHI can be computed at various points along the value chain, including ore extraction, smelting, and refining. Indeed, minerals undergo a multi-stage transformation process before they can be utilized in final applications. Initially, the raw minerals are extracted from deposits through mining activities, which are classified as upstream operations. Subsequently, the extracted minerals are transferred to smelters or refiners, where chemical refining and processing take place, known as midstream operations, transforming the minerals into fine particles with high purity levels, rendering them suitable for use in the final products. Finally, the refined metals are passed on to downstream actors who incorporate them into the manufacturing process to create the end products (Castillo and Purdy, 2022). Most criticality analyses focus on the country’s concentration of mineral production at the extraction stage, a choice driven primarily by data availability considerations.

In many cases, criticality studies are used to identify which minerals are subject to relatively higher supply risk, thereby distinguishing between different materials and identifying which markets require more vigilant monitoring. Although supplier diversity is generally considered in the literature to be a robust indicator of supply risk, it remains important to determine whether it is effective as a discriminative criterion for classifying different metals and minerals. This is a recurring observation in the literature reviewing criticality methodologies, consistently highlighting the lack of empirical evidence for widely used indicators (Achzet and Helbig, 2013; Frenzel et al., 2017; Helbig et al., 2021).

Only a few studies have highlighted the relevance of the HHI of production in this context, using different methodologies. Buchholz et al. (2022) focus on the largest mines for 12 mineral commodities over 1.5 years. They use big data analytics to investigate how specific risk events disrupt these mines. They analyze the impact of events such as COVID-19 measures taken by different countries and conclude that a global market with few suppliers would be more vulnerable to risk than a market with a large supplier base. However, their conclusion depends largely on their underlying assumption: “the potential impact has been quantified based on the global share of production from mines at risk.” Furthermore, the study only looks at 12 raw materials over a relatively short period of time. Brown (2018), though, shows that assessing supply concentration using only a snapshot index taken at a single point in time may inadequately measure potential supply concentration concerns. Therefore, examining the impact of HHI over such a truncated time period (less than two years) could lead to misleading results. Gleich et al. (2013) assess the relevance of the indicator by examining its impact on raw material prices. This methodology is grounded in the efficient market hypothesis, assuming that prices reflect current and future risks, i.e., economic scarcity, and thus capture a degree of criticality. This approach offers a more comprehensive perspective, encompassing a larger set of metals and minerals (42) over an extended period (26 years). However, the study adopts a time series perspective, considering every material independently. As a result, it cannot demonstrate whether the HHI is a relevant indicator for the entirety of metals and minerals, and thus a suitable means of differentiation.

In the United States, the Federal Trade Commission has established benchmark values, as outlined in their guidelines, to identify markets of concern (Federal Trade Commission, 2006): markets are categorized into three groups based on the HHI—unconcentrated markets (HHI below 1500), moderately concentrated markets (HHI between 1500 and 2500), and highly concentrated markets (HHI above 2500). Mineral criticality studies frequently incorporate the thresholds specified in the American Merger Guidelines when utilizing the HHI to quantify production concentration. This is done in two ways. Firstly, the thresholds are mentioned in the introduction to the analysis, which creates a framing bias for the reader but does not directly affect the results (Al Barazi et al., 2021; Buchholz et al., 2022). Secondly, some studies include these thresholds in their methodology. For instance, in their paper on supply risk for mineral commodities, Schneider et al. (2014) set a threshold for each selected indicator, including the HHI of production, above which supply risk is expected. The supply risk for each resource is then calculated by considering its proximity to this threshold. For the HHI of production, the threshold is set at 1500, in line with the thresholds defined by the US Department of Justice in the Merger Guidelines. Similarly, Rosenau-Tornow et al. (2009) use these thresholds to define their benchmarks for HHI values related to country concentration. However, these thresholds were established in the context of using the HHI as a proxy for the monopolistic structure of an industry, rather than for measuring the redundancy of the trading system, which is a more pertinent criterion in criticality studies. Furthermore, even in the context of mergers, these thresholds have been criticized for being arbitrary (Nocke and Whinston, 2022). The arbitrary nature of thresholds is also emphasized by Brown (2018) within the context of criticality studies. She highlights that the specific level at which the threshold for defining “high concentration” is established can significantly influence the interpretation of results in criticality assessments of minerals.

While the scientific community is generally less inclined towards adopting a sharply defined threshold value for criticality determination, policymakers tend to employ such values since they lead to easily understandable outcomes, as in the case of enumerative inventories of critical raw materials (Schrijvers et al., 2020). Consequently, it is essential to provide empirical evidence to support the validity of such indicators and the relevance of the thresholds used (Brown, 2018).

This paper tackles this crucial issue. Specifically, it aims to empirically assess the validity of a country production concentration indicator for evaluating the supply risk aspect of criticality and to examine whether a threshold exists within the HHI values to assign the criticality of specific non-fuel minerals. We go further than the aforementioned literature since, to the best of our knowledge, no study has assessed the relevance of the HHI of production as an indicator for distinguishing among various metals and minerals, nor has any study empirically attempted to determine an appropriate threshold for utilizing this indicator in the context of criticality studies. Our paper fills these gaps by investigating the impact of the production HHI on metal prices from a panel perspective and seeking to identify the presence of a threshold. To this end, we adopt the approach outlined in Gleich et al. (2013), which attempts to assess the validity of certain indicators, by examining their relationship with raw material prices.

Our results challenge the commonly held assumption that the variation of HHI has a greater impact on prices at higher HHI levels. Additionally, our findings suggest that a clear threshold does not exist to distinguish high-risk markets from less risky ones based on their concentration levels. Therefore, using the HHI as a supply risk indicator, particularly in conjunction with a threshold, may result in underestimating risks in less concentrated markets. Overall, our results contribute to a deeper understanding of metal criticality and provide actionable insights for policymakers and industry stakeholders to mitigate supply risks and ensure the sustainability of the energy transition. In particular, our findings and the associated thresholds offer a framework for policymakers and industry leaders to (i) identify markets where intervention (e.g., strategic stockpiles, diversification of

<footnote n="6">⁶ According to Le Coq and Paltseva (2009), the HHI’s emphasis on the larger suppliers makes it “suited to reflect the risks, associated with the non-diversified energy portfolio.”</footnote>
supply sources, trade policies...) is necessary, (ii) anticipate price and supply risks in metal markets undergoing structural changes, and (iii) develop policies tailored to the degree and nature of concentration and market stability.

The rest of the paper is organized as follows. Section 2 comprehensively describes the HHI data used in the model while Section 3 outlines our chosen models. Section 4 presents and discusses the results, and draws some policy implications. Finally, Section 5 summarizes our main findings.

## 2. The Herfindahl-Hirschman Index (HHI): calculation and stylized facts

### 2.1. HHI calculation

We construct a database that tracks the evolution of the HHI for a set of 63 metals and minerals that are key to today's economy (see Table 8 in Appendix A). The database spans the period from 1994 to 2021 at an annual frequency. To measure these concentrations, we use country-specific production data for these materials. Our primary sources for this purpose are the United States Geological Survey (USGS) and the British Geological Survey (BGS), both recognized as global references for minerals and metals data and statistics.

The USGS publishes an annual report called *The Minerals Yearbook*, which reviews the mineral and metal industries of both the United States and foreign countries. This yearbook comprises statistical data on various metals and minerals and offers information on economic and technical trends. First published in 1933, digital versions have been available on the USGS website since 1996. In the publication for year *i*, the USGS provides data of global primary production by country for a wide variety of raw materials for year *i* – 2. Consequently, we can extract production data from 1994 to 2021. This data availability defines the period of our study. For most materials listed, the data pertains to primary production (extracted from mining operations), while refining data is available for some metals.

Similarly, the BGS maintains its own database on the production and trade of minerals named the *World Mineral Statistic Datasets*. This data is published annually in three reports, including *World Mineral Production*, which contains production statistics, categorized by country, for a range of economically significant mineral commodities, encompassing ferrous and non-ferrous metals, industrial minerals, and hydrocarbons. The first publication of this dataset dates to 1913. While data for some metals are available before 1994, we opt to extract data from 1994 to ensure comparability with the USGS dataset.

While primarily relying on data from the USGS, we use BGS data in cases where USGS data is missing, and it serves as a robustness check for our HHI calculations. The HHI for raw material *m* at stage *s* and year *i* is defined as follows:

$$ \text{HHI}_{m,s,i} = \sum_{c \in P_{m,s}} (S_{c,m,s,i})^2 $$

where:

- $P_{m,s}$ is the set of all countries *c* that produce raw material *m* at stage *s*.

- $S_{c,m,s,i}$ is the share of country *c* in the global supply of the raw material *m* at stage *s* in the specified year *i*, expressed as a percentage.

- *s* corresponds either to mine production, refinery, or smelter activities.

In the USGS reporting, for some raw materials, minor producers are aggregated into the 'Other Country' category, resulting in a combined production denoted as $p_{other}$. In this case, we assume that each country within the 'Other Country' category produces less than the country

with the lowest production ($p_{min}$) among the available data.<fnref n="7" /> Applying this methodology, we obtained HHI data for 63 metals and minerals at various stages of their value chain. Most of these data points represent production concentration at the extraction level, but for certain metals, we also have data on concentration at the refining or smelting stages (see Table 8 in Appendix A).

### 2.2. Stylized facts: trends in HHI over the 1994–2021 period

#### 2.2.1. HHI at the extraction stage

The time evolution of HHI at the extraction stage exhibits diverse patterns across the studied metals and minerals (Fig. 1). Specifically, we observe five distinct categories of HHI trends. First, certain metals and minerals exhibit continuous HHI growth, indicating a rising market dominance over time. Second, another group maintains relatively stable HHI values, pointing to a consistent market share throughout the years. Third, some raw materials experience a decreasing trend in HHI, implying increased competition between countries within their respective markets. Fourth, there are cases where materials initially undergo growth before experiencing a subsequent decline. Fifth, conversely, we find instances where materials exhibit the reverse pattern, initially declining before witnessing growth.

In the period under study, most HHI series exhibit an increasing trend (40% of the analyzed series) indicating a concentration of primary production for a significant number of metals and minerals over the past two decades. This intensification in concentration occurs at varying rates, with the HHI for silver increasing only by 13 points per year on average, while for gallium,<fnref n="8" /> the rise amounts to over 400 HHI points annually (Table 1). Several factors contribute to this phenomenon, including geological considerations as countries possess differing mineral endowments and prioritize the extraction of highly concentrated ores. For instance, the Democratic Republic of the Congo (DRC) is a prominent cobalt producer due to its possession of nearly half of the world's cobalt reserves (USGS, 2023). Economies of scale and expertise are additional drivers of production concentration. Lastly, environmental, and social regulations (ecological and social dumping) can also lead to significant concentration in the production of certain metals.

A sustained decrease in HHI over the same period is relatively rare, representing only 16% of the studied series. Notably, this subset comprises gold, palladium, and platinum, three metals categorized as precious metals.<fnref n="9" /> This can be attributed to consistently high prices that make extraction profitable, even when deposits are not highly concentrated. For instance, artisanal and small-scale gold mining, which contributes to about 20% of global production and operates in 80 countries (Kumah, 2022), plays a role in lowering the gold HHI value. Some minerals such as talc, kaolin, bentonite, and gypsum, also exhibit a sustained decrease in HHI. In these cases, the decreasing trend can be explained by their large and well-distributed resources among various producing countries, contributing to a more balanced concentration of production across the globe (USGS, 2023). In 16% of cases, the HHI series display a pattern of growth followed by a subsequent decline over time. Notably, when we examine the leading producer of these materials at the point where the HHI reaches its maximum before decreasing, China emerges as the predominant producer in the majority of cases (Table 2). Also, the decline in HHI is often attributed to either a governmental decision to reduce production, typically in response to curbing domestic pollution, or a significant natural disaster that necessitated a substantial reduction in production.

<footnote n="7">⁷ All the details, as well as robustness checks, are provided in Appendix A.</footnote>

<footnote n="8">⁸ Gallium data is available only for the period 2007–2021.</footnote>

<footnote n="9">⁹ Silver is the only element in the precious metals category within our dataset that does not exhibit a declining HHI; nevertheless, as previously mentioned, its growth remains sluggish.</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Trends in production concentration: Evolution of the Herfindahl-Hirschman Index (HHI) at the extraction stage over the 1994–2021 period.</figcaption></figure>

Note: These graphs illustrate the evolution of the HHI values calculated at the mining stage for key metals and minerals from 1994 to 2021. Higher HHI values indicate greater production concentration. Data sources: USGS and BGS (see Section 2.1).

Antimony serves as a pertinent case study exhibiting a decreasing HHI from the period of 2008–2010 onwards. Classified as a metalloid, antimony plays a crucial role as an alloying element in the production of flame retardants, lead-acid batteries, and semiconductors. The reduction in HHI for antimony is explicitly linked to China’s pivotal position as the world’s leading antimony producer since the early 1980s.

