The Dynamic Relationships Among Green Technological Innovation, Government Policies, and the Low-Carbon Transformation of the Manufacturing Industry in the Yangtze River Economic Belt: An Analysis Based on the PVAR Model

Abstract

Green technological innovation, government policies, and the low-carbon transformation of the manufacturing industry are critical for promoting high-quality development in the Yangtze River Economic Belt. This study, based on input–output and total factor productivity theories, selects relevant variables and utilizes a PVAR model to analyze data from 11 provinces in the region from 2011 to 2023. The empirical results indicate that (1) green technological innovation and the low-carbon transformation of the manufacturing industry exhibit significant bidirectional causality, with the low-carbon transformation exerting a stronger positive impact on green innovation, underscoring the “demand–pull” effect. (2) Government policies provide initial impetus for both green innovation and low-carbon transformation but show signs of self-restriction and diminishing returns over time, reflecting a typical “policy lag–decay” pattern. (3) Variance decomposition highlights the dominant role of green technological innovation in driving long-term low-carbon transformation, while the direct impact of government policies remains limited, indicating that policy effectiveness is largely mediated through technological channels. These findings emphasize the importance of enhancing regional green innovation capacity, establishing dynamic policy feedback mechanisms, and fostering sustained technological advancement as key pathways to deepening the low-carbon transformation.

1. Introduction

According to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC): Climate Change 2023, the global average surface temperature increased by 1.1 °C from 2011 to 2020 compared to pre-industrial levels. Emissions of carbon dioxide and other greenhouse gases have surged, posing significant threats to socioeconomic activities and human safety. This poses one of the most significant threats to sustainable development in the 21st century [1], while the conflict between economic growth and environmental pollution is becoming increasingly pronounced [2]. Due to China’s extensive economic development model, which is characterized by high energy consumption, low output, and high pollution, the manufacturing sector has been the primary driver of economic growth [3]. Consequently, the low-carbon transformation of the manufacturing industry has become imperative for sustainable development. Green technological innovation, as highlighted in the 2023 Sustainable Development Financing Report, is an increasingly important engine for low-carbon economic growth and a current research focus [4,5].

The Yangtze River Economic Belt, as a strategically significant inland region, plays a crucial role in both China’s and the global economy. It boasts high industrialization but faces challenges due to its reliance on labor-intensive industries with low technological sophistication [6]. As a result, the presence of such traditional manufacturing clusters has necessitated industrial restructuring and management in cities along the Yangtze River as a key strategy for promoting high-quality development in the region [7]. Overall, the Yangtze River Economic Belt shoulders the dual responsibility of serving as a model for low-carbon economic development in other regions and spearheading the achievement of ‘peak carbon dioxide emissions’ [8,9,10].

Since the 2008 financial crisis, major developed countries have shifted their focus back to industrial economies, implementing re-industrialization strategies that have significantly accelerated the expansion of the manufacturing sector [11]. Nevertheless, this expansion has also exacerbated environmental crises, posing challenges to high-quality economic development and productivity growth. The low-carbon transformation has become a key solution to this problem, aiming to achieve sustainable development by fostering green, low-carbon economies and promoting high-quality growth through resource conservation, carbon emission reduction, and production efficiency optimization [12]. As the main sector for carbon emissions and the foundation for decarbonization, the manufacturing industry has perfected critical function in achieving peak carbon dioxide emissions and carbon neutrality goals [13,14].

Green technological innovation not only mitigates environmental impacts by improving resource efficiency and reducing emissions but also drives economic growth, making it a cornerstone of sustainable industrial development [15,16,17,18]. An increasing number of government agencies are recognizing the important role of green technological innovation in the low-carbon transformation of the manufacturing industry. For example, the OECD has worked to improve energy efficiency in manufacturing through technological innovation, and Japan’s ‘Green Factory’ program is promoting the use of green technological innovation to reduce the carbon intensity of the manufacturing industry. Therefore, green technological innovation, as a representative economic driving force, is a crucial tool for promoting low-carbon development and transformation [19].

This study makes three main contributions: First, from the perspective of input–output analysis and based on the total factor theory, we provide a comprehensive evaluation method for measuring green technological innovation indicators and apply a more objective weighting technique for these indicators. This approach is of significant importance for scientifically assessing green technological innovation. Second, we find that due to data availability limitations, many studies merely conduct statistical comparisons or qualitative discussions about the relationships among government policies, green technological innovation, and the low-carbon transformation of the manufacturing industry, often neglecting the potential time lags that may exist. Therefore, recognizing that economic and policy changes often exhibit delayed effects, this study explicitly incorporates time lags in its analysis to more accurately capture the dynamic interplay among key variables. Third, regarding model selection, previous studies have often relied on traditional econometric models such as baseline regressions and vector autoregression (VAR) models, which have certain limitations when analyzing dynamic relationships or data types. Therefore, this study adopts a more novel multivariate econometric tool, the Panel Vector Autoregression Regression (PVAR) model.

In conclusion, this paper clarifies the dynamic relationships between green technological innovation, government policies, and the low-carbon transformation of the manufacturing industry, offering valuable insights for China and other developing countries that are promoting high-quality economic development. The remainder of this paper is organized as follows: Section 2 reviews the literature on green technological innovation, government policies, and the low-carbon transformation of the manufacturing industry. Section 3 introduces the materials and methods used in this study. Section 4 discusses and presents the empirical results. Section 5 provides conclusions and policy recommendations. Figure 1 shows the 11 provinces along the Yangtze River Economic Belt involved in this paper.

