The Impact of Market-Oriented Carbon Regulation on the High-Quality Development of the Manufacturing Industry—Based on Double Machine Learning

Abstract

Promoting high-quality development of the manufacturing industry is an important strategy for China’s economic transformation and upgrading, as well as the realization of sustainable development, and the manufacturing industry is also a critical field for environmental regulation. What impact does market-driven carbon regulation have on the high-quality development of manufacturing firms? Taking the carbon emission trading pilot policy as a “quasi-natural experiment” of market-driven carbon regulation, this paper selects micro panel data from Chinese listed manufacturing enterprises spanning 2003 to 2021 and uses the double machine learning method to evaluate the effect of market-oriented carbon regulation on the high-quality development of the manufacturing industry. The study finds that the carbon emission trading pilot policy notably boosts the high-quality development of the manufacturing industry. Further mechanism analysis reveals that the policy has exerted a significant innovation effect, while the resource allocation effect is not yet significant. Heterogeneity analysis shows that the carbon emission trading pilot policy has a significant promotional effect on the high-quality development of the manufacturing industry in eastern and western regions, as well as state-owned and technology-intensive manufacturing industries. The research conclusions provide theoretical reference and practical insights for the construction of a national unified carbon market and the promotion of the green and low-carbon transformation of the manufacturing industry.

1. Introduction

In March 2024, the Report on the Work of the Government of the People’s Republic of China put forward initiatives to strengthen the development of ecological civilization, advance green and low-carbon development, as well as build a beautiful China where humans and nature coexist in harmony. China has long been confronted with the contradiction between extensive economic growth and ecological and environmental sustainability, making it imperative to explore a sustainable development path [1,2]. From the perspective of the evolution of environmental governance, China’s environmental regulation falls into two categories: command-driven and market-oriented. In the early stage, command-driven environmental regulation was dominant, distinguished by an overemphasis on administrative orders as well as inadequate utilization of market-oriented instruments [3]. China introduced market-oriented carbon emission regulation in 2013, launching pilot carbon emission trading schemes. In 2021, it set up the world’s largest unified national carbon emission trading market [4]. Carbon emission trading represents a typical form of market-oriented environmental regulation [5], and the establishment of the carbon market also marks the transition of China’s carbon regulation from a single command-driven model of environmental regulation to a parallel “command-driven combined with market-oriented” model of environmental regulation.

Facing increasingly prominent global warming and the urgent demand for high-quality development, the economic effects of carbon emission regulation (especially its impact on the manufacturing industry) have become a key focus of economic research [6]. China’s 14th Five-Year Plan clearly emphasizes focusing on the real economy, and highlights boosting the building of a strong manufacturing country and promoting the high-quality development of the manufacturing industry (HQDM; hereafter referred to as HQDM). Although China is known as the “world factory”, its manufacturing industry exhibits the traits of high energy consumption, high emissions, high pollution, and low added value [7,8]. This model has severely hindered China’s transition aimed at establishing a strong manufacturing country. Therefore, low-carbon transition has become an inherent requirement for the high-quality development of the manufacturing industry [9]. Currently, China’s environmental regulation is shifting from a single command-driven model to a parallel “command-driven combined with market-oriented” model. This gives rise to an urgent question to be addressed: What is the effect of market-oriented carbon regulation on the HQDM?

To address this question, this paper uses the pilot carbon emission trading policy (CETP, hereafter referred to as CETP) as a “quasi-natural experiment” for market-oriented carbon regulation. Based on the microdata of listed manufacturing enterprises from 2003 to 2021, it employs the double machine learning method (DML; hereafter referred to as DML) to assess the policy’s impact on the HQDM. Focusing on this typical form of market-oriented carbon regulation, this paper aims to answer two key questions through a systematic empirical study: What impact does carbon regulation have on the HQDM, and what mechanisms drive this impact? Additionally, is the policy effect contingent upon differences in regions, enterprise ownership types, and factor intensity? The empirical results indicate that the CETP exerts a significant promotional effect on the HQDM, and this effect is mainly achieved via the technological innovation mechanism. Scientifically clarifying the economic effects and mechanisms of market-oriented carbon regulation not only holds considerable theoretical value but also carries important practical significance amid China’s urgent practical needs for low-carbon transition and high-quality development.

2. Literature Review

The literature reviewed in this study mainly covers two aspects: the economic effects of market-oriented environmental regulation and the evaluation methods for policy effectiveness.

Regarding the economic effects of market-oriented environmental regulation, the overall findings indicate positive policy outcomes. For instance, environmental policies can induce technological innovation for emission reduction [2], especially green technological innovation [10], alleviate the short-term bias of corporate investment [11], and improve corporate performance [12]. Acemoglu et al. (2012) [13] found that the optimal environmental policy should include carbon taxes and research subsidies: carbon taxes are used to control carbon emissions, while research subsidies guide the direction of technological innovation. Broadstock et al. (2025) [14] identified a positive correlation between carbon pricing and stock returns in the energy sector. As a typical form of market-oriented environmental regulation, research on the economic effects of the CETP has continued to expand. Some studies argue that the CETP has significantly improved the TFP of emission-controlled enterprises [4], promoted corporate exports [15], and simultaneously driven corporate technological innovation [1,16]. Additionally, the CETP effectively reduces costs and boosts the allocation efficiency of production factors [17], and accelerates the substitution process of the energy consumption structure [18], lowering the proportion of profit-driven enterprises in the industry [19]. Meanwhile, Vakili et al. (2025) [20] revealed that carbon emission trading can notably reduce the life-cycle costs of carbon dioxide transportation projects in the UK. Marin et al. (2018) [21] discovered that the EU Emissions Trading System (EU ETS) has improved labor productivity. Oladapo et al. (2024) [22] revealed that carbon emission trading will promote GDP growth.