A government-driven decision to curtail antimony mining operations in 2010, in response to environmental concerns and safety issues, significantly contributed to this decline (USGS, 2023). Given China’s dominance, accounting for nearly 90% of global antimony production at the time, the production disruptions led to a substantial price surge in 2011. Similarly, the decline in HHI for lead, tin, REEs, and molybdenum
<figure><img src="image_5.png" /><figcaption>Fig. 1. (continued).</figcaption></figure>

<table><caption>**Table 1**

Trends in production concentration: Regression coefficients for metals and minerals (1994–2021).</caption><thead><tr><th>Raw material</th><th>Regression coefficient</th><th>Trend</th><th>Raw material</th><th>Regression coefficient</th><th>Trend</th></tr></thead><tbody><tr><td>tantalum</td><td>-146.281</td><td>Decreasing</td><td>phosphate-rock</td><td>45.737</td><td>Increasing</td></tr><tr><td>kaolin</td><td>-69.571</td><td>Decreasing</td><td>lithium</td><td>61.131</td><td>Increasing</td></tr><tr><td>platinum</td><td>-54.949</td><td>Decreasing</td><td>fluorspar</td><td>62.978</td><td>Increasing</td></tr><tr><td>palladium</td><td>-32.278</td><td>Decreasing</td><td>tungsten</td><td>64.060</td><td>Increasing</td></tr><tr><td>zirconium</td><td>-27.161</td><td>Decreasing</td><td>wollastonite</td><td>102.845</td><td>Increasing</td></tr><tr><td>talc</td><td>-22.322</td><td>Decreasing</td><td>asbestos</td><td>109.864</td><td>Increasing</td></tr><tr><td>gold</td><td>-20.033</td><td>Decreasing</td><td>graphite</td><td>129.243</td><td>Increasing</td></tr><tr><td>bentonite</td><td>-12.414</td><td>Decreasing</td><td>cobalt</td><td>131.806</td><td>Increasing</td></tr><tr><td>gypsum</td><td>-6.788</td><td>Decreasing</td><td>germanium</td><td>142.685</td><td>Increasing</td></tr><tr><td>silver</td><td>13.809</td><td>Increasing</td><td>yttrium</td><td>167.491</td><td>Increasing</td></tr><tr><td>niobium</td><td>20.059</td><td>Increasing</td><td>silicon</td><td>171.143</td><td>Increasing</td></tr><tr><td>manganese</td><td>24.751</td><td>Increasing</td><td>magnesite</td><td>183.807</td><td>Increasing</td></tr><tr><td>iron</td><td>29.663</td><td>Increasing</td><td>mercury</td><td>251.764</td><td>Increasing</td></tr><tr><td>zinc</td><td>31.527</td><td>Increasing</td><td>magnesium</td><td>265.179</td><td>Increasing</td></tr><tr><td>uranium</td><td>33.052</td><td>Increasing</td><td>gallium</td><td>414.387</td><td>Increasing</td></tr><tr><td>vanadium</td><td>38.926</td><td>Increasing</td><td></td><td></td><td></td></tr></tbody></table>

Note: This table presents the linear regression coefficients calculated for the HHI data of raw materials that exhibit a monotone HHI trend throughout the specified period (Fig. 1). Metals and minerals are arranged in ascending order based on their regression coefficients. Most of these trends show an upward trajectory, and the rate at which the HHI evolves varies significantly among the different elements studied.
<table><caption>**Table 2**
HHI peak year and leading producer market share: Key producer market dominance before declining concentration.</caption><thead><tr><th>Raw material</th><th>Year of max HHI</th><th>First producer country</th><th>Market share</th><th>Regression coefficient</th></tr></thead><tbody><tr><td>REE</td><td>2010</td><td>China</td><td>97.7</td><td>-550</td></tr><tr><td>antimony</td><td>2008</td><td>China</td><td>91.3</td><td>-399</td></tr><tr><td>arsenic</td><td>2011</td><td>China</td><td>66.6</td><td>-168</td></tr><tr><td>barite</td><td>2008</td><td>China</td><td>57.1</td><td>-108</td></tr><tr><td>beryllium</td><td>2014</td><td>USA</td><td>93.1</td><td>-440</td></tr><tr><td>copper</td><td>2006</td><td>Chile</td><td>35.5</td><td>-32</td></tr><tr><td>lead</td><td>2013</td><td>China</td><td>52.8</td><td>-114</td></tr><tr><td>strontium</td><td>2011</td><td>China</td><td>50.7</td><td>-119</td></tr><tr><td>tin</td><td>2011</td><td>China</td><td>49.2</td><td>-113</td></tr></tbody></table>

Note: This table presents the years of peak HHI values and the corresponding market share of the leading producer country. The ‘Year of max HHI’ column indicates the specific year when the Herfindahl–Hirschman Index reaches its highest value before starting to decrease. The ‘Market Share’ represents the proportion of production held by the leading producer country in that specific year.

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Global distribution of primary resource producers: Leading country by commodity count (1994–2021).</figcaption></figure>

Note: This figure displays the global distribution of primary resource producers, highlighting the countries dominating production across different materials over the period 1994–2021. It presents the number of primary commodities within our panel, for which each country holds the position of the leading producer at the upstream stage. Only countries leading in at least 3 commodities are individually listed, while all others are grouped under the ‘Other’ category based on their respective continents. This analysis is based on the raw mineral production data from the USGS and BGS datasets presented in Section 2.1.

in the 2010s can be attributed to production curtailments implemented as part of an environmental clean-up initiative led by Beijing (USGS, 2023). Additionally, the decline in HHI for REEs, starting in 2010, is also linked to China’s export restrictions on these elements, justified as a measure to conserve resources and protect the environment. This policy shift resulted in a substantial price surge for REEs in international markets, sparking increased investments in rare earth developments outside China. Consequently, despite China’s production rebound from 2016 onwards, the country’s market share declined due to growing exploitation in other regions of the world, which contributed to the rapid decrease in REE’s HHI since 2010 at a rate of –550 points per year (Table 2). The reduction in barite’s HHI is also attributed to the decrease in China’s production, although in this case, it is not due to a governmental decision but rather the result of extreme climatic conditions that significantly impacted Chinese production from 2009 to 2011. Coupled with increased fuel costs and robust global demand for barite, these circumstances led to a sharp increase in prices for Chinese barite. Consequently, the higher prices encouraged the entry of new players into the barite mining sector, particularly India, which resulted in a sustained decline in HHI (USGS, 2023).

Since the 1990s, a select group of countries have emerged as major players in primary resource production, dominating the supply of essential materials. Notably, China’s role as a significant producer experienced substantial growth from the 2010s onwards, leading to a shift in the dynamics at the expense of the United States. By 2009, China had claimed the top position as the leading producer of over half of all metals and minerals in our panel (Fig. 2). This shows that we have not only observed an increase in the concentration of global production for various commodities, but also a significant overall concentration of resources within China. However, despite China’s continued dominance

as a primary resource producer, there has been a decline in its market share since 2012, reflecting the impact of environmental policies implemented by the government (Fig. 3).<fnref n="10" /> Also, contextualizing Chinese production in relation to its consumption is essential as China is both the primary producer of metals and minerals and the largest consumer of these commodities (Frenzel et al., 2017).

### 2.2.2. HHI at the smelting stage

The concentration of smelter production for aluminum, copper, and tin exhibits an upward trend over the studied period (Fig. 4). In all three cases, the rise in HHI can be attributed to the expanding influence of the Chinese market on total production. China emerged as the leading player in tin smelting as early as 1993, with its market share steadily growing over time (Bonnet et al., 2022). Similarly, for aluminum and copper, China became the top producer in 2001 and 2004, respectively, leading to a noticeable shift in the HHI curves, coinciding with the moment when the country attained the position of the primary producer with an increasingly dominant market share.

### 2.2.3. HHI at the refinery stage

Likewise, the HHI series at the refinery stage for all metals with available refining data (metals shown in Fig. 5) exhibit an increasing trend. Notably, this upward trajectory in HHI values is consistently attributed to China’s production activities, signifying its progressive dominance in the refining processes of these metals.

<footnote n="10">¹⁰ The rationalization of industrial activities in China since 2010 should also be mentioned, with a wish to eliminate small actors for better control activities (Hache, 2019).</footnote>
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Market share dynamics: Total maximum production shares of top producers by country (1994–2021).</figcaption></figure>

Note: The graph displays the sum of the maximum market shares, representing the market share held by the first producer of each commodity, for each respective country. This analysis is based on the raw mineral production data from the USGS and BGS datasets presented in Section 2.1.

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Concentration dynamics: HHI evolution for selected materials at the smelting stage (1994–2021).</figcaption></figure>

Note: These graphs illustrate the evolution of concentration at the smelting stage. The HHI values reflect the degree of production concentration over time. Data sources: USGS and BGS (see Section 2.1).

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Concentration dynamics: HHI evolution for selected materials at the refinery stage (1994–2021).</figcaption></figure>

Note: These graphs illustrate the evolution of concentration at the refinery stage. The HHI values reflect the degree of production concentration over time. Data sources: USGS and BGS (see Section 2.1).
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Relationship between concentration and total annual production (1994–2021).</figcaption></figure>

Note: This plot depicts the relationship between concentration (HHI) and total annual production of the metals and minerals included in our panel. Total annual production is expressed in logarithmic terms and measured in metric tons of metal or mineral content per year.

It is noteworthy to compare the HHI values between the upstream and midstream stages.<fnref n="11" /> Taking copper and tin as examples, the concentration of production at the extraction stage has been decreasing for over 15 years, while the concentration at the refining stage is increasing. This dynamic is primarily driven by China's growth in the refining sector, even though China's tin extraction is declining. Regarding cobalt, both the extraction and refining HHIs show a comparable increasing trend, but the primary producer differs. The DRC dominates cobalt extraction, while China refines over 76% of global cobalt production in 2021. This reflects China's determination to secure its supplies and assert its hegemony in the global resources market. It also underscores its aim to move up the value chain and capture additional value downstream from ore, a sentiment echoed by many resource-producing countries. Notably, many countries have begun to restrict the export of unprocessed minerals. Indonesia banned the export of raw nickel ore in 2020 and has been followed by several lithium-rich African countries, including Ghana, Namibia, and Zimbabwe. The primary goal of these nations is to encourage investments in on-site ore processing, with a long-term objective of developing batteries within their territories. The Chinese dominance in the permanent magnet market is a successful example of value chain ascent, spanning from mining to the development of final technology. In his work, Pitron (2018) describes the Chinese strategy, starting with establishing a dominant position in rare earth mining and refining, and later assimilating foreign expertise in permanent magnet production.

## 2.3. Concentration as a function of total production

When examining the relationship between mining production concentration and total raw material production within the panel, we observe a negative relationship in the pooled regression. This implies that as the total quantity of mined mineral increases, its production concentration decreases. This initial finding suggests that metals or minerals produced in larger quantities tend to be shared among a greater number of actors. However, when we consider the individuality

of each metal and conduct a within-panel regression, the coefficient of regression between HHI and global production is positive (Fig. 6). This aligns with the earlier qualitative analysis, where we observed that the HHI of metals and minerals extraction generally shows a growing trend over time, while the production of metals and minerals also generally increases through time. As a result, we would expect to find a positive relationship between HHI and production.<fnref n="12" />

# 3. Data and methodology

Our analysis focuses on evaluating the HHI of a country's production concentration as a reliable indicator for measuring supply risk, specifically in distinguishing between different materials. Furthermore, we aim to analyze the presence of a distinct threshold in the HHI values for assigning the criticality of particular metals. Based on the hypothesis that metal prices can indicate to some degree their criticality (Gleich et al., 2013; Stepanek et al., 2013), we rely on a panel regression analysis to examine the impact of HHI on metal prices. The use of a panel data framework provides the significant advantage of working with a sizable dataset, thereby enhancing the statistical robustness of our findings. Furthermore, it is necessary to rely on a panel data approach because using a single metal's HHI values over time is insufficient for determining a consistent threshold due to their limited variability.

## 3.1. Data

Our dependent variable is the annual price of metals. Metal prices are measured in US dollars per metric ton and have been sourced from the USGS.<fnref n="13" /> Note that the prices reflect rates in the United States, serving as a representative estimate for the average cost of these raw materials in the country. As stated in the IRENA report (IRENA, 2023), not all metals and minerals have a fully global market presence. Nevertheless, after thoroughly comparing the USGS-derived prices with metal market rates obtained from alternative sources, a remarkable level of

<footnote n="11">¹¹ Given the proximity of HHI values between smelting and refining data, we can combine these two categories in the analysis. Although there is a slight difference for copper and tin, where the refining data accounts for secondary production, this has a negligible impact on the overall HHI.</footnote>

<footnote n="12">¹² In this analysis, we have excluded chromium from our panel due to data inconsistency, as its production data is expressed in gross weight rather than element content. To ensure consistency, we have retained only elements with production data expressed in element content.</footnote>

<footnote n="13">¹³ Data sources for all series are provided in Appendix D (Table 12).</footnote>
similarity is observed. The differences between these price series, on a median basis, tend to hover around a modest 3%, and their variations exhibit an even narrower median difference of approximately 0.3%. Detailed statistics are available in Appendix B (Table 10). Based on this empirical evidence, it is reasonable to consider the metal prices under examination as indicative of global market prices. However, this assumption cannot be uniformly applied to minerals such as salt, talc, and asbestos due to the lack of comprehensive global price data. Consequently, minerals have been excluded from the subsequent econometric analysis. This choice can also be justified by the fact that metals are more relevant than minerals in low-carbon technologies which deserve particular attention.<fnref n="14" /> Overall, our (unbalanced) panel is composed of 33 metals over the 1995–2021 period, corresponding to a total of 821 observations (see the list and descriptive statistics in Appendix C - Table 11). Following the common practice in the literature that examines commodity prices (Akram, 2009; Issler et al., 2014; Rubaszek et al., 2020), the metal prices have been transformed into real prices by deflating them by the US consumer price index (CPI).

