Industrial chain dynamics in the rare earth sector

China’s rare earth industry relies on a comprehensive industrial chain, spanning from upstream resource extraction to downstream technological applications, creating a distinct industrial advantage. However, despite this complete industrial chain, China’s position within the global rare earth value chain has yet to be fully realized. This is particularly evident in intermediate stages such as refining, where China faces increasing competitive pressure, as the U.S. and its allies gradually challenge its dominance in the global market. These countries are actively rebuilding the rare earth industrial chain through policies, legal frameworks, and equity transactions to reduce their dependency on China, particularly in refining, while simultaneously enhancing autonomy in downstream industries, especially in electric vehicles and renewable energy.

Existing literature highlights the asymmetry of China’s competitive advantage within the global rare earth value chain. Shuai et al. (2022) utilized a projection pursuit model to analyze China’s comparative advantage in rare earth products within the industrial chain, emphasizing that China holds a strong competitive edge in midstream and downstream sectors but lacks competitiveness in upstream mining activities [12]. Zuo et al. (2022) analyzed global rare earth trade data, noting a trend towards integration in the upstream and downstream sectors, while the midstream sector shows diversification [13]. However, these studies primarily focus on trade and production efficiency, without exploring in depth the effects of geopolitical factors, international sanctions, or changes in investment patterns on the rare earth industrial chain. Leng et al. (2021) employed social network analysis (SNA) to reveal China’s increasing technological innovation capacity in the rare earth industry, while still exhibiting a “strong upstream, weak downstream” structure [14]. While this finding enhances the understanding of China’s dominance in rare earth mining, it does not address how international competitors, particularly the U.S., use policies to influence this industry structure. Zhang et al. (2022) and Xia et al. (2023) examined competition across various stages of the rare earth industrial chain and found that competition is most intense in downstream markets, particularly in sectors related to clean energy technologies [15,16]. However, existing studies have not sufficiently addressed domestic policy changes in China, especially in response to international pressures, and how these factors influence the adjustment of China’s rare earth industrial chain. These dynamics significantly affect the competitive landscape of the global rare earth market.

Recent studies further emphasize supply chain integration dynamics. For instance, Severson et al. (2023) conducted an integrated supply chain analysis for rare earth elements under global electrification scenarios, highlighting the need for diversified sourcing to mitigate risks in clean energy transitions [17]. Similarly, Xu et al. (2025) examined interdependence in rare earth element supply between China and the United States using a multi-layer network approach, revealing how trade linkages stabilize global chains despite geopolitical tensions [18].

While existing research provides valuable insights into the rare earth industrial chain, there remains a significant gap in understanding how global geopolitical shifts impact the competitiveness of the rare earth industry chain. However, these studies often employ static models such as vector error correction models (VECM) or basic regression analyses, lacking time-varying perspectives that account for evolving geopolitical and market shifts over time [12,13]. Therefore, this study will employ a TVP-VAR model to quantify the dynamic relationships between different stages of the rare earth industrial chain, addressing these methodological gaps by incorporating time-varying parameters to analyze the effects of Chinese policies and international market changes. This theme of industrial chain dynamics underscores the need for models that capture evolving inter-segment relationships, setting the stage for examining linkages with broader markets such as clean energy.

Clean energy–rare earth linkages and energy-finance interactions

With the global energy transition, the share of renewable energy in global energy supply has steadily increased, with rare earth elements playing a critical role in this transformation. In recent years, the scale of clean energy equipment construction has significantly grown, particularly in the wind and solar sectors. According to the International Energy Agency, global renewable energy capacity additions reached approximately 510 GW in 2023, a nearly 50% increase compared to the previous year [19]. China’s newly added PV capacity in 2023 was comparable to the total global installation in 2022, while wind power capacity grew by 66%, with PV panels accounting for two-thirds of the global renewable energy capacity additions.

Post-pandemic economic recovery and the response to the global energy crisis have greatly accelerated investments in clean energy. From 2021 to 2023, the annual growth rate of clean energy investment reached 24%, far exceeding the 15% growth in fossil fuel sectors [20]. This surge has directly boosted demand for rare earths, which are critical raw materials in clean energy technologies, including wind power, solar energy, and electric vehicles [21].