However, Nong et al. (2020) [23] documented that when all industries in Vietnam participate in the emissions trading market, real GDP will decrease by 1.78%. Tran et al. (2019) [24] also found that carbon emission trading may cause a slight contraction in Australia’s real GDP and real household consumption. Dewaelheyns et al. (2023) [25] further observed that the increased “carbon risk” induced by the EU ETS leads to a decline in the value of enterprises with insufficient carbon allowances. Jia et al. (2023) [26] revealed that carbon emission trading also exerts a negative impact on the TFP of regional enterprises. These findings suggest that the economic effects of carbon trading policies are uncertain and may produce either positive or negative economic effects.

It can be concluded that the core feature of market-oriented environmental regulation is that emitters are required to pay for their emissions, with examples including carbon emission trading and carbon taxes. In terms of measuring environmental regulation, there are two primary approaches: first, measurement through proxy policies, such as the CETP and carbon tax policies; second, indirect measurement via proxy variables—for instance, using indicators like energy prices [2] and the share of environmental pollution control investment to GDP [12,27]. These proxy variables are highly subjective, reflecting only the performance of environmental regulation in a certain aspect rather than environmental regulation itself, which may lead to measurement bias [28,29]. Meanwhile, among the aforementioned studies on environmental regulation, few have examined the influence of market-oriented carbon regulation on the manufacturing industry. Therefore, this study employs the CETP as a proxy for carbon regulation and evaluates the actual effect of carbon regulation on the HQDM under the condition of effectively avoiding subjective biases in measurement indicator selection.

In terms of environmental regulation evaluation methods, existing studies mainly adopt difference-based methods such as DID [5,9], PSM-DID [30,31], and staggered DID [32]. However, these traditional methods share a common limitation: they impose strict restrictions on the dimension of control variables. When high-dimensional control variables are introduced, multicollinearity is likely to occur, which in turn leads to estimation bias—namely, the problem of “the curse of dimensionality”. With the rapid integration of machine learning into the field of econometrics, its application in policy evaluation has gradually increased. Chernozhukov et al. (2018) [33] were the first to propose that Double Machine Learning (DML) could be applied to policy effect evaluation. Since then, Yang et al. (2020) [34] used DML to test the effect of large-N auditors on audit quality and found that large-N auditors positively influence audit quality. Taking the “Broadband China” strategy as a “quasi-natural experiment”, Zhang and Li (2023) [35] used DML to confirm that the popularization of network infrastructure significantly promotes green growth of cities. Additionally, Zhang et al. (2022), Bodory et al. (2022), and Farbmacher et al. (2022) [36,37,38] used DML to assess the economic and social effects of night subway operation, the employment effect of vocational training, and the health effect of medical insurance, respectively—all of which verified the effectiveness of this method. The core advantage of DML lies in its ability to handle high-dimensional variables: it automatically screens high-dimensional control variables, effectively avoiding the multicollinearity problem (i.e., the “curse of dimensionality”) caused by high-dimensional variables in traditional methods [35].

The study’s marginal contributions are primarily reflected in three aspects: First, from the perspective of research design, this study takes the CETP as the proxy policy for market-oriented carbon regulation. By effectively avoiding subjective biases during the choice of measurement indicators, it explores the impact of the CETP on the HQDM. Second, in terms of research methods, the double machine learning (DML) method is applied to recognize policy impacts. As a nonparametric regression model, DML does not require prespecifying a functional form and has notable advantages in high-dimensional data processing and nonparametric prediction. This allows it to avoid the “curse of dimensionality” and model misspecification bias associated with traditional parametric regression [39]. Therefore, in this study, an exhaustive set of control variables is incorporated, which are selected from two dimensions: 14 variables at the enterprise-level and 16 variables at the city-level, amounting to a total of 30 control variables. In contrast, difference-based methods such as DID and PSM-DID, which are commonly used in previous studies, are limited by the dimension of control variables. They tend to suffer from multicollinearity due to high-dimensional variables and thus struggle to overcome the limitation of the “curse of dimensionality”. Third, regarding mechanism identification, this study conducts an in-depth examination of the mechanism by which carbon regulation impacts the HQDM. It proposes that carbon regulation may have both positive and negative impacts on technological innovation and resource allocation, and verifies the actual mechanism outcomes through empirical tests. Meanwhile, it systematically examines the heterogeneity of policy effects across regions, enterprises with different ownership types, and enterprises with different factor intensities.

3. Theoretical Mechanisms

The theoretical foundation of carbon emission trading is rooted in Coase’s property rights theory. Specifically, emission rights, with carbon dioxide as their subject, are characterized by the attribute of property rights. First, the carbon emission rights of market participants are clearly defined; on the basis of total carbon emission control, the commodity attribute is endowed with carbon emission rights, and the negative environmental impacts caused by corporate production are priced in the market. Through market transactions, enterprises bear the cost of carbon emissions, thereby achieving the Pareto optimality of resource allocation. Thus, this research puts forward the following hypothesis:

Hypothesis 1.

The CETP can boost the TFP of the manufacturing industry, which is to say, promote the HQDM.