The explanatory variable is the country HHI computed at the mine production level, presented in detail in the previous section.

Turning to the control variables, we use the five variables most found in the literature that investigates the dynamics of metal prices and, more generally, commodity prices. First, we consider the real price of Brent crude oil, which exerts its influence on metal prices through two primary channels.<fnref n="15" /> On the one hand, oil can be regarded as a proxy for global economic growth, thus impacting metal prices through its effect on demand. This relationship is supported by the literature, which indicates that commodities used as inputs in the production process typically escalate during periods of strong global economic activity (Erten and Ocampo, 2013). This is notably the case for metals used in sectors such as manufacturing, transportation, and energy. On the other hand, the extraction and refining processes of metals require a significant amount of energy, predominantly derived from fossil fuels. In the literature, this energy demand is estimated to account for 5% to 10% of the global primary energy supply (Aramendia et al., 2023). Therefore, fluctuations in oil prices have an impact on the production costs of metals, creating potential cost-push effects on metal prices (Akram, 2009; Lombardi et al., 2012).

Second, fluctuations in the US dollar can also act as a driver of metal prices. Since metals are commonly traded in US dollars, a depreciation of the US currency leads to a lower price for importers. Consequently, importers' demand for metals increases, ultimately resulting in higher prices. Conversely, when the US dollar appreciates, it becomes costlier for importers to purchase metals, leading to potentially reduced demand and lower commodity prices (Akram, 2009). We use the broad US dollar real effective exchange rate from the FRED database.

Third, metals and minerals are fundamental inputs in industrial production. For instance, strategic metals like cobalt, lithium, and REE are essential for producing electronics, vehicles, and renewable energy technologies. As previously mentioned, the rise in industrial production related to renewable energy infrastructure and electric vehicles has strongly intensified demand for critical metals. Therefore, an increase in industrial production triggers higher consumption of metals and minerals, which, in turn, has an impact on their prices. To capture this relationship as an explanatory variable, we rely on US real manufacturing and trade industries sales, which measures the combined value of the manufacturing, wholesale trade and retail trade industries. This

is an indicator of whether production is increasing or decreasing, thus providing insights into the evolution of global economic activity and, in turn, the demand for strategic metals.<fnref n="16" />

Fourth, mineral and metal prices can also be influenced by short-term interest rates. Frankel (2008) presents the theoretical link between interest rates and commodity prices, demonstrating a negative relationship between them. This negative correlation can be attributed to several factors. Firstly, interest rates influence metal markets through investment dynamics. A lower interest rate encourages a shift in investments from financial markets to commodity assets as it reduces the opportunity cost of holding non-yielding assets like metals. Then, it increases the incentive to hold inventories due to reduced carrying costs and diminishing the motivation for early extraction of exhaustible commodities. Low interest rates indeed reduce storage costs, increasing stockpiling behavior and stimulating demand for strategic metals. These combined effects lead to an increase in metal demand and a decrease in metal supply, ultimately resulting in higher commodity prices. We use the US LIBOR rate as a proxy for the US interest rate, as in Akram (2009).

Fifth, the influence of uncertainty on metal prices has been widely explored in the literature. Uncertainty can impact metal prices by amplifying the effects of an economic recession, as global economic growth is a key driver of commodity prices. Moreover, heightened uncertainty may induce increased risk aversion among investors, leading to a rise in the desired risk premium, subsequently hampering investment prospects (Byrne et al., 2013; Chen et al., 2022). Investors may shift from industrial metals to safer assets, lowering demand for strategic materials. As geopolitical events tend to generate uncertainty, they can create supply chain shocks for metals, leading to price volatility. The volatility index (VIX) traded in the Chicago Board Options Exchange can be used to proxy uncertainty, as a measure of the implied volatility of S&P 500 index options and reflects the uncertainty of the stock market.

Finally, the ore concentration is often cited as one of the primary factors influencing production costs, which, in turn, can ultimately impact metal prices. However, several studies have shown that there is no direct link between resource scarcity and market prices, indicating that current market prices are not reliable indicators of resource depletion (Seyhan et al., 2012; Henckens et al., 2016). Vidal (2021) explains this phenomenon by highlighting that technological innovation has thus far offset the decline in mineral concentration. As a result, we do not consider the concentration of minerals in deposits as an explanatory variable in our model.

With the exception of the interest rate, all series are transformed into first-logarithmic differences to ensure stationarity.<fnref n="17" />

<footnote n="14">¹⁴ Additionally, none of the parameters obtained from the panel regression exclusively conducted on mineral data attains statistical significance.</footnote>

<footnote n="15">¹⁵ The Brent crude oil price benchmark was chosen over the WTI because it is the world's most important crude oil benchmark, responsible for pricing nearly 70% of globally traded crude oil (Imsirovic and Chapman, 2022). As shown in Appendix G, using WTI leads to similar results, illustrating the robustness of our findings to the choice of the oil price series.</footnote>

<footnote n="16">¹⁶ Other variables exist such as the shipping freight cost (Baltic Dry Index). This index reflects shipping rates for major raw materials, and serves as a gauge of global demand for minerals and metals, providing insights into the overall economic activity. Another usual variable is the industrial production index of OECD, China, Brazil, India, and Russia, measuring the output of industrial sectors in the respective countries. In the present study, we have selected the US real manufacturing and trade industries sales as the proxy for industrial production because it exhibits the highest significance in our model.</footnote>

<footnote n="17">¹⁷ We used the second-generation unit root test for panel data proposed by Demetrescu et al. (2006) that allows for cross-dependence across the panel units. We applied this test to the price series and HHI series, which are the only ones that vary according to the *N* individuals of the panel (metals). The remaining variables depend solely on the time section of the panel. This test is a modification of Choi's inverse-normal combination test that can be used when the *N* p-values are not independent. The results, reported in Appendix E Table 13, show that the logged price series cannot be considered stationary, as the test fails to reject the null at a 10% significance level. The outcomes for the logged HHI series are dependent on the chosen specification, yet the test never displays significance at the 5% level.</footnote>
## 3.2. Panel regressions

To address our research questions, we consider four panel regression models:

### Model 1

$$ \Delta \ln price_{i,t} = \alpha_i + \beta_1 \Delta \ln HHI_{i,t} + \beta_2 \Delta \ln oil_t + \beta_3 \Delta \ln er_t + \beta_4 ir_t + \beta_5 \Delta \ln vix_t + \beta_6 \Delta \ln is_t + \epsilon_{i,t} \quad (1) $$

### Model 2

$$ \Delta \ln price_{i,t} = \alpha_i + \beta_{11} \Delta \ln HHI_{i,t} + \beta_{12} I_{HHI_{i,t}} + \beta_{13} \Delta \ln HHI_{i,t} * I_{HHI_{i,t}} + \beta_{2} \Delta \ln oil_t + \beta_{3} \Delta \ln er_t + \beta_{4} ir_t + \beta_{5} \Delta \ln vix_t + \beta_{6} \Delta \ln is_t + \epsilon_{i,t} \quad (2) $$

### Model 3

$$ \Delta \ln price_{i,t} = \alpha_i + \beta_{11} \Delta \ln HHI_{i,t} + \beta_{12} I_{\Delta \ln HHI_{i,t}} + \beta_{13} \Delta \ln HHI_{i,t} * I_{\Delta \ln HHI_{i,t}} + \beta_{2} \Delta \ln oil_t + \beta_{3} \Delta \ln er_t + \beta_{4} ir_t + \beta_{5} \Delta \ln vix_t + \beta_{6} \Delta \ln is_t + \epsilon_{i,t} \quad (3) $$

### Model 4

$$ \Delta \ln price_{i,t} = \alpha_i + \beta_{11} \Delta \ln HHI_{i,t} + \beta_{12} I_{HHI_{i,t}} + \beta_{122} I_{\Delta \ln HHI_{i,t}} + \beta_{131} \Delta \ln HHI_{i,t} * I_{HHI_{i,t}} + \beta_{132} \Delta \ln HHI_{i,t} * I_{\Delta \ln HHI_{i,t}} + \beta_{14} \Delta \ln HHI_{i,t} * I_{HHI_{i,t}} * I_{\Delta \ln HHI_{i,t}} + \beta_{2} \Delta \ln oil_t + \beta_{3} \Delta \ln er_t + \beta_{4} ir_t + \beta_{5} \Delta \ln vix_t + \beta_{6} \Delta \ln is_t + \epsilon_{i,t} \quad (4) $$

The variable price$_{i,t}$ represents the price of metal i at time t, while HHI$_{i,t}$ denotes the corresponding country HHI computed at the mine production level. The variables oil$_{i,t}$, er$_{i,t}$, vix$_{i,t}$, ir$_{t}$ and is$_{t}$ represent the oil price, exchange rate, VIX index, interest rate, and industries sales, respectively, at time t, all independent of i. The constant vector α$_{i}$ reflects the unobserved effects. The random error terms are denoted by ϵ$_{i,t}$ . Model (1) simply examines the effect of a change in HHI on the metal price. In the other models, two dummy variables are introduced: I$_{HHI_{i,t}}$ takes the value of 0 when HHI$_{i,t}$ is below a certain threshold and 1 otherwise. Similarly, I$_{Δln HHI_{i,t}}$ is derived from the absolute value of Δln HHI$_{i,t}$. Mathematically, this is expressed as:

$$ I_{HHI_{i,t}} = \begin{cases} 0 & \text{if } HHI_{i,t} < t_{HHI} \\ 1 & \text{if } HHI_{i,t} \ge t_{HHI} \end{cases} \quad \text{with } t_{HHI} \in [0, 10000] \quad (5) $$

$$ I_{\Delta \ln HHI_{i,t}} = \begin{cases} 0 & \text{if } |\Delta \ln HHI_{i,t}| < t_{\Delta \ln HHI} \\ 1 & \text{if } |\Delta \ln HHI_{i,t}| \ge t_{\Delta \ln HHI} \end{cases} \quad \text{with } t_{\Delta \ln HHI} \in [0, 1] \quad (6) $$

Incorporating these variables into Eqs. (2) to (4) enables differentiation of the effects of an HHI variation on prices based not only on the HHI level but also on the magnitude of this variation. In Model (2) we include the interaction dummy variable I$_{HHI_{i,t}}$ alongside Δln HHI$_{i,t}$, in order to explore the interplay between the level of the HHI and the fluctuation of the HHI on price changes. Similarly, within Eq. (3), a corresponding investigation is made by including the dummy variable I$_{Δln HHI_{i,t}}$. The latter represents the absolute value of the annual HHI variation and aims to capture the impact of pronounced HHI fluctuations. In Model (4), we take into account the interaction of the three variables: Δln HHI$_{i,t}$, I$_{HHI_{i,t}}$, and I$_{Δln HHI_{i,t}}$, which enables us to examine how a metal price responds to changes in HHI, considering the extent of the variation and HHI's level. This specification outlines four regimes as detailed in Table 3.

Moreover, the inclusion of the dummy variable I$_{HHI_{i,t}}$ can provide evidence of the existence of a threshold within the HHI values. Instead of arbitrarily fixing a threshold value as in most of the previous literature, we check all the possible thresholds by performing a loop over

<table><caption>**Table 3**
Metal price responses to changes in HHI: Metal price fluctuation regimes delineated in Model (4).</caption><thead><tr><th>I<sub>HHI<sub>i,t</sub></sub></th><th>HHI level</th><th>I<sub>ΔlnHHI<sub>i,t</sub></sub></th><th>HHI variation</th><th>Model parameters</th><th>Regime effect</th></tr></thead><tbody><tr><td>0</td><td>Low</td><td>0</td><td>Low</td><td>β<sub>11</sub></td><td>β<sub>low,low</sub></td></tr><tr><td>0</td><td>Low</td><td>1</td><td>High</td><td>β<sub>11</sub> + β<sub>132</sub></td><td>β<sub>low,high</sub></td></tr><tr><td>1</td><td>High</td><td>0</td><td>Low</td><td>β<sub>11</sub> + β<sub>131</sub></td><td>β<sub>high,low</sub></td></tr><tr><td>1</td><td>High</td><td>1</td><td>High</td><td>β<sub>11</sub> + β<sub>131</sub> + β<sub>132</sub> + β<sub>14</sub></td><td>β<sub>high,high</sub></td></tr></tbody></table>

Note: Model (4) delineates four regimes based on the levels and variations of HHI. The effect of HHI variations on prices for each regime is captured by the parameters of Eq. (4) in the 'Model parameters' column. The overall name for these parameters is provided in the 'Regime effect' column.

the values of the variable t$_{HHI}$, ranging from 0 to 10,000. Differences in the results based on the value of t$_{HHI}$ could be a positive indication of a threshold. The chosen value would be the one leading to the most empirically significant results. This method leads us to select a threshold value equal to 2700. This value corresponds to a market that is quite highly concentrated, such as those of cobalt and lithium. The same method is applied to the dummy variable I$_{Δln HHI_{i,t}}$, resulting in a value of 0.1, which corresponds to a 10% change in HHI.<fnref n="18" />

In this analysis, we did not use a dynamic model because the results did not show significance when incorporating the lagged endogenous variable (see Appendix G). Similarly, the outcomes lack significance when accounting for the lagged variable of interest (Δln HHI$_{i,t}$$_{−}$$_{1}$). However, the issue of endogeneity is not a substantial concern within the scope of our econometric model due to several factors. Mining, the first stage in the value chain of metal production, depends on external factors unrelated to the price of raw materials. These factors include the mining endowment of the producing country and prevailing environmental and social regulations. Moreover, the start of mine operations is primarily a government decision driven by sovereignty considerations rather than economic concerns. In addition, although mining investment is highly correlated with metal prices, its effect on production and, consequently, on the HHI, may take several years to materialize. According to IEA (2021), the average lead time from discovery to production is about 17 years. The period from discovery through exploration to feasibility accounts for most of this time, with the remaining period (construction planning and construction to production) averaging about 4.5 years.

