Constraint or catalyst? Unraveling the nonlinear relationship between industrial linkages and CO₂ emissions

Summary

Industrial linkages shape production efficiency, resource allocation, and technology diffusion, yet their environmental consequences remain underexplored. This paper investigates the relationship between industrial linkages and sectoral CO₂ emissions. We construct weighted forward and backward linkage indicators based on input-output tables, covering 24 harmonized sectors across 30 Chinese provinces. Empirical findings reveal an inverted-U relationship between industrial linkages and CO₂ emissions: stronger linkages are initially associated with higher emissions, but beyond a threshold they are linked to lower emissions. Mechanism analysis identifies three impact channels: output scale effect, technological innovation effect, and energy intensity effect. Furthermore, we construct a measure of regional industrial linkage structures to help identify key areas for emissions reduction. The results highlight regions such as Anhui, Henan, Liaoning, and Shaanxi as priority zones for targeted emissions mitigation. Our study provides empirical insights and policy implications for understanding the role of industrial linkages in reducing carbon emissions.

Graphical abstract

Highlights

• •An inverted U-shaped relationship exists between industrial linkages and CO₂ emissions
• •Output scale, technological innovation, and energy intensity are the underlying mechanisms
• •Regional industrial linkage structures help identify key areas for emissions reduction

Economics; Energy sustainability; Environmental policy

Introduction

The UN Environment Programme emphasizes the critical need for all countries to expedite comprehensive green transitions to realize the goals of the Paris Agreement. Mitigating carbon emissions while sustaining economic growth has become a central challenge.^1,2 Adjusting industrial structure is a critical component in achieving green transformation and lowering carbon emissions.^3,4 However, industrial structure adjustment may also impose short-term economic costs on certain industries. In particular, the phase-out of carbon-intensive capacity, tighter environmental regulations, and the reallocation of capital and labor toward cleaner sectors may weaken output growth, profitability, or employment in traditional industries during the transition process.⁵ As a result, green transformation often involves balancing environmental gains with transitional economic pressures across sectors. Therefore, greater attention should be paid to how industrial linkages influence carbon emissions from a holistic perspective,⁶ as production linkages across industries can shape both the environmental effectiveness and economic costs of structural change. Unlike industrial structure, industrial linkages capture inter-sector dependence and production-chain transmission, directly affecting how shocks, technologies, and emissions propagate across the economy. Understanding the relationship between industrial linkages and carbon emissions can help policymakers better coordinate industrial restructuring with green and low-carbon transition goals.

Industries are connected through supply chains in which upstream sectors provide intermediate inputs to downstream sectors, while downstream demand feeds back to upstream production.^7,8 These industrial linkages shape resource allocation, production efficiency, and structural transformation, and may therefore have important implications for energy-related CO₂ emissions. However, stronger linkages may generate conflicting environmental effects: they can expand production scale and energy demand, but they may also facilitate technology diffusion and efficiency improvement. Understanding this relationship is particularly important in China, where deep industrial networks coexist with ambitious carbon reduction targets and substantial regional heterogeneity. Examining China’s experience may also provide useful insights for other emerging economies undergoing rapid industrialization. Taking China as a case study, we examine whether industrial linkages exert nonlinear effects on sectoral carbon emissions.

Our study explores the nonlinear nexus between industrial linkages and sectoral CO₂ emissions. The study contributes to the literature in three ways. First, we advance the theoretical understanding of the environmental consequences of production networks by arguing that industrial linkages generate competing effects on emissions. We test and document a nonlinear relationship between industrial linkages and sectoral energy-related CO₂ emissions across Chinese provinces and industries.

Second, we deepen the mechanism-based explanation of how industrial linkages shape carbon emissions. We explore the potential mechanisms from output scale effect, technological innovation effect, and energy intensity effect, which can better explain the dynamic nexus between industrial linkages and sectoral energy-related CO₂ emissions. This mechanism framework helps reconcile why industrial linkages may initially intensify CO₂ emissions but later support carbon mitigation as production systems upgrade.

Third, we extend the analysis to regional structural implications. We construct interpretable indicators of regional industrial linkage composition and use them to identify priority areas where weak production connectivity coincides with high emissions. Rather than proposing a purely technical index, this framework translates sector-level evidence into place-based decarbonization guidance and offers practical support for coordinating industrial upgrading with emissions reduction.

The remainder of this article is organized as follows. The literature review section summarizes related studies, while the theoretical analysis section develops the conceptual framework and research hypotheses. The results section describes the data, empirical strategy, and main findings. Finally, the discussion section interprets the results, highlights their implications, and concludes the study.

Literature review

Existing studies primarily explore the relationship between production networks and carbon emissions, with most research concentrating on embodied emissions and their determinants within input-output (I-O) frameworks. Industrial linkages refer to collaborative interactions among firms across different stages of production chains, which aim to enhance competitiveness and resilience. These linkages are closely associated with structural transformation and industrial upgrading, and are fundamentally driven by imbalances in industrial structure, providing a theoretical foundation for analyzing inter-sectoral I-O relationships.