2. Theoretical Analysis and Literature Review

2.1. Theoretical Analysis

From a theoretical perspective, the interaction between government policies, green technological innovation, and the low-carbon transformation of the manufacturing industry can be interpreted through multiple lenses. According to the Porter Hypothesis, well-designed environmental regulations can stimulate technological innovation that offsets the cost of compliance and enhances competitiveness [20]. Meanwhile, the Environmental Kuznets Curve suggests an inverted U-shaped relationship between economic growth and environmental degradation, implying that technological progress, supported by policy incentives, can shift the turning point toward earlier low-carbon transformation [21]. Furthermore, total factor productivity theory highlights that integrating environmental and innovation factors into productivity assessment allows for a more accurate reflection of the synergistic effects of green innovation and policy on industrial upgrading [22]. These theories collectively underscore the dynamic and feedback-driven nature of the relationships among green innovation, government intervention, and industrial low-carbon transformation, providing a conceptual basis for this study’s empirical framework.

2.2. Green Technological Innovation and the Low-Carbon Transformation of Manufacturing

Traditional manufacturing, as an important driver of economic development, can promote high-quality economic growth by transitioning from an extensive production model to a green and low-carbon one. Green technological innovation serves as a cornerstone of sustainable development, and this relationship has attracted widespread attention [23,24,25]. The role of green technological innovation in the low-carbon transformation of manufacturing can be categorized into direct and indirect effects.

In terms of direct effects, numerous studies indicate that the effectiveness of green technology innovation in promoting low-carbon transformation is positively correlated with the province’s low-carbon transformation index. The further development of green and other low-carbon technologies can enhance companies’ decarbonization efficiency, and this effect is more significant for low-emission enterprises. Conversely, the low-carbon transformation of manufacturing also has a reciprocal effect on green technological innovation, encouraging companies to improve production technologies and raise their level of green innovation [26,27,28,29,30].

In terms of indirect effects, green core capabilities play an intermediary role in the relationship between low-carbon technological innovation and corporate performance. Moreover, low-carbon technological innovation has a significantly positive impact on manufacturing enterprise performance [31]. Green technological innovation, which is intrinsically connected to the low-carbon transformation of manufacturing, serves as a catalyst for advancing a green and low-carbon technological revolution. By fostering continuous innovation, it significantly strengthens the momentum for green transformation, thereby facilitating long-term sustainable economic and social development.

2.3. Government Policies and Green Technological Innovation

Research on the impact of government policies on green technological innovation has been explored from various angles, and three main viewpoints can be identified: Firstly, the positive impact of policies on green technological innovation. Various government policy measures, including command and incentive measures, social willingness, policy volume, policy effectiveness, and policy implementation capacity [32,33,34,35,36,37], as well as government subsidies, regulation, and oversight [38,39], have played a significant role in promoting green technological innovation in enterprises. Secondly, policies can also negatively impact green technological innovation. In regions with weak financial infrastructure and low small and medium-sized enterprise activity levels, local governments often have limited resources, leading to prolonged policymaking cycles and relatively high implementation costs. In such areas, the “free-rider” behavior of governments in policy formulation negatively impacts the development of green technological innovation in SMEs [40,41,42,43]. Finally, the relationship between policies and green technological innovation often exhibits non-linear patterns. Some studies suggest a U-shaped or inverted U-shaped relationship between government policies and technological innovation [44,45]. These findings highlight the complexity of the non-linear relationship between government policies and green technological innovation, suggesting that policymakers should carefully balance both regulatory intensity and methods to achieve a dynamic balance in promoting green innovation.

2.4. Government Policies and the Low-Carbon Transformation of Manufacturing

Local government fiscal subsidies, tax rewards and penalties, as well as central government supervision, reward and punishment mechanisms, and transfer payments, play a crucial role in shaping the low-carbon transformation of the manufacturing sector. In general, effective government policies can promote green, low-carbon transformation. In financially developed regions, government policy plays a crucial role in steering high-carbon industries and enterprises toward low-carbon transition. By implementing regulatory frameworks and incentivizing sustainable practices, policies facilitate the shift of traditional manufacturing toward a greener and more sustainable trajectory [46,47,48,49].

Using a “green low-carbon transformation incentive-driven analysis model”, researchers have demonstrated that incentive-driven government policies play a significant role in driving low-carbon transformation [50]. At the same time, government policies can effectively drive urban low-carbon transformation by fostering the digital economy. Other studies further confirm that by formulating targeted incentives and optimizing governance mechanisms, governments can not only promote the low-carbon transformation of manufacturing but also lead manufacturing to achieve sustainable development goals. To accelerate the low-carbon transformation of manufacturing, governments have also introduced various emerging green policies, such as carbon emissions trading policies, which have a significant effect on green manufacturing, achieving higher technological levels, cleaner energy structures, and greener industrial structures [51,52,53,54]. Hence, studying government policies that drive the low-carbon transformation of manufacturing holds substantial theoretical and strategic significance.

Notably, while prior studies have frequently documented bidirectional and non-linear relationships among government policies, green technological innovation, and low-carbon transformation, the underlying mechanisms remain insufficiently unpacked. Empirical findings indicate that stringent environmental regulations can exert a dual effect on green innovation: initial phases typically stimulate technological advancement, while excessively stringent enforcement may impose high compliance costs that inhibit further innovation, resulting in an inverted U-shaped dynamic [55]. Moreover, the interaction between green technological innovation and low-carbon transformation typically manifests as a reinforcing feedback loop: improvements in green innovation enhance the efficiency and effectiveness of decarbonization efforts, while increasing demands for low-carbon transformation create stronger incentives for firms to pursue further technological breakthroughs, resulting in mutually accelerating progress toward sustainability goals [56]. The direction and magnitude of these relationships are further moderated by contextual variables such as institutional quality, market maturity, and industrial heterogeneity, underscoring the need for nuanced analysis that transcends linear assumptions.