Building on these linkages, several studies have delved into energy-finance interactions, such as price spillovers and market correlations. Several studies have explored the relationship between clean energy and the rare earth market. Ding et al. (2024) examined the relationship between global warming, renewable energy consumption, and the rare earth market, finding that during the COVID-19 pandemic, global warming and renewable energy utilization had a positive short-term effect on the rare earth market [22]. However, this study did not investigate how policy changes might affect long-term demand dynamics in the rare earth market. Apergis and Apergis (2017) noted a temporal correlation between rare earth prices and renewable energy, but did not explore in depth the GPR impacting the rare earth market [23]. Fritz and Schiefer (2009) analyzed the impact of rare earth metal prices on clean energy indices using a multi-factor market model, revealing a negative correlation between rare earth prices and the performance of certain clean energy stocks during periods of price increase [24]. While this finding is of practical significance, it does not adequately consider the broader impacts of global economic fluctuations on clean energy investment patterns. Madaleno et al. (2023) studied the spillover effects between rare earth elements and renewable energy, noting that these effects vary with market conditions and time frames [25]. This research provides valuable insights into the relationship between rare earth markets and renewable energy market fluctuations, but has not thoroughly explored the influence of geopolitical tensions on these spillover effects. Recent research has advanced understanding of clean energy market spillovers and dynamic connectedness. Ye et al. (2023) analyzed time-varying spillovers between rare earth prices and renewable energy sectors, showing heightened connectedness during market volatility periods [26]. Gao et al. (2024) explored higher-order moments connectedness between rare earth and clean energy markets from a multiscale perspective, uncovering asymmetric risk transmissions that vary across short- and long-term horizons [27]. While insightful, many of these analyses rely on static vector autoregression (VAR) models or correlation-based approaches, which overlook time-varying connectedness and asymmetric effects in spillovers [23,24]. This limitation hinders a full understanding of how GPR and economic fluctuations dynamically influence the rare earth-clean energy nexus. These themes highlight the interconnectedness of energy transitions and financial markets, yet gaps persist in dynamic analyses, which this review addresses next through theoretical frameworks.

Theoretical framework for industrial chain and market dynamics

Several theoretical channels have been proposed in the literature to influence industrial industrial chains, including the bullwhip, capacity-constraining, cost-compensating, and contagion effects [28–31]. These theories provide a robust foundation for analyzing how exogenous shocks influence the interactions within the rare earth market. A ubiquitous challenge in industrial chain design is the “bullwhip effect” [28], wherein small fluctuations in downstream customer demand result in significant alterations in upstream production levels [32–35]. The capacity constraint effect reflects the fact that changes in the production and market demand for upstream raw materials can significantly affect the maximum production capacity of midstream and downstream products within the industrial chain [30,36]. The cost compensation effect suggests that price changes in midstream and downstream products may influence the market prices of upstream raw materials through subsidies to production costs [31]. The market contagion effect refers to the potential for external shocks to impact the prices of mid- and downstream products within the industrial chain due to the interconnectedness of the market [37–39].

Building upon the aforementioned models, this paper examines the pathways through which the clean energy market influences the interconnectedness among product markets in the rare earth industry chain (see Fig 1). The rare earth market is exposed to potential risks from the evolution of the clean energy market, which can trigger exogenous shocks to the prices, demand, and supply of products within the rare earth industry chain. These effects represent distinct pathways through which the clean energy market impacts the interconnectedness of rare earth industry chain product markets.

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Fig 1. Mechanisms and pathways for clean energy market to influence the product market of rare earths industrial chain.

https://doi.org/10.1371/journal.pone.0342223.g001

Pathway 1 describes the route through which the clean energy market induces the bullwhip effect in the rare earth industry chain. Growth in the clean energy market serves as a major driver of demand for rare earth minerals [24]. Consequently, to meet the increased demand, there is a need to expand the supply of downstream products in the industrial chain, implying that upstream production must also increase, further amplifying the bullwhip effect (Pathway 1).

However, as demand grows, the prices of downstream products in the rare earth industry chain are likely to rise, allowing downstream manufacturers to realize higher profits. This situation incentivizes rare earth recycling companies to increase the recycling of discarded rare earth products, thus boosting the secondary supply of upstream rare earth products. This initiative reduces the dependency of downstream products on primary upstream raw materials [40,41], thereby alleviating the capacity constraint effect (Pathway 2).

Pathways 3 and 4 illustrate how the clean energy market affects the cost compensation and contagion effects within the price connectivity of the rare earth industry chain. As clean energy technologies become more widespread, the strategic importance and economic value of rare earth metals are further emphasized. For companies that simultaneously produce upstream, midstream, and downstream products in the rare earth industry chain, an increase in downstream product prices can lead to higher production profits, which can then subsidize the relatively low returns from upstream raw material production. This implies that price changes in downstream products, driven by the clean energy market, may affect the market prices and profitability of upstream products (Pathway 3). Moreover, as fluctuations in the energy market affect the rare earth market [25,42], the volatility in the clean energy market can cause price fluctuations in the rare earth industry chain through market contagion effects (Pathway 4).

In summary, while existing literature illuminates industrial chain dynamics, clean energy–rare earth linkages, and energy-finance interactions, significant unknowns persist, including the time-varying impacts of geopolitical shifts, asymmetric spillovers in market connectedness, and the integration of supply chains under electrification pressures. Methodological gaps, such as reliance on static VAR or VECM models, further limit insights into evolving relationships. This study addresses these voids by employing advanced time-varying models like TVP-VAR and NARDL to empirically analyze dynamic risk transmissions, asymmetric effects, and policy influences within the rare earth industry chain, offering a more nuanced understanding of its interplay with the clean energy market.