One strand of the literature estimates embodied carbon emissions across countries and sectors, including studies on China, India, Japan, and the United States.^9,10,11,12 These studies generally show that sectors occupying central positions in production networks tend to have higher embodied emissions.¹³ A second strand of literature examines the drivers of sectoral carbon emissions. Final demand expansion significantly increases emissions through production-chain transmission.¹⁴ Natural resource endowments, economic development levels, and structural factors are also important determinants of sectoral emissions.^14,15 A third strand of literature emphasizes that industrial linkages not only reflect intermediate input flows but also capture the transmission of labor, capital, and technology across sectors, thereby forming complex production networks. Within such networks, energy-related CO₂ emissions propagate through supply-chain interactions, making it essential to examine the underlying transmission mechanisms. Empirical studies based on I-O analysis, STIRPAT, SFA, and CGE models have shown that inter-industry connections significantly shape both the scale and structure of emissions.^16,17 For instance, energy-intensive upstream industries such as metals, electricity, and fossil fuel extraction are closely linked to downstream production activities and exert strong effects on emissions through supply-chain propagation.¹⁸ In addition, carbon-intensive material industries (e.g., steel and cement) constitute important sources of embodied emissions in downstream sectors.¹⁹ Transport and logistics sectors further amplify emissions through energy-intensive freight activities.²⁰ Conversely, service sectors such as wholesale, retail, and finance may contribute to emission reduction by improving allocation efficiency and facilitating structural upgrading.²¹

Despite the valuable contributions of prior literature, two limitations remain. First, most existing studies treat industrial linkages primarily as an accounting channel for measuring embodied emissions,^11,12 rather than as an explanatory structural factor that may independently shape sectoral environmental performance. Second, limited attention has been paid to whether the effects of industrial linkages are nonlinear. Addressing these gaps is particularly important for emerging economies such as China, where energy-related emissions account for the majority of total CO₂ emissions and industrial networks remain central to economic activity. Understanding how industrial linkages influence sectoral CO₂ emissions can therefore provide useful guidance for industrial upgrading and low-carbon transition policies.

Theoretical analysis

Industrial linkages reflect the intensity of inter-industry connections within production networks, where upstream sectors provide intermediate inputs to downstream sectors and downstream demand feeds back into upstream production.^7,8 By shaping the organization of production, resource allocation, and inter-sectoral coordination, industrial linkages can exert important but potentially conflicting effects on sectoral CO₂ emissions. Theoretically, the environmental impact of industrial linkages can be understood as the result of two competing forces: a scale expansion effect and a reallocation and efficiency effect. The interaction among these effects suggests that the environmental impact of industrial linkages may be inherently nonlinear.

First, industrial linkages tend to expand production scale through intensified I-O connections. Industrial restructuring and spatial reallocation may increase emissions in the short run due to the construction of new facilities and capital investment, which are typically energy-intensive processes.^21,22 As industries become more interconnected, intermediate demand increases and production chains lengthen, which amplifies overall economic activity.²³ This expansion typically leads to higher energy consumption, particularly in the early stages of development when production remains relatively energy-intensive and relies more heavily on fossil fuels. As a result, the scale expansion effect implies a positive relationship between industrial linkages and CO₂ emissions. There is also considerable evidence that industry linkages generate positive output scale effects.²⁴ From a micro-level perspective, the “cost correlation effect” incentivizes firms to strengthen their linkages with others, aiming to lower operational costs from suppliers.²⁵ Meanwhile, firms can ensure a reliable consumer market through backward linkages.²⁴ There exists a strong correlation between industry linkages and the output scale,²⁶ indicating that stronger linkages may facilitate a larger output scale under similar conditions.

Second, industrial linkages may also generate a reallocation and efficiency effect that mitigates emissions. Stronger inter-industry connections facilitate specialization, improve the division of labor, and enhance coordination across sectors.^27,28 These processes can promote the diffusion of cleaner technologies,²⁹ optimize resource allocation,³⁰ and reduce redundant production through cross-industry learning effects.³¹ Conflicts within industrial sectors are gradually mitigated as their coordination capabilities improve, while factors such as technological advancements and policy frameworks become increasingly mature and stable.³² Meanwhile, strengthened linkages are conducive to reducing energy intensity in this stage.^33,34 Better integration of supply chains due to industry linkages can promote cross-industry collaboration to reduce energy intensity.^35,36

Recent studies also suggest that the relationship between industrial linkages and carbon emissions may be nonlinear and heterogeneous across sectors and regions.^37,38 In particular, the environmental effects of industrial linkages may vary with the level of industrial integration, technological innovation, and energy intensity, potentially exhibiting threshold or inverted U-shaped patterns.^39,40 Therefore, the relationship between industrial linkages and sectoral CO₂ emissions is expected to exhibit an inverted U-shaped pattern. According to the analyses above, we propose the following hypotheses.

H1: there exists an inverted U-shaped nexus between industry linkages and sectoral energy-related CO₂ emissions.

H2: sectoral CO₂ emissions can be affected by industry linkages through output scale effect, technological innovation effect, and energy intensity effect

Results

Variable selection

Explained variable: sectoral energy-related carbon emissions

This study estimates energy-related carbon emissions for two-digit industrial sectors across 30 provinces over time. The calculation is based on sector-level consumption data for 19 energy types (raw coal, cleaned coal, other washed coal, briquettes, coke, coke oven gas, other gas, other coking products, crude oil, gasoline, kerosene, diesel oil, fuel oil, LPG, refinery gas, other petroleum products, natural gas, heat, electricity) combined with the standard emission factors provided by the IPCC guidelines. The energy consumption data are sourced from provincial statistical yearbooks in China, which provide officially reported energy use at the aggregated industrial sector level.

Explanatory variables: industrial linkages

Following Sun et al. (2020),¹³ we construct industrial weighted forward linkages (WFLs) and weighted backward linkages (WBLs) using the absolute weighted method (AWM) based on Leontief and Ghosh I-O frameworks. These weighted indicators account for sectoral scale differences and capture the structural position of industries within production networks. Detailed calculations are provided in the Method Details section.

Figures 1 and 2 present the distributions of lnWFL and lnWBL among sectors and regions across years. The distribution of lnWFL exhibits right skewness, indicating that most sectors maintain relatively low forward industry linkages. In contrast, the distribution of lnWBL approximates a normal distribution, suggesting a more balanced distribution of backward industry linkages across sectors in China.

Figure 1.

Distributions of lnWFL

Notes: The distribution of lnWFL is right-skewed, indicating that most sectors exhibit relatively weak forward industry linkages.

Figure 2.

Distributions of lnWBL

Notes: The distribution of lnWBL is approximately normal, suggesting a more balanced dispersion of backward industry linkages across sectors in China.