As can be inferred from Coase’s property rights theory mentioned above, the market transaction of carbon emission rights enables the achievement of Pareto optimality in their allocation and enhances productivity. Meanwhile, based on Marx’s analysis of the factors affecting productivity, there are two primary pathways to improve productivity: first, accelerating technological progress, which requires increasing R&D investment, and introducing advanced technologies; second, optimizing factor allocation, with a focus on addressing resource misallocation from an institutional perspective [40]. Accordingly, this study explores the influence mechanism of the CETP on the HQDM from two dimensions: the innovation effect and the resource allocation effect. The innovation effect acts on technological innovation through the dual perspectives of the “compliance cost hypothesis” and the “innovation compensation hypothesis”; while the resource allocation effect may affect resource allocation efficiency through two channels: optimal resource allocation and resource misallocation.

3.1. Innovation Effect

The innovation effect of the CETP exerts both positive and negative impacts.

Regarding the positive impacts, the following can be concluded: ① Based on the “innovation compensation hypothesis” perspective, when enterprises face increased cost pressure due to purchasing carbon allowances, they are motivated instead to increase innovation input and achieve technological innovation [41]. This offsets the cost pressure brought by the CETP, generates an innovation compensation effect, and thereby promotes the improvement of TFP in the manufacturing industry. ② The potential advantage of carbon emission trading lies in two aspects: it not only regulates the total volume of carbon emissions but also allows enterprises to sell surplus carbon allowances to obtain additional economic benefits [42]. Therefore, carbon emission trading provides enterprises with a “sustained and dynamic economic incentive” for technological innovation. Green technological innovation can not only enhance enterprises’ competitiveness in the market and gain greater economic benefits, but also improve their social reputation [18], which further stimulates enterprises to expand investment in technological innovation.

As for the negative impact, the price of carbon trading affects enterprises’ production costs. From the perspective of the “compliance cost hypothesis”, when enterprises’ carbon allowances are insufficient to meet production needs, they must purchase additional allowances from the carbon market. This increases their production costs and crowds out their investment in technological innovation.

Drawing on the above analysis, the actual policy effect of the CETP on technological innovation remains to be further verified. Therefore, this study puts forward the following hypotheses:

Hypothesis 2a.

The CETP induces technological innovation and promotes the HQDM.

Hypothesis 2b.

The CETP crowds out technological innovation and inhibits the HQDM.

Hypothesis 2c.

The CETP exerts an inducing effect and a crowding-out effect on technological innovation that are roughly equivalent, thus having no significant impact on the HQDM.

3.2. Resource Allocation Effect

The CETP’s resource allocation effect on HQDM is primarily positive. The CETP optimizes the allocation of factors across enterprises. Carbon emission trading transforms carbon emissions from a free public resource into a crucial scarce resource [4,5]. The CETP can enhance enterprises’ flexibility in emission reduction by sending clear market price signals [43] and optimizing the allocation of carbon allowances among enterprises, enabling enterprises to reach emission reduction goals at the lowest cost.

Based on the above analysis, in the mature stage of the carbon market, the CETP can improve resource allocation and promote the HQDM. However, in the early stage of carbon market development, the CETP may not exert a notable impact on resource allocation. Moreover, the market price may fail to reflect the real supply and demand situation, which could instead disrupt resource allocation and lead to a certain degree of resource misallocation.

Hypothesis 3a.

The CETP optimizes resource allocation and promotes the HQDM.

Hypothesis 3b.

The CETP causes resource misallocation and inhibits the HQDM.

Hypothesis 3c.

Due to the imperfect construction of the carbon market, the CETP has no significant impact on the HQDM.

To summarize, the specific impact mechanisms of carbon regulation are illustrated in Figure 1.

4. Research Design

4.1. Policy Background, Variables, and Data

In June 2013, the first carbon market in China was put into operation for trading in Shenzhen. Subsequently, a total of seven local pilot carbon markets were put into operation one after another in Beijing, Tianjin, and more. In December 2016, the Fujian carbon market was put into operation, becoming the eighth pilot. By then, the pilot program had covered eight entities, including three provinces and five cities. In July 2021, the national carbon market officially started its operation. The CETP mainly involves each pilot region establishing an emissions trading market based on its own actual conditions. Its core logic is as follows: first, each pilot carbon market sets an emission control threshold for carbon emissions volume or benchmark emission intensity in accordance with the local industrial structure characteristics and the central government’s carbon intensity constraints [16].

To assess the influence of the CETP on the HQDM, this study chooses A-share listed firms on the Shanghai and Shenzhen Stock Exchanges during 2003 to 2021 as the study sample. To exclude abnormal samples and ensure the validity of sample selection, this study eliminates the following enterprises in accordance with the common practices in existing literature: ① ST and *ST enterprises with consecutive losses; and ② enterprises with severe data missing. Meanwhile, linear interpolation is employed to supplement partially missing data of individual enterprises, and finally, 404 listed manufacturing enterprises are selected. Data for the variables in this study are mainly sourced from the China Stock Market & Accounting Research (CSMAR) Database and the China City Statistical Yearbook. Given the lag effect of pilot policy execution, this study sets the implementation timelines of the CETP as follows: Shenzhen (2013); Beijing, Tianjin, Shanghai, Chongqing, Hubei, and Guangdong (2014); and Fujian (2017).

4.2. Research Methods

To evaluate the impact of carbon regulation on the HQDM, this research employs the double machine learning (DML) method. First, drawing on the research of Robinson (1988) [44] and Chernozhukov et al. (2018) [33], a partially linear model (1) is built.

$$Y_{it}={\beta }_1{P}_{it}+g_0\left(X_{it}\right)+U_{it}, E\left[U_{it}|X_{it},P_{it}\right]=0$$

(1)

$$P_{it}=m_0\left(X_{it}\right)+V_{it}, E\left[V_{it}|X_{it}\right]=0$$

(2)

In the equation, the dependent variable $Y_{it}$ represents the high-quality development level of manufacturing enterprise i in year t, which is measured by the total factor productivity (TFP); $P_{it}$ denotes a policy dummy variable. $g_0\left(X_{it}\right)$ and $m_0\left(X_{it}\right)$ are unknown functions, where $X_{it}$ is a group of control variables; $U_{it}$ and $V_{it}$ denote error terms, and their corresponding conditional means are 0. Equation (1) serves as the primary equation, and Equation (2) is the auxiliary one.