Theoretically, this research contributes by advancing key concepts such as asymmetry—distinguishing responses to positive (e.g., demand surges) versus negative (e.g., policy restrictions) shocks—and time-varying effects, capturing regime changes like those induced by geopolitical tensions or electrification policies. Empirically, it innovates through a novel integration of TVP-VAR for evolving spillovers, ARDL for long-run equilibria, and NARDL for nonlinear asymmetries, applied to a unique dataset of monthly rare earth returns and clean energy indices from 2015–2023, enabling robust quantification of market dynamics that prior static approaches overlook.

Methodology

Time-varying parameter vector autoregression (TVP-VAR).

Our research applied the TVP-VAR methodology to explore the evolving spillovers among product markets at each phase of the Chinese PV industry chain. The TVP-VAR model was originally put forward by Primiceri, n.d. (2005) [43]. This model presents a distinctive benefit, as it can capture nonlinear relationships that vary over time among economic variables. It achieves this by permitting variations in the coefficients and variance covariance matrices over time [44–46]. As per Antonakakis et al. (2020) [47], this model has two key advantages. First, it helps to settle the problem of selecting the best scrolling window size. Second, it avoids to loss valuable observations and hence is also suitable for short samples.

The TVP-VAR model, as proposed by Primiceri, n.d. (2005) [43], can be expressed as:

(1)

where is an N × 1 vector of observed variables, is an N × 1 time-varying intercept vector, are N × N time-varying coefficient matrices for lags k = 1 to p, and is an N × 1 error vector with time-varying covariance matrix . The covariance matrix is decomposed as where is a lower triangular matrix with ones on the diagonal, and is a diagonal matrix of stochastic volatilities.

Following Diebold and Yılmaz (2014) [48], the TVP-VAR is transformed into its vector moving average (VMA) representation based on Wold’s theorem:

(2)

where are N × N time-varying coefficient matrices in the VMA representation.

The generalized impulse response function (GIRF), denoted as , measures the response of variable j to a shock in variable i over horizon H:

(3)

where , and is the j-th diagonal element of . The GIRF is scaled as:

(4)

with an N × 1 selection vector with 1 in the i-th position and 0 elsewhere.

The generalized forecast error variance decomposition (GFEVD), , represents the proportion of the H-step-ahead forecast error variance of variable i attributable to shocks in variable j:

(5)

Normalized as,

(6)

Subsequently, we compute the aggregate spillover index using GFEVD as follows:

(7)

The spillover index present in Eq. (7) usually demonstrates the spilling over of shocks from one variable towards other variables under examination. However, to conduct a more comprehensive analysis of directional linkages, this study categorizes them into three types: directional spillovers passed on to others; directional spillovers received from others; and net spillovers (Table 1).

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Table 1. Spillover indices and their interpretations.

https://doi.org/10.1371/journal.pone.0342223.t001

First, we analyze the directional spillovers that are passed on to other variables (j) when variable (i) sends its shocks as demonstrated in Eq. (8):

(8)

Second, we examine the impacts of shocks that variable i experiences from other variables j in Eq. (9).

(9)

Finally, subtract Eq. (9) from Eq. (8) to obtain a net spillover. To calculate the net spillover, we deduct the directional spillover received from other parties from the directional spillover transmitted to them.

(10)

Eq. (10) illustrates how variable i affects the network being analyzed. Hence, a positive indicates that variable i exerts a stronger impact on the network than the network has on itself. Conversely, a negative indicates that the network motivates variable i.

We selected the TVP-VAR model because it is well-suited for capturing the dynamic and evolving nature of interactions among the product markets of the rare earth industry chain, especially given the rapid changes in the clean energy market and the external shocks that might impact this chain. The model allows us to track how the relationships between variables shift over time, which is crucial when dealing with time series data that is subject to changing economic conditions [47].

Furthermore, the TVP-VAR model is advantageous because it addresses the limitations inherent in models that use fixed parameters, providing a more flexible framework that can adapt to time-varying relationships. The ability to estimate time-varying parameters enables us to better understand the evolution of spillovers across different phases of the industry chain, especially under changing external conditions, such as shifts in policy or market dynamics.

However, limitations of the TVP-VAR model must be acknowledged. One key limitation is the complexity of estimation, as time-varying parameters require more computational resources and are prone to overfitting when the sample size is small. This can lead to potential biases if not properly managed. Additionally, while the model is highly flexible, it may struggle to adequately model nonlinearities or capture long-term equilibrium relationships that are often of interest in industrial chain analyses. In this context, we complement the TVP-VAR with other models, such as ARDL and NARDL, to investigate both long-term and short-term effects.

Autoregressive distributed lag model (ARDL) and nonlinear autoregressive distributed lag model (NARDL).