Figure 3 reveals the trend of average industry linkages in various provinces across years. The WFL indicator remained largely stable throughout the sample period, while the WBL indicator exhibited significant fluctuations. Some regions present significant rises in the WBL index,such as Beijing, Chongqing, and Hainan, indicating a strengthening of backward linkages during this period. While regions such as Fujian, Hubei, and Jiangsu display stable trends in the WBL index, reflecting minimal changes in industry linkages.

Figure 3.

Trend in industrial linkages across 30 provinces

Note: The figure illustrates trends in average industry linkages across 30 provinces. The WFL index remains largely stable over time across provinces, whereas the WBL index exhibits greater temporal and regional variation. Some provinces (e.g., Beijing, Chongqing, and Hainan) show notable increases in WBL, while others (e.g., Fujian, Hubei, and Jiangsu) display relatively stable patterns.

The distribution of weighted forward and backward linkages across sectors in 2017 reveals several notable patterns. First, in terms of forward industrial linkages, sectors such as Agriculture, Production and supply of electricity and heat, and wholesale and retail exhibit relatively higher levels. It suggests that these sectors play a key role in supplying inputs and supporting the production activities of downstream industries. Second, regarding backward industrial linkages, sectors including Food manufacturing and tobacco, metal smelting and rolling, and electrical machinery and equipment manufacturing show relatively higher values. It indicates that these sectors rely heavily on intermediate inputs and are more strongly connected to upstream industries through demand-driven linkages. The development of these sectors requires a substantial amount of intermediate goods input, which drives the output of upstream sectors through the demand-pull effect.⁶

Control variables

Drawing on previous research,^41,42 we select several control variables as follows: (1) industry output share (Share_ind), that is the proportion of industry output in the total industrial sectors; (2) industry profitability (Prof_ind), measured by the total industry operating surplus; (3) industry carbon emission intensity (CI_ind), calculated by sectoral carbon emissions per unit of output; (4) industry production tax (Tax_ind), measured using the share of net production taxes in industry added value; (5) industry labor scale (Labor_ind), measured by the share of labor remuneration in industry added value; (6) regional economic development level (lngdp), measured by regional gross domestic product; (7) regional openness (lnexp), measured using total value of regional export; (8) regional innovation level (RD), measured by the regional R&D investment intensity. Table 1 reports the descriptive statistics of the main variables. The summary statistics indicate substantial variation across province-industry observations, suggesting sufficient cross-sectional and temporal heterogeneity for empirical identification.

Table 1.

Description results of variables

Variable	Variable meaning	Obs.	Mean	Std. dev.
lnCE	sectoral energy-related carbon emissions (logarithmic form; 10,000 tons)	2132	3.28	2.56
lnWFL	industrial weighted forward linkages (logarithmic form)	2188	0.52	0.39
lnWBL	industrial weighted backward linkages (logarithmic form)	2147	0.68	0.72
Share_ind	proportion of sectoral output scale in industrial output	2186	0.04	0.05
Prof_ind	logarithm of total operating surplus (trillion yuan)	2058	2.70	1.85
Tax_ind	net production tax share	2188	0.19	0.18
Labor_ind	labor factor share	2185	0.12	0.08
Lngdp	logarithm of regional gross product (10,000 yuan)	2189	8.71	1.16
Lnexp	total regional exports	2189	16.37	1.83
RD	regional R&D investment intensity	2186	0.01	0.01

Data

The I-O tables are derived from Provincial Bureaus of Statistics (PBSs) of China; the raw data of sectoral energy consumption are derived from the CEADs Database; and the raw data of other variables are from PBS and the CEIC Database. All variables used in this research are shrunk by 1% to minimize the influence of extreme samples on the baseline empirical results. Due to the publication years of regional I-O tables by PBS, the sample period in this paper includes 1997, 2002, 2007, 2012, and 2017. Meanwhile, the regions of Tibet, Hong Kong, Macau, and Taiwan are not considered due to the unavailability of data.

The sectoral classification of I-O tables is based on China’s national economic industrial classification system, in which two-digit sectors represent major industry categories in the national accounts. Due to revisions in the national industrial classification standards over time, the naming conventions and classification structures of two-digit sectors vary across I-O tables in different years. To ensure consistency and comparability across I-O tables from 1997 to 2017, we construct a harmonized sector classification by aggregating and aligning sector definitions across different years. The harmonization procedure follows three principles.

(1) Industries with identical economic meaning but slightly different naming conventions across I-O tables are treated as the same sector. This ensures consistency in sector identification over time despite changes in nomenclature. (2) When the level of disaggregation varies across different I-O tables (for example, general equipment manufacturing and special equipment manufacturing are reported separately in some years but combined in others), we adopt a “higher-level consistency” rule. Specifically, we aggregate such sectors into a unified category (e.g., “General and special equipment manufacturing”) to maintain comparability across time. (3) We retain only industrial sectors in the empirical analysis. Since the dependent variable—carbon emissions—is constructed based on sectoral energy consumption data, which are only available for industrial sectors from the province-level PBS.

This harmonization procedure allows us to construct a consistent panel dataset of industrial sectors across different I-O tables while preserving the comparability of sectoral economic structure and environmental outcomes over time. The harmonized sectors are shown in Table S2 in the SI Appendix. The detailed mapping between original sectors in the 1997–2017 I-O tables and the corresponding harmonized sectors is reported in Tables S3 and S4 in SI Appendix to ensure transparency and replicability.

Empirical strategy

We estimate the baseline model using a high-dimensional fixed effects (HDFE) ordinary least squares (OLS) specification, which controls for unobserved heterogeneity across provinces, industries, and years. Further details on the empirical specification are provided in the Method Details section.

