Global Value Chain Embedding and Total Factor Productivity in Carbon Emission Reduction: A Multi-Country Analysis of the Paper Industry

Abstract

Against the backdrop of carbon reduction and low-carbon economic development, this study takes the global paper industry chain as its research subject and employs the SBM-GML model and input–output model to measure the low-carbon TFP and value chain embedding levels of 42 major global economies from 2001 to 2021. Using fixed-effects and threshold effect models, the study examines both the overall and stage-specific impacts of value chain embedding on low-carbon TFP. The results reveal that between 2001 and 2021, while the low-carbon TFP of major countries in the global paper industry chain steadily increased, significant disparities persisted among them. Most countries experienced low-carbon TFP growth driven by technological progress, whereas only a few high low-carbon TFP nations also demonstrated upward trends in technical efficiency. The division of labour position in the value chain significantly promoted low-carbon TFP at a ratio of 1:0.26. In contrast, the low-carbon TFP effects of participation displayed a nonlinear impact with a threshold of 0.21: it exerted an insignificant inhibitory effect in the initial stage but, upon crossing the threshold, resulted in a significant positive effect with a ratio of 1:0.13. These findings highlight the importance of optimizing GVC strategies to achieve sustainable industrial transformation and growth.

1. Introduction

Since the global financial crisis, there has been a growing tide of anti-globalization sentiments in developed countries, triggered by events such as trade wars, the COVID-19 pandemic, and regional conflicts [1]. At the same time, latecomer countries, including China, have been steadily integrating into the global production network, leading to a comprehensive restructuring of the global value chain (GVC) [2]. In these processes of decoupling and embedding, all countries are striving to occupy more high value-added industrial segments, aiming to achieve sustainable resource utilization and environmentally friendly economic development by shifting the focus from gross domestic product (GDP) growth to total factor productivity (TFP) and low-carbon TFP improvement. Due to differing attitudes of countries towards the GVC and their shared pursuit of improving low-carbon TFP, the impact of participating in GVC and dividing labour in low-carbon TFP has become a widely debated topic in academia. However, most studies analyze heterogeneous industries, regions, and specific external conditions [3,4], leading to different conclusions and complicating discussions on the actual impact of GVC integration.

Against this backdrop, the 2015 adoption of the United Nations Sustainable Development Goals (SDGs) brought global attention to sustainable production models characterized by “reducing consumption, increasing output, and improving quality”. The 2016 Paris Agreement, which set a target of achieving net-zero emissions by 2050, further spurred nations into action, promoting low-carbon economic development. In recent years, major economies, including China, have announced carbon peaking and carbon neutrality goals with corresponding timelines. These developments position “Low Carbon Total Factor Productivity (TFP)” as a critical standard for assessing industrial sustainable development, providing a novel perspective for addressing these issues.

Compared with green total factor productivity, which measures various pollutants, low-carbon TFP focuses on carbon emissions as the core metric, effectively bridging the differences and commonalities between economic growth and environmental protection. By incorporating the rigid constraint of carbon peaking, it transforms environmental factors into measurable, scarce resources. Moreover, the long-term goal of carbon neutrality offers a clear direction for optimizing resource allocation in economic activities. At a time when economies are transitioning from extensive to intensive growth models, examining the TFP effects of GVC participation from a carbon reduction perspective provides accurate evidence of the economic implications of industrial participation in GVC and actionable recommendations for environmentally friendly growth.

The paper industry serves as a representative sector due to its significant contributions to national economies and its high levels of resource consumption and carbon emissions. This industry highlights the urgent need for transformation to enhance low-carbon TFP. By integrating cross-country analyses, this study offers valuable insights for high-quality and sustainable industrial growth worldwide. Furthermore, this research introduces a refined analytical framework that integrates nonlinear threshold models, addressing the heterogeneous impacts of GVC embedding across regions and industries. These contributions highlight the novelty of this study, offering valuable perspectives for achieving high-quality and sustainable economic growth in alignment with global climate targets.

This study addresses these critical issues by exploring the interplay between GVC embedding and low-carbon TFP, focusing on gaps in the existing literature. Specifically, it examines three key dimensions: (1) the nuanced interactions between value chain positioning and multi-factor productivity in a low-carbon context, addressing the heterogeneity of impacts across industries and countries; (2) the quantification of GVC participation and division of labour on low-carbon TFP within the global paper industry, along with the nonlinear threshold effects of GVC participation; (3) practical policy recommendations for achieving sustainable industrial transformation in alignment with global climate goals, such as the Paris Agreement and the Sustainable Development Goals (SDGs).

The research is structured as follows: Section 2 presents a comprehensive review of research findings on low-carbon TFP and its determinants. Section 3 summarizes the transmission mechanisms of the impact of GVC embedding on low-carbon TFP and proposes research hypotheses. Section 4 utilizes the slack-based measure and global Malmquist–Luenberger (SBM-GML) model and input–output theory to calculate low-carbon TFP and GVC embedding levels. A threshold effect model examines the nonlinear impact of GVC embedding. Section 5 assesses the development of low-carbon TFP in the paper industry of different countries through theoretical mechanisms and tests. Section 6 compares the results with the existing literature, followed by discussion. Finally, Section 7 presents research conclusions and policy recommendations.

2. Literature Review

2.1. Current Status of Low-Carbon Total Factor Productivity Research

The Japanese economists Kaya and Yokobori [5] first introduced the concept of low-carbon TFP through the notion of ’carbon productivity’ in 1993. They examined the economic benefits of a unit of carbon emissions by comparing the value of GDP with carbon emissions over specific periods. This measure belongs to ‘single-factor’ carbon productivity. The method has the advantages of being simple to calculate and avoiding potential correlations between input data and independent variables [6]. However, it does not consider the substitutability between carbon emissions and other factors, such as capital, labour, and energy. Therefore, the results may not fully and accurately reflect a country’s true production efficiency and competitiveness [7]. In the comprehensive development phase, widely accepted in low-carbon economic theory and practice, the total factor carbon productivity (TFCP) becomes an important complement to traditional total factor productivity. This indicator, known as Low Carbon Total Factor Productivity, is an important tool in the academic world for measuring economic sustainability and growth efficiency.

Against this backdrop, scholars have investigated the development and influencing factors of low-carbon TFP from different theoretical perspectives and empirical models. Hu and Liu [8] calculated the level of low-carbon TFP in the Australian construction industry using the data envelopment analysis (DEA), demonstrating the feasibility of achieving both industrial growth and carbon reduction targets through technological advancement. Su et al. [9] examined how renewable energy technology innovation positively impacts TFCP through channels such as technological advancement and efficiency improvement. Bai and Sun [10] used the SBM-GML method to investigate the main drivers of low-carbon TFP growth, including cost, innovation, and demand. It was suggested that a combination of legal, economic, and administrative measures should be implemented to promote low-carbon growth patterns at the enterprise level. Similarly, Wang et al. [11], focusing on China’s agricultural sector, employed an SBM model to test the positive role of regional economic development in enhancing low-carbon TFP. The studies above outline the current development status and key characteristics of low-carbon TFP, providing valuable insights for analyzing the heterogeneous impacts across countries in the context of the GVC restructuring.

2.2. The Impact of Global Value Chain Embedding on Low Carbon Total Factor Productivity

Regarding the environmental and economic impacts of the GVC embedding, Sun and Wang [12] examined the ‘productivity effect’ of GVC embedding from a micro perspective. They showed that domestic enterprises can enhance TFP by introducing and absorbing international advanced technologies. Additional research has revealed that the productivity effect is counterbalanced by the technological suppression effect of multinational enterprises (MNEs), ultimately resulting in an inverted U-shaped effect [13,14]. In a similar theoretical framework, research on the relationship between carbon emissions and GVC embedding can be viewed from two perspectives: advocating carbon reduction through technological progress and efficiency improvement [15], or intensifying carbon emissions through the pollution haven effect of developed countries’ capture [16]. Yan et al. [17] also suggested that carbon emissions embedded in value chain trade could lead to a “pollution haven effect” at the regional level. Wang et al. [18] proposed a threshold model that integrates the conclusions. They stated that changes in the division of labour linkages have a nonlinear effect on carbon emission intensity due to value chain embedding [19].