To further investigate the asymmetric effects of China’s clean energy market on the connectivity of the rare earth industry chain, this study employs both the ARDL and NARDL models. The ARDL model is particularly advantageous due to its flexibility in handling small sample sizes and accommodating variables integrated at different levels, such as I(0) or I(1). This model allows for the simultaneous estimation of long-run and short-run parameters, providing valuable insights into the dynamic equilibrium of the system [49].

However, while the ARDL model is widely used, it assumes symmetric relationships between variables. Such an assumption may not be appropriate in contexts where variables exhibit different impacts depending on whether they increase or decrease. Financial time series, including those related to the rare earth and clean energy sectors, often demonstrate nonlinear behaviors, where a positive shock may yield a different effect compared to a negative shock. To better capture these potential nonlinearities, we introduce the NARDL model, developed by Shin et al. (2014) [50]. The NARDL model facilitates the estimation of asymmetric short- and long-run effects, offering a nuanced understanding of how positive and negative changes in the clean energy market differentially influence the rare earth industry chain.

Empirically, NARDL is justified for asymmetric economic relationships, as it decomposes variables into positive and negative partial sums to capture threshold effects often seen in commodity markets [51]. For instance, in energy economics, NARDL has revealed asymmetric pass-throughs in oil prices to inflation or growth, where negative shocks (price falls) have stronger impacts due to sticky adjustments [50]. In this study, BDS test results confirming nonlinearity in series like NEI further support NARDL, enabling robust analysis of how clean energy declines disrupt rare earth connectivity more than increases enhance it, addressing gaps in linear models.

The ARDL model is specified as [49]:

(11)

where is the dependent variable, is a k × 1 vector of regressors, is the error correction term, are long-run coefficients, and are short-run coefficients, and is the error term.

To illustrate, we constructed an ARDL model using the New Energy Index (NEI) to analyze its impact on the total connectivity (TC) of China’s rare earth industry chain:

(12)

Here, TC represents the total connectivity index of China’s rare earth industry chain, NEI is the new energy index, GPR is the geopolitical risk index, EPU is the economic policy uncertainty index, and TPU is the trade policy uncertainty index.

In the NARDL framework, asymmetry is introduced by decomposing explanatory variables (e.g., NEI) into positive and negative components using partial sum processes:

(13)(14)

The NARDL model is:

(15)

This decomposition captures how increases (positive shocks) and decreases (negative shocks) in clean energy indices differentially affect rare earth connectivity. Theoretically, asymmetry is expected because positive shocks (e.g., policy incentives boosting EV/PV demand) may enhance chain integration linearly, while negative shocks (e.g., trade restrictions) could amplify disruptions due to supply chain rigidities and investor risk aversion, consistent with nonlinear behaviors in commodity markets [50].

For example, using the NEI, we constructed a NARDL model to explore how positive and negative changes in the NEI influence the rare earth industry chain’s connectivity:

(16)

The formula is as follows: represents long-run coefficient of positive changes in NEI, represents long-run coefficient of negative changes in NEI, denotes short-run coefficient of positive changes in NEI, denotes short-run coefficient of negative changes in NEI, is cumulative short-run impact of positive changes, and is cumulative short-run impact of negative changes.

While the ARDL and NARDL models offer powerful tools for analyzing relationships, they are not without limitations. The ARDL model assumes linearity, which may oversimplify relationships in contexts characterized by large, nonlinear changes. Both models also require assumptions about cointegration and stationarity, which may not always hold in real-world data. The NARDL model, while addressing asymmetry, introduces additional complexity by decomposing variables into positive and negative changes, making interpretation more challenging and increasing the risk of overfitting.

By integrating the ARDL and NARDL models, this study captures both dynamic spillovers and asymmetric effects, offering a comprehensive framework for analyzing the interactions between China’s clean energy market and the rare earth industry chain.

The selected models complement each other as follows: TVP-VAR captures time-varying spillovers and regime changes (e.g., policy shifts), addressing RQ1 and H1 on dynamic risk transmission; ARDL establishes symmetric long-run equilibria, supporting RQ3 and H3 on policy optimization; NARDL uncovers asymmetries in positive/negative shocks, central to RQ2 and H2 on differential effects. This synergy is significant for the hypotheses, as it allows testing evolving (TVP-VAR), balanced (ARDL), and nonlinear (NARDL) relationships in volatile markets [43,49,50].

To visually summarize how these models interrelate in the analytical process, Fig 2 provides a step-by-step methodological flowchart. This diagram illustrates the sequential pipeline, starting from data preparation and diagnostics, proceeding through TVP-VAR for capturing time-varying dynamics and spillovers, followed by ARDL and NARDL for examining symmetric and asymmetric effects, and concluding with interpretation and robustness validation.