Main results

The baseline model results are presented in Table 2. It can be seen that, regardless of whether time and region fixed effects are included, the coefficient of the linear term of forward industry linkages (lnWFL) is positive and the coefficient of its quadratic term (lnWFL2) is negative. Similarly, the coefficient of lnWBL is positive, and the coefficient of lnWBL2 is negative. These findings indicate an inverted U-shaped relationship between industry linkages and sectoral carbon emissions, first promoting and then inhibiting emissions. From a numerical perspective, the estimated turning point for forward industrial linkages is approximately 0.89 in lnWFL, while that for backward industrial linkages is approximately 1.82 in lnWBL. Only a limited share of observations lies beyond these estimated thresholds.

Table 2.

The relationship between industry linkages and carbon emissions

	(1) lnCE	(2) lnCE	(3) lnCE	(4) lnCE
lnWFL	1.9473∗∗∗	1.8537∗∗∗
	(0.3884)	(0.4079)
lnWFL2	−1.0705∗∗∗	−1.0461∗∗∗
	(0.2301)	(0.2529)
lnWBL			0.4199∗∗∗	0.4896∗∗∗
			(0.1373)	(0.1195)
lnWBL2			−0.1008∗	−0.1345∗∗∗
			(0.0579)	(0.0480)
Controls	yes	yes	yes	yes
Region FE	yes	yes	yes	yes
Industry FE	yes	yes	yes	yes
Year FE	yes	yes	yes	yes
Industry-year FE	yes	yes	yes	yes
Region-year FE	no	yes	no	yes
Observation	2,002	2,002	1,964	1,964
R2	0.7923	0.8081	0.7941	0.8105

∗∗∗ represents p < 0.01, ∗∗ indicates p < 0.05, and ∗ signifies p < 0.1; values in () are the robust standard errors clustered at the industry-year level. This notation is used consistently in the following tables.

Robustness check

Endogeneity issue

Potential endogeneity may arise from reverse causality and omitted time-varying factors. On the one hand, changes in sectoral carbon emissions may induce adjustments in production organization, thereby affecting industrial linkages. On the other hand, unobserved factors such as industrial policies, technological progress, and environmental regulation may simultaneously influence both industrial linkages and carbon emissions. To address potential endogeneity concerns, we construct the Bartik instrumental variable (IV) for industrial linkages, referring to Goldsmith-Pinkham et al. (2020).⁴³ The intuition is that initial industry linkage levels capture pre-existing structural differences, while aggregate growth reflects broader changes in the industrial linkage environment over time. Specifically, we interact the initial level of industrial linkages in the base year (1997) with the growth rate of industrial linkages at the provincial level. The IV is constructed as Equation 1 and 2.

$$Barti{k}_{WFL}=WFL1997\times \left(1+Growt{h}_{WFL}\right)$$ (Equation 1)

$$Barti{k}_{WBL}=WBL1997\times \left(1+Growt{h}_{WBL}\right)$$ (Equation 2)

where WFL1997 and WBL1997 denote the initial values of forward and backward linkages for each province-industry unit. Growth_WFL and Growth_WBL represent the growth rate of industrial linkages at the provincial level. Regarding the identification conditions, the relevance requirement is satisfied because the interaction between initial linkage levels and subsequent growth generates strong variation that is highly correlated with the observed industrial linkages. The exogeneity condition relies on the fact that the initial linkage structure in 1997 is predetermined and not directly affected by contemporaneous shocks to sectoral carbon emissions. The consistency between OLS and IV estimates provides additional support for the stability of our findings. Table 3 exhibits the IV-GMM regression outcomes.

Table 3.

IV-GMM estimation of the relationship between industry linkages and carbon emissions

	(1) lnCE	(2) lnCE
lnWFL	4.3661 ∗∗
	(1.8757)
lnWFL2	−3.1413 ∗∗
	(1.2705)
lnWBL		2.1316 ∗∗∗
		(0.6280)
lnWBL2		−0.7233 ∗∗∗
		(0.064)
Control	yes	yes
Kleibergen-Paap rk LM	24.377 [0.000]	27.392 [0.000]
Kleibergen-Paap rk Wald F	11.504 {7.03}	12.664 {7.03}
Region FE	yes	yes
Industry FE	yes	yes
Year FE	yes	yes
Industry-year FE	yes	yes
Observation	1166	1081

We take the logarithm of Bartik IVs and the squared terms as the instrumental variables for the industry linkages variable and their square terms in the above IV-GMM regression models. The values in [ ] are the p value of Kleibergen-Paap rk LM test, the values in {} are the 10% level critical values of Kleibergen-Paap rk Wald F test. The observations are less than the baseline results since the data for certain sectors in the initial year (1997) is missing.

The first-stage regression results of the LM test and Wald F test indicate that there are no weak instruments or weak identification issues. The results suggest that Bartik IVs used in our study serve as valid instrumental variables. The regression coefficients for lnWFL and lnWBL are both positive at a 10% significance level. Meanwhile, estimated coefficients for lnWFL2 and lnWBL2 are both negative, passing the 5% and 1% significance levels. The results in Table 3 suggest that, after solving the endogeneity issues, the inverted U-shaped nexus between industry linkages and sectoral energy-related carbon emissions still exists.

Controlling for policy and industry-specific confounders

To further address potential confounding factors, this study additionally controls for policy and industry-specific influences that may affect sectoral carbon emissions. Specifically, we introduce a dummy variable for high energy-consuming industries, which captures sectors with systematically higher energy use relative to the regional industry-level average. In addition, we control for the implementation of carbon emission trading policies by constructing a policy indicator based on the rollout of regional carbon markets across provinces and industries. The results reported in columns (1) and (2) of Table 4, remain qualitatively unchanged. The coefficients on lnWFL and lnWBL are positive, while those on lnWFL2 and lnWBL2 are negative, continuing to support the existence of an inverted U-shaped relationship. This suggests that the main findings are robust to controlling for industry heterogeneity and carbon policy interventions.

Table 4.