However, comprehensive research on the impact of the GVC embedding on low-carbon TFP are scarce, and the conclusions of the analyses differ significantly. Xu et al. [20] and Xu and Han [21] examined the transmission pathways and industry differentiation from the perspective of GVC embedding, using industry-specific data from China. Xie et al. [22] demonstrated that both upstream and downstream embedding levels in the GVC have a significant positive impact on low-carbon TFP. The authors used the value-added accounting method to separately calculate the effects of GVC embedding participation and position on single-factor carbon productivity. They found that the former has a facilitating effect, while the latter shows a U-shaped relationship. The results from the Trade in Value Added (TIVA) database indicate that the GVC participation has a positive impact on single-factor carbon productivity. However, the GVC position is significantly negatively correlated with China’s industrial carbon productivity. Li et al. [23] examined the impact of forward and backward participation (embedding) in GVC on the carbon emission efficiency of China’s manufacturing sector. Additionally, they analyzed the role of different embedding patterns in promoting the Central and Eastern European region by incorporating value chain length indicators.

2.3. Summary and Innovation Points

Although the existing literature has shed some light on the impact of GVC embedding on low-carbon TFP, several issues still require clarification. One of the main issues is the absence of unified concepts and classification methods for value chain embedding; the existing research on GVC embedding exhibits various conceptual approaches, including classifications based on value chain length, participation, and division of labour position, which has resulted in a relatively confusing summary of the transmission mechanisms of embedding behaviour on low-carbon TFP, and has implications for the comparability and representativeness of empirical findings as well. In addition, many studies have primarily focused on macro-level examinations of industrial sectors within a single country and industrial comparisons based on variations in factor intensity. However, they lack focus on a specific industry and have not conducted multi-country examinations of its entire participant chains. The heterogeneity of the impact based on the division of labour positions is the fundamental characteristic that distinguishes GVC embedding from other influencing factors. Finally, some studies that rely on the analysis of single-factor carbon productivity results may need to improve their underlying assumptions and data accuracy.

Therefore, this study refines the connotations of GVC embedding from the perspectives of division of labour positions and participation. Based on this refinement, the two main arguments currently influencing low-carbon TFP, namely technology spillover effects and technology suppression effects, are reorganized and matched with specific mechanisms. Subsequently, this study examines the paper industry as the subject of investigation due to its pressure to transition towards carbon emission reduction. The entire paper industry chain involving all major economies worldwide is analyzed using input–output tables. The study analyzes the realistic impacts and trends of each country’s embedding in this industry chain on their own low-carbon TFP. The aim of this approach is to provide more convincing general conclusions regarding the effects of the GVC embedding in the low-carbon economy field.

3. Theoretical Mechanism and Research Hypotheses

3.1. The Impact of Global Value Chain Division of Labour Positions on Low-Carbon Total Factor Productivity

According to the definition provided by neoclassical economic theory, TFP, also known as the Solow residual, is the most critical indicator for measuring technological progress and efficiency in production [24]. It represents the ratio of output to the input costs of labour, capital, and other material resources within a multi-input, multi-output framework, reflecting the average output per unit of total input over a specific industry or period. In practical applications, TFP is commonly defined as the ratio of total output to total input, capturing the total output achievable under existing technology given a certain level of total input. Changes in TFP over time indicate improvements in production efficiency. This concept and measurement methodology can be traced back to Solow’s investigation into the sources of economic growth [25].

As a foundational contribution to neoclassical economic growth theory, Solow’s study first identified that economic growth stems from two sources: the increase in output due to the growth in input factors such as labour and capital, and the improvement in production efficiency resulting from advancements in factor technology, cost reduction, and product quality improvement. The latter is defined as TFP. Low-carbon TFP, in turn, represents the application of TFP theory within the context of the low-carbon economy, serving as a critical tool for analyzing a nation’s sustainable economic growth.

The definition of the GVC, according to the United Nations Industrial Development Organization, includes various value-added activities from upstream to downstream in the production process. These activities comprise design, product development, manufacturing, marketing, delivery, consumption, after-sales services, and final recycling [26]. The activities can be categorized into high-end and low-end positions based on the amount of value added. This classification resembles a ’smile curve’ with peaks in design and product development, a trough in manufacturing, and peaks again in marketing and after-sales services.

The high-end segments of the GVC often involve technology research and development and service activities, offering high added value and minimal environmental pollution. In contrast, the low-end processing and manufacturing segments imply lower added value and higher carbon emissions, resulting in a lower low-carbon TFP. Therefore, from a long-term perspective and to maximize social welfare, a country is likely to actively enhance its division of labour position in specific industry chains by catching up, learning, and innovating in international advanced technologies. In this process, the GVC acts as a conduit for technology spillover effects and positive externalities, providing valuable opportunities for the high-quality transformation and upgrading of industries in developing countries [27].

3.2. The Impact of Global Value Chain Participation on Low-Carbon Total Factor Productivity

In the context of extensive international trade in intermediate goods, a country’s degree of participation in the GVC reflects its contribution to and dependence on the GVC [28,29]. This process of value chain participation is also accompanied by the creation and competition of advanced production and emission reduction technologies. On one hand, deep involvement in the global production network enables a country to gain access to relevant advanced technologies. This can occur through passive technology spillover in adjacent intermediate stages and proactively adopting “learning by doing” methods amid intense international competition [30,31]. These approaches effectively promote the improvement of low-carbon TFP. On the other hand, participating extensively in the GVC and expanding economic activities excessively can result in increased carbon emissions and draw the attention of major international buyers and multinational corporations. This, in turn, can hinder technology spillover due to various technological trade barriers, which can keep the country locked in its existing production stages [32]. As a result, the enhancement of low-carbon TFP can be significantly inhibited.

In reality, technology spillover and technology suppression effects often coexist in the process of GVC participation, and the balance and ultimate impact between them depend greatly on the country’s position in specific industry chains. When a country’s primary production activities focus on the high-end segments of the GVC, it acts as both the creator and owner of advanced technologies, making it more favourable to amplify the positive effects of efficiency improvements in further technological competition, while avoiding the hindering effects of technological barriers. In this case, the increase in GVC participation is more likely to manifest as a positive impact on low-carbon TFP. However, when a country’s industrial sectors are more concentrated in the low-end processing and manufacturing segments, the lower technological intensity and significant challenges in catching up make it more vulnerable to being captured by technologically advanced countries and companies. Through methods such as transferring pollution-intensive segments, it not only hinders the improvement of low-carbon TFP but also leads the industry into a more severe low-end lock-in and “pollution haven” dilemma [33].

3.3. Summary

Based on the current literature review of international division of labour theory, value chain theory, and comparative advantage theory, as well as the analysis of the impact mechanism of value chain embedding on low-carbon TFP, the following hypotheses are proposed:

H1: 

The enhancement of the division of labour positions in the GVC promotes the growth of low-carbon TFP.

H2: 

The increase in the participation level in the GVC has both technology spillover and technology suppression effects on low-carbon TFP, and the outcome will exhibit a nonlinear impact depending on the differences in industry division of labour positions.