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Fig 2. Methodological flowchart.

https://doi.org/10.1371/journal.pone.0342223.g002

Data

The dataset comprises 17 variables, primarily monthly time series data spanning from February 2015 to August 2023 (Table 2). Rare earth industry chain products include upstream (Praseodymium-Neodymium Oxide (PNO), Dysprosium Oxide (DO), Neodymium Oxide (NO), Praseodymium Oxide (PO)), midstream (Dysprosium Metal (DM), Neodymium Metal (NM), Praseodymium Metal (PM), Pr-Nd Alloy (PNA), Dy-Fe Alloy (DFA)), and downstream (Nd-Fe-B (NFB)) items, sourced from the Shanghai Nonferrous Metals Network via the Wind database. Clean energy market proxies are the CSI New Energy Index (NEI), CSI New Energy Vehicle Index (NEVI), CSI Wind Power Industry Index (WIND), and CSI Photovoltaic Industry Index (SOLAR), obtained from the CSI Index website (www.csindex.com.cn). Control variables include the Geopolitical Risk Index (GPR), Economic Policy Uncertainty Index (EPU), and Trade Policy Uncertainty Index (TPU), accessed from the Economic Policy Uncertainty website (www.policyuncertainty.com). GPR captures interstate tensions and threats, potentially affecting commodity market information flows. EPU and TPU, per Davis et al. (2019), quantify policy-related uncertainties impacting metal market connectivity [52].

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Table 2. Detailed description of variables.

https://doi.org/10.1371/journal.pone.0342223.t002

The sample covers monthly data from February 2015 to August 2023, selected primarily due to data availability from the specified sources. This period encompasses key policy milestones and structural shifts relevant to the rare earth and clean energy sectors, including China’s 2015 rare earth resource tax reforms, the 2020 Export Control Law implementation (which influenced price surges), and the 2022 Russia-Ukraine conflict’s impact on global commodity markets. These events allow for analysis of dynamic spillovers amid evolving geopolitical and economic uncertainties, aligning with the study’s focus on time-varying interactions.

Prior to estimation, we conducted unit root tests to assess stationarity: Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski-Phillips-Schmidt-Shin (KPSS). Results indicated mixed integration orders, with most variables I(1) at levels but I(0) after first differencing, justifying ARDL/NARDL use. Cointegration was tested via ARDL bounds approach [49], confirming long-run relationships where F-statistics exceeded critical bounds.

To detect nonlinear dependencies, we applied the BDS test [53], which rejects the null of independent and identical distribution (iid) for key series like TC and NEI, confirming nonlinearity and supporting the use of asymmetric models like NARDL.

Model lag orders were selected using Akaike Information Criterion (AIC) for TVP-VAR to optimize fit, and Schwarz Information Criterion (SIC) for ARDL/NARDL to favor parsimony, with maximum lags of 4 based on data length.

Table 3 provides descriptive statistics for each variable. We calculated the returns for each market i at time t using the formula, where p represents the spot prices of Chinese rare earth products and new energy market indices. Using this return data, we explored the correlations among the products in the rare earth industrial chain. The monthly prices and return changes for PNO, DO, NO, PO, DM, NM, PM, PNA, DFA, and NFB are illustrated in Fig 3.

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Table 3. Descriptive statistics for all variables.

https://doi.org/10.1371/journal.pone.0342223.t003

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Fig 3. Fluctuations in prices and returns of rare earth industry chain products from February 2015 to August 2023.

https://doi.org/10.1371/journal.pone.0342223.g003

In December 2020, with the formal implementation of China’s Export Control Law, prices of rare earth-related products began to soar rapidly, reaching their peak in March 2022. From March 2022, the impact of the Russia-Ukraine conflict, which resulted in a spike in commodity prices, partially reduced the profit margins of rare earth companies. This has resulted in reduced demand for rare earths, resulting in a gradual decline in their prices. Fig 3 illustrates significant fluctuations in the returns of all markets, particularly in 2022. Table 3 shows that among all rare earth products, NO exhibits the highest average returns and volatility. Except for NFB, the positive skewness coefficients indicate that nine series are right-skewed. In the new energy markets, NEVI exhibits the highest average returns, whereas SOLAR demonstrates the highest volatility. All variables in the new energy markets exhibit right-skewed distributions. Regarding kurtosis coefficients, except for DO, all variables demonstrate noticeable leptokurtic distributions. Apart from PNO, DO, NO, PNA and NEVI, the Jarque-Bera statistics show elevated values which reject the null hypothesis and indicate that all variables are not normally distributed.

Robustness checks

To ensure result stability, we conducted sub-sample analyses: (1) pre-2020 (February 2015–November 2020) to isolate pre-Export Control Law effects, and (2) post-2020 (December 2020–August 2023) amid heightened volatility. Additionally, alternative proxies were tested, such as replacing GPR with the International Country Risk Guide (ICRG) political risk index and EPU with global EPU variants. Across specifications, spillover patterns and asymmetric effects remained consistent, with minor variations in magnitude during volatile periods, affirming the models’ reliability.

TVP-VAR results: Static and dynamic connectivity

This study examines the connectivity of rare earth industry chain product markets using the TVP-VAR method, with the optimal lag order determined by the AIC over a forecast range of 10. Initially, conventional spillover methods were applied to evaluate spillover effects and provide a deeper understanding of the interconnections among rare earth industry chain product markets. Table 4 presents the static connectivity indices for various variables.