# 4. Empirical results, discussion, and policy implications

## 4.1. Results

Table 4 presents the results of the four regression models considered, estimated for the thresholds set at t$_{HHI}$ = 2700 and t$_{Δln HHI}$ = 0.1. Before discussing our main variables of interest, let us briefly comment on the control variables.

The significant and positive correlation between oil and metal prices underscores the cost-driven nature of the extraction and refining processes—a result that acts in favor of the transition towards renewable energy within mining operations to mitigate cost volatility. As expected, the positive link between industrial production and metal prices confirms the strategic importance of these materials in global economic activity, particularly in growth sectors like renewable energy and electric vehicles. Exchange rate fluctuations also appear as significant drivers of metal prices, pointing to the interconnectedness of global trade and—to a lesser extent—financial systems with metal markets.

<footnote n="18">¹⁸ Although the Panel Smooth Regression Model specification would have been an interesting alternative approach at a first sight, it cannot be implemented in our context as demonstrated in Appendix H.</footnote>
<caption>**Table 4**</caption>

Estimation results of fixed-effects regressions: Impact of concentration and control variables on metal prices.

<table><thead><tr><th></th><th>Model 1</th><th>Model 2</th><th>Model 3</th><th>Model 4</th></tr></thead><tbody><tr><td>Δ ln HHI<sub>t,t</sub></td><td>-0.04<br>(0.09)</td><td>0.04<br>(0.12)</td><td>-0.38<br>(0.24)</td><td>-0.75**<br>(0.31)</td></tr><tr><td>Δ ln oil<sub>t</sub></td><td>0.14**<br>(0.07)</td><td>0.14**<br>(0.07)</td><td>0.14**<br>(0.06)</td><td>0.14**<br>(0.06)</td></tr><tr><td>Δ ln er<sub>t</sub></td><td>-1.70***<br>(0.35)</td><td>-1.70***<br>(0.36)</td><td>-1.69***<br>(0.35)</td><td>-1.71***<br>(0.36)</td></tr><tr><td>Δ ln is</td><td>0.89***<br>(0.31)</td><td>0.88***<br>(0.32)</td><td>0.89***<br>(0.31)</td><td>0.88***<br>(0.31)</td></tr><tr><td>Δ ln vix<sub>t</sub></td><td>0.02<br>(0.04)</td><td>0.01<br>(0.04)</td><td>0.02<br>(0.04)</td><td>0.02<br>(0.04)</td></tr><tr><td>ir<sub>t</sub></td><td>-0.00<br>(0.01)</td><td>-0.00<br>(0.01)</td><td>-0.00<br>(0.01)</td><td>-0.00<br>(0.01)</td></tr><tr><td>I<sub>HHI,t</sub></td><td></td><td>-0.01<br>(0.03)</td><td></td><td>-0.00<br>(0.04)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>HHI,t</sub></td><td></td><td>-0.12<br>(0.18)</td><td></td><td>0.70<br>(0.48)</td></tr><tr><td>I<sub>Δln HHI,t</sub></td><td></td><td></td><td>-0.03<br>(0.02)</td><td>-0.01<br>(0.04)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub></td><td></td><td></td><td>0.41<br>(0.26)</td><td>0.95***<br>(0.34)</td></tr><tr><td>I<sub>Δln HHI,t</sub> * I<sub>Δln HHI,t</sub></td><td></td><td></td><td></td><td>-0.02<br>(0.05)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub> * I<sub>Δln HHI,t</sub></td><td></td><td></td><td></td><td>-0.96*<br>(0.52)</td></tr><tr><td>Num. obs.</td><td>821</td><td>821</td><td>821</td><td>821</td></tr></tbody></table>

Note: The dependent variable is the log differentiated prices of metals Δln price. The variables Δln oil, Δln er, Δln vix, and Δln is denote the variation rate of oil price, exchange rate, VIX index, and Industries sales, respectively. *ir* denotes the US interest rate. Δln HHI is the variation rate of the country metal production concentration and I<sub>HHI</sub> and I<sub>Δln HHI</sub> are the dummy variables computed for the threshold values of t<sub>HHI</sub> = 2700 and t<sub>Δln HHI</sub> = 0.1. These thresholds are chosen according to the methodology presented in the previous section, and the decision relies on the results presented in Appendix F. To provide consistent results, we apply the Newey and West robust covariance estimators, the corresponding standard errors are in parentheses.

In the first panel regression model, the HHI has no impact on price dynamics. This is also the case in Models (2) and (3). Furthermore, the interaction terms in both models are not significant; a result which remains consistent regardless of the considered threshold (see Figs. 7 and 8 in Appendix F).<fnref n="19" /> The most interesting findings concern Model (4). Indeed, the parameters associated with Δln HHI<sub>t,t</sub>, Δln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub>, and Δln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub> * I<sub>Δln HHI,t</sub> are statistically significant at conventional confidence levels. Based on this finding, to examine the impact of metal production concentration on their prices, it is essential to consider both the HHI level and the extent of HHI variation. In this context, the estimated value of the parameter β<sub>11</sub> related to the variable Δln HHI<sub>t,t</sub> is negative (−0.75). This implies that for HHI values below 2700 and for HHI fluctuations below 10%, HHI fluctuations and commodity price fluctuations have an inverse relationship. The estimated parameter value associated with the interaction variable Δln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub> is positive and greater than the absolute value of the preceding parameter (β<sub>11</sub> + β<sub>132</sub> = 0.2). This suggests that when the HHI is below 2700 and the HHI variation is above 10%, the HHI variation has a positive effect on price variation. The estimated parameter value associated with the interaction variable Δln HHI<sub>t,t</sub> * I<sub>Δln HHI,t</sub> is also positive but lower than the absolute value of the first parameter (β<sub>11</sub> + β<sub>131</sub> = −0.05). However, it is not statistically significant at conventional confidence levels (pvalue = 14%). Finally, the parameter

<caption>**Table 5**</caption>

Impact of HHI fluctuations on metal prices by HHI level and variation magnitude.

<table><thead><tr><th></th><th>low</th><th>Low</th><th>High</th><th>High</th></tr></thead><tbody><tr><td>HHI level</td><td>Low</td><td>Low</td><td>High</td><td>High</td></tr><tr><td>HHI variation</td><td>Low</td><td>High</td><td>Low</td><td>High</td></tr><tr><td>parameter</td><td>β<sub>low,low</sub></td><td>β<sub>low,high</sub></td><td>β<sub>high,low</sub></td><td>β<sub>high,high</sub></td></tr><tr><td>effect on price</td><td>-0.75</td><td>0.2</td><td>-0.05</td><td>-0.06</td></tr></tbody></table>

Note: This table summarizes the results of Model (4), with t<sub>HHI</sub> = 2700 and t<sub>Δln HHI</sub> = 0.1.

linked to the variable Δln HHI<sub>t,t</sub> * I<sub>HHI,t</sub> * I<sub>Δln HHI,t</sub> is significant and the overall effect of HHI variation when the HHI is above 2700 and the HHI variation exceeds 10% is captured by: β<sub>11</sub> + β<sub>131</sub> + β<sub>132</sub> + β<sub>14</sub> = −0.06. Therefore, in that case, the HHI variation has a negative impact on price variation. Additionally, we observe that the effect of HHI on prices is more pronounced for lower HHI levels, where a 1-point HHI variation results in a price change of either 0.2 points or 0.75 points, depending on the magnitude of the variation.

Table 5 summarizes our main findings. For relatively low concentrations of mining production (HHI below 2700) and modest concentration variations (<10%), an increase in HHI generally leads to a downward effect on prices. However, when the HHI is low (<2700) and concentration variation is large (>10%), the effect is reversed and a rise in HHI tends to increase commodity prices. Finally, when both the HHI level and the HHI variation are high, a negative coefficient is observed, indicating that a decrease in HHI leads to higher prices.<fnref n="20" />

## 4.2. Discussion and policy implications

We have shown that the effect of HHI variation on metal prices depends on the magnitude of the HHI change, irrespective of whether we examine high or low HHI values. If metal production is diversified, a small change in HHI (less than 10%) will negatively impact prices. This can be illustrated by commodities characterized by low HHI values and high prices, such as precious metals, where a price increase induces even small producers (e.g., gold) to augment production, leading to a reduction in HHI. This can be attributed to increased competition among diverse producers, where even small changes in production concentration significantly influence market dynamics. For example, a slight reduction in supply diversity due to geopolitical tensions or production constraints can generate price spikes, as in the cobalt market during times of heightened demand for batteries used in electronic devices (smartphones, laptops) or for heat-resistant alloys for aerospace, medical applications, and the chemical industry. In cases of larger HHI variations, the inverse effect is observed.

Within the scope of our analysis, the dummy variable I<sub>Δln HHI,t</sub> can be considered a proxy for disturbances or shocks to material production. A minor fluctuation in HHI indicates the absence of market disruption, while a substantial fluctuation signifies market disturbance. A significant HHI shift can be traced back to a sudden drop in major producers' production or a decline in output from smaller producers, which magnifies the dominance of the leading producer. This variable allows us to account for the vulnerability of metal markets to external shocks—such as disruptions caused by resource nationalism or export bans (e.g., Indonesia's nickel ore export ban)—which amplify instability in relatively diversified markets. More specifically, among the six geopolitical risks to the supply of materials listed by IRENA, five have the potential to cause production disruptions that could impact HHI. These risks include resource nationalism, mineral cartels, political instability and social unrest, export restrictions, as well as external

<footnote>* p < 0.1.</footnote>

<footnote>** p < 0.05.</footnote>

<footnote>*** p < 0.01.</footnote>

<footnote n="19">¹⁹ We obtain the same results (available upon request to the authors) when testing homogeneity against the Panel Smooth Transition Regression alternative.</footnote>

<footnote n="20">²⁰ These results hold for other HHI threshold values (see Figs. 9 to 12). The threshold 2700 was chosen as it is the value that gives the most empirically significant results.</footnote>
shocks (IRENA, 2023).<fnref n="21" /> Consequently, our findings indicate that a disruption in markets with lower concentration positively affects prices but has a negative effect in markets with higher concentration. This latter phenomenon can be illustrated by cases such as antimony and REEs, where a significant decline in HHI can be attributed to a reduction in production by the dominant producer, leading to shortages in the market. Under the assumption that a major commodity producer can more easily reduce the HHI in the short term by lowering production than increase it, market participants may view a negative impact as riskier. This is due to the potential increase in prices resulting from the decisions of a few key players which underscores the rationale for avoiding excessively concentrated commodity markets.

Nonetheless, disruption has a four-fold greater impact in less concentrated markets compared to their more concentrated counterparts in absolute terms. This apparently paradoxical result can be explained by the stabilizing effect on prices provided by cartels' market power.

As previously mentioned, redundancy is widely acknowledged as a key factor in enhancing the resilience of networks, including trade systems (Kharrazi et al., 2020). By diversifying supply chains, redundancy reduces vulnerability to disruptions in contexts where multiple producers face varying shocks (Sprecher et al., 2015). It also ensures a more competitive and resilient pricing structure under normal conditions. This has implications for policy advocating for diversification of supply sources, particularly for critical raw materials essential to renewable energy technologies. However, in the case of metals, we show that reduced redundancy—reflected in higher production concentration— can have a stabilizing effect on prices. By consolidating control over production and pricing, entities such as cartels can help mitigate price volatility, thereby reducing the supply risks associated with market fluctuations. Importantly, price stabilization is key for advancing the energy transition (Balciar et al., 2019). Stable commodity prices provide a more predictable environment for planning and investment in renewable energy technologies, which are highly sensitive to market uncertainties. A notable example is Indonesia, a leading producer of tin, which in 2013 established the Indonesia Commodity and Derivatives Exchange with the aim of stabilizing tin prices (Pitron, 2018).

A comparable situation can be observed for other raw materials like oil, where OPEC strives to maintain prices at a fair level, a phenomenon highlighted in the literature (Brémond et al., 2012; Pescatori and Nazer, 2022). The role of OPEC in stabilizing oil prices mirrors the ability of major metal producers, such as China for REE, to influence global pricing. However, this stability may come at the cost of increased geopolitical risks and potential supply vulnerabilities, as disruptions to a key supplier can have outsized impacts on the market.