Based on the theoretical mechanism analysis, this study initially constructs a baseline model to examine the overall impact of the GVC participation and division of labour on the low-carbon TFP of the paper industry in various regions:

$$LCTF{P}_{it}={\alpha }_0+{\alpha }_{1}GVC\text{\_}P{A}_{it}+{\alpha }_{2}GVC\text{\_}P{O}_{it}+{\alpha }_3{X}_{it}+{\nu }_i+{\nu }_t+{\epsilon }_{it}$$

(1)

where i = 1, 2, …, N represents different countries, t = 1, 2, …, T represents time, LCTFP is the dependent variable under investigation: the low-carbon TFP of the paper industry, GVC_PA and GVC_PO are two types of explanatory variables under investigation, referring to the participation and division of labour position in the GVC of the paper industry, X represents a series of control variables, and α is the corresponding coefficient vector. According to the research hypotheses, α₂ is positive, indicating that low-carbon TFP increases with the rise in division of labour position. The sign of α₁ is uncertain, reflecting the varying impact of the participation index on low-carbon TFP across different stages of value chain embedding. v_i and v_t are the fixed effects for regions and years, respectively, and ε_it is the random disturbance term.

The theoretical mechanism diagram, as derived from the above analysis, is shown in Figure 1:

4. Model Specification and Variable Selection

The econometric analysis in this study utilizes a panel regression model to examine the relationship between GVC embedding and low-carbon TFP. Given the longitudinal nature of the dataset, which spans 42 countries over a 20-year period, a panel data approach is particularly suitable as it allows for the control of unobserved heterogeneity across countries and over time.

4.1. Primary Model Specification

4.1.1. Threshold Effects Model

The threshold effects model is rooted in the nonlinear econometric framework proposed by Hansen (1999) [34], which is widely used to examine structural breaks and threshold dynamics in panel data. This model is particularly suited for exploring how the effects of independent variables vary across regimes defined by a threshold variable. In the context of this study, the threshold effects model is applied to investigate the nonlinear impact of GVC embedding on low-carbon TFP, with GVC participation serving as the threshold variable.

Equation (2) provides the mathematical specification of the threshold effects model:

$$\begin{array}{l}LCTF{P}_{it}={\mu }_i+{\beta }_{1}GVC\text{\_}P{A}_{it}\times I(GVC\text{\_}P{O}_{it}\le \gamma )+{\beta }_1^{\prime }GVC\text{\_}P{A}_{it}\times I(GVC\text{\_}P{O}_{it}>\gamma )+\\ {\beta }_2{X}_{it}+{\omega }_{it}\end{array}$$

(2)

where the main variable meanings are as mentioned above, TFP_it represents the low-carbon total factor productivity for country i at time t. GVC_PA_it and GVC_PO_it indicate GVC participation and division of labour metrics. X_it denotes other control variables. I(·) is an indicator function that defines the regimes based on the threshold variable q_it, taking the value 1 if the corresponding condition is met and 0 otherwise, γ is a specific threshold value, β is the corresponding coefficient vector, μ_i reflects individual effects in different economies, and ω_it is the random disturbance term. The model can be expanded into a multiple-threshold model depending on specific circumstances.

This model assumes that the relationship between GVC embedding and low-carbon TFP may change when the GVC participation level exceeds a critical threshold γ. For instance, in lower participation regimes (q_it ≤ γ), GVC effects may be constrained by factors such as limited technological capacity or low resource utilization efficiency. Conversely, in higher participation regimes (q_it > γ), the positive effects of advanced technological spillovers and enhanced division of labour may become more pronounced.

The application of this model enables the study to capture the heterogeneous effects of GVC embedding across different stages of value chain integration. By estimating γ, the study identifies the critical participation level that differentiates these regimes, providing actionable insights into how countries can transition to higher productivity stages.

The threshold effects model is particularly appropriate for this study for the following reasons: (1) It captures nonlinearity in the relationship between GVC embedding and low-carbon TFP, reflecting the complexity of value chain dynamics; (2) It accounts for potential heterogeneity across countries by incorporating unobserved fixed effects (μ_i); (3) It provides a clear interpretation of regime shifts, enabling policymakers to identify critical participation levels for enhancing low-carbon TFP.

4.1.2. Slack-Based Measure and Global Malmquist–Luenberger Index Model

To accurately calculate the low-carbon TFP of the paper industry in various countries, the study references the estimation method proposed by Färe et al. [35]. It employs the SBM-GML index to assess the low-carbon TFP of all major countries in the paper industry chain during the research period.

Assuming each country is a decision-making unit (DMU), with each unit using N inputs: x = (x₁,…,x_N)ϵ$R_N^{+}$, producing M desired outputs: y = (y₁,…,y_m)ϵ$R_M^{+}$, and I undesired outputs: b = (b₁,…,b_I)ϵ$R_I^{+}$. The input–output vector for country k in period t is represented as (x^k,t, y^k,t, b^k,t). The feasible production set P^t(x^t) considering input and undesired output constraints for the current period can be expressed as the following:

$$P^t(x^t)=\left\{\begin{array}{c}\hfill (y^t,b^t)\mid {\displaystyle \sum _{k=1}^K{\lambda }_k^t{x}_{kn}^t\le x_{kn}^t;}\hspace{1em}{\displaystyle \sum _{k=1}^K{\lambda }_k^t{y}_{km}^t\ge y_{km}^t;}\hspace{1em}{\displaystyle \sum _{k=1}^K{\lambda }_k^t{b}_{ki}^t\ge b_{ki}^t;}\hspace{1em}{\displaystyle \sum _{k=1}^K{\lambda }_k^t=1,{\lambda }_k^t\ge 0}\hfill \end{array}\right\}$$

(3)

where ${\lambda }_k^t$ is the weight for each cross-sectional observation, and when ${\lambda }_k^t$ ≥ 0, production technology follows the Constant Returns to Scale (CRS) assumption, when ${\lambda }_k^t$ ≥ 0 and ${\mathsf{\sum }}_{k=1}^k$ ${\lambda }_k^t=1$, it follows the Variable Returns to Scale (VRS) assumption. Considering the comparability and consistency of the production frontier, the production possibility set in Equation (3) is transformed into a global-based production possibility set P^G(x):

$$P^G(x)=P^1(x^1)\cup P^2(x^2)\cup P^3(x^3)\cup \cdots \cup P^t(x^t)$$

(4)

Based on this, the study, following the estimation method of Fukuyama and Weber [36], defines the global SBM directional distance function as:

$$\begin{array}{l}{S}_V^G(x^{t,k^{\prime }},y^{t,k^{\prime }},b^{t,k^{\prime }},g^x,g^y,g^b)=\underset{s^x{s}^y{s}^b}{\max }{\displaystyle \frac{\frac{1}{N}{\displaystyle \sum _{n=1}^N\frac{s_n^x}{g_n^x}+\frac{1}{M+I}({\displaystyle \sum _{m=1}^M\frac{s_m^y}{g_m^y}+}{\displaystyle \sum _{i=1}^I\frac{s_i^b}{g_i^b}})}}{2}}\\ S.t.\left\{\begin{array}{c}\begin{array}{ccc}{\displaystyle \sum _{k=1}^K{\lambda }_k^t{x}_{kn}^t+s_n^x=x_{k^{\prime }n}^t;}& {\displaystyle \sum _{k=1}^K{\lambda }_k^t{y}_{km}^t-s_m^y=y_{k^{\prime }m}^t;}& {\displaystyle \sum _{k=1}^K{\lambda }_k^t{b}_{ki}^t+s_i^b=b_{k^{\prime }i}^t;}\end{array}\\ \hfill \begin{array}{c}{\displaystyle \sum _{k=1}^K{\lambda }_k^t=1,{\lambda }_k^t\ge 0;}\hspace{1em}{s}_n^x\ge 0;\hspace{1em}{s}_m^y\ge 0;\hspace{1em}{s}_i^b\ge 0;\end{array}\hfill \end{array}\right\}\end{array}$$

(5)

where (x^t,k′, y^t,k′, b^t,k′) represents the input, desired output, and undesired output vector of the paper industry of country k in period t, (g^x, g^y, g^b) is the directional variable representing the reduction in inputs, increase in desired outputs, and decrease in undesired outputs, ($S_n^x$, $S_m^y$, $S_i^b$) is the slack vector of inputs, desired outputs, and undesired outputs. $S_n^x$ represents input redundancy, $S_m^y$ represents desired outputs insufficiency, and $S_i^b$ represents excessive undesired outputs. When $S_n^x$, $S_i^b$ > 0, it indicates that the actual inputs and undesired outputs exceed the boundary values, and when $S_m^y$ > 0, it means that the actual desired outputs are less than the boundary values.