Given X, taking the conditional expectation of both sides of Equations (1) and (2) yields:

$$E\left(Y_{it}|X_{it}\right)={\beta }_{1}E\left(P_{it}|X_{it}\right)+g_0\left(X_{it}\right)+\underset{=0}{\underbrace{E\left(U_{it}|X_{it}\right)}}$$

(3)

$$E\left(P_{it}|X_{it}\right)=m_0\left(X_{it}\right)+\underset{=0}{\underbrace{E\left(V_{it}|X_{it}\right)}}$$

(4)

Subtracting Equation (3) from Equation (1):

$$Y_{it}-E\left(Y_{it}|X_{it}\right)={\beta }_1(P_{it}-E\left(P_{it}|X_{it}\right))+U_{it}$$

(5)

Stage 1: Machine Learning Estimation

Estimating values $\widehat{E\left(Y_{it}|X_{it}\right)}$ and $\widehat{E\left(P_{it}|X_{it}\right)}$ are obtained by predicting $E\left(Y_{it}|X_{it}\right)$ and $E\left(P_{it}|X_{it}\right)$ through machine learning, which embodies the implication of double machine learning. Substituting them into the above Equation (5) yields:

$$Y_{it}-\widehat{E\left(Y_{it}|X_{it}\right)}={\beta }_1(P_{it}-\widehat{E\left(P_{it}|X_{it}\right))}+{error}_{it}$$

(6)

To facilitate the deduction below, let $l_0\left(X_{it}\right)=E\left(Y_{it}|X_{it}\right)$, ${\widehat{l}}_0\left(X_{it}\right)$ = $\widehat{E\left(Y_{it}|X_{it}\right)}$, ${\widehat{m}}_0\left(X_{it}\right)=\widehat{E\left(P_{it}|X_{it}\right)}$, and ${\widehat{V}}_{it}=P_{it}-{\widehat{m}}_0\left(X_{it}\right)$. Then Equation (6) becomes (7):

$$Y_{it}-{\widehat{l}}_0\left(X_{it}\right)={\beta }_1\left(P_{it}-{\widehat{m}}_0\left(X_{it}\right)\right)+{error}_{it}={\beta }_1{\widehat{V}}_{it}+{error}_{it}$$

(7)

Stage 2: OLS Estimation

Equation (7) uses the Ordinary Least Squares (OLS) method to obtain the OLS estimator ${\widehat{\beta }}_1$ of ${\beta }_1$:

$${\widehat{\beta }}_1={\left({\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\widehat{V}}_{it}\left[Y_{it}-{\widehat{l}}_0\left(X_{it}\right)\right]$$

(8)

After derivation, it can be obtained that

$$\begin{array}{c}\sqrt{n}\left({\widehat{\beta }}_1-{\beta }_1\right)={\left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{\sqrt{n}}}{\displaystyle \sum _{i=1}^n}\left[m_0\left(X_{it}\right)-{\widehat{m}}_0\left(X_{it}\right)+V_{it}\right]\left\{U_{it}+\left[{\widehat{m}}_0\left(X_{it}\right)-m_0\left(X_{it}\right)\right]{\beta }_1+l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right\}\hfill \\ =\underset{=c}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{\sqrt{n}}}\sum _{i=1}^n\left[m_0\left(X_{it}\right)-{\widehat{m}}_0\left(X_{it}\right)\right]U_{it}}}-\underset{=d}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{{\beta }_1}{\sqrt{n}}}\sum _{i=1}^n{\left[m_0\left(X_{it}\right)-{\widehat{m}}_0\left(X_{it}\right)\right]}^2}}+\hfill \\ \underset{=e}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{\sqrt{n}}}\sum _{i=1}^n\left[m_0\left(X_{it}\right)-{\widehat{m}}_0\left(X_{it}\right)\right]\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]}}+\underset{=f}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{\sqrt{n}}}{V}_{it}{U}_{it}}}+\hfill \\ \underset{=g}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{{\beta }_1}{\sqrt{n}}}\sum _{i=1}^n{V}_{it}\left[m_0\left(X_{it}\right)-{\widehat{m}}_0\left(X_{it}\right)\right]}}+\underset{=h}{\underbrace{{\left({\displaystyle \frac{1}{n}}\sum _{i=1}^n{{\widehat{V}}_{it}}^2\right)}^{-1}{\displaystyle \frac{1}{\sqrt{n}}}\sum _{i=1}^n{V}_{it}\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]}}\hfill \end{array}$$

(9)

Since $V_{it}$ is correlated with $l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)$, with the specific impact path of $V_{it}$→$P_{it}$→$Y_{it}$→${\widehat{l}}_0\left(X_{it}\right)$, and the convergence rate of the single prediction bias $l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)$ to 0 is slower than that of the product term of the two prediction biases, $h$ does not necessarily converge to 0 in probability. Ultimately, this causes $\sqrt{n}\left({\widehat{\beta }}_1-{\beta }_1\right)$ to also fail to converge to 0 in probability, implying that ${\widehat{\beta }}_1$ is not an unbiased estimator of ${\beta }_1$.