Overall, our findings challenge the conventional assumption that market disruptions have a greater impact on prices for metals whose production is highly concentrated. Furthermore, our analysis indicates the absence of a clear threshold to differentiate high-risk metals from lower-risk ones based solely on production concentration levels. This raises questions about the reliability of concentration-based metrics, such as the HHI, in criticality assessments, particularly when rigid thresholds are applied, as it may lead to underestimating risks in less concentrated markets. In addition, our results underscore the key role played by fluctuations in concentration production as an indicator of supply disruption. While most criticality assessment methodologies emphasize the absolute level of concentration, the potential for changes in concentration requires greater attention. This perspective aligns with findings by Nocke and Whinston (2022) in the context of mergers analysis and extends them to the domain of metal criticality.

Our study highlights the critical need for careful monitoring of metal supply chains, even those that appear diversified. Particular

attention should be paid to potential changes in production concentration, which can arise from various factors. One such factor is the geographic clustering of mines. For instance, the “Lithium Triangle”, a region spanning Argentina, Chile, and Bolivia, hosts numerous lithium mines across different countries, contributing to the diversification of global lithium production. However, this geographic proximity exposes these operations to shared risks, such as climate-related events (e.g., droughts). Such simultaneous disruptions could significantly reduce production in all three countries,<fnref n="22" /> further consolidating Australia’s dominant position as a global lithium supplier. Another factor to consider when assessing the potential for changes in production concentration is the number of different host metals associated with a metal that has a high degree of companionality.<fnref n="23" /> Metals with a single host metal are particularly vulnerable to supply disruptions affecting that specific host. For example, germanium, which is almost exclusively a co-product of zinc, faces heightened supply risks due to its dependency on a single host. In contrast, metals like silver, which are co-products of multiple host metals (e.g., copper, gold, lead, and zinc), benefit from a more diversified production base. This diversification decreases the likelihood of significant changes in production concentration. These two factors—geographic clustering and companionality—illustrate the complexities involved in understanding supply risks. However, they represent only a subset of the variables that can influence production concentration.

A more detailed and context-specific analysis could reveal additional insights, enabling stakeholders to better anticipate changes in production dynamics and identify which metals require closer monitoring. Such an analysis would be helpful in drawing tailored policy recommendations aiming at reducing dependency on a few dominant suppliers and enhancing supply chain resilience among the various strategies and trade policies that can be followed: (i) developing domestic mining capabilities through policies including financial incentives for mining, (ii) promoting partnerships with emerging suppliers by establishing agreements with resource-rich regions such as Africa, South Asia, and Latin America, (iii) facilitating cross-border resource-sharing agreements to reduce over-reliance on specific regions, (iv) encouraging the development of recycling technologies for metals like cobalt, lithium, and REE, (v) supporting exploration and processing capacity in diverse regions to decentralize the production chain, and (vi) constituting and maintaining strategic stockpiles that can serve as buffers during supply shocks, price spikes or geopolitical tensions. These examples of policy recommendations aim to lower the potential risk of supply disruption, but also to balance immediate supply chain resilience with long-term sustainability, ensuring that critical materials are available to meet the growing demands of the energy transition and associated green technologies.

### 4.3. Beyond the HHI

As previously discussed, the HHI calculated at the country production level remains the most widely used metric to evaluate the supply risk component of criticality. However, ongoing research aims to refine this indicator by incorporating complementary metrics to better capture the complexities of supply risk. One key refinement involves enhancing the geopolitical relevance of the production concentration indicator by incorporating the political and economic stability of producing countries. This adjustment is often implemented by weighting the HHI with the World Bank’s Worldwide Governance Indicators (WGI), based on the premise that a higher production share in politically unstable countries increases geopolitical risk. This approach has been adopted

<footnote n="21">²¹ The final risk type is market manipulation, which refers to phenomena like short squeezing, market cornering, spoofing, and insider trading. However, these risks do not affect production and are thus not accounted for in our models.</footnote>

<footnote n="22">²² Currently, Bolivia’s lithium production remains very limited.</footnote>

<footnote n="23">²³ The degree of companionality is defined as “the degree to which a metal is obtained largely or entirely as a by-product of one or more host metals from geologic ores” (Nassar et al., 2015).</footnote>
by the European Commission in its criticality assessments (European Commission, 2010) and is integrated into the methodology developed by Graedel et al. (2012). However, the concept of political stability remains ambiguous and subject to various biases, as the correlation between governance quality and political stability is neither strictly linear nor universally consistent. Furthermore, the causal relationship between political instability and supply risks warrants further empirical study. To better integrate geopolitical risk, some studies propose considering the political and strategic interactions among market actors. For example, Hache et al. (2019) suggest using a net export dependency index for producers to complement traditional market concentration metrics or net import dependency indices for consumers. Complementary indicators, such as material substitutability and recyclability rates, are also employed to account for potential supply offsets (European Commission, 2010). Helbig et al. (2016) extended this framework by incorporating the domestic production capacity of importing countries, emphasizing its importance in mitigating supply disruptions—an improvement later adopted by the European Commission in its 2017 criticality assessment.

Alternative approaches to measuring concentration along the value chain of metals have also been proposed, leading to results that sometimes differ from those presented in this paper. Gemechu et al. (2016), for instance, suggest computing the HHI based on the share of each producer country in an importing country's total imports rather than global production. Another approach considers corporate concentration, which generally compounds the geographical concentration of production (IRENA, 2023). Faubert et al. (2024) explore the capital ownership structures of leading publicly traded companies engaged in critical raw material extraction, measuring the geographical distribution of shareholders. Their resulting concentration index reveals differences compared to our findings for certain metals, including cobalt and lithium.

Despite these developments, more sophisticated approaches face challenges related to data availability, which limits the broader application of such indicators (European Commission, 2010). Data availability remains a fundamental issue in criticality assessments, as it directly impacts the comparability of analyses across different metals. Other indicators, like the convenience yield of commodity futures, have also been tested as proxies for commodity availability to measure supply risk (Stepanek et al., 2013). However, this approach is constrained by the fact that not all metals have sufficiently liquid futures markets to derive meaningful convenience yields.

Such methodological gaps in the measurement of supply risk reflect broader critiques of the criticality concept itself. Criticality is inherently context-dependent, varying across geographic regions and entities, and evolving with technological advancements and geopolitical shifts. As Eggert (2011) aptly observes, “criticality is in the eye of the beholder.”

These methodological uncertainties underline why no singular framework can adequately address all supply security challenges, necessitating the adoption of diverse and complementary policy approaches for securing critical raw materials. The strategies implemented in the United States, Europe, and key producer nations such as Australia and Canada reflect a growing international recognition of the pivotal role strategic metals play in global technological competition. According to the IEA, more than 230 regulations concerning critical materials have been enacted across nearly 25 countries or regions, with nearly half introduced in recent years. These measures encompass a broad range of aforementioned policies, including the establishment of critical material lists, the introduction of updated mining laws, and initiatives aimed at fostering the development of domestic resources. Additionally, they include efforts to forge new international collaborations, enforce stricter environmental standards for mining, and, in some instances, create or expand strategic material stocks to enhance industrial resilience against external disruptions.

## 5. Conclusion

The Herfindahl-Hirschman Index applied to world production of a given commodity by country is a fundamental component of most raw material criticality assessments. This operates on the premise that analyzing mineral supply concentration is crucial since increased concentration heightens the potential risk of supply disruption.

In the present paper, we rely on a large panel of 33 metals to analyze the influence of HHI on market prices. Interestingly, our results challenge the commonly held assumption since they indicate that the variation of HHI has more impact on prices at lower HHI levels. Furthermore, our findings question the existence of a threshold that clearly distinguishes high-risk markets from less risky ones based on their concentration levels. Hence, using the HHI as a supply risk indicator, especially in conjunction with a threshold, may result in underestimating risks in less concentrated markets. Additionally, our paper highlights the importance of assessing the potential for fluctuations in production concentration, since it directly influences the impact of HHI on prices. This variable, which poses a challenge to measurement, has yet to be included in studies on criticality.

Our results are relevant for policymakers and industry leaders as scrutinizing the variation in HHI may help them identify markets where intervention is necessary, anticipate price and supply risks in markets undergoing structural changes, and implement strategies tailored to the degree and nature of concentration and market stability. Our paper can be extended in several ways. First, it would be relevant to weight the HHI measured at the country level by the country's level of governance, to account for institutional quality considerations. Second, our study does not consider the recycling of metals, as it assesses concentration at the mining level. Although recycling rates for many metals are still low, recycling has the potential to significantly affect the concentration of metal production (at the refining stage) and provide a measure of sovereignty over these materials for countries without significant mining resources. Therefore, it would be instructive to replicate our study with HHI values calculated at the refining stage, allowing for the inclusion of recycling data when assessing the impact of concentration on commodity prices. Third, since all world production may not be available for consumption by any country (Thomas et al., 2022), it would be interesting to consider market availability instead of production concentration as a measure of supply diversity. Finally, acknowledging that criticality is a complex notion that cannot be fully captured by prices, using multi-dimensional models that account for the supply-risk dimension, environmental and social factors, and geopolitical risks, would be a promising extension to provide valuable tools for policymakers and stakeholders in resource management in the context of the energy transition and sustainable development. These avenues are left for future research.

### CRediT authorship contribution statement

**Pauline Bucciarelli:** Writing – original draft, Writing – review and editing, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Emmanuel Hache:** Writing – original draft, Writing – review and editing, Supervision, Methodology, Funding acquisition, Conceptualization. **Valérie Mignon:** Writing – original draft, Writing – review and editing, Supervision, Methodology, Conceptualization.

## Appendix A. HHI calculation

### A.1. USGS 'other country' category

In the USGS reporting, for some raw materials, minor producers are aggregated into the 'Other Country' category, resulting in a combined production denoted as $p_{other}$. In this case, we assume that each country
<table><caption>**Table 6**
Comparison of HHI statistics: Impact of HHI adjustment for minor producers.</caption><thead><tr><th></th><th>HHI Adjustment</th><th>HHI wo Adjustment</th><th>HHI w Adjustment</th><th>HHI Adjustment %</th></tr></thead><tbody><tr><td>mean</td><td>11.223</td><td>3075.467</td><td>3086.690</td><td>7.520</td></tr><tr><td>std</td><td>29.076</td><td>2152.209</td><td>2146.427</td><td>2.119</td></tr><tr><td>min</td><td>0.000</td><td>497.691</td><td>517.388</td><td>0</td></tr><tr><td>25%</td><td>0.015</td><td>1518.263</td><td>1530.770</td><td>0.003</td></tr><tr><td>50%</td><td>1.348</td><td>2382.732</td><td>2391.428</td><td>0.048</td></tr><tr><td>75%</td><td>7.828</td><td>3917.357</td><td>3917.382</td><td>0.440</td></tr><tr><td>max</td><td>321.394</td><td>9776.956</td><td>9776.962</td><td>22.022</td></tr></tbody></table>

Note: (i) HHI wo Adjustment represents the calculation excluding the 'Other Country' category, (ii) HHI w Adjustment is the total HHI after including the fictitious country adjustment (sum of HHI wo Adjustment and HHI Adjustment), (iii) HHI Adjustment % indicates the contribution of the fictitious country adjustment to the overall HHI.

<table><caption>**Table 7**
Relative differences between USGS and BGS data with and without HHI adjustment.</caption><thead><tr><th></th><th>Relative difference wo Adjustment</th><th>Relative difference w Adjustment</th></tr></thead><tbody><tr><td>mean</td><td>10.179</td><td>9.657</td></tr><tr><td>std</td><td>11.739</td><td>11.277</td></tr><tr><td>min</td><td>0.017</td><td>0.012</td></tr><tr><td>25%</td><td>2.609</td><td>2.424</td></tr><tr><td>50%</td><td>6.637</td><td>6.022</td></tr><tr><td>75%</td><td>13.883</td><td>13.277</td></tr><tr><td>max</td><td>143.370</td><td>142.242</td></tr></tbody></table>

Note: The 'Relative difference' refers to the percentage difference between USGS and BGS data, calculated with and without the HHI Adjustment. Lower relative differences indicate better alignment and comparability between the datasets when the HHI Adjustment is considered.

within the 'Other Country' category produces less than the country with the lowest production ($p_{min}$) among the available data. To account for this, we introduce n fictitious countries, each hypothetically producing $\frac{p_{min}}{2}$ of the commodity. The value of n is determined as the floor of the ratio $P_{other}/P_{min}$. Employing the previously mentioned formula, we calculate what we refer to as the 'HHI Fictitious Country Adjustment'.

The 'HHI Fictitious Country Adjustment' has a minimal effect on the overall HHI calculation, with an average adjustment value of 11.2 and a standard deviation of 29 observed across all materials and throughout the entire period (Table 6). Despite its seemingly negligible impact, the adjustment retains importance, particularly for certain metals. Specifically, in cases where the 'Other Country' category significantly contributes to the total production, the fictitious country adjustment can have a more notable influence on the HHI calculation. Accurately accounting for these smaller producers through the introduction of fictitious countries becomes essential to preserve the integrity of the HHI analysis and ensure a comprehensive representation of market concentration. Moreover, in the case of comparable data between the USGS and the BGS, the relative difference between the datasets is observed to be lower when considering the inclusion of the 'HHI Fictitious Country Adjustment', as depicted in Table 7.