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Table 4. Static spillover indices.

https://doi.org/10.1371/journal.pone.0342223.t004

The total connectivity among markets is 31.2%, indicating substantial interactions and a lack of market independence within the rare earth industry chain. This aligns with Madaleno et al. (2023) [26], who found varying spillovers between rare earths and renewables, but our time-varying focus reveals higher connectivity during policy surges, extending their static analysis by capturing regime shifts. PM and NFB emerge as the primary net contributors to spillover effects. Key findings include:

Upstream Market: PNO generates the largest spillover effect on other products, dominating the upstream market alongside NO and PO. These products are pivotal in transmitting risks across the industrial chain, consistent with the bullwhip effect where upstream demand fluctuations amplify downstream volatility [28].

Midstream Market: NM exhibits a spillover effect of 162%, significantly influencing NO. This highlights the midstream market’s role as a critical node for risk propagation and interaction.

Downstream Market: The downstream market is primarily impacted by PM and receives significant spillovers from upstream products. PNO, NO, and PNA are the major recipients of market spillovers, while DM is the largest net recipient of risk premiums.

Product Connectivity: The strongest connectivity among rare earth products occurs between NO and NM, indicative of efficient information transmission within these markets. In contrast, the weakest connectivity is observed between DO and NFB, reflecting limited interaction between these products.

The static connectivity analysis provides an overview of the average level of connectivity, but it does not capture the dynamic fluctuations in connectivity over time. This section presents the time-varying connectivity of China’s rare earth industry chain product market.

Fig 4 illustrates the total connectivity of returns among rare earth industry chain product markets over time. The total connectivity fluctuates between 30% and 33%, indicating notable spillover effects among these markets. Due to exogenous shocks affecting the Chinese rare earth market, the spillover effects exhibit considerable time-varying characteristics.

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Fig 4. Time-varying total connectivity of China’s rare earth industry chain product market.

Note: This figure illustrates the dynamic total spillover index (in percentage terms) among rare earth product returns from February 2015 to August 2023. The y-axis represents the connectivity index (%), ranging from 25% to 35%, while the x-axis denotes time on a monthly scale with labeled years (2015−2023). Blue shaded areas highlight significant structural shift periods, such as policy announcements (e.g., May 2015 tariff cancellation) and external shocks (e.g., 2020 COVID-19), where connectivity exceeds 32% (1 standard deviation above mean). Peaks indicate heightened risk transmission due to clean energy demand surges.

https://doi.org/10.1371/journal.pone.0342223.g004

Key Moments in Dynamic Connectivity and Structural Shifts:

May 2015 (Policy Shift): The Chinese Ministry of Commerce’s cancellation of rare earth export tariffs, amid a global commodity recovery, spiked connectivity to ~32%, as investors capitalized on improved trade, boosting upstream-midstream linkages (see Fig 3 peak). This policy-driven peak echoes Hanif et al. (2023)’s COVID spillovers [42], but our results show stronger upstream transmission in recovery phases, highlighting rare earths’ sensitivity to domestic policies over global shocks.

July 2017 (Renewable Energy Push): The National Energy Administration’s “13th Five-Year Plan” for renewables drove a surge to 33%, reflecting heightened demand from clean energy growth, with midstream products like NM transmitting risks downstream. Consistent with Bouri et al. (2023)’s volatility connectedness [54], but our study emphasizes midstream roles in renewables push, differing by quantifying 33% peaks tied to plan implementation.

2018-2019 (Trade War Effects): Connectivity dipped to ~30% during US-China trade tensions, indicating structural shifts from tariffs disrupting supply chains, increasing volatility in upstream products like PNO (Fig 4 shows net receivers).

2020−2021 (COVID-19 Disruption): Amid pandemic supply chain breaks, connectivity fluctuated wildly, with downstream NFB as a net transmitter, highlighting economic resilience but policy needs for diversification.

April 2023 (Green Recovery): Post-COVID “Two Sessions” and green development white paper pushed connectivity to 32.89%, signaling renewed investor confidence in rare earths for energy transition.

Fig 5 shows the net connectivity of individual rare earth industry chain products over time. Products exhibit either negative net connectivity, acting as receivers of shocks, or positive net connectivity, acting as transmitters of shocks. The findings are consistent with the trends observed in total connectivity and highlight significant time variations.

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Fig 5. Time-varying net connectivity of various products within China’s rare earth industry chain.

Note: This multi-panel figure displays net spillover indices (in percentage terms) for key rare earth products (e.g., PNO, DO, NM, Nd-Fe-B) over February 2015 to August 2023. Each panel’s y-axis shows net connectivity (%), with x-axis as monthly time series labeled by year. Positive values indicate net transmitters, negative as receivers. Shaded regions mark significance, emphasizing shifts like NFB’s consistent transmitter role.

https://doi.org/10.1371/journal.pone.0342223.g005

Key Products as Contributors or Receivers: NFB consistently emerged as the primary contributor to overflow effects, particularly following major clean energy announcements. DFA was a net contributor for most of the sample period but transitioned to a net receiver in late 2017.In early 2021, DO shifted from being a net receiver to a net contributor of spillover effects.