The SBM function is primarily used to estimate the static low-carbon TFP of each production decision unit. To reflect the dynamic characteristics of low-carbon TFP changes, the study further utilizes the GML index formula proposed by Oh [37] on this basis:

$$GM{L}_t^{t+1}={\displaystyle \frac{1+S_V^G(\begin{array}{cc}{x}^t,y^t,b^t;& g^x,g^y,g^b\end{array})}{1+S_V^G(\begin{array}{c}{x}^{t+1},y^{t+1},b^{t+1}; g^x,g^y,g^b\end{array})}}$$

(6)

where a GML index greater than 1 indicates an increase in low-carbon TFP, while a value less than 1 suggests a decline.

4.1.3. Multi-Regional Input–Output Model

The Multi-Regional Input–Output (MRIO) model encompasses information on production, demand, and bilateral trade among multiple countries globally. MRIO effectively avoids the “double-counting” issue associated with traditional export trade accounting in addition to allowing the calculation of domestic output created by foreign demand in terms of value-added trade. Therefore, the model is chosen to examine the GVC participation and division of labour in the paper industry across different countries. According to the MRIO model, a country s’ exports (E_sr) to any country r consists of two parts: intermediate exports (A_srX_r) and final goods exports (Y_sr). According to the total trade accounting framework, a country s’ exports to country r can be decomposed into 16 parts of value-added and duplicative calculations, as follows:

$$\begin{array}{l}{E}_{sr}={(V_s{B}_{ss})}^T\#Y_{sr}+{(V_s{L}_{ss})}^T\#(A_{sr}{B}_{rr}{Y}_{rr})+{(V_s{L}_{ss})}^T\#(A_{sr}{\displaystyle \sum _{t\ne s,r}^G{B}_{rt}{Y}_{tt}})+{(V_s{L}_{ss})}^T\#(A_{sr}{B}_{rr}{\displaystyle \sum _{t\ne s,r}^G{Y}_{rt}})\\ +{(V_s{L}_{ss})}^T\#(A_{sr}{\displaystyle \sum _{t\ne s,}^G{\displaystyle \sum _{ru\ne s,t}^G{B}_{rt}{Y}_{tu}}})+{(V_s{L}_{ss})}^T\#(A_{sr}{B}_{rr}{Y}_{rs})+{(V_s{L}_{ss})}^T\#(A_{sr}{\displaystyle \sum _{t\ne s,r}^G{B}_{rt}{Y}_{ts}})\\ +{(V_s{L}_{ss})}^T\#(A_{sr}{B}_{rs}{Y}_{ss})+{(V_s{L}_{ss})}^T{\#(\mathrm{A}}_{\mathrm{sr}}{\displaystyle \sum _{\mathrm{t}\ne \mathrm{s}}^{\mathrm{G}}{\mathrm{B}}_{\mathrm{rs}}{Y}_{st}})+{\left({\mathrm{V}}_{\mathrm{s}}{\mathrm{B}}_{\mathrm{ss}}{-\mathrm{V}}_{\mathrm{s}}{\mathrm{L}}_{ss}\right)}^{\mathrm{T}}\#(A_{sr}{X}_r)+{(V_r{B}_{rs})}^T\#Y_{sr}\\ +{(V_r{B}_{rs})}^T\#(A_{sr}{L}_{rr}{Y}_{rr})+{(V_r{B}_{rs})}^T\#(A_{sr}{L}_{rr}{E}_{r*})+{({\displaystyle \sum _{t\ne s,r}^G{V}_t}{B}_{ts})}^T\#Y_{sr}+{({\displaystyle \sum _{t\ne s,r}^G{V}_t}{B}_{ts})}^T\#(A_{sr}{L}_{rr}{Y}_{rr})\\ +{({\displaystyle \sum _{t\ne s,r}^G{V}_t}{B}_{ts})}^T\#(A_{sr}{L}_{rr}{E}_{r*})\end{array}$$

(7)

where # denotes the block matrix dot product; A_ss and A_sr are the direct consumption coefficient matrices within country s and the mutual demand coefficient matrix between production sectors of countries s and r, respectively; B_ss, B_rr, B_rt, B_rs, and B_ts are the classical Leontief inverse matrices; L_ss and L_rr are the Leontief inverse matrices within countries s, r, and t, respectively, and L_ss = (I − A_ss)⁻¹; V_s, V_r, and V_t are the value-added coefficient vectors for countries s, r, and t, respectively; X_r and E_r* are the total output vector and total export vector for country r (both N × 1 column vectors); Y_ss and Y_sr are the vectors representing the production used to satisfy domestic demand and final demand for country r, respectively.

If we denote the 16 parts on the right side of Equation (7) as vectors T₁ to T₁₆, then the equation can be transformed as follows:

$$E_{sr}=T_1+T_2+\cdots +T_{16}={\displaystyle \sum T_n}$$

(8)

The specific meanings of each part are shown in

Table 1. Specific meanings of decomposition parts in MRIO from the value-added perspective.

Component	Symbol	Decomposition	Symbol	Code
Domestic value-added absorbed by foreign countries	DVA	Domestic value-added embodied in final goods exports	DVA_FIN	T1
		Intermediate goods exports absorbed directly by the importing country	DVA_INT	T2
		Intermediate goods exports absorbed by the importing country through direct production for re-export to a third country	DVA_INTREX	T3 + T4 + T5
Domestic value-added returned and absorbed domestically	RDV	/	/	T6 + T7 + T8
Foreign value-added	FVA	Value-added implied by exports to the importing country	MVA	T11 + T12
		Value-added implied by exports to other countries	OVA	T14 + T15
Pure double-counting parts	PDC	Pure double counting from the domestic account	DDC	T9 + T10
		Pure double counting from the foreign account	FDC	T13 + T16

Note: All value-added vectors are column vectors of N × 1.

:

4.2. Variable Selection and Data Sources

4.2.1. Dependent Variable: Low-Carbon Total Factor Productivity

For the research objectives, the expected output for low-carbon TFP calculation was defined as the total output of a nation’s paper industry. The relevant data were sourced from the WIOD (The World Input Output Database (WIOD) is developed by the European Commission, Research Directorate General, and the 2016 version covers input and output data for 56 sectors in 43 countries from 2000 to 2014) and the ADB MRIO (The Asian Development Bank MRIO (ADBMRIO) is a database housing the multiregional input–output tables and derived indicators across multiple economies covering various time periods (2000, 2007–2021)) databases. The undesired output was identified as the carbon dioxide emissions from the paper industry sector of a nation. The data used in this study was obtained from two sources: the WIOD for the years 2001–2016, and the EDGAR-IND (The Emissions Database for Global Atmospheric (EDGAR-IND) database is an independent global greenhouse gas and air pollution anthropogenic emission database developed by the European Union Statistical Office) database for the years 2017–2021. This study then presents consolidated annual carbon emissions for the manufacturing industry of each country. Additionally, it estimates the carbon emissions for the paper industry based on corresponding proportions. The inputs required for low-carbon TFP calculation include labour, capital, and energy factors. Employment in the paper industry, total energy consumption, and nominal capital stock are used as indicators. Data are sourced from the WIOD-SEA (WIOD-Socio Economic Accounts (SEA) provides industry-level data on employment, capital stocks, gross output, and value added in millions of local currency, both at current and constant prices), ILOSTAT (The International Labour Organization (ILO) Department of Statistics serves as the United Nations’ focal point for labour statistics. It develops international standards to improve the measurement of labour issues and enhance international comparability), pwt100 (The Penn World Table (PWT) version 10.00 is a database containing information on the relative levels of income, output, input, and productivity for 183 countries between 1950 and 2019), and the World Bank database. For capital-related indicators, the study further converts data based on annual exchange rate changes from databases such as IMF-IFS (The International Financial Statistics (IFS) of the International Monetary Fund (IMF) is one of the Fund’s principal statistical datasets and has been available since January 1948), EUROSTAT, and Internal Revenue Service (IRS) to obtain accurate input factor data.