3. Data and Methods

3.1. Data and Processing

To study the impact of green technological innovation, government policies, and the low-carbon transformation of manufacturing on the high-quality economic development of the Yangtze River Economic Belt, we collected data from 2011 to 2023 covering the following regions: Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Guizhou, and Yunnan. The chosen time frame is based on two considerations: data availability and comprehensiveness, as well as the introduction of the Yangtze River Economic Belt concept in 2013. By comparing data before and after 2013, we can assess the impact of the Yangtze River Economic Belt initiative on the economic development of the provinces and cities along the Yangtze River.

Due to factors such as data entry errors or systemic changes during data collection, some of the original data contain minor gaps. To better reflect the trends and fluctuations in the data, we applied a second-order exponential smoothing method, which has been effectively utilized in empirical environmental studies for trend correction and noise reduction [57]. The basic formula for this method is as follows:

$$\begin{array}{c}{x}_{it}^{(1)}=\alpha x_{it-1}+(1-\alpha )x_{it-1}^{(1)}\\ x_{it}^{(2)}=\alpha x_{it}^{(1)}+(1-\alpha )x_{it-1}^{(2)}\\ {\alpha }_{it}=2x_{it}^{(1)}-x_{it}^{(2)}\\ {\beta }_{it}={\displaystyle \frac{\alpha }{1-\alpha }}(x_{it}^{(1)}-x_{it}^{(2)})\\ x_{it+m}={\alpha }_{it}+{\beta }_{it}m\end{array}$$

(1)

where $x_{it}^{(1)}$ and $x_{it}^{(2)}$ denote the first and second-order exponential smoothing values for region $i$ in year $t$, ${\alpha }_{it}$ and ${\beta }_{it}$ represent the linear smoothing parameters for region $i$, $\alpha$ is the linear smoothing parameter, and $x_{it+m}$ signifies the predicted value for region $i$ in period $(t+m)$.

3.2. Variable Description

For green technological innovation, we constructed an efficiency evaluation system based on the total factor productivity theory from an input–output perspective. Traditional measurements of green technological innovation efficiency typically include inputs such as labor and capital, as well as expected outputs. However, they fail to account for the negative impact of energy consumption and environmental pollution on economic growth, which may introduce biases and fail to accurately reflect the factors influencing regional economic growth [58]. Therefore, this study incorporates energy input, R&D investment, and undesirable outputs into the evaluation system to ensure that the measurement results balance both economic efficiency and environmental efficiency.

To quantify government policies, we analyzed the frequency of key terms related to environmental protection, energy consumption, and green development in government work reports from prefecture-level cities along the Yangtze River. This text-mining approach provides an indirect measure of governmental emphasis on green and low-carbon development [59]. We selected keywords related to environmental protection, environmental pollution, energy consumption, development concepts, green production, green living, green ecology, and green construction. The ratio of the total number of these keywords to the total word count of the government work reports serves as an indicator of the government’s emphasis on and investment in green and low-carbon development. The use of such comprehensive policy indicators aligns with the notion of innovation policy mixes, which recognize that sustainability transitions require a combination of regulatory, financial, and institutional measures rather than isolated policies [60]. However, it should be noted that while this indicator reflects the government’s emphasis in official documents, it fails to fully capture actual enforcement intensity, consistency over time, and real-world effectiveness, which limits its comprehensiveness [61].

The low-carbon transformation of the manufacturing industry is a complex process that encompasses technological innovation, enhancements in production efficiency, and rigorous environmental impact mitigation measures. To measure the progress of green transformation in the manufacturing sector, we selected “electricity generation”, “value added by manufacturing”, and “carbon emissions” as core indicators, which reflect key aspects of sustainability performance [62]. These indicators are closely linked to achieving sustainability goals in manufacturing and represent the three core dimensions of low-carbon transformation: environmental sustainability, economic contribution, and effective carbon footprint management. The specific indicator system is shown in

Table 1. Selected variables and their descriptions.

Index	Symbol	Description
Labor input	LI	Manufacturing employment per thousands of people
R&D investment	RI	Hundred million yuan of internal expenditure of R&D funds
Capital input	CI	Hundred million yuan of the net fixed assets of manufacturing enterprises above designated size
Energy input	EI	Tons of standard coal in total energy consumption in manufacturing
Earnings output	FO	Manufacturing new product sales revenue per ten thousand yuan
Innovation output	IO	A unit of green invention patents granted
Industrial wastewater discharge	IWE	Ten thousand tons of industrial wastewater discharge
Industrial sulfur dioxide emissions	ISDE	Ten thousand tons of industrial sulfur dioxide emissions
Industrial smoke and dust emissions	ISAD	Ten thousand tons of industrial smoke and dust emissions
Generating capacity	PG	Hundreds of millions of kilowatt-hours of renewable energy generation
Manufacturing value added	MVA	Hundred million yuan of manufacturing value added
Carbon emission	CE	Ten thousand tons of carbon dioxide emissions
Government policy	GP	Percentage of keyword frequency
Green technology innovation	GTI	Green technology innovation efficiency value
Low-carbon transformation in manufacturing	MTE	Efficiency value of low-carbon transition in manufacturing industry

.

Table 2. Descriptive statistics of variables.