Robustness check

	(1) lnCE	(2) lnCE	(3) lnCE	(4) lnCE	(5) lnCE
lnWFL	1.9450∗∗∗			1.6833∗∗∗
	(0.3935)			(0.1962)
lnWFL2	−1.0819∗∗∗			−0.9557∗∗∗
	(0.2410)			(0.1199)
lnWBL		0.5194∗∗∗			0.9662∗∗∗
		(0.1184)			(0.0779)
lnWBL2		−0.1418∗∗∗			−0.3258∗∗∗
		(0.0477)			(0.0326)
lnLink			104.8202∗∗∗
			(30.9276)
lnLink2			−1,740.2395∗∗∗
			(564.7719)
Controls	yes	yes	yes	yes	yes
Region FE	yes	yes	yes	yes	yes
Industry FE	yes	yes	yes	yes	yes
Year FE	yes	yes	yes	yes	yes
Industry-year FE	yes	yes	yes	yes	yes
Region-year FE	yes	yes	yes	yes	yes
Observation	2,002	1,964	2,002	8,230	8,118
R2	0.8136	0.8162	0.8076	0.8311	0.8359

Replace industry linkages variables

The benchmark regression uses the AWM to measure the industry linkages of each industry and examines the relationship between industry linkages and industry carbon emissions. Furthermore, this study constructs an unweighted average industry correlation coefficient (Link) based on direct consumption coefficient a and direct distribution coefficient b for a robustness check. The calculation method of Link is shown as follows.

First, calculate the linkages of sector i and sector j. The calculation formula of link_ij is shown as Equation 3. a_ij(a_ji) is the direct consumption coefficient, which signifies the ratio of the intermediate input of sector i(j) to sector j(i) to the overall input of sector j(i). b_ij(b_ji) is the direct distribution coefficient, which is the proportion of total output of sector i(j) flowing to sector j(i).

$${link}_{ij}=\left(a_{ij}+b_{ij}+a_{ji}+b_{ji}\right)/4$$ (Equation 3)

Second, calculate the average industry linkages of sector i, that is, Link_i. The formula is exhibited in Equation 4; n denotes the number of sectors.

$${Link}_i=\frac{1}{n}{\sum }_j\left({link}_{ij}\right)$$ (Equation 4)

We replace the explanatory variables by the logarithm form of average industry linkages lnLink and its squared term lnLink2 in the baseline model. The results are shown in column (3) of Table 4. It is evident that the regression coefficient for the linear term of the average industry correlation is positive and that of the squared term is negative, both passing the 1% level significance check. These results also suggest the inverted U shape relationship between industry linkages and sectoral energy-related carbon emissions.

Extending the sample using interpolation

The sample period of this study spans from 1997 to 2017. Given that official I-O tables are only available for selected benchmark years (2002, 2007, 2012, and 2017), we address this limitation by constructing interpolated I-O data for the missing years. Specifically, we apply a linear interpolation method based on the benchmark I-O tables for 2002, 2007, and 2012 to generate annual province-level I-O information over the period 1997–2017. This approach is commonly used in the literature for low-frequency I-O data, as it allows for a more continuous representation of structural changes over time while preserving the underlying cross-sectional variation.^44,45,46 Based on the interpolated dataset, we re-estimate the baseline model. The results are reported in columns (4) and (5) of Table 4. The estimated coefficients remain consistent with those in the baseline regressions, with the linear terms being positive and the squared terms being negative.

Mechanism test

Output scale effect

If industry linkages can increase sectoral carbon emissions through output scale effects, then the larger the industry scale, the stronger the effect of industry linkages on sectoral carbon emissions. The regression results of the output scale mechanism effect in Table 5 indicate that estimated coefficients of lnWFL × Scale and lnWBL × Scale are both positive, showing that the higher the industry scale, the more obvious energy-related carbon emissions increasing effect of industry linkages.

Table 5.

Mechanism test

	(1) lnCE	(2) lnCE	(3) lnCE	(4) lnCE	(5) lnCE	(6) lnCE
lnWFL × Scale	1.8366∗∗
	(0.8496)
lnWBL × Scale		1.5152∗∗∗
		(0.4686)
lnWFL × Tech			−0.0825∗∗∗
			(0.0207)
lnWBL × Tech				−0.0175∗
				(0.0105)
lnWFL × EI					0.3884∗∗∗
					(0.0938)
lnWBL × EI						0.0168
						(0.0584)
Controls	yes	yes	yes	yes	yes	yes
Region FE	yes	yes	yes	yes	yes	yes
Industry FE	yes	yes	yes	yes	yes	yes
Year FE	yes	yes	yes	yes	yes	yes
Industry-year FE	yes	yes	yes	yes	yes	yes
Region-year FE	yes	yes	yes	yes	yes	yes
Observation	1,964	1,964	1,964	1,964	1,964	1,964
R2	0.8313	0.8321	0.8118	0.8099	0.8137	0.8098

These results confirm the inference proposed above, and support the hypothesis that industry linkages may promote the industry output scale, subsequently leading to an increase in their energy-related carbon emissions levels. Industry linkages can not only provide manufacturers with a stable source of intermediate input through forward linkage, but also ensure a reliable consumer market through backward linkages.²⁴ For the sectors, the increase in industry linkages has a positive output effect, thereby increasing energy-related carbon emissions at the production end.

Technological innovation effect

If industry linkages reduce sectoral energy-related carbon emissions through technological innovation effects, then we can infer that greater technological innovation reduces the promotion effect of industry linkages on sectoral carbon emissions. The regression coefficient of lnWFL × Tech in column (3) is negative, and that of lnWBL × Tech in column (4) is negative at the 10% level. The results suggest that technological innovation strengthens the energy-related carbon emissions reduction effect of industrial forward linkages and industrial backward linkages. The results can indirectly infer that forward linkages may affect sectoral energy-related carbon emissions through technological innovation.

Industries with high industrial linkages have closer ties with other industries, making the technological spillover effect between industries more obvious, thus conducive to carbon emission reduction. However, the upstream industries are mainly large-scale monopoly resource-based industries and have weak spillover effects on knowledge and technology. Thus, the technological promotion effect of industrial backward linkages may be less than that of industrial forward linkages.