Differences Between Upstream and Midstream Products: Most upstream and midstream products (PNO, DO, NO, DM, NM, and PNA) acted as primary receivers of spillover effects. DM exhibited weaker overflow effects, whereas NFB displayed stronger effects. Compared to other receivers, DM and PNA demonstrated greater hedging capabilities, suggesting potential advantages, particularly concerning NFB.

Changes in the clean energy market significantly enhance the connectivity of the rare earth industry chain, highlighting how market shocks strengthen inter-product relationships. The connectivity patterns among products vary distinctly depending on the stages of rare earth-related policy implementation and the broader impacts of clean energy market dynamics.

As the influence of the clean energy market on rare earth market performance continues to grow, its implications for investors and businesses are expected to further drive the connectivity of the entire rare earth industry chain. Therefore, this study emphasizes the potential impact of China’s clean energy market on the rare earth industry chain, which will be explored further in the subsequent sections.

ARDL results: Symmetric effects

The changes in the clean energy market represent a key source of risk for the rare earth industry chain’s product markets. To explore the relationship between the Chinese clean energy market and the rare earth industry chain product market, we employed the ARDL and NARDL models. Based on the AIC and BIC, an optimal lag order of 8 was selected.

Before estimation, we conducted unit root tests on the data to ensure their suitability for ARDL and NARDL analysis. The ADF, PP and KPSS tests confirmed that all variables were either integrated at order zero I(0) or one I(1), meeting the data stationarity requirements. Table 5 presents the results of these unit root tests.

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Table 5. Unit root tests.

https://doi.org/10.1371/journal.pone.0342223.t005

Table 6 shows the ARDL regression results and cointegration tests, revealing a long-run relationship between the overall connectivity of the rare earth industry chain and the clean energy market variables (NEI, NEVI, WIND, and SOLAR). The models also incorporate GPR, EPU, and TPU as control variables.

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Table 6. ARDL regression results.

https://doi.org/10.1371/journal.pone.0342223.t006

The results indicate that all types of clean energy markets significantly influence the connectivity of the rare earth industry chain:

Short-Run Effects: NEI, NEVI, WIND, and SOLAR exhibit significant positive effects on the overall connectivity. For instance, a 1% increase in NEVI leads to a short-term decrease in connectivity by 0.009%. Meanwhile, NEI, WIND, and SOLAR have significant positive impacts with a lag of one period. Long-Run Effects: Connectivity is negatively impacted by SOLAR, with a 1% increase in solar market activity reducing connectivity by 0.223%. This negative long-run SOLAR effect mirrors Apergis & Apergis (2017)‘s correlations between rare earth prices and renewables [23], but our ARDL framework shows equilibria stabilization, implying rational adjustments not fully captured in their temporal analysis. This suggests that in the long run, participants in the rare earth market respond rationally, aligning their investments with broader market trends.

Cointegration test results for all four models exceed the critical values at the 5% significance level, confirming the presence of a long-run relationship characterized by asymmetry. However, the nonlinearity of these relationships suggests that linear ARDL models may not fully capture the dynamics, warranting further exploration through NARDL models.

The ARDL models highlight the critical role of clean energy market dynamics in shaping the connectivity of rare earth industry chains. The significant short-run impacts emphasize the sensitivity of rare earth markets to immediate changes in clean energy demand. Conversely, the long-run effects suggest that market participants adapt their strategies to align with rational expectations. However, the asymmetric effects and the complexity of these interactions warrant further investigation using nonlinear models to better understand the evolving dynamics.

Economically, the positive short-run effects imply that surges in clean energy indices prompt rapid investor reallocation toward rare earth products, enhancing chain integration and potentially reducing short-term price volatility through diversified demand. In contrast, the negative long-run SOLAR coefficient suggests that as solar markets mature, they stabilize rare earth connectivity by encouraging efficient supply chain adjustments, but this could signal over-reliance on solar demand, advising policymakers to diversify renewable incentives to mitigate risks.

NARDL results: Asymmetric effects

The NARDL regression results, shown in Table 6, shed light on the intricate relationship between the clean energy market and the connectivity of the rare earth industry chain, supplemented by cointegration test findings. The cointegration tests reject the null hypothesis of no cointegration across all models, indicating a nonlinear long-term linkage between rare earth industry connectivity and key clean energy market variables, including NEI, NEVI, WIND, and SOLAR. These results reveal a complex, asymmetric dynamic between the clean energy sector and the rare earth industry’s overall connectivity.