	Number	Minimum	Median	Maximum	Standard	Kurtosis	Skewness
LI	143	0	0.44	1	0.34	1.59	0.06
RI	143	0	0.34	1	0.32	1.84	0.42
CI	143	0	0.48	1	0.32	1.71	0.06
EI	143	0	0.52	1	0.34	1.60	−0.04
FO	143	0	0.44	1	0.32	1.84	0.27
IO	143	0	0.32	1	0.33	1.88	0.46
IWE	143	0	0.14	1	0.35	3.02	1.31
ISDE	143	0	0.24	1	0.40	1.29	0.33
ISAD	143	0	0.45	1	0.32	1.79	0.11
PG	143	0	0.48	1	0.32	1.84	0.00
MVA	143	0	0.44	1	0.33	1.79	0.22
CE	143	0	0.43	1	0.30	1.97	0.20
GP	143	0	0.46	1	0.29	2.25	0.13

presents the descriptive statistics of the normalized variables. The results indicate that, after normalization, industrial sulfur dioxide emissions have the highest variance, indicating the fluctuations in ISDE are larger compared to other variables. For normally distributed data, the expected median after normalization should be 0.5. However, the median values of R&D investment, innovation output, and industrial wastewater discharge deviate significantly from the expected median, suggesting that their data may exhibit non-normal distribution characteristics. Kurtosis analysis reveals that most of all variables are less than the threshold of 3 except IWE, indicating that the distribution of these variables are relatively dispersed, with lighter tails and fewer extreme values. Skewness analysis shows that the skewness of energy input is less than 0, indicating a left-skewed distribution. The remaining variables exhibit right-skewed distributions, where industrial wastewater discharge exhibits the longest tail. The presence of non-normal distribution characteristics in the variables suggests that we cannot apply traditional OLS models for analysis. Furthermore, considering potential issues such as endogeneity, we employ the PVAR model for researching.

3.3. Method

3.3.1. Principal Component Analysis

After constructing the indicators for green technological innovation and the low-carbon transformation of manufacturing, it is necessary to link these indicators using a set of weights. Unlike traditional weighting techniques such as equal weights or entropy weight method, we adopt an innovative approach by employing the unsupervised learning algorithm principal component analysis (PCA) to assign weights. As shown in Table 2, the distribution of the data for various indicators mostly exhibits non-normal characteristics, with weak or inconsistent correlations among indicators. This contradicts the assumptions required for the entropy weight method. However, by leveraging the component matrix and variance explanation in weight assignment, we can avoid this issue and obtain more objective weight results with fewer assumptions.

(1) Determine the linear combination coefficients ${\sigma }_{nm}$ of the secondary indicator $x_m$ in each principal component $F_n$. Specifically, this is calculated using the eigenvalues ${\alpha }_n$ from the total variance analysis table and the eigenvectors ${\beta }_n^m$ corresponding to each indicator in the component analysis table. The formula is ${\sigma }_{nm}={\displaystyle \frac{{\beta }_n^m}{\sqrt{{\alpha }_n}}}$. This allows each principal component $F_n$ to be expressed as the following linear combination:

$$F_n= {\sigma }_{n1}{x}_1+{\sigma }_{n2}{x}_2+\dots +{\sigma }_{nm}{x}_m$$

(2)

where $m,n=1,2,\dots l$ with $l$ indicating the number of secondary indicators.

(2) Use the variance contribution rate of the principal components to determine the comprehensive score coefficient. When using principal component analysis to calculate weights, negative weights may appear. To avoid this and better reflect the actual impact of each secondary indicator on the primary indicator, this study applies a coordinate translation method in the calculation of the comprehensive score coefficient. Specifically, for each linear combination coefficient ${\sigma }_{nm}$, we subtract the minimum value of the corresponding principal component ${\sigma }_{nm}$. Let the variance contribution rate of the first $p$ principal component eigenvalues be $\phi$, and let the comprehensive score coefficient corresponding to each indicator be ${\gamma }_n$. Then,

$${\gamma }_n={\displaystyle \frac{{\displaystyle {\sum }_{m=1}^n{\phi }_n({\sigma }_{nm}-\min ({\sigma }_{nm}){|}_{n=n_0})}}{{\displaystyle {\sum }_{k=1}^p{\phi }_k}}}$$

(3)

(3) Normalize the comprehensive score coefficients to obtain the weights. Let $\omega$ represent the weight corresponding to the secondary indicator. Then,

$${\omega }_n={\displaystyle \frac{{\gamma }_n}{{\displaystyle {\sum }_{i=1}^n{\gamma }_n}}}$$

(4)

Table 3. Weight value of green technology innovation.

Primary Index	Secondary Index	Tertiary Indicators	PCA Weigh
$GTI$	Input index	Labor input	3.9884%
		R&investment	13.9260%
		Capital input	39.9493%
		Energy input	1.2823%
	Expected output	Earnings output	9.1987%
		Innovation output	12.7295%
	Undesirable output	Industrial wastewater	3.5649%
		Industrial sulfur dioxide	10.5885%
		Industrial smoke dust	4.7723%

presents the weight distribution of indicators for green technological innovation. It can be observed that capital input and R&D investment have the largest weights, indicating the significant driving force of input in the development of green technological innovation. In terms of output, earnings output accounts for 9.20% and 12.73%, respectively, highlighting the positive role of input in the development of green technological innovation. For undesirable outputs, it can be seen that industrial sulfur dioxide is an important factor affecting the development of green technological innovation, while industrial wastewater and industrial dust emissions also have significant impacts. Figure 2 visualizes the provincial distribution of green technological innovation values post-weight assignment, where darker shades represent higher values.