To address the correlation issue between $V_{it}$ and $l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)$ Chernozhukov et al. (2018) [33] proposed the cross-fitting method, which involves splitting the sample. A portion of the sample is used for the machine learning estimation in the first stage to obtain ${\widehat{l}}_0\left(X_{it}\right)$ and the other samples are used for the OLS estimation in the second stage. Given that the sample data satisfy the independent and identically distributed assumption, $V_{it}$ and $l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)$ are relatively independent. Thus the following is observed:

$$\begin{array}{c}E\left\{{\displaystyle \frac{1}{\sqrt{n}}}{\displaystyle \sum _{i=1}^n}{V}_{it}\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]\right\}={\displaystyle \frac{1}{\sqrt{n}}}{\displaystyle \sum _{i=1}^n}{E}_{X_{it}}E\left\{V_{it}\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]|X_{it}\right\}\hfill \\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{1}{\sqrt{n}}}\sum _{i=1}^n{E}_{X_{it}}\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]\underset{=0}{\underbrace{E\left\{V_{it}|X_{it}\right\}}}=0\end{array}$$

(10)

$$\begin{array}{c}\mathrm{V}\mathrm{a}\mathrm{r}\left\{{\displaystyle \frac{1}{\sqrt{n}}}{\displaystyle \sum _{i=1}^n}{V}_{it}\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]\right\}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}E\left\{{V_{it}}^2{\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]}^2\right\}\hfill \\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{1}{n}}\sum _{i=1}^{n}E{V_{it}}^{2}E{\left[l_0\left(X_{it}\right)-{\widehat{l}}_0\left(X_{it}\right)\right]}^2\to 0\end{array}$$

(11)

Therefore, under this condition, $h$ converges to 0 in mean square. $\sqrt{n}\left({\widehat{\beta }}_1-{\beta }_1\right)$ will also converge to 0 in probability; in large samples, ${\widehat{\beta }}_1$ will converge to ${\beta }_1$, making ${\widehat{\beta }}_1$ an unbiased estimator of ${\beta }_1$.

In summary, it can be concluded that predicting $E\left(Y_{it}|X_{it}\right)$ and $E\left(P_{it}|X_{it}\right)$ through machine learning—specifically via double machine learning—enables avoidance of the “curse of dimensionality” triggered by high-dimensional control variables. Meanwhile, cross-fitting conducted via machine learning allows for obtaining an unbiased estimator of the coefficient ${\beta }_1$. Based on the analysis of the partially linear model above, when the functional form of the covariate function is unknown, the application of the double machine learning method can yield unbiased estimates of the treatment effect.

4.3. Variable Selection

(1)

Dependent Variable

Based on the method of Niu and Yan (2021) [45], his study employs TFP as the indicator of the HQDM.

(2)

Control Variables

The core explanatory variable is Tctrade, which is a dummy variable representing the CETP. Beyond the core explanatory variable, control variables are selected from two perspectives: micro-level enterprises and macro-level cities. Micro-level enterprise control variables, drawing on relevant studies in existing literature [46,47], mainly encompass variables from two dimensions—enterprise characteristic indicators and enterprise financial indicators—totaling 14 variables. Specifically, the first dimension includes enterprise characteristic variables: Listing Years (Age), Firm Size (Size), Ownership (Soe), Export Status (Import), Board Size (Board), Independent Director Ratio (Dep), and Ownership Concentration (Toph); the second dimension comprises enterprise financial indicators: Asset-Liability Ratio (Rate), Capital Intensity (Kl), Enterprise Liquidity (Flow), Return on Assets (Profit), Enterprise Growth (Grow), Market Value (Mva), and Corporate Investment (Inv). Macro-level city control variables, as referenced in relevant research from the existing literature [48,49,50], primarily encompass variables across three dimensions: regional development status characteristics, government behavior characteristics, and market environment characteristics, totaling 16 variables. Specifically, the first dimension includes regional development status indicators: Economic Development Level (Gdp), Urbanization Level (Urb), Industrial Structure (Stru), Population Density (Pde), Income Level (Wage), Transportation Infrastructure (Road), and Internet Penetration (Int); the second dimension covers government behavior-related variables: Government Expenditure (Gov), Foreign Capital Utilization (Fdi), Fiscal Decentralization (Fdp), Government R&D Input (RD), Education Investment (Exp), and SOE Reform (Nsoe); and the third dimension comprises market environment indicators: Marketization Level (Mkt), Degree of Opening-up (Open), and Financial Development Level (Finance).

The main variables’ definitions and descriptive statistics are presented in

Table 1. Definitions of main variables.