This suggests that accounting for the fictitious country addition in the HHI calculation leads to a reduced disparity between USGS and BGS data, enhancing the comparability and alignment of their results. In this paper, we will refer to the Herfindahl-Hirschman Index calculation that incorporates the 'HHI Fictitious Country Adjustment' simply as HHI.

## A.2. Final data

In total, we obtained HHI data for 63 metals and minerals at various stages of their value chain. Most of these data points represent market concentration at the extraction level, but for certain metals, we also have data on concentration at the refining or smelting stages. By considering both the raw material and the stage of the value chain, we have a total of 69 HHI series. The distribution of these values between our two sources is shown in Table 8.

<table><caption>**Table 8**
Data source by material and stage in the supply chain.</caption><thead><tr><th>Stage</th><th>USGS</th><th>BGS</th></tr></thead><tbody><tr><td>Mine</td><td>REE, antimony, asbestos, barite, bauxite, bentonite, beryllium, boron, chromium, cobalt, copper, diatomite, feldspar, fluorspar, gallium gold, graphite, gypsum, iron, lead, lithium, magnesite, magnesium, manganese, mercury, molybdenum, nickel, niobium, palladium, perlite, phosphate-rock, platinum, potash, rhenium, salt, silicon, silver, strontium, sulfur, talc, tantalum, tin, titanium, tungsten, vanadium, vermiculite, yttrium, zinc.</td><td>arsenic, bentonite, gallium, germanium kaolin sillimanite, uranium, wollastonite zirconium.</td></tr><tr><td>Smelting</td><td></td><td>aluminum, copper, tin.</td></tr><tr><td>Refinery</td><td>cadmium, indium, tellurium.</td><td>alumina, cobalt, copper, lead, nickel, selenium, tellurium.</td></tr></tbody></table>

Note: Metals such as bentonite, gallium, and tellurium, appear in both the 'USGS' and 'BGS' columns due to the data collection process. For some years, BGS data were used when USGS data were either unavailable or considered unreliable.

<table><caption>**Table 9**
Differences in HHI values obtained from (i) USGS and BGS data and (ii) World Mining Data (WMD) data (2013–2021).</caption><thead><tr><th></th><th>Relative difference</th><th>Relative difference abs</th></tr></thead><tbody><tr><td>mean</td><td>-0.019</td><td>0.111</td></tr><tr><td>std</td><td>0.184</td><td>0.148</td></tr><tr><td>min</td><td>-1.098</td><td>0</td></tr><tr><td>25%</td><td>-0.064</td><td>0.024</td></tr><tr><td>50%</td><td>0.004</td><td>0.065</td></tr><tr><td>75%</td><td>0.067</td><td>0.136</td></tr><tr><td>max</td><td>0.344</td><td>1.098</td></tr></tbody></table>

Note: The 'Relative difference' represents the percentage difference between the final dataset and WMD data.

## A.3. Robustness checks

The calculations conducted in Table 7 serve as a preliminary assessment of the robustness of the obtained results by comparing the HHIs obtained from the USGS and BGS sources. Additionally, a third source, the World Mining Data (WMD), an annual publication of the Federal Ministry Republic of Austria, is used. This publication reports the productions of 65 minerals and computes the HHI values between 2013 and 2021, utilizing data from various sources, including the USGS. We analyze the difference between the HHIs obtained solely from USGS and BGS data and those from WMD over this period. On average, the difference is approximately 10%, indicating that the calculations based solely on USGS or BGS data are relatively reliable (Table 9).
<table><caption>**Table 10**
Metal price differences: USGS data compared to alternative data sources.</caption><thead><tr><th>Metal</th><th>Source</th><th>price diff</th><th>Δln price diff</th></tr></thead><tbody><tr><td>REE</td><td>Dysprosium Metal Dy/ TREM=99% Dom. - SMM</td><td>-0.303</td><td>0.014</td></tr><tr><td>aluminum</td><td>Aluminum 99.7% Cash U$/MT - LME</td><td>0.084</td><td>0.090</td></tr><tr><td>antimony</td><td>Antimony 99.65% CIF NWE U$/MT- Refinitiv</td><td>0.046</td><td>0.008</td></tr><tr><td>arsenic</td><td>Arsenic Metal =99.5% Domestic - SMM</td><td>0.168</td><td>0.349</td></tr><tr><td>bauxite</td><td>Bauxite Australia Al:48-50,Si:6-7- SMM</td><td>0.740</td><td>1.669</td></tr><tr><td>bismuth</td><td>China Bismuth Ingot 99.99% - SMM</td><td>0.093</td><td>-0.147</td></tr><tr><td>cadmium</td><td>Cadmium 99.99% CIF NWE U$/LB - Refinitiv</td><td>-0.120</td><td>0.610</td></tr><tr><td>chromium</td><td>Chromium =99.2%, Coarse Particle - SMM</td><td>-36.084</td><td>-0.068</td></tr><tr><td>cobalt</td><td>Cobalt Cash - LME</td><td>0.076</td><td>0.096</td></tr><tr><td>copper</td><td>Copper Grade A Cash U$/MT - LME</td><td>0.031</td><td>-0.046</td></tr><tr><td>gallium</td><td>Gallium Ingots CIF NWE U$/KG - Refinitiv</td><td>0.356</td><td>-0.315</td></tr><tr><td>germanium</td><td>Germanium 50ohm CIF NWE U$/KG- Refinitiv</td><td>0.053</td><td>-0.500</td></tr><tr><td>gold</td><td>Gold Spot - LME</td><td>0.007</td><td>0.025</td></tr><tr><td>graphite</td><td>Graph spherical 99.9 FOB China - Fastmarket MB</td><td>-1.039</td><td>0.758</td></tr><tr><td>indium</td><td>Indium CIF NWE U$/KG - Refinitiv</td><td>0.182</td><td>0.460</td></tr><tr><td>lead</td><td>Lead Cash U$/MT - LME</td><td>0.240</td><td>-3.783</td></tr><tr><td>lithium</td><td>Lithium Metal =99%, Battery Grade - SMM</td><td>0.036</td><td>0.948</td></tr><tr><td>magnesium</td><td>Magnesium Ingot Shanghai-Wenxi - SMM</td><td>0.495</td><td>1.310</td></tr><tr><td>manganese</td><td>EMM =99.7% Major Prodcctn Region - SMM</td><td>-422.723</td><td>-0.322</td></tr><tr><td>mercury</td><td>China Mercury Metal 99.999% EXW - Bloomberg</td><td>0.998</td><td>0.216</td></tr><tr><td>molybdenum</td><td>Molybdenum Cash Comp U$/MT - LME</td><td>0.051</td><td>1.125</td></tr><tr><td>nickel</td><td>Nickel Cash U$/MT - LME</td><td>-0.001</td><td>0.008</td></tr><tr><td>selenium</td><td>Selenium CIF NWE U$/LB - Refinitiv</td><td>0.107</td><td>-0.449</td></tr><tr><td>silicon</td><td>Silicon Lumps CIF NWE U$/MT- Refinitiv</td><td>-0.016</td><td>0.435</td></tr><tr><td>silver</td><td>Silver, Handy&Harman (NY) U$/Troy OZ - Handy&Harman</td><td>-0.096</td><td>0.066</td></tr><tr><td>strontium</td><td>China Strontium Metal 99% EXW - Bloomberg</td><td>-76.269</td><td>0.681</td></tr><tr><td>tantalum</td><td>China Tantalum Pentoxide 99.5% EXW - Bloomberg</td><td>-0.163</td><td>-1.019</td></tr><tr><td>tellurium</td><td>Tellurium =99.99% Domestic - SMM</td><td>-0.131</td><td>0.149</td></tr><tr><td>tin</td><td>Tin 99.85% Cash U$/MT - LME</td><td>0.038</td><td>0.130</td></tr><tr><td>tungsten</td><td>Tungsten Ferro CIF NWE U$/KG- Refinitiv</td><td>-0.108</td><td>1.094</td></tr><tr><td>yttrium</td><td>China Yttrium Metal 99.9% - Bloomberg</td><td>0.093</td><td>0.030</td></tr><tr><td>zinc</td><td>SHG Zinc 99.995% Cash U$/MT - LME</td><td>0.074</td><td>-0.280</td></tr><tr><td>zirconium</td><td>China Zirconium Carbonate ZrHfO2 40% EXW - Bloomberg</td><td>-1.533</td><td>-1.889</td></tr></tbody></table>

Note: The 'price diff' and '$\Delta\ln price$ diff' columns show the average relative differences between metal price data from USGS and those from the source indicated in the 'Source' column. The differences are calculated respectively on the raw level data and after applying logarithmic differentiation.

## Appendix B. Price benchmark

See Table 10.

## Appendix C. Descriptive statistics

See Table 11.

## Appendix D. Sources

See Table 12.

## Appendix E. Second-generation panel unit root test

See Table 13.

## Appendix F. Empirical results

See Figs. 7–12.

## Appendix G. Robustness tests

See Tables 14 and 15.

## Appendix H. Panel smooth transition regression (PSTR)

We first considered the possibility of using PSTR models to investigate the likely non-linear relationship between metal prices and HHI variations. However, our research shows statistical significance only with the inclusion of two threshold variables—the HHI level and the magnitude of HHI variations—which is not consistent with a PSTR specification, as further illustrated.

Within the PSTR framework (Gonzalez et al., 2017), the additive model can account for two different transition variables. The model specification is presented as follows:

$$y_{it} = \theta_0 x_{it} + \theta_1 x'_{it} G_1(s_{1, it}; \gamma_1, c_1) + \theta_2 x'_{it} G_2(s_{2, it}; \gamma_2, c_2)$$

where:

* $y_{it}$ is the dependent variable

* $x_{it}$ is the vector of explanatory variables

* $x'_{it}$ is the vector of explanatory variables in the non-linear part

* $s_{k, it}$ is an observable transition variable

* $G_k(s_{k, it}; \gamma_k, c_k)$ is a transition function bounded between zero and one, where $\gamma_k$ is the slope parameter indicating the speed of transition between the extreme values, whereas the threshold parameter $c_k$ points to where the transition takes place.

If we apply this specification to our data, $s_{1, it}$ corresponds to $HHI_{1, it}$ and $s_{2, it}$ to $|\Delta\ln HHI_{1, it}|$. Then, our dummy variables correspond to the extreme values of the transition functions $G_1(s_{1, it}; \gamma_1, c_1)$ and $G_2(s_{2, it}; \gamma_2, c_2)$ (see Tables 16 and 17).
<table><caption>**Fig. 7.** Estimated parameters of Eq. (2) based on dummy variable thresholds.</caption><thead><tr><th>t<sub>HHI</sub></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>1500</td><td>-0.25</td><td>0.22</td><td>0.14</td><td>-1.69</td><td>0.02</td><td>0.00</td><td>0.90</td></tr><tr><td>1600</td><td>-0.16</td><td>0.12</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>0.00</td><td>0.88</td></tr><tr><td>1700</td><td>-0.17</td><td>0.13</td><td>0.14</td><td>-1.71</td><td>0.01</td><td>0.00</td><td>0.91</td></tr><tr><td>1800</td><td>-0.11</td><td>0.07</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>0.00</td><td>0.91</td></tr><tr><td>1900</td><td>-0.07</td><td>0.03</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.90</td></tr><tr><td>2000</td><td>-0.09</td><td>0.06</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>0.00</td><td>0.91</td></tr><tr><td>2100</td><td>-0.11</td><td>0.08</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.91</td></tr><tr><td>2200</td><td>0.04</td><td>-0.09</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.87</td></tr><tr><td>2300</td><td>0.10</td><td>-0.18</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>-0.00</td><td>0.87</td></tr><tr><td>2400</td><td>0.07</td><td>-0.15</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>-0.00</td><td>0.88</td></tr><tr><td>2500</td><td>0.04</td><td>-0.11</td><td>0.14</td><td>-1.71</td><td>0.01</td><td>-0.00</td><td>0.88</td></tr><tr><td>2600</td><td>0.01</td><td>-0.07</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>-0.00</td><td>0.89</td></tr><tr><td>2700</td><td>0.04</td><td>-0.12</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>-0.00</td><td>0.88</td></tr><tr><td>2800</td><td>-0.02</td><td>-0.05</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>0.00</td><td>0.88</td></tr><tr><td>2900</td><td>0.00</td><td>-0.08</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>-0.00</td><td>0.89</td></tr><tr><td>3000</td><td>0.01</td><td>-0.09</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>-0.00</td><td>0.89</td></tr><tr><td>3100</td><td>0.01</td><td>-0.09</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>-0.00</td><td>0.89</td></tr><tr><td>3200</td><td>0.02</td><td>-0.11</td><td>0.14</td><td>-1.68</td><td>0.01</td><td>-0.00</td><td>0.87</td></tr><tr><td>3300</td><td>0.01</td><td>-0.12</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>0.00</td><td>0.89</td></tr><tr><td>3400</td><td>0.03</td><td>-0.17</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>0.00</td><td>0.89</td></tr><tr><td>3500</td><td>0.01</td><td>-0.15</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>0.00</td><td>0.89</td></tr><tr><td>3600</td><td>0.02</td><td>-0.17</td><td>0.14</td><td>-1.70</td><td>0.01</td><td>0.00</td><td>0.89</td></tr><tr><td>3700</td><td>0.01</td><td>-0.16</td><td>0.13</td><td>-1.71</td><td>0.01</td><td>0.00</td><td>0.89</td></tr><tr><td>3800</td><td>-0.09</td><td>0.13</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.91</td></tr><tr><td>3900</td><td>-0.09</td><td>0.12</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.90</td></tr><tr><td>4000</td><td>-0.07</td><td>0.09</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.89</td></tr><tr><td>4100</td><td>-0.08</td><td>0.13</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.90</td></tr><tr><td>4200</td><td>-0.08</td><td>0.13</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.90</td></tr><tr><td>4300</td><td>-0.09</td><td>0.15</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.90</td></tr></tbody></table>