3.3.2. PVAR Model

The PVAR model, based on the multivariate system equation [63], combines the advantages of panel analysis and the vector autoregressive (VAR) model. It constructs an endogenous system by transforming all variables into endogenous variables within the system for unrestricted treatment, allowing for a more objective analysis of the potential relationships between green technological innovation, government policies, and the low-carbon transformation of the manufacturing industry. The PVAR model also avoids the need for prior hypothesis testing and the specification of independent and dependent variables, making it easier to explore the impact of each variable and its lagged values on the correlations and interactions with other variables in the model. Furthermore, compared to the VAR model, PVAR uses panel data, which allows for a greater variety of observations [64], thereby controlling for the interference of missing variables on the results.

Compared with prior studies that have adopted PVAR models in environmental economics, the novelty of this study lies in two aspects. First, rather than relying on simple macro-level policy indicators or static indices, we construct a dynamic, text-mining-based proxy for government policy intensity, which better captures temporal variations in policy emphasis. Second, while earlier PVAR applications typically overlook the multi-dimensionality of green technological innovation by using single-factor proxies, our framework integrates a comprehensive, multi-indicator system for GTI based on total factor productivity theory and undesirable outputs, thereby enhancing the robustness of the empirical analysis. These innovations allow us to not only examine standard dynamic interrelations but also reveal deeper lag structures and potential feedback effects that have been underexplored in the existing literature.

The following settings are made for the PVAR model:

$$Y_{it}={\alpha }_0+{\displaystyle \sum _{i=1}^n{\alpha }_j{Y}_{i,t-j}+{\delta }_t+{\eta }_i}+{\mu }_{it}$$

(5)

where $Y_{it}$ represents the system’s endogenous variables—green technological innovation, government policies, and the low-carbon transformation of manufacturing. i, t represent the region and time dimensions, respectively. n denotes the number of lags, j indicates the lag period, ${\alpha }_j$ represents the regression coefficient matrix for the j lag period, ${\delta }_t$ refers to the time effect, ${\eta }_i$ represents the individual (or regional) effect, and ${\mu }_{it}$ stands for the random disturbance term, which accounts for effects beyond the time and individual effects.

Before conducting empirical research using the PVAR model, we need to examine the cross-sectional dependence between variables. Cross-sectional dependence is a crucial issue, and neglecting it may lead to severe estimation bias and distortion of magnitudes [65]. Given that the number of cross-sections in this study is smaller than the length of the time series, we adopt the LM method based on the seemingly unrelated regression (SUR) model proposed by Breusch and Pagan. The Breusch–Pagan LM test involves performing an OLS estimation on the regression model to obtain the residuals $\widehat{{\mu }_i}$, and then calculating ${\widehat{{\mu }_i}}^2$ and the variance ${\widehat{\sigma }}^2={\displaystyle \raisebox{1ex}{$SSE$}\!\left/ \!\raisebox{-1ex}{$N$}\right.}$. This is followed by obtaining $p_i={\displaystyle \raisebox{1ex}{${\widehat{{\mu }_i}}^2$}\!\left/ \!\raisebox{-1ex}{${\widehat{\sigma }}^2$}\right.}$ and setting up an auxiliary regression $p_i=X\beta +v$. The LM test statistic has the following form:

$$LM=N\times SSR~{\chi }^2(N-1)$$

(6)

After performing the cross-sectional dependence test, we need to examine the unit roots of the selected variables. The presence of a unit root indicates that the series is non-stationary. For the unit root test, this study employs Dickey’s ADF test [66]. The ADF test has the following form:

$$\Delta y_t={\beta }^{’}z(t)+\gamma y_{t-1}+{\displaystyle \sum _{j=1}^p{\varphi }_j\Delta y_{t-j}}+{\epsilon }_t$$

(7)

where $z(t)=\{0,1,(1,t)\}$ represents the deterministic part of $y$, ${\sigma }^2$ is a Gaussian white noise sequence with mean 0 and variance ${\epsilon }_t$, and $\beta ,\gamma ,{\varphi }_j$ are the coefficient vectors corresponding to $z(t),y_{t-1},\Delta y_{t-j}$, respectively. Once it is confirmed that the selected variables do not have unit roots, we proceed with the cointegration test. The cointegration test is conducted to determine whether there exists a long-term stable relationship between the panel data and to assess whether the panel data regression is a spurious regression. If the Breusch–Pagan LM test indicates no cross-sectional dependence, we should use first-generation test methods, such as the Pedroni test. The equation for the Pedroni test is as follows:

$$\Delta y_{it}={\alpha }_i+{\delta }_{i}t+X_{it}^{’}{\beta }_i+u_{it},i=1,\dots ,N;t=1,\dots ,T$$

(8)

where ${\delta }_{i}t$ is the time trend term, and it allows the long-term coefficient $\beta$ to vary with the individual-specific coefficient i. ${\alpha }_i$ represents the difference generated after considering the time trend. $u_{it}$ is the residual generated from the differenced model. In terms of the test statistics, there are three within-group statistics: the panel variance ratio statistic, the panel-$\rho$ and panel-t statistics, and two between-group statistics: the between-group-$\rho$ and between-group-t statistics.

Figure 3 presents the framework of the empirical study in this paper, and the specific results are discussed in Section 4.

4. Empirical Results

Before the analysis, we first test the stationarity of the data. Only if the data are stationary can the PVAR model be used. To facilitate the subsequent calculation of the GMM estimator, we need to ensure that the data satisfy the first-difference moment conditions, which requires applying forward orthogonal transformation or taking the first difference of the data. We choose to apply first-order differencing and test the stationarity of each differenced series using LLC, IPS, and ADF tests. Next, we consider the lag order of the model. We use multiple information criteria, including the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the Hannan–Quinn Information Criterion (HQIC), with the results presented in

Table 4. Information criterion values corresponding to each lag order of variables.