Variable Type	Variable Symbol			Variable Name	Variable Definition
Dependent Variable	TFP			Total Factor Productivity	Total factor productivity estimated by the LP method
Explanatory Variable	Tctrade			Pilot Policy of Carbon Emission Rights Trading	Dummy variable
Control Variables	Enterprise-level	Enterprise Characteristics	Age	Listing Years	Current year—Listing year
			Size	Firm Size	Total assets
			Soe	Ownership	State-owned enterprise = 1; Non-state-owned enterprise = 0
			Export	Export Status	Exporting enterprise = 1; Non-exporting enterprise = 0
			Board	Board Size	Number of board directors
			dep	Independent Director Ratio	Number of independent directors/Total number of directors
			Toph	Ownership Concentration	Shareholding ratio of the largest shareholder
		Enterprise Financial Status	Rate	Asset-Liability Ratio	Total liabilities/Total assets
			Kl	Capital Intensity	Net fixed assets/ Number of employees
			Flow	Enterprise Liquidity	Net cash flow from operating activities/Total assets
			Profit	Return on Assets	Net profit/Total assets
			Grow	Enterprise Growth	growth rate of net assets
			Mva	Market Value	Total market value/Total assets
			Inv	Enterprise Investment	Investment in fixed assets, intangible assets, and other long-term assets
	City-level	Regional Development Status	Gdp	Economic Development Level	GDP/Total population
			Urb	Urbanization Level	Urbanization rate
			Stru	Industrial Structure	Added value of the secondary industry/Added value of the tertiary industry
			Pde	Population Density	Population per unit area
			Wage	Income Level	Per capita wage
			Road	Transportation Infrastructure	Highway mileage/ Total population
			Int	Internet Penetration	Number of Internet users
		Government Behavior	Gov	Government Expenditure	Fiscal expenditure/GDP
			Fdi	Foreign Capital Utilization	utilized foreign direct investment/GDP
			Fdp	Fiscal Decentralization	Budgetary fiscal revenue/Budgetary fiscal expenditure
			RD	Government R&D Input	Per capita government fiscal expenditure on R&D
			Exp	Education Input	Fiscal education expenditure/GDP
			Nsoe	SOE Reform	Number of urban private and individual employees/ Total number of employees
		Market Environment	Mkt	Marketization Level	Marketization Index of Chinese Provinces
			Open	Degree of Opening-up	export trade volume/GDP
			Fin	Financial Development Level	Balance of deposits and loans of financial institutions/GDP

and

Table 2. Descriptive statistics of main variables.

Variable Type	Variable Symbol			Number of Observations	Mean	Standard Deviation	Min	Max
Dependent Variable	TFP			7503	11.42	0.90	7.85	14.84
Explanatory Variable	Tctrade			7675	0.15	0.35	0	1
Control Variables	Enterprise -level	Enterprise Characteristics	Age	7675	25.79	2.95	20	32
			Size	7675	126.76	343.09	1.26	9194.15
			Soe	7675	0.71	0.45	0	1
			Export	7675	0.03	0.17	0	1
			Board	7675	9.17	1.86	0	18
			dep	7675	0.363	0.058	0.00	0.80
			Toph	7675	36.617	15.435	3.39	89.99
		Enterprise Financial Status	Rate	7675	0.48	0.18	−0.09	1.00
			Kl	7675	1.90	2.58	0.17	80.47
			Flow	7675	0.04	0.07	−0.47	0.48
			Profit	7675	0.03	0.05	−0.53	0.40
			Grow	7675	0.06	0.36	−1.27	10.35
			Mva	7675	203.88	579.54	4.58	25,564.3
			Inv	7675	2.48	7.77	0	146.18
	City -level	Regional Development Status	Gdp	7656	2.24	1.11	0.25	5.27
			Urb	7616	0.66	0.19	0.11	1.00
			Stru	7669	1.09	0.78	0.19	32.12
			Pde	7656	1131.60	1318.70	15.67	8854.08
			Wage	7656	5.68	3.68	0.00	19.77
			Road	7342	20.46	15.32	1.15	357.90
			Int	7656	273.46	522.29	0.06	9114.00
		Government Behavior	Gov	7675	0.14	0.05	0.04	0.57
			Fdi	7249	0.03	0.03	0.00	0.39
			Fdp	7656	0.69	0.21	0.03	1.54
			RD	7656	0.15	0.11	0.00	0.69
			Exp	7656	0.02	0.01	0.00	0.13
			Nsoe	7628	0.39	0.17	0.018	0.99
		Market Environment	Mkt	7675	9.20	19.53	2.47	422.00
			Open	7468	4.09	8.26	0.03	80.17
			Fin	7656	1.36	0.71	0.11	7.45

.

5. Empirical Results

5.1. Baseline Results

Based on the study by Yang et al. (2020) [34], the Gradient Boosting (GradBoost) algorithm outperforms other machine learning algorithms in evaluation, namely Random Forest (RF), Lasso (LassoCV), and Neural Network (nnet). Therefore, this study adopts Gradient Boosting (GradBoost) to construct a prediction model and uses five-fold cross-validation to evaluate the model’s fitting effect and optimize its parameters, thereby providing a reliable predictive foundation for the causal effect estimation of double machine learning. It should be noted that five-fold cross-validation refers to randomly dividing the dataset into 5 mutually exclusive and equally sized subsets: Four subsets are used for model training, and the one remaining subset (validation set) is employed to generate prediction results. The regression results are shown in

Table 3. Impact of carbon regulation on the HQDM.

Variable	TFP
	(1)	(2)
Tctrade	0.153 *** (0.033)	0.097 *** (0.034)
Control Variable First-order Term	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes
Sample Size	6771	6771

Note: *** denote statistical significance at the 1% levels, respectively. Standard errors are in parentheses.

. The coefficients of Tctrade are all statistically significant and positive at the 1% level. This indicates that the CETP significantly improves the TFP of the manufacturing and promotes the HQDM, thus verifying Hypothesis 1.

5.2. Robustness Analysis

5.2.1. Sample Selection

(1)

Winsorization

This study winsorizes the dependent variable TFP at the 1% and 5% levels, then re-evaluates the policy effect using the DML. The regression results are presented in columns (1) to (4) of

Table 4. Estimation results of sample winsorization and exclusion of municipalities.

Variable	TFP
	1% Winsorization		5% Winsorization		Exclusion of Municipalities
	(1)	(2)	(3)	(4)	(5)	(6)
Tctrade	0.153 *** (0.033)	0.09 *** (0.035)	0.148 *** (0.030)	0.09 *** (0.034)	0.155 *** (0.040)	0.095 ** (0.042)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes
Sample Size	6771	6771	6771	6771	5436	5436

Note: ** and *** denote statistical significance at the 5%, and 1% levels, respectively. Standard errors are in parentheses.