The NARDL regression models (N1: NEI, N2: NEVI, N3: WIND, and N4: SOLAR) incorporate GPR, EPU, and TPU as control variables. Asymmetric effects are evident in both the short and long run, with the PV market demonstrating significant short- and long-run impacts on rare earth connectivity, while other clean energy markets exhibit primarily long-run asymmetric influences, as confirmed by Wald test results in Table 8.

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Table 7. NARDL regression results.

https://doi.org/10.1371/journal.pone.0342223.t007

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Table 8. Asymmetric response tests.

https://doi.org/10.1371/journal.pone.0342223.t008

In the short run, the results for Model N1 indicate that a 1% increase (decrease) in NEI reduces (raises) rare earth industry chain connectivity by 0.015%, reflecting symmetric short-run effects. Similar patterns are observed for NEVI and WIND. However, the impact of SOLAR stands out with pronounced asymmetry: a 1% increase (decrease) in SOLAR raises (lowers) connectivity by 0.066% (0.058%). These SOLAR asymmetries extend Ding et al. (2024)‘s positive short-term effects during COVID [22], but our NARDL reveals stronger disruptions from negatives. These findings underscore the significant role of clean energy markets in shaping short-term dynamics within the rare earth industry chain. For instance, rising returns in the new energy vehicle and wind energy markets encourage investors to stabilize rare earth material industrial chains to secure consistent returns, thereby reducing market volatility, as per contagion theory in interconnected markets [37]. Conversely, declining returns can heighten investor risk aversion, leading to temporary disruptions. Nevertheless, the optimistic market outlook and strong government backing for clean energy help cushion the adverse effects on rare earth market volatility. In the PV market, government-led initiatives to integrate photovoltaics into residential infrastructure have closely tied its growth to daily life. When PV returns increase, investors intensify short-term investments in related rare earth products, boosting connectivity. On the other hand, declines in PV returns trigger minimal short-term adjustments due to long-term confidence in the market’s resilience and potential.

Table 7 also presents the long-run coefficients of clean energy markets on rare earth industry connectivity. Models N1, N2, and N3 suggest that NEI, NEVI, and WIND exert no significant long-term effects, highlighting rational investor behavior and the stabilizing influence of long-term expectations on market volatility. In contrast, Model N4 (SOLAR) reveals pronounced long-term asymmetry: a 1% increase (decrease) in SOLAR reduces (raises) connectivity by 0.205% (0.192%). This long-run finding builds on Gao et al. (2024)‘s higher-order connectedness, but differentiates by showing positive shocks’ saturation effects [27], unique to China’s PV dominance. This finding underscores the pivotal role of the PV market in stabilizing the rare earth industrial chain. Positive shocks, such as rising PV returns, mitigate risk spillovers by bolstering industrial chain stability through integrated supply chains under electrification [17]. Conversely, persistent negative shocks, like sustained declines in returns, prompt gradual portfolio adjustments, leading to increased volatility.

Among clean energy markets, the PV market has the most substantial influence on rare earth connectivity. Negative short-term shocks in PV returns have a more pronounced impact than positive ones, although their long-term effects are muted. In contrast, positive long-term shocks yield greater connectivity benefits, highlighting the PV market’s stabilizing influence. Table 8 confirms the statistical significance of these asymmetric relationships, with PV market returns closely tied to rare earth industrial chains, further emphasizing the sector’s central role in the global energy transition.

Overall, variations in China’s clean energy market demonstrate a mix of nonlinear and asymmetric effects on rare earth industry connectivity. Rapid fluctuations in NEV and wind energy markets can influence investor sentiment, creating temporary spillovers. However, robust government support fosters rational investment decision-making, reducing overall volatility. The PV market stands out due to its strong integration into daily life and policy prioritization, amplifying its impact on rare earth connectivity. Over time, the clean energy market has promoted greater transparency and rational investor behavior, gradually diminishing the frequency and intensity of connectivity disruptions within the rare earth industry chain.

From an economic viewpoint, the asymmetric SOLAR short-run effects indicate that positive shocks foster bullish market behavior, driving investment inflows and tighter chain linkages, while negative shocks trigger risk-averse pullbacks, exacerbating volatility—consistent with contagion effects [37]. In the long run, the stronger negative impact from positive SOLAR changes implies market saturation, where excess demand leads to overcapacity and reduced connectivity, urging policies like strategic reserves to balance supply [10].

Robustness discussion

To validate the findings, we compare ARDL and NARDL results. ARDL reveals symmetric short-run positives for clean energy indices and a consistent negative long-run SOLAR effect, aligning with NARDL’s asymmetric SOLAR impacts, suggesting robustness in solar’s stabilizing role. Consistencies include non-significant long-run effects for NEI/NEVI/WIND across models, indicating rational market adaptation. Differences highlight NARDL’s capture of asymmetries, e.g., stronger short-run SOLAR positives, underscoring nonlinearity. Sub-sample tests (pre/post-2020) and alternative proxies (e.g., ICRG for GPR) confirm these patterns, with minor volatility variations, affirming the models’ reliability in depicting clean energy-rare earth dynamics.