4.2.2. Independent Variable: Global Value Chain Participation and Division of Labour

The research adopts the analytical method proposed by Wang et al. [29], representing the forward and backward participation of a nation’s specific sector in the GVC as the following:

$$GVCP{t}_f={\displaystyle \frac{V\text{\_}GVC\text{\_}S}{v{a}^{\prime }}}+{\displaystyle \frac{V\text{\_}GVC\text{\_}C}{v{a}^{\prime }}}={\displaystyle \frac{\stackrel{⌢}{V}L{A}^{F}BY}{v{a}^{\prime }}}$$

(9)

$$GVCP{t}_b={\displaystyle \frac{V\text{\_}GVC\text{\_}S}{Y^{\prime }}}+{\displaystyle \frac{V\text{\_}GVC\text{\_}C}{Y^{\prime }}}={\displaystyle \frac{VL{A}^{F}B\stackrel{⌢}{Y}}{Y^{\prime }}}$$

(10)

where va’ represents the destination of value-added or industry GDP of a specific sector in a nation, Y’ denotes the source of value-added for the final output of a specific sector in a nation. V_GVC_S and V_GVC_C, respectively, represent the portions of simple GVC activities and complex GVC activities remaining in a nation’s total production activities after deducting pure domestic production and traditional international trade activities. Based on this, the GVC participation of a specific sector in a nation can be expressed as the following:

$$GVC\text{\_}Participation=GVCP{t}_f+GVCP{t}_b$$

(11)

The larger this index, the higher the degree of participation in the GVC.

Furthermore, according to the GVC division of labour measurement proposed by Koopman et al. [28], the GVC division of labour status of a specific sector in a nation is represented as the following:

$$GVC\text{\_}Position=\ln (1+GVCP{t}_f)-\ln (1+GVCP{t}_b)$$

(12)

The larger this index, the closer it is to the upstream of the value chain.

Using the above measurement methods, the study, based on the UIBE GVC INDEX (The UIBE GVC INDEX system is a secondary (derived) database developed by theGVC research team of the University of International Business and Economics under the leadership of Professor Zhi Wang. It is based on the current mature methods of value-added trade accounting and analysis, processed from the original data of the World ICIO Database) system, extracts and calculates the GVC participation and division of labour data for the paper industry of various countries from 2001 to 2021 using data from the WIOD and ADBMRIO databases. Specifically, we selected the raw data from WIOD as the core data for the first stage. In subsequent periods, we began with overlapping years containing relevant indicators from both databases. Using the trend ratios of the values in ADBMRIO, we reasonably estimated the years not included in WIOD. This allowed us to obtain comparable data for global value chain participation and division of labour positions over the study period. The WIOD includes a total of 42 major global economies within the paper industry value chain. From the perspective of geographic location and socio-political conditions, these 42 countries encompass three distinct groups: Asia–Pacific countries representing developing economies, EU member states mostly comprising developed nations, and New World countries such as the United States, Canada, and Australia. Notably, these three groups exhibit significant differences in carbon reduction policies, making them well suited for subsequent heterogeneity analysis to better validate the research hypotheses. Therefore, examining the selected countries will provide robust insights into the mechanisms through which value chain embedding impacts low-carbon TFP across different nations.

4.2.3. Control Variables

Industrial Structure (IS): Calculated by the proportion of a nation’s paper industry output to the total output of the manufacturing industry. The manufacturing industry is a core sector influencing environmental protection and economic growth. Given the overlay of carbon reduction constraints and scale effects, countries are actively promoting policies in the paper industry towards cleaner and high-tech sectors. Therefore, it is predicted that this indicator will have a positive structural effect. The relevant data are sourced from the WIOD and ADBMRIO databases.

Energy Consumption Structure (ES): Calculated by the proportion of coal consumption in a nation’s paper industry to the total energy consumption of the industry. A higher proportion of coal consumption, compared to clean energy, leads to more carbon dioxide emissions, hindering the improvement of low-carbon TFP. The data used is sourced from the WIOD for the years 2001–2016. For the years 2017–2021, the data are estimated based on the ratio of coal consumption in the overall industry, as reported in the ’World Energy Statistics Yearbook.’ The list of variables’ descriptions is reported in

Table 2. Variables descriptions and sources.

Variables	Definitions	Main Sources	Links
Expected output	Industrial total output	WIOD, ADBWRIO	https://www.rug.nl/ggdc/valuechain/wiod/ (accessed on 30 April 2024) https://kidb.adb.org/globalization (accessed on 30 April 2024)
Undesired output	Industrial carbon dioxide emissions	WIOD, EDGAR-IND	https://www.rug.nl/ggdc/valuechain/wiod/ (accessed on 30 April 2024) https://edgar.jrc.ec.europa.eu/gallery?release=v70ghg&substance=CO2_excl_short-cycle_org_C&sector=IND (accessed on 30 April 2024)
Labour input	Industrial employment	WIOD-SEA, ILOSTAT, pwt100, World Bank Databese, IMF-IFS	https://www.rug.nl/ggdc/valuechain/wiod/wiod-2016-release (accessed on 30 April 2024) https://ilostat.ilo.org/data/ (accessed on 30 April 2024) https://www.rug.nl/ggdc/productivity/pwt/ (accessed on 30 April 2024) https://data.worldbank.org/ (accessed on 30 April 2024) https://data.imf.org/?sk=4c514d48-b6ba-49ed-8ab9-52b0c1a0179b (accessed on 30 April 2024)
Capital input	Industrial nominal capital stock
Energy input	Industrial total energy consumption
GVC participation	Industrial degree of participation in the GVC	WIOD, ADBWRIO	https://www.rug.nl/ggdc/valuechain/wiod/ (accessed on 30 April 2024) https://kidb.adb.org/globalization (accessed on 30 April 2024)
GVC position	Industrial position in the GVC
Industrial structure	Proportion of paper industry output to the total output of the manufacturing industry
Energy consumption structure	Proportion of coal consumption in paper industry to the total energy consumption of the industry	WIOD, World Energy Statistics Yearbook	https://www.rug.nl/ggdc/valuechain/wiod/ (accessed on 30 April 2024) https://digitallibrary.un.org/record/4037837?v=pdf (accessed on 30 April 2024)

.

5. Results

5.1. Current State and Trends of Low-Carbon Total Factor Productivity

Before examining the productivity impact of value chain integration, the study first utilizes the SBM-GML model to incorporate various input and output data. This is performed to calculate the low-carbon TFP development and changes in the paper industry of major countries and regions worldwide from 2001 to 2021. Based on the above settings, the GML index reflects the dynamic characteristics of low-carbon TFP and is further decomposed into technical efficiency change (EC) and best practice gap change (BPC). This decomposition provides a basis for understanding the basic dynamics and preparing data for subsequent impact analysis.

Table 3. Average low-carbon TFP and its decomposition in the paper industry of various countries from 2001 to 2021.