Note: Rows represent the threshold value $t_{HHI}$ applied to the $I_{HHI}$ variable, while columns indicate the explanatory variables in the model. The dummy column corresponds to $\Delta \ln HHI * I_{HHI}$. Each cell shows the estimated parameter from the fixed effects panel regression for the given threshold and variable. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<table><caption>**Fig. 8.** Estimated parameters of Eq. (3) based on dummy variable thresholds.</caption><thead><tr><th>t<sub>ΔHHI</sub></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>0.05</td><td>-0.27</td><td>0.24</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.06</td><td>-0.34</td><td>0.32</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>0.00</td><td>0.88</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.07</td><td>-0.41</td><td>0.40</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.08</td><td>-0.38</td><td>0.37</td><td>0.14</td><td>-1.72</td><td>0.02</td><td>0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.09</td><td>-0.27</td><td>0.27</td><td>0.14</td><td>-1.69</td><td>0.02</td><td>-0.00</td><td>0.88</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.1</td><td>-0.38</td><td>0.41</td><td>0.14</td><td>-1.69</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.11</td><td>-0.23</td><td>0.24</td><td>0.14</td><td>-1.69</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.12</td><td>0.00</td><td>-0.04</td><td>0.14</td><td>-1.69</td><td>0.01</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.13</td><td>-0.10</td><td>0.08</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.14</td><td>-0.11</td><td>0.09</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.15</td><td>-0.07</td><td>0.05</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.16</td><td>-0.10</td><td>0.07</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.17</td><td>-0.05</td><td>0.00</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.18</td><td>-0.07</td><td>0.04</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.19</td><td>-0.07</td><td>0.04</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.2</td><td>-0.08</td><td>0.04</td><td>0.14</td><td>-1.72</td><td>0.01</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.21</td><td>-0.03</td><td>-0.03</td><td>0.14</td><td>-1.72</td><td>0.01</td><td>-0.00</td><td>0.90</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.22</td><td>-0.03</td><td>-0.03</td><td>0.14</td><td>-1.71</td><td>0.01</td><td>-0.00</td><td>0.90</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.23</td><td>-0.02</td><td>-0.05</td><td>0.14</td><td>-1.71</td><td>0.02</td><td>-0.00</td><td>0.89</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.24</td><td>-0.04</td><td>-0.02</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.90</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.25</td><td>-0.01</td><td>-0.08</td><td>0.14</td><td>-1.70</td><td>0.02</td><td>-0.00</td><td>0.90</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Note: Rows represent the threshold value $t_{ΔHHI}$ used to compute the $I_{ΔHHI}$ variable, while columns indicate the explanatory variables in the model. The dummy column corresponds to $ΔlnHHI * I_{ΔHHI}$. Each cell shows the estimated parameter from the fixed effects panel regression for the given threshold and variable. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<figure><img src="image_11.png" /><figcaption>Fig. 9. Estimated parameters for ΔlnHHI in Eq. (4) based on dummy variable thresholds.</figcaption></figure>

Note: Rows represent the threshold values applied to the $I_{HHI}$ variable, while columns indicate the threshold values applied to the $I_{ΔlnHHI}$ variable. Each cell shows the estimated parameter of the ΔlnHHI variable from the fixed effects panel regression for the corresponding thresholds. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<figure><img src="image_12.png" /><figcaption>Fig. 10. Estimated parameters for ΔlnHHI * IHHI in Eq. (4) based on dummy variable thresholds.</figcaption></figure>

Note: Rows represent the threshold values applied to the I<sub>HHI</sub> variable, while columns indicate the threshold values applied to the I<sub>ΔlnHHI</sub> variable. Each cell shows the estimated parameter of the ΔlnHHI * IHHI variable from the fixed effects panel regression for the corresponding thresholds. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<figure><img src="image_13.png" /><figcaption>Fig. 11. Estimated parameters for ΔlnHHI * I<sub>ΔlnHHI</sub> in Eq. (4) based on dummy variable thresholds.</figcaption></figure>

Note: Rows display the threshold values applied to the I<sub>HHI</sub> variable, while columns indicate the threshold values applied to the I<sub>ΔlnHHI</sub> variable. Each cell shows the estimated parameter of the ΔlnHHI * I<sub>ΔlnHHI</sub> variable from the fixed effects panel regression for the corresponding thresholds. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<figure><img src="image_14.png" /><figcaption>Fig. 12. Estimated parameters for ΔlnHHI * IHHI * IΔlnHHI in Eq. (4) based on dummy variable thresholds.</figcaption></figure>

Note: Rows represent the threshold values applied to the IHHI variable, while columns indicate the threshold values applied to the IΔlnHHI variable. Each cell shows the estimated parameter of the ΔlnHHI * IHHI * IΔlnHHI variable from the fixed effects panel regression for the corresponding thresholds. Significance levels are represented by cell colors: blue for 10%, green for 5%, and yellow for 1%.
<table><caption>**Table 11**

Descriptive statistics (1995–2021).</caption><thead><tr><th rowspan="2">Metal</th><th colspan="4">HHI</th><th colspan="4">Δln HHI</th><th colspan="4">Δln price</th></tr><tr><th>mean</th><th>std</th><th>min</th><th>max</th><th>mean</th><th>std</th><th>min</th><th>max</th><th>mean</th><th>std</th><th>min</th><th>max</th></tr></thead><tbody><tr><td>REE</td><td>7061</td><td>2041</td><td>3409</td><td>9559</td><td>0.004</td><td>0.129</td><td>-0.418</td><td>0.349</td><td>0.087</td><td>0.439</td><td>-0.850</td><td>1.229</td></tr><tr><td>antimony</td><td>6479</td><td>1428</td><td>3547</td><td>8359</td><td>-0.018</td><td>0.092</td><td>-0.229</td><td>0.139</td><td>0.049</td><td>0.317</td><td>-0.468</td><td>0.834</td></tr><tr><td>arsenic</td><td>3768</td><td>1086</td><td>1636</td><td>5116</td><td>0.028</td><td>0.167</td><td>-0.36</td><td>0.62</td><td>-0.009</td><td>0.291</td><td>-0.535</td><td>0.562</td></tr><tr><td>bauxite</td><td>1795</td><td>123</td><td>1520</td><td>1997</td><td>-0.001</td><td>0.074</td><td>-0.21</td><td>0.16</td><td>-0.016</td><td>0.093</td><td>-0.213</td><td>0.146</td></tr><tr><td>beryllium</td><td>6073</td><td>1576</td><td>3906</td><td>8716</td><td>0.012</td><td>0.141</td><td>-0.378</td><td>0.458</td><td>0.027</td><td>0.141</td><td>-0.266</td><td>0.376</td></tr><tr><td>chromium</td><td>2560</td><td>249</td><td>2102</td><td>2982</td><td>0.008</td><td>0.107</td><td>-0.149</td><td>0.252</td><td>-0.007</td><td>0.248</td><td>-0.404</td><td>0.721</td></tr><tr><td>cobalt</td><td>2590</td><td>1207</td><td>1361</td><td>5268</td><td>0.046</td><td>0.116</td><td>-0.185</td><td>0.271</td><td>-0.029</td><td>0.404</td><td>-0.81</td><td>0.788</td></tr><tr><td>copper</td><td>1372</td><td>173</td><td>1105</td><td>1663</td><td>0</td><td>0.054</td><td>-0.073</td><td>0.145</td><td>0.035</td><td>0.223</td><td>-0.324</td><td>0.564</td></tr><tr><td>germanium</td><td>6898</td><td>1587</td><td>3321</td><td>8923</td><td>0.012</td><td>0.149</td><td>-0.388</td><td>0.369</td><td>-0.018</td><td>0.282</td><td>-0.513</td><td>0.430</td></tr><tr><td>gold</td><td>712</td><td>177</td><td>517</td><td>1150</td><td>-0.029</td><td>0.036</td><td>-0.088</td><td>0.064</td><td>0.035</td><td>0.127</td><td>-0.182</td><td>0.275</td></tr><tr><td>graphite</td><td>4105</td><td>1382</td><td>1530</td><td>6292</td><td>0.032</td><td>0.194</td><td>-0.531</td><td>0.436</td><td>0.007</td><td>0.177</td><td>-0.344</td><td>0.463</td></tr><tr><td>iron</td><td>1888</td><td>144</td><td>1592</td><td>2049</td><td>0.014</td><td>0.042</td><td>-0.06</td><td>0.072</td><td>0.036</td><td>0.153</td><td>-0.149</td><td>0.394</td></tr><tr><td>lead</td><td>1941</td><td>673</td><td>894</td><td>3195</td><td>0.032</td><td>0.082</td><td>-0.135</td><td>0.159</td><td>0.043</td><td>0.181</td><td>-0.320</td><td>0.503</td></tr><tr><td>lithium</td><td>2785</td><td>585</td><td>1880</td><td>4263</td><td>0.018</td><td>0.127</td><td>-0.208</td><td>0.275</td><td>0.019</td><td>0.234</td><td>-0.545</td><td>0.529</td></tr><tr><td>magnesium</td><td>5602</td><td>2386</td><td>1820</td><td>8138</td><td>0.039</td><td>0.105</td><td>-0.121</td><td>0.327</td><td>-0.002</td><td>0.180</td><td>-0.311</td><td>0.446</td></tr><tr><td>manganese</td><td>1431</td><td>245</td><td>1132</td><td>2091</td><td>0.018</td><td>0.067</td><td>-0.093</td><td>0.219</td><td>0.007</td><td>0.341</td><td>-0.421</td><td>1.328</td></tr><tr><td>mercury</td><td>4940</td><td>2252</td><td>1718</td><td>8533</td><td>0.053</td><td>0.261</td><td>-0.399</td><td>0.758</td><td>0.032</td><td>0.321</td><td>-0.518</td><td>0.829</td></tr><tr><td>molybdenum</td><td>2418</td><td>241</td><td>1967</td><td>2846</td><td>-0.007</td><td>0.074</td><td>-0.115</td><td>0.227</td><td>0.005</td><td>0.436</td><td>-0.888</td><td>1.122</td></tr><tr><td>nickel</td><td>1157</td><td>204</td><td>909</td><td>1839</td><td>0.012</td><td>0.106</td><td>-0.209</td><td>0.246</td><td>0.027</td><td>0.292</td><td>-0.605</td><td>0.466</td></tr><tr><td>niobium</td><td>8046</td><td>418</td><td>7214</td><td>9025</td><td>0.004</td><td>0.05</td><td>-0.122</td><td>0.103</td><td>0</td><td>0.205</td><td>-0.257</td><td>0.253</td></tr><tr><td>palladium</td><td>3426</td><td>311</td><td>2932</td><td>4017</td><td>-0.004</td><td>0.044</td><td>-0.097</td><td>0.059</td><td>0.084</td><td>0.309</td><td>-0.598</td><td>0.677</td></tr><tr><td>platinum</td><td>5866</td><td>571</td><td>4450</td><td>6796</td><td>-0.005</td><td>0.079</td><td>-0.191</td><td>0.232</td><td>0.016</td><td>0.147</td><td>-0.275</td><td>0.334</td></tr><tr><td>rhenium</td><td>3134</td><td>566</td><td>2006</td><td>4243</td><td>-0.008</td><td>0.13</td><td>-0.35</td><td>0.2</td><td>-0.027</td><td>0.385</td><td>-0.479</td><td>1.605</td></tr><tr><td>silicon</td><td>3293</td><td>1486</td><td>1125</td><td>4997</td><td>0.057</td><td>0.111</td><td>-0.143</td><td>0.369</td><td>0.028</td><td>0.189</td><td>-0.408</td><td>0.452</td></tr><tr><td>silver</td><td>952</td><td>122</td><td>751</td><td>1152</td><td>0.015</td><td>0.058</td><td>-0.111</td><td>0.122</td><td>0.037</td><td>0.194</td><td>-0.283</td><td>0.526</td></tr><tr><td>strontium</td><td>3132</td><td>505</td><td>2548</td><td>4210</td><td>0.007</td><td>0.103</td><td>-0.251</td><td>0.16</td><td>0.019</td><td>0.207</td><td>-0.306</td><td>0.802</td></tr><tr><td>tantalum</td><td>3435</td><td>1428</td><td>1474</td><td>6175</td><td>-0.030</td><td>0.253</td><td>-0.601</td><td>0.699</td><td>0.015</td><td>0.554</td><td>-1.810</td><td>1.834</td></tr><tr><td>tin</td><td>2227</td><td>450</td><td>1508</td><td>2983</td><td>0.005</td><td>0.103</td><td>-0.228</td><td>0.218</td><td>0.046</td><td>0.236</td><td>-0.304</td><td>0.636</td></tr><tr><td>tungsten</td><td>6456</td><td>741</td><td>4526</td><td>7579</td><td>0.017</td><td>0.075</td><td>-0.135</td><td>0.213</td><td>0.06</td><td>0.268</td><td>-0.372</td><td>0.979</td></tr><tr><td>vanadium</td><td>3684</td><td>474</td><td>3203</td><td>4950</td><td>0.015</td><td>0.07</td><td>-0.183</td><td>0.193</td><td>0.031</td><td>0.495</td><td>-0.915</td><td>0.999</td></tr><tr><td>yttrium</td><td>8947</td><td>1188</td><td>4921</td><td>9777</td><td>0.038</td><td>0.11</td><td>-0.024</td><td>0.455</td><td>-0.035</td><td>0.334</td><td>-0.517</td><td>1.080</td></tr><tr><td>zinc</td><td>1292</td><td>290</td><td>856</td><td>1769</td><td>0.02</td><td>0.062</td><td>-0.112</td><td>0.125</td><td>0.021</td><td>0.249</td><td>-0.589</td><td>0.830</td></tr><tr><td>zirconium</td><td>2806</td><td>289</td><td>2120</td><td>3361</td><td>-0.013</td><td>0.071</td><td>-0.231</td><td>0.138</td><td>0.033</td><td>0.312</td><td>-0.948</td><td>1.025</td></tr></tbody></table>