Energy intensity effect

Similarly, if industry linkages reduce sectoral energy-related carbon emissions by lowering energy intensity, then sectors with lower energy intensity will experience a more pronounced carbon reduction effect from industry linkages.

Columns (5) and (6) in Table 5 display the empirical findings related to the energy intensity effect. The regression estimated coefficient of lnWFL × EI is positive, passing the 1% level of significance test, while that of lnWBL × EI cannot pass the 10% significance level test. These outcomes indicate that for industries with lower energy intensity, the effect of forward industry linkages on carbon emissions is more negative. Thus, it can be inferred that forward industry linkages can affect sectoral energy-related carbon emissions through reducing energy intensity, but backward industry linkages may not.

Further analysis

The baseline results indicate that industrial linkages may exert heterogeneous environmental effects across stages of structural development. While stronger industrial linkages can initially raise emissions through scale expansion, they may also facilitate technological diffusion and efficiency improvement over time. To translate these sector-level findings into regional implications, this section examines whether the composition of regional industrial linkages is associated with carbon emissions and identifies areas with greater structural mitigation potential.

Measuring regional industrial structure

We construct summary indicators of regional industrial linkage composition based on the distribution of sectors with different linkage intensities. Specifically, sectors are classified into three groups according to their relative WFLs and WBL.

Weak-linkage sectors: both WFL and WBL are below the sample mean; strong-linkage sectors: both WFL and WBL are above the sample mean; intermediate-linkage sectors: all remaining sectors. We calculate the share of regional value added accounted for by sectors in each group:

$${Low}_{it}=\sum _l{g}_{ilt}/\sum _{j=1}^{24}{g}_{ijt}$$ (Equation 5)

$${Middle}_{it}=\sum _m{g}_{imt}/\sum _{j=1}^{24}{g}_{ijt}$$ (Equation 6)

$${High}_{it}=\sum _h{g}_{iht}/\sum _{j=1}^{24}{g}_{ijt}$$ (Equation 7)

In Equations 5, 6, and 7, l, m, and h represent weak-linkage-, intermediate-linkage-, and strong-linkage groups, and g represents the industrial added value. These indicators do not aim to create a purely technical index; rather, they provide an interpretable summary of how regional production activity is distributed across sectors with different linkage positions.

Regional linkage structure and carbon emissions

To examine whether regional industrial linkage composition is associated with carbon emissions, we estimate the following model as Equation 8, where fixed effects include province, industry, year, and industry-year effects.

$${lnCE}_{ijt}={\beta }_0+{\beta }_1\mathit{ln}{Low}_{it}+{\beta }_2\mathit{ln}{Middle}_{it}+{\beta }_3\mathit{ln}{High}_{it}+{\beta }_4{con}_{ijt}{+\lambda }_t+{\mu }_i+{\theta }_j+{\rho }_{jt}+{\epsilon }_{ijt}$$ (Equation 8)

The estimation results shown in Table 6 indicate that the coefficient on lnLow is significantly positive at the 5% level. This suggests that provinces with a larger share of output concentrated in weak-linkage sectors tend to exhibit higher sectoral carbon emissions. By contrast, the coefficients on lnMiddle and lnHigh are statistically insignificant. These findings suggest that carbon emissions are more strongly associated with the persistence of weak production connectivity than with the expansion of already well-connected sectors.

Table 6.

The impact of regional industry linkages structure on carbon emissions

	(1) lnCE	(2) lnCE
lnLow	0.2314∗∗	0.2274∗∗
–	(0.1029)	(0.1026)
lnMiddle	−0.1173	−0.1119
–	(0.1184)	(0.1164)
lnHigh	0.1393	0.1388
–	(0.1044)	(0.1091)
Controls	yes	yes
Region FE	yes	yes
Industry FE	yes	yes
Year FE	yes	yes
Industry-year FE	no	yes
Observation	1,966	1,966
R2	0.7733	0.7887

Building on the above findings, we develop a practical screening framework to identify regions with greater structural mitigation potential. A province is classified as a priority area for carbon mitigation when it simultaneously exhibits: (1) above-median sectoral carbon emissions in a given year; and (2) above-median share of weak-linkage sectors (Low) in the same year.

This dual criterion captures two dimensions simultaneously: current emissions pressure and structural upgrading potential. Regions with high emissions but relatively strong industrial connectivity may require technology-oriented decarbonization strategies, whereas regions with both high emissions and weak production linkages may benefit more from supply-chain integration, industrial coordination, and structural upgrading policies.

Based on this framework, provinces such as Anhui, Henan, Liaoning, and Shaanxi are repeatedly identified as priority regions during the sample period (see Table 7). Most of these provinces are generally characterized by relatively carbon-intensive industrial structures, indicating a higher dependence on energy-intensive production activities. At the same time, they tend to exhibit weaker internal production connectivity compared with more developed regions, reflecting less efficient inter-industry coordination and limited spillover effects within their industrial systems.

Table 7.

Key areas for carbon emissions reduction

Year	Key areas of carbon emissions reduction	Median of ACEs	Median of low
1997	Liaoning; Shandong; Shanxi; Sichuan; Zhejiang	2.916	0.182
2002	Guangdong; Henan; Hunan; Liaoning; Shanxi	3.229	0.152
2007	Anhui; Guangdong; Henan; Hunan; Inner Mongolia; Jilin; Liaoning	3.384	0.156
2012	Anhui; Guangdong; Henan; Hubei; Shaanxi	3.837	0.192
2017	Anhui; Henan; Hunan; Liaoning; Shaanxi	3.960	0.171

Discussion

This study constructs measures of forward and backward industrial linkages for 24 merged two-digit sectors across 30 provinces in China over the period 1997–2017, and examines their relationship with sectoral energy-related CO₂ emissions. The empirical findings reveal a robust nonlinear relationship between industrial linkages and emissions, characterized by an inverted U-shaped pattern. This nonlinear relationship reflects the coexistence of competing effects associated with industrial linkages. Further analysis suggests that this relationship operates through three key channels: output scale, technological innovation, and energy intensity. While the scale effect initially dominates, leading to higher emissions, the technological and efficiency effects gradually offset and eventually outweigh it. This mechanism highlights the importance of considering both expansion and efficiency dimensions when evaluating the environmental consequences of industrial linkages.