Country	LCTFP	EC	BPC	Country	LCTFP	EC	BPC
Malta	0.650	1.000	1.053	Australia	0.023	0.937	1.234
United States	0.584	1.000	1.048	Portugal	0.023	0.955	1.081
Luxembourg	0.438	1.013	1.199	Slovak Republic	0.022	1.004	1.106
Ireland	0.391	1.000	1.100	Romania	0.022	0.985	1.114
China	0.286	1.085	1.954	Hungary	0.019	0.936	1.096
Japan	0.134	0.987	1.189	France	0.019	0.876	1.308
Overall	0.088	0.952	1.192	Canada	0.018	0.945	1.357
Estonia	0.077	0.892	1.164	Czech Republic	0.018	0.961	1.077
Croatia	0.076	1.271	1.171	United Kingdom	0.017	0.888	1.407
Norway	0.074	0.934	1.123	Poland	0.015	0.946	1.068
Denmark	0.050	0.958	1.088	Italy	0.014	0.887	1.478
Switzerland	0.047	0.919	1.144	Spain	0.014	0.867	1.240
Germany	0.041	0.868	1.746	Korea, Republic of	0.012	0.991	1.481
Latvia	0.038	0.965	1.123	Bulgaria	0.012	0.928	1.102
Greece	0.035	0.965	1.092	Turkey	0.009	0.922	1.084
Finland	0.029	0.927	1.159	Taiwan	0.009	0.925	1.079
Netherlands	0.026	0.912	1.239	Mexico	0.006	0.886	1.190
Belgium	0.026	0.934	1.095	Brazil	0.005	0.895	1.195
Sweden	0.025	0.916	1.172	Russia	0.004	1.015	1.145
Lithuania	0.025	0.929	1.105	Indonesia	0.003	0.916	1.068
Austria	0.024	0.931	1.088	India	0.001	0.920	1.072
Slovenia	0.023	0.949	1.107

Data Source: Calculated by the authors.

shows the average values of relevant indicators for each region, sorted in descending order of low-carbon TFP.

The table above shows that out of the 42 major economies involved in the global paper industry chain, Malta (MLT) has the highest level of low-carbon TFP, with an average value of 0.66 during the study period. In contrast, India (IND) has the lowest indicator value, standing at approximately 0, indicating significant regional differences. Moreover, only six countries, including China, exhibit low-carbon TFP values higher than the overall average, once again emphasizing a significant hierarchical development pattern in low-carbon TFP across regions. Additionally, concerning the decomposition of the GML index, the growth of low-carbon TFP in most countries and regions is attributed to the change in the best practice gap, i.e., ‘technological progress’. This means increasing output without increasing input by using technological advancements. The technical efficiency indicators of the top five countries, including China, also support the growth of low-carbon TFP. This suggests that, at the current technological level, these countries can further utilize their existing technology by improving coordination among various resource elements. Based on this analysis, it can be concluded that to achieve growth in low-carbon TFP from the perspective of indicator connotation, countries should continue to improve their technological levels while simultaneously focusing on innovation and exploration of their own technical efficiency. This provides valuable insights into the specific practical direction of each country in value chain integration.

Based on the measurement of low-carbon TFP and its constituent indicators across countries, the study focused on China as a high-performing country. By examining China’s technological advancements and efficiency improvements since 2001, we evaluated the significant roles of BPC and EC in driving low-carbon TFP improvements. As the world’s largest producer and consumer of paper and paperboard, China has long been aware of the paper industry’s challenges, such as high energy consumption, strong resource dependence, and significant pollution emissions. Over the years, the country has continuously promoted a low-carbon transformation of the industry through various measures, steadily increasing its low-carbon TFP. Specifically, in promoting technological progress, China has actively developed water- and energy-saving technologies and equipment, integrating them with advanced automation systems and intelligent control systems to optimize labour efficiency. In enhancing technical efficiency, the country has adopted new biomass and low-temperature thermal energy as alternatives to traditional coal-fired power. Additionally, outdated equipment, such as cooling towers and wastewater recycling systems, has been replaced, upgraded, and restructured to significantly improve production efficiency. These measures have rapidly advanced the low-carbon transformation of China’s paper industry over the past decade, turning a traditionally high-pollution sector into a key contributor to clean production. As a result, the low-carbon TFP of China’s paper industry now ranks among the highest in the world.

5.2. Baseline Regression

Using the collected data on low-carbon TFP levels and other key variables, a fixed-effects model is employed in this study to conduct a baseline test on the actual effects of the growth in GVC participation and division of labour status in the paper industry of different countries (regions). Firstly, descriptive statistics are performed on each variable, and the results are showed in

Table 4. Descriptive statistics of each variable.

Variable	Sample Size	Mean	Standard Deviation	Minimum	Maximum
LCTFP	882	0.081	0.177	0.001	1.000
GVC_PA	882	0.611	0.252	0.145	1.454
GVC_PO	882	0.063	0.107	−0.181	0.445
IS	882	0.060	0.032	0.011	0.197
ES	882	0.060	0.118	0.000	0.764

Data Source: Calculated by the authors.

.

The table above shows that all necessary variable data for the study has been obtained and that the sample sizes meet the research requirements. It is clear that, with the exception of the value chain division of labour status, all indicators have positive values based on the minimum and mean values. The absolute variations in each variable are not significant, and the evolving trends are relatively stable, although the possibility of thresholds cannot be ruled out. On this basis, we conducted unit root and cointegration tests on the sample data to ensure the validity of the results. The corresponding results are presented in

Table 5. Unit root and cointegration tests results.

Variable	Chi2	p Value	Kao Cointegration Test	Statistic	p Value
LCTFP	120.713	0.005	Modified Dickey–Fuller t	−1.782	0.037
GVC_PA	102.298	0.085	Dickey–Fuller t	−1.783	0.037
GVC_PO	124.604	0.003	Augmented Dickey–Fuller t	2.110	0.017
d.IS	890.895	0.000	Unadjusted modified Dickey–Fuller t	−3.705	0.000
ES	147.665	0.000	Unadjusted Dickey–Fuller t	−2.844	0.002

Data Source: Calculated by the authors.

.

As shown in the table above, all variables used in this study passed the unit root and cointegration tests at the 10% significance level, making them suitable for constructing panel data for the subsequent regression analysis. In the model selection process, we considered the adaptability of cross-sectional models and panel models based on the basic characteristics of the sample data and the primary research questions. Since the main goal of this study is to examine the impact of different stages of value chain embedding on low-carbon TFP in the paper industry of various countries, and, considering that during the study period, the 42 major economies in the global paper industry chain were at various stages of international division and participation, with differing trends over time, the panel model was deemed more suitable than the cross-sectional model. This is because the panel model can better reflect the temporal variation characteristics of the sample data. Therefore, this study selects the panel model for analysis.

After conducting a preliminary econometric analysis of the data, the study proceeds to the overall regression test for the variables mentioned above. Both fixed-effects and random-effects models were considered, and a Hausman test was conducted to determine the appropriate model. The results (Chi-squared = 15.27, p-value = 0.004) indicate that the fixed-effects model is more suitable at a 1% significance level. This choice is justified for the following reasons: (1) Fixed effects control for country-specific, time-invariant factors such as institutional quality and geographic characteristics; (2) The model mitigates omitted variable bias by focusing on within-country variations; (3) It is well suited for analyzing the effectiveness of policy interventions like GVC integration strategies. These assumptions were verified through diagnostic tests for heteroskedasticity, serial correlation, and cross-sectional dependence. The estimation results are shown in

Table 6. Baseline regression results.

Variable	GVC_PA	GVC_PO	IS	ES
Coefficient	0.018 (0.33)	0.264 *** (3.27)	2.219 *** (7.78)	−0.390 *** (−6.38)

Note: *** represents significance level at 1%. The values in parentheses are t-statistics.

.

From the table above, it can be observed that, except for the variable of GVC participation, the parameter results for the other variables in the model have passed the significance test at the 1% level. Specifically, among the control variables, for every 1% increase in the industrial structure indicator, the low-carbon TFP is expected to increase by 2.22%. This shows that under the constraints of a low-carbon economy, paper industries in various countries are generally shifting towards a clean and sustainable development model, contributing to the improvement of the industry’s low-carbon TFP. For every 1% increase in the energy consumption structure indicator, the low-carbon TFP is expected to decrease by 0.39%. This indicates that the consumption of traditional energy sources, such as coal, significantly hinders the transformation of the paper industry. As for the two types of explanatory variables, the division of labour status has a promoting effect on low-carbon TFP. For every 1% increase in this indicator, the corresponding low-carbon TFP is expected to increase by 0.26%, which supports Hypothesis H1. However, the participation indicator does not show a significant regression result, suggesting a possible nonlinear relationship between the two variables, partially confirming the theoretical mechanism mentioned earlier.