Note: This table presents descriptive statistics for each material in the panel over the 1995–2021 period. The panel consists solely of metals and metalloids from the materials described in Fig. 1, except for two: bauxite, a mineral containing alumina and thus representing aluminum (a metal), and graphite, which, although not classified as a metal, is essential to battery technologies (for which market data is available). Additionally, the panel excludes four metals, namely boron, uranium, gallium, and titanium, due to limited data availability.

<table><caption>**Table 12**</caption><caption>Data sources.</caption><thead><tr><th>Variable</th><th>Source</th></tr></thead><tbody><tr><td>Metal and mineral HHI</td><td>USGS and BGS</td></tr><tr><td>Metal price</td><td>USGS</td></tr><tr><td>BRENT crude Oil price</td><td>FRED - code: POILBREUSDM</td></tr><tr><td>Broad US dollar real effective rate</td><td>FRED - code: RTWEXBGS</td></tr><tr><td>Industries sales</td><td>FRED - code: CMRMTSPL</td></tr><tr><td>US LIBOR</td><td>FRED - code: IR3TIB01USM156N</td></tr><tr><td>VIX</td><td>Bloomberg</td></tr><tr><td>US consumer price index</td><td>FRED - code: CPIAUCSL</td></tr></tbody></table>

Hence, through correspondence, employing the additive model ne-
cessitates that the model satisfies the condition:

$$ \beta_{11} + \beta_{132} + \beta_{11} + \beta_{131} = \beta_{11} + \beta_{131} + \beta_{132} + \beta_{14} $$

$$ \beta_{11} = \beta_{14} $$

Conversely, the model with interaction variables developed in the paper gives:

$$ \beta_{11} \neq \beta_{14} $$

Using the additive model does not offer sufficient degrees of freedom, making it unsuitable for our analysis.

This problem of multiple regimes has been addressed in a time series context in van Dijk and Franses (1999). The authors develop a Multiple Regime Smooth Transition AutoRegressive (MRSTAR) model

<table><caption>**Table 13**

Panel unit root tests – *p*-values.</caption><thead><tr><th>Variable</th><th>With linear trend</th><th>With constant</th><th>Without constant</th></tr></thead><tbody><tr><td>ln price</td><td>0.17</td><td>0.38</td><td>0.77</td></tr><tr><td>Δln price</td><td>1.7 × 10<sup>-5</sup></td><td>1.2 × 10<sup>-6</sup></td><td>1.8 × 10<sup>-8</sup></td></tr><tr><td>ln(HHI)</td><td>0.67</td><td>0.19</td><td>1</td></tr><tr><td>Δln(HHI)</td><td>1.2 × 10<sup>-67</sup></td><td>7.8 × 10<sup>-76</sup></td><td>1.9 × 10<sup>-105</sup></td></tr></tbody></table>

Note: This table reports the *p*-values of the second-generation unit root test for panel data proposed by Demetrescu et al. (2006). The test is based on the *p*-values from *N* independent ADF tests, with the number of lags determined by the Akaike Information Criterion (AIC). The null hypothesis is the presence of a unit root. Columns specify the deterministic kernel used in the test.

that allows the definition of a four-regime model.<fnref n="24" />

$$ y_t = [\phi_1 x_t(1 - G_1(s_{1,t}; \gamma_1, c_1)) + \phi_2 x_t G_1(s_{1,t}; \gamma_1, c_1)][1 - G_2(s_{2,t}; \gamma_2, c_2)] + [\phi_3 x_t(1 - G_1(s_{1,t}; \gamma_1, c_1)) + \phi_4 x_t G_1(s_{1,t}; \gamma_1, c_1)]G_2(s_{2,t}; \gamma_2, c_2) $$

The MRSTAR model could be adapted to our problem, though it has not yet been extended to panel data.

<footnote n="24">²⁴ Obtained by ‘encapsulating’ two different two-regime LSTAR models.</footnote>
<table><caption>**Table 14**

Robustness tests: Dynamic model estimation and sensitivity to the oil price series.</caption><thead><tr><th rowspan="2"></th><th colspan="2">difference GMM</th><th colspan="2">individual fixed effects</th></tr><tr><th>Model 1 lag</th><th>Model 4 lag</th><th>Model wo CV</th><th>Model WTI</th></tr></thead><tbody><tr><td>Δ ln price<sub>t,t-1</sub></td><td>0.01<br>(0.06)</td><td>0.02<br>(0.06)</td><td></td><td></td></tr><tr><td>Δ ln HHI<sub>t,t</sub></td><td>-0.02<br>(0.08)</td><td>-1.04<sup>***</sup><br>(0.39)</td><td>-0.54<br>(0.35)</td><td>-0.76<sup>**</sup><br>(0.31)</td></tr><tr><td>Δ ln HHI<sub>t,t-1</sub></td><td>0.10<br>(0.08)</td><td>0.10<br>(0.08)</td><td></td><td></td></tr><tr><td>Δ ln oil<sub>t</sub></td><td>0.17<sup>**</sup><br>(0.07)</td><td>0.17<sup>**</sup><br>(0.07)</td><td>0.11<br>(0.07)</td><td></td></tr><tr><td>Δ ln er<sub>t</sub></td><td>-1.43<sup>***</sup><br>(0.37)</td><td>-1.54<sup>***</sup><br>(0.36)</td><td>-1.87<sup>***</sup><br>(0.37)</td><td></td></tr><tr><td>Δ ln is</td><td>1.05<sup>***</sup><br>(0.35)</td><td>1.03<sup>***</sup><br>(0.33)</td><td>0.92<sup>***</sup><br>(0.31)</td><td></td></tr><tr><td>Δ ln vix<sub>t</sub></td><td>0.03<br>(0.04)</td><td>0.04<br>(0.04)</td><td>0.01<br>(0.04)</td><td></td></tr><tr><td>ir<sub>t</sub></td><td>-0.00<br>(0.01)</td><td>-0.00<br>(0.01)</td><td>0.00<br>(0.00)</td><td></td></tr><tr><td>I<sub>HHI,t</sub></td><td></td><td>-0.08<br>(0.07)</td><td>-0.00<br>(0.04)</td><td>0.00<br>(0.04)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>HHI,t</sub></td><td></td><td>1.14<sup>**</sup><br>(0.46)</td><td>0.65<br>(0.52)</td><td>0.71<br>(0.48)</td></tr><tr><td>I<sub>ΔlnHHI,t</sub></td><td></td><td>-0.00<br>(0.06)</td><td>-0.03<br>(0.04)</td><td>-0.01<br>(0.04)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>ΔlnHHI,t</sub></td><td></td><td>1.30<sup>***</sup><br>(0.42)</td><td>0.85<sup>**</sup><br>(0.38)</td><td>0.95<sup>***</sup><br>(0.34)</td></tr><tr><td>I<sub>HHI,t</sub> * I<sub>ΔlnHHI,t</sub></td><td></td><td>-0.02<br>(0.07)</td><td>-0.01<br>(0.05)</td><td>-0.02<br>(0.05)</td></tr><tr><td>Δ ln HHI<sub>t,t</sub> * I<sub>HHI,t</sub> * I<sub>ΔlnHHI,t</sub></td><td></td><td>-1.39<sup>***</sup><br>(0.50)</td><td>-1.06<sup>*</sup><br>(0.56)</td><td>-0.97<sup>*</sup><br>(0.52)</td></tr><tr><td>Num. obs.</td><td>898</td><td>898</td><td>821</td><td>821</td></tr><tr><td>Num. obs. used</td><td>753</td><td>753</td><td></td><td></td></tr></tbody></table>

Note: The dependent variable is the log differentiated price of metals Δln price. The variables Δln oil, Δln er, Δln vix, and Δln is denotes the variation rate of oil price, exchange rate, VIX index, and Industries sales, respectively. *ir* denotes the US interest rate. Δln HHI denotes the variation rate of the country metal production concentration, and I<sub>HHI</sub> and I<sub>ΔlnHHI</sub> are the dummy variables computed for the threshold values of t<sub>HHI</sub> = 2700 and t<sub>ΔlnHHI</sub> = 0.1. GMM stands for the Generalized Method of Moments. Model 1 lag and Model 4 lag correspond to the dynamic form of Model (1) and Model (4), respectively. Model wo CV corresponds to Model (4) without the control variables, and Model WTI uses the WTI price benchmark for oil instead of Brent in Model (4). To provide consistent results, we apply the Newey and West robust covariance estimators for the fixed effect specification, the corresponding standard errors are in parentheses.

* p < 0.1.

** p < 0.05.

*** p < 0.01.

<table><caption>**Table 15**

Impact of HHI fluctuations on metal prices by HHI level and variation magnitude — Robustness tests.</caption><thead><tr><th></th><th>β<sub>low,low</sub></th><th>β<sub>low,high</sub></th><th>β<sub>high,low</sub></th><th>β<sub>high,high</sub></th></tr></thead><tbody><tr><td>Model 4 lag</td><td>-1.04</td><td>0.27</td><td>0.11</td><td>0.02</td></tr><tr><td>Model wo CV</td><td>-0.54</td><td>0.32</td><td>0.11</td><td>-0.10</td></tr><tr><td>Model WTI</td><td>-0.76</td><td>0.20</td><td>-0.04</td><td>-0.05</td></tr></tbody></table>

Note: This table corresponds to Table 5 for the models presented in Table 14.

<table><caption>**Table 16**

Parameter correspondence with the PSTR additive model.</caption><thead><tr><th>I<sub>HHI,t</sub>/G<sub>1</sub></th><th>I<sub>ΔlnHHI,t</sub>/G<sub>2</sub></th><th>Regime parameter</th><th>Article parameters</th><th>PSTR parameters</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>β<sub>1,low,low</sub></td><td>β<sub>11</sub></td><td>θ<sub>0</sub></td></tr><tr><td>0</td><td>1</td><td>β<sub>1,low,high</sub></td><td>β<sub>11</sub> + β<sub>132</sub></td><td>θ<sub>1</sub></td></tr><tr><td>1</td><td>0</td><td>β<sub>1,high,low</sub></td><td>β<sub>11</sub> + β<sub>131</sub></td><td>θ<sub>2</sub></td></tr><tr><td>1</td><td>1</td><td>β<sub>1,high,high</sub></td><td>β<sub>11</sub> + β<sub>131</sub> + β<sub>132</sub> + β<sub>14</sub></td><td>θ<sub>1</sub> + θ<sub>2</sub></td></tr></tbody></table>

<table><caption>**Table 17**

Parameter correspondence with the MRSTAR additive model.</caption><thead><tr><th>I<sub>HHI,t</sub>/G<sub>1</sub></th><th>I<sub>ΔlnHHI,t</sub>/G<sub>2</sub></th><th>Regime parameter</th><th>Article parameters</th><th>MRSTAR parameters</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>β<sub>1,low,low</sub></td><td>β<sub>11</sub></td><td>Φ<sub>1</sub></td></tr><tr><td>0</td><td>1</td><td>β<sub>1,low,high</sub></td><td>β<sub>11</sub> + β<sub>132</sub></td><td>Φ<sub>2</sub> - Φ<sub>1</sub></td></tr><tr><td>1</td><td>0</td><td>β<sub>1,high,low</sub></td><td>β<sub>11</sub> + β<sub>131</sub></td><td>Φ<sub>3</sub> - Φ<sub>1</sub></td></tr><tr><td>1</td><td>1</td><td>β<sub>1,high,high</sub></td><td>β<sub>11</sub> + β<sub>131</sub> + β<sub>132</sub> + β<sub>14</sub></td><td>Φ<sub>4</sub> - Φ<sub>1</sub></td></tr></tbody></table>

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