Lags	AIC	BIC	HQIC
1	−3.59434 *	−2.56325 *	−3.17613 *
2	−3.02473	−1.68785	−2.48382
3	2.41974	4.10883	3.10023
4	−1.67542	0.424874	−0.83532

Note: * denote the minimum value for all lags.

. Based on the principle of minimizing the information criteria, the optimal lag order of the model is determined to be 1.

4.1. BP-LM Test, Unit Root Test, and Cointegration Test Results

The results of the BP-LM test are shown in

Table 5. BP-LM test result.

Variables	Chibar2	Prob > Chibar2
GTI	0.00	1.0000
GP	0.00	1.0000
MTE	0.00	1.0000

, which represents the cross-sectional dependence test and serves as the basis for subsequent econometric methods and empirical results. The results indicate that the null hypothesis cannot be rejected for any variable, implying no cross-sectional dependence among them. This indicates that the variables are cross-sectionally independent. Based on this result, we adopt first-generation test methods in the subsequent analysis.

After confirming the absence of cross-sectional dependence, we conducted the traditional ADF unit root test, with results presented in

Table 6. Unit root test.

Variables	Statistic	Value	p-Value
GTI	Z	−7.5812	0.0000
	L	−8.6700	0.0000
	Pm	12.3570	0.0000
GP	Z	−13.0053	0.0000
	L	−20.3904	0.0000
	Pm	33.3665	0.0000
MTE	Z	−9.2009	0.0000
	L	−13.0292	0.0000
	Pm	20.4018	0.0000

. Under the ADF test, the Z, L, and Pm statistics reject the null hypothesis for all variables at the 1% significance level, indicating that they are stationary and free from unit root problems. Therefore, we proceeded to the cointegration test.

We conducted the Pedroni cointegration test based on three statistics: the Modified Phillips–Perron t, Phillips–Perron t, and Augmented Dickey–Fuller t, with the results shown in

Table 7. Pedroni cointegration test findings.

Variables	Statistic	Value	p-Value
GTI	Modified P–P	2.9775	0.0015
	P–P	−3.1629	0.0008
	ADF	−3.3287	0.0004
GP	Modified P–P	1.7423	0.0407
	P–P	−9.0185	0.0000
	ADF	−9.5261	0.0000
MTE	Modified P–P	2.5044	0.0061
	P–P	−6.5321	0.0000
	ADF	−3.6446	0.0001

. The results show that all three statistics are statistically significant at the 5% level, rejecting the null hypothesis. This confirms a long-term cointegration relationship among the three variables, making the PVAR model suitable for analyzing their dynamic interactions.

4.2. Panel Vector Autoregression Regression (PVAR) Analysis

Given the absence of cross-sectional dependence among the variables in this study, we employ the system GMM approach to analyze their relationships and the core regression outcomes presented in

Table 8. Regression coefficient and significance level based on PVAR model.

Explained Variable	Explanatory Variable	Lags	Regression Coefficient	p Value
GTI	GTI	1	0.0164	0.892
	GP	1	−0.0190	0.068
	MTE	1	0.0349	0.022
GP	GTI	1	1.7716	0.239
	GP	1	−0.3415	0.000
	MTE	1	0.2483	0.436
MTE	GTI	1	1.3660	0.003
	GP	1	0.0164	0.582
	MTE	1	−0.3209	0.004

. In the green technological innovation equation, the coefficient of the first-order lagged term of green innovation is 0.0164 and not statistically significant, indicating weak short-term persistence. This suggests that although green innovation exhibits cumulative effects, its inertia is insufficient in the short run, which may be attributed to long R&D cycles, slow diffusion of innovation, and limited incentive structures. Government policy exerts a negative impact on green innovation, with a coefficient of −0.0190 significant at the 10% level, implying that although policies are intended to promote innovation, issues such as an excessive focus on assessment indicators at the expense of substantive outcomes may dampen firms’ enthusiasm for innovation, especially during the early stages of implementation. In contrast, the influence of manufacturing low-carbon transformation on green innovation is significantly positive, reflecting the “pressure effect” whereby market demand for low-carbon products and cleaner production processes effectively stimulates firms’ innovation activities.

In the government policy equation, the lagged term of policy is significantly negative, indicating a strong self-adjustment mechanism. Policy implementation tends to follow a stepwise evaluation and adjustment approach, which aligns with the incremental pattern characteristic of local government governance in China. The short-term effects of green innovation and low-carbon transformation on policy are not significant, suggesting that these factors are insufficient to induce rapid policy responses in the short run, revealing a time-lagged feedback mechanism from enterprises to policymakers.

In the manufacturing low-carbon transformation equation, the lagged term of low-carbon transformation is significantly negative, indicating short-term inertia constraints. This reflects both the substantial upfront investments and high adjustment costs associated with low-carbon transition, as well as deeper structural imbalances in regional economic development. Provinces in the upper reaches of the Yangtze River, which are characterized by weaker industrial structures and high dependence on resource-based industries, have experienced slower progress in low-carbon transformation. In contrast, downstream developed regions, leveraging strong industrial foundations and superior innovation capabilities, have demonstrated greater resilience in advancing low-carbon transformation. The impact of green innovation on low-carbon transformation is notably significant and positive, underscoring the critical role of technological advancement as a key pathway to achieving decarbonization goals. The direct effect of government policy on low-carbon transformation is not significant, indicating that its influence is mainly exerted through indirect channels. The GMM regression results indicate that green innovation serves as a key driver of low-carbon transformation, while low-carbon transformation also facilitates deeper progress in green innovation to a certain extent. However, government policy exhibits a “strong-then-weak” dynamic feature in the short term, with clear signs of implementation delays and feedback lags. Moreover, regional disparities amplify the complexity of these relationships. Quantitative results show that provinces in the lower reaches of the Yangtze River—such as Shanghai, Zhejiang, and Jiangsu—consistently display higher values of green technological innovation, government policy intensity, and low-carbon transformation compared with midstream and upstream regions such as Chongqing and Sichuan, providing a direct illustration of interregional differences. Since PVAR is a dynamic model, the coefficients and significance levels obtained from the regression may not fully capture the true relationships between the variables. To more accurately describe the dynamic interdependencies among these variables, we utilize impulse response functions and variance decomposition.