5.3. Endogeneity Test

Considering the potential high autocorrelation of low-carbon TFP as the dependent variable and the possible bidirectional causality with the independent variables, the study builds on the above static decomposition and adopts a System GMM model, as referenced by Yao and Xia [38]. By introducing the first-order lag term of the dependent variable into Equation (1), the dynamic model verifies the mechanism by which value chain embedding influences low-carbon TFP and alleviates potential endogeneity issues in the baseline model. The specific model settings are as follows, and the estimation results are shown in

Table 7. Endogeneity effect test results.

LCTFPt−1	0.616 ***	GVC_PA	0.056 ***	GVC_PO	0.349 ***	IS	3.606 ***
ES	−0.106 ***	AR(1)	0.075 (−1.78)	Ar(2)	0.147 (1.45)	Hansen Tset	0.137 (41.94)

Note: *** represents significance level at 1%, the z statistic and chi-square distribution are in parentheses.

.

$$LCTF{P}_{it}={\beta }_0+{\beta }_{1}LCTF{P}_{it-1}+{\beta }_{2}GVC\text{\_}P{A}_{it}+{\beta }_{3}GVC\text{\_}P{O}_{it}+{\beta }_4{X}_{it}+{\nu }_i+{\nu }_t+{\epsilon }_{it}$$

(13)

The table above shows that the AR(1) results are significant, the AR(2) results are not significant, and the Hansen test results are also not significant, indicating that the selected model is valid. Furthermore, the coefficients in the table show little deviation from the baseline regression results, suggesting that the endogeneity problem is not severe and does not affect the reliability of the model results.

5.4. Threshold Effect Test

After examining the promoting effect of value chain division of labour status on low-carbon TFP, the study, based on linear analysis, further explores a nonlinear relationship between participation indicators and low-carbon TFP using the division of labour status indicator as a threshold variable. The relevant parameter results are presented in

Table 8. Threshold effect test results.

Threshold Value	0.210	F Value	51.30	p Value	0.040	5% Critical Value	45.872
GVC_PA_0	−0.019	GVC_PA_1	0.126 ***	IS	2.137 ***	ES	−0.423 ***

Note: *** represents significance level at 1%.

.

The table above shows that there is a significant single threshold effect between low-carbon TFP and the GVC participation indicator. Specifically, when the division of labour status is below 0.21, the participation indicator has a non-significant negative impact on the paper industry’s low-carbon TFP. However, if the division of labour status index exceeds the threshold value, a 1% increase in participation will lead to a significant 0.13% increase in the corresponding low-carbon TFP level. This demonstrates the substantial additive effect of the high-end position in the GVC on technical spillover effect of participation. This result once again validates the theoretical mechanism and research hypothesis H2.

Based on these econometric results, the study uses the division of labour status threshold value as a boundary to group the corresponding impact on the paper industry of the 42 countries studied. The threshold phase diagram is illustrated in Figure 2 below.

The figure above shows that, between 2001 and 2021, only four countries—Finland, Sweden, Portugal, and Russia—had an average value chain division of labour status exceeding the threshold of 0.21 in the global paper industry chain. This indicates that an increase in participation at this point would significantly promote the improvement of low-carbon TFP. In contrast, for the other 38 countries (regions), including China, an increase in participation has no significant impact on their low-carbon TFP or may even have an inhibitory effect. This implies that, in this context, the improvement of the division of labour status is a prerequisite for promoting low-carbon development in the industry. In addition, it should be noted that the numerical value of this threshold will vary depending on the industrial sector, research period, and major countries in the industry chain, within the theoretical framework of this study.

5.5. Robustness Test

To ensure the robustness of the findings, additional diagnostic tests were conducted. First, we addressed potential heteroskedasticity by employing robust standard errors. Serial correlation was tested using the Wooldridge test, and necessary corrections were applied where serial correlation was detected. Furthermore, cross-sectional dependence was assessed due to the global nature of the data, and adjustments were incorporated to account for cross-country interactions.

The threshold model confirms the existence of a participation threshold. However, variations in energy policies and industrial structures across countries may introduce extreme values that interact with GVC embedding, potentially affecting the reliability of the results. To address this, we adopted the truncation method proposed by Chen et al. [40], performing a 1% bilateral truncation on key control variables, including energy structure and industrial structure data. This approach reduces the influence of extreme values on the regression results. After truncation, the R² of the threshold model increased from 0.17 to 0.18, while the significance and signs of core independent variables remained consistent, confirming the robustness of the model (

Table 9. Robustness test results.

Variable	GVC_PA	GVC_PO	IS	ES	—
Coefficient	0.026 (0.48)	0.243 *** (3.03)	2.378 *** (8.17)	−0.454 *** (−6.91)	—
Threshold Value	0.210	p Value	0.040	GVC_PA_0	−0.013
GVC_PA_1	0.125 ***	IS	2.292 ***	ES	−0.476 ***

Note: *** represents significance level at 1%.

).

5.6. Heterogeneity Test

Based on the analysis of the entire sample of countries, and to separate the potential impact of key socio-political factors on global value chain embedding and low-carbon total factor productivity, while also considering the sample size and the effectiveness of empirical results, this paper divides the 42 economies into two groups: EU countries and non-EU countries. These countries not only exhibit significant differences in industrial development strategies and global value chain embedding but also have varying carbon reduction policies.

The majority of EU countries are developed nations that focus on carbon pricing as a core strategy, aiming to control carbon emissions through a unified carbon trading system and market forces. On the other hand, other countries, including developing countries in the Asia–Pacific region as well as new-world countries like the United States, Canada, and Australia, all of which focus on significant investments or fiscal incentives in green industries, use methods such as tax credits to rapidly promote industry growth and achieve carbon reduction.

Therefore, conducting a heterogeneity analysis on these two groups of countries will further refine the mechanism through which global value chain embedding affects low-carbon total factor productivity in different countries. The threshold effect test results are presented in

Table 10. Heterogeneity effect test results.

Group	EU Country	Threshold Value	0.212 ***	F Value	63.67	5% Critical Value	45.764
GVC_PA_0	−0.032	GVC_PA_1	0.147 ***	IS	2.132 ***	ES	−0.166
Group	Non-EU Country	Threshold Value	0.009 *	F Value	9.62	5% Critical Value	11.270
GVC_PA_0	−0.965 ***	GVC_PA_1	0.262 *	IS	1.774 **	ES	−0.476 ***

Note: *, **, and *** represent significance levels at 10%, 5%, and 1%, respectively.

.

As shown in the table above, there is a significant single-threshold effect between low-carbon TFP and GVC embedding in both categories of economies. Specifically, for EU countries and non-EU countries, a 1% increase in initial GVC participation corresponds to a decrease in low-carbon TFP by 0.0318% and 0.965%, respectively. However, once the GVC position surpasses the thresholds of 0.21 and 0.01, a 1% increase in GVC participation leads to an increase in low-carbon TFP by 0.15% and 0.26%, respectively. The threshold for non-EU countries is lower, but the pre- and post-threshold effects of GVC participation are larger than those for EU countries. This indicates that while EU countries, benefiting from established technology transfer systems and resource-sharing policies, experience relatively stable effects of GVC embedding across different stages of development, the impact of GVC participation caused by technological progress is more controllable. In contrast, non-EU countries, despite encountering challenges such as low-end lock-in and technological barriers in the early stages of development, exhibit significant positive impacts on low-carbon TFP once their GVC position exceeds the corresponding threshold.