. After excluding extreme values and controlling for the interaction terms and quadratic terms of the control variables, the coefficients of Tctrade remain statistically significant and positive. This result aligns with the baseline regression results.

(2)

Exclusion of Municipalities

This study excludes the samples of the four centrally administered municipalities: Beijing, Tianjin, Shanghai, and Chongqing. The empirical results are presented in columns (5) to (6) of Table 4. It can be observed that the coefficients of Tctrade remain statistically significant and positive, which proves the robustness of the baseline results.

5.2.2. Replacing the Estimation Method of the Dependent Variable

This study uses the OP method, GMM method [6], OLS method, and FE method [46] to replace the LP method for estimating the TFP of listed manufacturing firms, to conduct robustness tests. The regression results are presented in columns (1) to (8) of

Table 5. Estimation results by replacing the estimation method of the dependent variable.

Variable	TFP
	OP		GMM		OLS		FE
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Tctrade	0.112 ** (0.048)	0.156 *** (0.055)	0.117 ** (0.047)	0.123 ** (0.054)	0.140 *** (0.028)	0.092 *** (0.033)	0.125 *** (0.028)	0.090 *** (0.033)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes	No	Yes
Sample Size	6771	6771	6771	6771	6771	6771	6771	6771

Note: ** and *** denote statistical significance at the 5%, and 1% levels, respectively. Standard errors are in parentheses.

below. Regardless of whether the interaction terms and quadratic terms of the control variables are controlled for, the coefficients of Tctrade remain statistically significant and positive at least at the 5% significance level. Moreover, these coefficients are close to the corresponding estimated coefficients from the LP method, indicating that the baseline regression results are robust.

5.2.3. Resetting the DML Model

(1)

Adjusting the Sample Split Ratio

According to the research by Chernozhukov et al. (2018) [33], in the case of small samples, splitting the research sample equally into four or five groups reduces the loss of sample information and yields more robust estimation results compared to splitting it into two groups. This study splits the sample at a ratio of 1:3—where the ratio of the sample for machine learning prediction to that for regression estimation is 1:3—to conduct a robustness test. The results are presented in columns (1) and (2) of

Table 6. Estimation results of resetting the double machine learning model.

Variable	TFP
	Sample Split Ratio : (1 : 3)		Stacked Regression		Interaction Model
	(1)	(2)	(3)	(4)	(5)	(6)
Tctrade	0.148 *** (0.033)	0.093 *** (0.034)	0.099 * (0.056)	0.061 * (0.036)	0.091 *** (0.004)	0.0761 *** (0.0069)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes
Sample Size	6771	6771	6771	6771	6771	6771

Note: * and *** denote statistical significance at the 10% and 1% levels, respectively. Standard errors are in parentheses.

. It can be observed that the coefficients of Tctrade all remain statistically significant and positive at the 1% level, indicating that the baseline regression results are robust.

(2)

Replacing the Machine Learning Algorithm: Stacked Regression

This study employs Stacked Regression to conduct policy evaluation. The estimation results are presented in columns (3) and (4) of Table 6. The coefficients of Tctrade are all statistically significant and positive, which also indicates that the baseline empirical results are robust.

(3)

Replacing the Machine Learning Model: Interaction Model

With reference to Chernozhukov et al. (2018) [33], this study further constructs a more general interaction model to account for the impact of this heterogeneity.

$$Y_{it}=g_0\left(P_{it},X_{it}\right)+U_{it}, \mathrm{E}\left[U_{it}|X_{it},P_{it}\right]=0$$

(12)

$$P_{it}=m_0\left(X_{it}\right)+V_{it}, \mathrm{E}\left[V_{it}|X_{it}\right]=0$$

(13)

The treatment effect obtained from this model is ${\beta }_1=E[g_0\left(P_{it}=1,X_{it}\right)-g_0\left(P_{it}=0,X_{it}\right)]$. The derivation process of the estimated parameters is consistent with that of the partially linear model. The regression results are presented in columns (5) and (6) of Table 6. It can be seen that the coefficients of variable Tctrade all remain statistically significant and positive at the 1% level, indicating that the CETP promotes the HQDM. This also shows that the baseline empirical results hold robustness.

5.3. Further Analysis Based on Impact Mechanisms and Heterogeneity

5.3.1. Analysis of Impact Mechanisms

(1)

Innovation Effect

Carbon regulation may affect the HQDM via technological innovation. To verify whether this transmission mechanism is valid, this study selects the ratio of R&D expenditure to operating income as the proxy variable for technological innovation [51] to conduct an empirical test.

Table 7. Estimation results of the innovation effect.

Variable	Inno
	(1)	(2)
Tctrade	0.009 * (0.005)	0.019 *** (0.005)
Control Variable First-order Term	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes
Sample Size	4142	4142

Note: * and *** denote statistical significance at the 10% and 1% levels, respectively. Standard errors are in parentheses.

reports the corresponding regression results. The coefficients of variable Tctrade are all statistically significant and positive, indicating that this policy promotes the technological innovation of the manufacturing industry. Together with the mechanism analysis from the prior section, this is because the innovation-induced effect of the “innovation compensation hypothesis” is stronger than the innovation crowding-out effect of the “compliance cost hypothesis”, thus generating a positive innovation effect. Hypothesis 2a is verified, while Hypotheses 2b and 2c are rejected.