In addition, the results indicate substantial regional heterogeneity. Regions with relatively weaker industrial linkage structures tend to exhibit higher emission levels, suggesting that the organization of production networks plays an important role in shaping environmental outcomes. Identifying such regions helps to better target emission reduction efforts and improve the effectiveness of place-based policies.

These findings contribute to the existing literature by emphasizing the role of industrial linkages as a structural determinant of emissions,^9,10,11,12 rather than merely an accounting framework. They also complement prior studies on production networks and environmental performance by uncovering a nonlinear relationship and its underlying mechanisms.

Based on the findings of this paper, three policy implications are proposed:

First, dynamically adjust energy-related carbon emissions reduction and industrial policies. The findings of our study reveal that carbon emissions reduction strategies should be dynamically adjusted according to different stages of industry linkages. The initial focus should be on promoting green technology and clean energy applications to reduce carbon intensity. After entering the mature stage, policymakers should focus on strengthening the industry linkages to guide the low-carbon transformation of the industrial sectors.

Second, promote industrial technological innovation and reduce energy intensity. The findings of this paper show that technological innovation and energy intensity are important paths for industry linkages to reduce sectoral energy-related carbon emissions. Therefore, in order to better leverage the environmental benefits of industry linkages, the government should focus on inter-industry linkages in technological progress and energy efficiency. For example, establish a sharing mechanism and taxation support for technology exchanges between industries.

Third, optimize the industry linkage structure and promote balanced development. Based on our study, the weaker the regional industry linkages, the higher the sectoral carbon emissions. Thus, the government should optimize the industry linkage structure to mitigate carbon emissions. Specifically, policies should be made to promote R&D investment, cross-industry technological innovation collaboration, encourage the vertical deepening and horizontal expansion of the industrial chain, and build a more balanced industrial development pattern.

Limitations of the study

Several limitations of the study should be acknowledged. First, the analysis relies on I-O tables that are available at multi-year intervals, which may not fully capture short-term dynamics. Second, the study focuses on China, and the generalizability of the findings to other contexts may be limited. Future research could address these limitations by employing higher-frequency data and extending the analysis to other emerging economies.

Resource availability

Lead contact

Further information and requests should be directed to the lead contact, Chuanwang Sun (scw@xmu.edu.cn).

Materials availability

No new materials were generated by this work.

Data and code availability

• •This paper analyzes publicly available datasets, which are listed in the key resources table.
• •The original data sources include publicly available input-output tables, sectoral energy consumption data, and socioeconomic indicators. Processed data used for the empirical analysis are available from the lead contact upon reasonable request.
• •The code for data processing and empirical analysis was written in Stata and is available from the Lead Contact upon reasonable request. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

The authors wish to express their sincere gratitude to the National Natural Science Foundation of China (grant nos. 72574085, 72204098), the General Program of the National Fund of Philosophy and Social Science of China (grant no. 23BJL130), and the Major Program of National Fund of Philosophy and Social Science of China (grant no. 21&ZD109).

Author contributions

Z.C., conceptualization, methodology, formal analysis, and writing – original draft preparation; M.Y., conceptualization and visualization; S.C., formal analysis and visualization; D.W., methodology and visualization; Q.L., supervision and writing – original draft preparation; C.S., supervision, project administration, and writing – review and editing.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Sectoral energy-related carbon emissions	Bureaus of Statistics of China; CEADs Database	https://www.stats.gov.cn; https://www.ceads.net.cn/
Industrial weighted forward linkages	Bureaus of Statistics of China	https://www.stats.gov.cn
Industrial weighted backward linkages	Bureaus of Statistics of China	https://www.stats.gov.cn
Proportion of sectoral output scale in industrial output	Bureaus of Statistics of China	https://www.stats.gov.cn
Total operating surplus	Bureaus of Statistics of China	https://www.stats.gov.cn
Net production tax share	Bureaus of Statistics of China	https://www.stats.gov.cn
Labor factor share	Bureaus of Statistics of China	https://www.stats.gov.cn
Regional gross product	Bureaus of Statistics of China; CEIC Database	https://www.stats.gov.cn; https://insights.ceicdata.com.cn/login
Total regional exports	Bureaus of Statistics of China; CEIC Database	https://www.stats.gov.cn; https://insights.ceicdata.com.cn/login
Regional R&D investment intensity	Bureaus of Statistics of China; CEIC Database	https://www.stats.gov.cn; https://insights.ceicdata.com.cn/login
Software and algorithms
Stata software	Stata	https://www.stata.com/
Visual Studio Code	Microsoft	https://code.visualstudio.com

Method details

Explanatory variables: Industrial linkages

According to Sun et al., (2020a), this paper employs the absolute weighted method (AWM) method to calculate industrial weighted forward linkages (WBL) and weighted backward linkages (WFL) of various industries in different provinces. The calculation methods based on the Leontief and Ghosh input-output systems are as follows. The use of weighted linkage measures aims to mitigate the influence of sector size and capture the structural position of industries within the production network. Unweighted indicators may be dominated by large sectors with higher output or demand. By incorporating net total output as weights, WBL and WFL adjust for scale effects and provide a more accurate representation of inter-industry linkages.

The measurement of industrial linkages is based on I-O tables. There are two main types of I-O tables: competitive and non-competitive tables. Competitive I-O tables do not distinguish between imported and domestically produced intermediate inputs, whereas non-competitive I-O tables explicitly separate these two components. In this study, we employ non-competitive I-O tables. Table S1 in SI Appendix presents the structure of the non-competitive I-O table.