For the control variables, the share of the paper industry in GDP positively affects low-carbon TFP, with a 1% increase leading to a rise of 2.13% and 1.77% for EU and non-EU countries, respectively. Conversely, an increase in coal consumption as a proportion of energy structure by 1% reduces low-carbon TFP by 0.17% and 0.47%, respectively. These results highlight that the paper industry in EU countries is relatively more environmentally sustainable, while non-EU countries are called upon to direct their efforts towards enhancing the resilience and sustainability of their industries.

6. Discussion

6.1. Results Comparison

Among the numerous existing studies on low-carbon TFP, this study selects the paper industry, located at the forefront of carbon reduction actions, as the subject of investigation. It conducts international comparisons from the perspective of value chain embedding. The results drawn have a certain representativeness and differ from the existing literature in some aspects. Firstly, compared to more macro-level studies on the overall manufacturing industry, this study focuses on the paper industry, explicitly pointing out the varied impact effects on low-carbon TFP among 42 major countries in this value chain due to differences in the division of labour and participation [41,42]. Secondly, compared to many papers that discuss a single promoting or inhibiting effect of value chain embedding, this paper integrates existing research perspectives and proposes a nonlinear impact mechanism considering both the division of labour and participation. It empirically identifies the important threshold value of 0.2095 in the paper industry [43,44]. Finally, compared to some studies that solely examine the carbon productivity of single factors, this paper measures the input levels of other factors such as capital, labour, and technology in various stages of the industry chain [17,45]. By combining this with a precise definition of value chain embedding, the paper provides conclusions and recommendations that align more with the actual economic operating laws and contribute to promoting comprehensive industrial transformation and upgrading.

Furthermore, regarding the positions of the 42 countries in Figure 2 and the differences in the impact of the GVC embedding, there may be several reasons. Firstly, for the four countries in the upper part of the figure, Finland and Russia have abundant timber resources [46], and, similar to Sweden and Portugal [47,48], possess high production and processing technologies and international divisions of labour status in the paper industry. They have already entered a virtuous cycle of increasing participation and low-carbon TFP growth. Secondly, economies such as China, located in the lower right part of the figure, have achieved a high level of value chain participation. However, due to a lack of crucial technology needed to ascend to the high end of the GVC, further embedding into the value chain may hinder the growth of low-carbon TFP. They are already in a typical “low-end lock-in” situation [49]. Lastly, other economies located in the lower-left quadrant of the figure have low participation and division of labour status in the international paper industry chain. During the research period, they remained in an intermediate zone between the two aforementioned patterns. In the next stage of industrial development, they must choose between advancing technology or focusing on expanding scale. The development direction will depend on the resource endowments and future development plans of each country.

6.2. Validity, Reliability, and Generalisability

Against the backdrop of the transition to a low-carbon economy, this study focused on the global paper industry chain and redefined the accurate connotations of value chain embedding using participation and division of labour indicators. It then delved into the theoretical mechanisms and effects of both on low-carbon TFP at a fundamental level. Using the SBM-GML model and input–output model, the study calculated the low-carbon TFP, value chain embedding levels, and their trends for 42 major economies worldwide from 2001 to 2021. Fixed-effect and threshold-effect models were employed to examine the overall and stage-specific impacts of value chain embedding on low-carbon TFP. The methods and data used above have been widely recognized in the academic community [50,51]. The study considers the longer-term period during which all major world economies undergo economic development transitions, including the key influencing factors faced at both economic and environmental levels, when selecting study subjects, determining the research period, and considering other variables. As a result, the obtained results are considered reliable and generalizable.

6.3. Implications

Taking the paper industry as an example, this study verifies the impact mechanism of the GVC embedding on low-carbon TFP. It provides theoretical and empirical evidence for the extensive implementation of carbon reduction actions in other industries in the next stage. Meanwhile, at a critical period when countries worldwide are striving to achieve the 2030 Sustainable Development Goals (SDGs) as scheduled, the main findings of this paper also contribute to assessing the role of the paper industry and other key national economic sectors in achieving Goal 9: Promote inclusive and sustainable industrialization and foster innovation, Goal 12: Ensure sustainable consumption and production patterns, and Goal 13: Take urgent action to combat climate change and its impacts. These insights help to clarify directions for sustainable industrial transformation in the next phase. Furthermore, the Paris Agreement has set a target of achieving net-zero emissions by 2050. For policymakers and other stakeholders, focusing on the embeddedness of specific industries into GVCs and establishing rational domestic industrial trade division and value chain participation networks will help create a more conducive environment for current sustainability initiatives. This will ultimately facilitate the realization of corresponding policy objectives.

7. Conclusions and Recommendations

The main research findings in this study have certain reference significance for the sustainable development of both the paper industry and other major industries in various countries. First, insufficient technological utilization efficiency is often the main constraint on low-carbon TFP growth in many countries, despite advancements in technological development. Therefore, in the next stage, relevant production sectors should pay close attention to the technological elements of industrial transformation. To ensure balanced development of low-carbon TFP at the conceptual level, the focus should be on exploring the efficiency improvement space of existing technologies, while continuing to innovate in key technological areas.

Second, the status of the GVC division not only significantly promotes the improvement of industrial low-carbon TFP, but is also a crucial prerequisite for the effective promotion of low-carbon TFP with the participation level of the value chain. In response, efforts should be made to encourage enterprises to go global, actively expand overseas business, and simultaneously raise industry production technology standards. Attracting high-level foreign investment widely is also crucial to accelerate the integration of various key aspects of the industry into the global production and trade network. On the other hand, a focus should be placed on examining the dynamics of value chain embedding and major issues in various industry sectors, including the paper industry. Efforts in research and development and service in the industry are needed, utilizing approaches such as technology introduction, technological innovation, and learning by doing to break free from the “low-end lock” situation. The aim is to achieve synchronous improvement in the level of value chain embedding and the low-carbon TFP of the industry.

Third, reasonable energy consumption and industrial structures have become important benchmarks for measuring the progress of industrial transformation and upgrading. Research indicates that the paper industry in various countries has shown a clear trend towards sustainable development in recent years due to clean and low-carbon policies [52]. This trend has had a positive impact on the industry’s low-carbon TFP. In the next stage, relevant incentive policies should be accelerated in formulation and implementation to support the growth and development of low-carbon production enterprises and green industries. This support should also encourage other high-emission entities to actively reduce carbon emissions and improve efficiency. Meanwhile, efforts should be made to accelerate the pace of energy structure adjustment. It is essential to actively explore and implement feasible solutions that replace traditional coal fuel with various clean energy sources. Promoting resource-intensive and environmentally friendly low-carbon production models within each industry will contribute positively to simultaneously achieving economic growth and environmental protection goals.

Limitations and Reflections

In reality, the degree of vertical specialization in the international division of labour often varies significantly due to the unique characteristics of different industries. When an industry or a key segment is highly concentrated and monopolized by a few countries, the significance of discussing the impact of the GVC embedding on low-carbon TFP is reduced. Furthermore, specific economic and environmental factors that can influence low-carbon TFP may differ between industries, which can affect the expression of related empirical results. Therefore, to improve the existing value chain embedding mechanisms, separate tests for different industries should be conducted to better understand their impact effects. Regarding research methods, one can choose from various empirical approaches based on the specific influencing factors of each industry. The results obtained can then be compared to establish a general and applicable investigative paradigm for the methodological aspect of low-carbon TFP research. Moreover, this study uses the low-carbon TFP indicator to measure the development quality and sustainability of the paper industry. However, since this indicator only includes carbon dioxide as an undesirable output and does not account for various energy inputs in the calculation process, the results have certain limitations in assessing the industry’s level of clean production and guiding its future development. This issue could be further addressed and refined in future analyses of related industries. Finally, due to limitations in obtaining core data, the study period in this paper ends in 2021. Public health and politico-economic events that have occurred globally in recent years may have influenced the expression of the result coefficients to some extent. To address this, further research can be conducted on related issues once the latest data becomes available in the next phase.