4.3. Stability Test

Furthermore, we analyzed the model’s stability. We assessed the model’s stability based on the AR root diagram. If the characteristic roots lie within the unit circle, this suggests that the model is stable. As shown in

Table 9. Model eigenvalue table.

Eigenvalue		Modulus
Real	Imaginary
−0.2931	−0.1992	0.3544
−0.2931	0.1992	0.3544
−0.2458	0.0000	0.2458

, both the values and moduli of characteristic roots lie within the unit circle, confirming the stability of the system GMM regression results. This result is further illustrated in Figure 4.

4.4. Granger Causality Test

The Granger causality test determines whether the inclusion of lagged values of an independent variable can improve the prediction of the dependent variable, thereby assessing the predictive influence of one variable on another. In this study, to gain deeper insights into the relationships among GTI, GP, and MTE, we conducted a Granger causality test, the results of which are shown in

Table 10. Granger causality analysis.

Independent Variable–Dependent Variable	chi2	df	Prob > chi2
GTI→GP	3.330	1	0.068
GTI→MTE	5.231	1	0.022
GP→GTI	1.384	1	0.239
GP→MTE	0.599	1	0.436
MTE→GMI	8.761	1	0.003
MTE→GP	0.303	1	0.582

. Table 10 shows that GTI and MTE exhibit bidirectional Granger causality at the 5% significance level, indicating a two-way causality relationship. GTI is a Granger cause of GP at the 10% significance level, indicating a unidirectional causal relationship from GP to GTI. This conclusion aligns with the system GMM results.

4.5. Impulse Response Analysis

The PVAR regression results focus solely on the impact relationships among variables but do not examine the dynamic effects when a variable is subjected to a shock from another. The impulse response function (IRF) addresses this issue by offering a clear depiction of the dynamic interactions following a shock to a variable. In this study, we conducted 500 Monte Carlo simulations in Stata18 to obtain the dynamic responses of each variable to shocks over 0 to 10 periods. The upper and lower curves denote the bounds of the 95% confidence interval, while the middle curve depicts the estimated IRF values. The results are shown in Figure 5.

Figure 5 indicates that the shock variables and response variables include green technological innovation, government policies, and the low-carbon transition of the manufacturing industry. This study performs a longitudinal analysis of the impulse response graph.

When green technological innovation is subjected to external shocks, government policy exhibits a clear positive response in the first period but quickly turns negative in the second period and gradually stabilizes thereafter. Meanwhile, the low-carbon transformation of the manufacturing industry also shows a significant short-term negative effect initially. This phenomenon reveals that, although green technological innovation stimulates policy responses and market expectations in the short term, the actual transformation of innovation outcomes lags behind. Enterprises bear high R&D costs and substantial investment in transformation, leading to a temporary disconnect in low-carbon transformation benefits. Additionally, significant disparities in regional economic structures and technological foundations—particularly in the less-developed midstream and downstream areas—limit the spillover effects of green innovation, resulting in an overall “initial surge followed by suppression” pattern. This reflects the crucial impact of technology diffusion barriers and uneven policy implementation capacity on short-term negative effects.

When government policy experiences a shock, both green technological innovation and the low-carbon transformation of the manufacturing industry display immediate positive responses, indicating that policy can effectively stimulate enterprise innovation enthusiasm and promote low-carbon practices in the short term. However, this stimulus effect gradually diminishes over subsequent periods, reflecting a typical “policy lag–decay” pattern. This not only illustrates the inherent life-cycle effect of policies but also exposes execution-level issues such as “policy-heavy on issuance, light on enforcement”, along with enterprises’ tendency to respond actively in the early stages but lose momentum later. Moreover, the strong “assessment-oriented” focus in policy design means that some local governments prioritize short-term achievements, resulting in insufficient long-term incentives and limiting the sustained depth of policy impact.

When the low-carbon transformation of the manufacturing industry is impacted, green technological innovation shows a weak initial response but quickly strengthens in the second and third periods, stabilizing thereafter. This indicates that low-carbon transformation, through a market “pressure mechanism”, effectively stimulates corporate green innovation momentum in the medium term, especially in regions with strong low-carbon market demand and mature green industrial chains. However, in the long run, this facilitative effect is constrained by innovation path dependency, technological bottlenecks, and market saturation, making it difficult to sustain. Meanwhile, the feedback effect of low-carbon transformation on government policy remains weak, highlighting that the current policy system is predominantly characterized by a top-down “policy-driven” model, with insufficient bottom-up feedback mechanisms—suggesting that policy feedback channels need further strengthening.

4.6. Variance Decomposition

As the complement of impulse response analysis, variance decomposition can analyze and compare the relative importance of each variable to the given endogenous variable. Additionally, it assesses the cumulative contribution of the same variable to an endogenous variable across different forecasting periods. Therefore, to gain a more precise understanding of the internal relationships among green technological innovation, government policies, and low-carbon transformation of the manufacturing industry, this paper employs variance decomposition with 500 Monte Carlo simulations over 10 periods. The main results are shown in

Table 11. Variance decomposition results of each variable.