Assume that the economy contains n industrial sectors. Let Z^d denotes the n×n matrix of domestic intermediate inputs, and Z^m denotes the n×n matrix of imported intermediate inputs. Let x be the n × 1 vector of total output, and y the n × 1 vector of final demand. The value-added vector v is a 1×n row vector. Final demand includes consumption (Con), investment (Inv), and exports (Ex). Con and Inv are further decomposed into domestic and imported components, so that final demand can be expressed as y = y^d+y^m.

According to the row-balance condition of the IO table, we have:

$${\sum }_{j=1}^n{Z}_{ij}^d+y_i^d=x_i$$ (Equation 9)

In matrix form:

$$A^{d}Xc+y^d=A^{d}x+y^d=x$$ (Equation 10)

where A^d = Z^d(X)⁻¹ is the domestic input coefficient matrix, X = diag(x) is the diagonal matrix constructed from the output vector x, and c=(1,1,⋯,1)′, then Xc = x. The Leontief model can thus be written as:

$$x={\left(I-A^d\right)}^{-1}{y}^d$$ (Equation 11)

where ${\left(I-A^d\right)}^{-1}{y}^d$ is the Leontief inverse matrix, denoted by L.

According to the column-balance condition of the IO table:

$${\sum }_{i=1}^n{Z}_{ij}^d+{\sum }_{i=1}^n{Z}_{ij}^m+v_j=x_j^{\prime }$$ (Equation 12)

In matrix form:

$$c^{\prime }{Z}^d+c^{\prime }{Z}^m=X^{\prime }{B}^d+X^{\prime B^m}+v=X^{\prime }$$ (Equation 13)

where B^d=(X)⁻¹Z^d is the domestic output (distribution) coefficient matrix, and B^m=(X)⁻¹Z^m is the imported distribution coefficient matrix. The Ghosh model can therefore be expressed as:

$$x^{\prime }=v{\left(I-B^d-B^m\right)}^{-1}$$ (Equation 14)

where ${\left(I-B^d-B^m\right)}^{-1}$ is the Ghosh inverse matrix, denoted by G.

To avoid overestimating domestic production induced by domestic final demand, we remove the contribution of imported intermediate inputs. The net domestic final demand is defined as:

$$y^{dn}=y^d-{A^m\left(I-A^d\right)}^{-1}{y}^d$$ (Equation 15)

where A^m = Z^m(X)⁻¹ is the imported input coefficient matrix. This adjusted final demand captures domestic consumption, domestic investment, and exports excluding imported intermediate inputs, thereby addressing the double-counting problem in conventional trade statistics (Koopman et al., 2012).

Based on the adjusted framework, weighted backward linkages (WBL) are computed using weights derived from net final demand, while weighted forward linkages (WFL) are based on value-added weights. Specifically:

$$WBL=\left(\mathrm{Y}{L}^{\prime }c\right)/\left(\frac{1}{n}{c}^{\prime }\mathrm{x}\right)$$ (Equation 16)

$$WFL=\left(\text{VG}c\right)/\left(\frac{1}{n}{c}^{\prime }\mathrm{x}\right)$$ (Equation 17)

where Y = diag(y^dn) and V = diag(v) are diagonal matrices constructed from net final demand and value-added vectors, respectively. $L={\left(I-A^d\right)}^{-1}$ is the Leontief inverse matrix, capturing the total (direct and indirect) input requirements induced by one unit of final demand. $G={\left(I-B^d-B^m\right)}^{-1}$ is the Ghosh inverse matrix, reflecting the total output distribution effects generated by primary input changes. The denominator $\left(\frac{1}{n}{c}^{\prime }\mathrm{x}\right)$ represents the average industrial linkage intensity across all sectors in the economy and serves as a normalization term to ensure that WFL and WBL are comparable across sectors in relative terms.

According to Equation 16 and 17, this paper calculates the indexes of WFL and WBL for 24 merged two-digit sectors in 30 provinces.

Empirical strategy

To examine the relationship between industrial linkages and sectoral CO₂ emissions, we estimate the baseline model using a high-dimensional fixed effects (HDFEs) ordinary least squares (OLSs) specification as Equation 10. This approach allows us to control for the unobserved heterogeneity across provinces, industries, time, thereby mitigating concerns arising from omitted variable bias at multiple levels.

$$\mathit{ln}{CE}_{ijt}={\beta }_0+{\beta }_1\mathit{ln}{X}_{ijt}+{\beta }_2\mathit{ln}{X2}_{ijt}+{\beta }_3{con}_{ijt}+{\lambda }_t+{\mu }_i+{\theta }_j+{\rho }_{jt}+{\delta }_{it}{\epsilon }_{ijt}$$ (Equation 18)

In Equation 10, i denotes province, j represents two-digit sector, t denotes year. The explained variable CE represents sectoral energy-related carbon emissions; X denotes the main explanatory variable, industrial weighted forward linkage (WFL) and weighted backward linkage (WBL), X2 is the square term; con represents the control variables. ε is the error term. λ, μ , θ, ρ, and δ respectively represents the time fixed effect, region fixed effect, industry fixed effect, industry-year joint fixed effects, and province-year joint fixed effects. Specifically, the inclusion of province fixed effects captures time-invariant regional characteristics; industry fixed effects account for persistent sectoral heterogeneity in production technology and energy intensity; and time fixed effects absorb common macroeconomic shocks. In addition, industry-year and province-year fixed effects control for evolving sectoral trends and region-specific macro dynamics. Given this high-dimensional fixed effects structure, the baseline OLS estimates are interpreted as conditional associations rather than strict causal effects.

Quantification and statistical analysis

Statistical analyses were conducted using Stata software. Statistical significance is denoted by ∗, ∗∗, and ∗∗∗ corresponding to the 10%, 5%, and 1% levels, respectively.