Response Variable	Number of Periods	Shock Variable
		GTI	GP	MTE
GTI	1	1.000	0.000	0.000
	5	0.961	0.029	0.010
	10	0.961	0.029	0.010
GP	1	0.007	0.993	0.000
	5	0.050	0.943	0.006
	10	0.050	0.943	0.006
MTE	1	0.040	0.005	0.955
	5	0.263	0.009	0.728
	10	0.263	0.009	0.728

.

The variance decomposition results of green technological innovation indicate that its variation is primarily dominated by its own dynamics. Specifically, in the first period, the self-explanatory power of green technological innovation reaches 1.000. By the fifth and tenth periods, this value slightly decreases to approximately 0.961. The contributions of government policy and the low-carbon transformation of the manufacturing industry remain minimal throughout, both staying below 0.03. This suggests that green technological innovation possesses a strong self-driven characteristic, with its accumulation and development mainly relying on its own trajectory. Direct external interventions have yet to produce statistically significant impacts. This indirectly reflects that, although policy and market environments continuously emphasize the importance of green transformation, the implementation and diffusion of green innovation are still predominantly endogenous and have not yet been propelled by strong external driving forces.

The variance decomposition of government policy presents a typical feature of policy endogeneity. Both in the short term and the long term, the self-explanatory power of government policy remains high, decreasing only slightly from 0.993 in the first period to 0.943 in the tenth period. The impacts of green technological innovation and the low-carbon transformation of the manufacturing industry remain very limited. This result reveals that the current policy system mainly operates through top-down internal formulation and adjustment mechanisms. It has not yet formed an effective dynamic pathway where enterprise innovation or low-carbon transformation outcomes exert upward pressure to optimize policy. This highlights the weakness of the policy feedback mechanism and signals a certain degree of self-circulation risk within the policy framework. In the long term, if effective feedback from the market and enterprises is lacking, policies may lose their adaptability and long-term effectiveness.

The variance decomposition of the low-carbon transformation of the manufacturing industry is the most noteworthy. In the first period, its variation is mainly explained by itself, with a contribution rate of 0.955. In the medium and long term, its self-explanatory rate declines significantly, dropping to around 0.728 in both the fifth and tenth periods. In contrast, the explanatory power of green technological innovation rises continuously, increasing from 0.04 in the first period to 0.263 in the fifth and tenth periods. This highlights the pivotal role of green technological innovation in driving the low-carbon transformation of the manufacturing industry and confirms that green innovation is a crucial force in achieving deep and sustained low-carbon transformation. Meanwhile, the explanatory power of government policy for the low-carbon transformation remains very low, not exceeding 0.01 even in the long term. This indicates that the direct effect of policy is relatively limited, and its influence is exerted more through indirect pathways. These findings suggest that future policies should focus more on building a transformation model centered on innovation-driven mechanisms rather than relying solely on traditional administrative directives and regulatory measures.

5. Conclusions and Suggestions

Based on the PVAR model analysis of panel data from 11 provinces along the Yangtze River Economic Belt, this study investigates the dynamic relationship among green technological innovation (GTI), government policies (GP), and the low-carbon transformation of the manufacturing industry (MTE). The empirical findings reveal that bidirectional causality exists between GTI and MTE, but the positive effect of MTE on GTI is stronger than the reverse. This finding aligns with the demand–pull hypothesis, suggesting that pressure from the low-carbon transformation of the manufacturing sector stimulates green technological innovation as firms respond to regulatory and market-driven decarbonization imperatives. Additionally, government policy impacts are short-term and self-limiting, showing an initial promotional effect followed by a decay, which suggests lagged administrative responses and a wait-and-see effect after initial intervention. Variance decomposition shows that over time, GTI becomes a dominant contributor to MTE, affirming its long-term strategic role in supporting sustainable industrial transformation.

Drawing upon our empirical findings, we propose the following recommendations to enhance green technological innovation and facilitate the low-carbon transformation of the manufacturing industry. First, due to the marked regional disparity in GTI and MTE performance, one-size-fits-all innovation strategies are ineffective. Tailored policies should be implemented to promote inclusive green innovation. Policymakers should create localized innovation matching funds for provinces with underdeveloped GTI capabilities, support green innovation clusters that align with provincial industrial strengths such as green textiles in Jiangxi or eco-manufacturing in Chongqing, and promote horizontal interprovincial spillovers through policy-guided collaborative R&D networks and IP-sharing platforms. Secondly, this study shows a self-restriction tendency in government policies. Instead of one-off policy shocks, sustained and staggered policies are more effective in maintaining momentum. Governments are encouraged to introduce multi-stage policy portfolios, combining upfront fiscal incentives with delayed tax credits or penalties, develop real-time monitoring systems for MTE and GTI indicators to enable feedback-driven policy adjustment, and avoid abrupt withdrawal of policies that could undermine innovation continuity. Third, as GTI’s contribution to MTE rises significantly over time, it is crucial to ensure its sustained accumulation and regional dissemination. Policymakers should develop a Yangtze River Green Innovation Diffusion Index based on interprovincial impulse response data, form technology sharing alliances between high-GTI provinces and lower-GTI ones to bridge the transformation gap and establish a Low-Carbon Technology Exchange Platform integrating government, industry, and academia to promote modular technology transfers and adaptive learning.

Despite the valuable insights gained from this study, certain limitations must be acknowledged. Among them, the biggest limitation is the regional limitation. We only take the Yangtze River Economic Belt as a sample for the study. Future research should extend the geographical scope of analysis to enhance the generalizability of the findings. Second, we recognize that high-quality regional development is not limited to green and low-carbon aspects. Future research can explore additional determinants of sustainable economic growth and conduct similar empirical investigations to provide a more holistic perspective.