(2)

Resource Allocation Effect

Carbon regulation may also affect the HQDM through the resource allocation effect. To test the influence of this transmission mechanism, this research uses capital allocation efficiency as the proxy variable of resource allocation efficiency [31] and draws on the investment level-investment opportunity sensitivity model [52] to examine the impact of the CETP on resource allocation efficiency. The investment level-investment opportunity sensitivity model is used to measure the sensitivity of a firm’s investment level to changes in investment opportunities. A higher sensitivity coefficient indicates that the firm is more capable of adjusting its investment behavior in response to investment opportunities, and its resource allocation efficiency is usually higher. The model is as follows:

$$A_{it}{=P}_{it}\times {Roa}_{it}$$

(14)

$${Invest}_{it}={\beta }_1{A}_{it}+g_0\left(X_{it}\right)+U_{it}, \mathrm{E}\left[U_{it}|X_{it},A_{it}\right]=0$$

(15)

$$A_{it}=m_0\left(X_{it}\right)+V_{it}, \mathrm{E}\left[V_{it}|X_{it}\right]=0$$

(16)

In this model ${Invest}_{it}$ denotes corporate investment level, calculated as (cash paid for asset purchases minus cash received from asset disposals) divided by total assets. ${Roa}_{it}$ stands for return on assets (ROA), representing a firm’s investment opportunities. $P_{it}$ is a policy dummy variable. $A_{it }$ represents the interaction term of $P_{it }$ and ${Roa}_{it}$. The definitions of the remaining variables are consistent with those in Model (1) and Model (2). The empirical results are shown in columns (1) and (2) of

Table 8. Estimation results of resource allocation effect.

Variable	Invest2021		Invest2020		Invest2019		Invest2018
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Tctrade	−0.030 (0.029)	−0.007 (0.030)	−0.059 * (0.032)	−0.034 (0.029)	−0.049 (0.035)	−0.017 (0.037)	−0.059 (0.038)	−0.018 (0.035)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes	No	Yes
Sample Size	6768	6768	6500	6500	6193	6193	5887	5887

Note: * denotes statistical significance at the 10% levels, respectively. Standard errors are in parentheses.

. The coefficient of Tctrade is negative and insignificant, indicating that the CETP has no significant impact on enterprises’ capital allocation efficiency. We also examined the CETP’s resource allocation effect across three time periods: 2003–2020, 2003–2019, and 2003–2018. As observed in Columns (3) to (8) of Table 8, when controlling for the interaction terms and quadratic terms of control variables, the estimated coefficients of Tctrade are all insignificant. This further confirms that the CETP has no significant impact on enterprises’ capital allocation efficiency. A possible reason is that the economic effect of the pilot carbon market depends on market liquidity [4], and its resource allocation effect is also highly dependent on the degree of improvement of the carbon market. However, China’s pilot carbon markets are still in the early phase of development [3], and the carbon markets within these emission trading regions have not yet been comprehensively and effectively established. Moreover, the pilot carbon markets in China are mutually independent, and cross-market carbon quota trading is not possible. Meanwhile, the market coverage is limited, lacking sufficient participation from industries and entities, which may affect the operational effect of the policy [53]. Thus, the resource allocation effect of the pilot carbon market is not significant. This verifies Hypothesis 3c, while Hypotheses 3a and 3b are rejected.

5.3.2. Analysis of Heterogeneity

This study further explores the heterogeneity in terms of location conditions, enterprise ownership, and technology intensity.

(1)

Location Conditions

China exhibits significant differences in geographical conditions, which could result in heterogeneity regarding the impact of carbon regulation on the HQDM. To examine such regional heterogeneity, referring to the regional division approach [54], this research categorizes the sample into three regions: eastern, central, and western. The results of the regression are shown in

Table 9. Estimation results of regional heterogeneity.

Variable	TFP
	Eastern Region		Central Region		Western Region
	(1)	(2)	(3)	(4)	(5)	(6)
Tctrade	0.160 *** (0.043)	0.106 ** (0.043)	−0.041 (0.117)	−0.173 * (0.103)	−15.703 (1486.961)	2.056 ** (0.856)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes
Sample Size	4045	4045	1722	1722	1004	1004

Note: *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parentheses.

. As shown in the table, after controlling for the interaction terms and quadratic terms of control variables, the coefficients of Tctrade in the eastern and western regions are both positive and statistically significant, while the coefficient in the central region is significantly negative. The potential reasons are as follows:

Firstly, facing carbon emission constraints, the eastern region, relying on its strong economic strength, has prominent advantages in technological innovation, production structure adjustment, and resource allocation optimization. Additionally, its more mature market economy and carbon market, coupled with sufficient resource mobility, enable it to offset the negative impact of carbon emission constraints, ultimately promoting the improvement of TFP in the manufacturing industry. Secondly, the western region has a weak economic foundation but a solid ecological base. Local governments take this characteristic into account when formulating pilot carbon trading policies, resulting in relatively loose carbon constraints brought by the policy. Enterprises in this region can offset the negative impact of carbon constraints through moderate technological innovation or resource allocation optimization, thereby also promoting TFP improvement. Thirdly, the central region has a weaker ecological base than the western region and falls behind the eastern region in economic strength and carbon market maturity. When confronting stronger carbon constraints, it finds it difficult to eliminate the negative impact of carbon constraints through technological innovation or resource allocation optimization, which in turn inhibits the improvement of manufacturing TFP. This study further conducts robustness tests on the research results of the western region, including winsorization and exclusion of provincial capitals. The regression results are shown in

Table 10. Estimation results of sample winsorization and exclusion of provincial capital.

Variable	TFP
	1% Winsorization		5% Winsorization		Exclusion of Provincial Capital
	(1)	(2)	(3)	(4)	(5)	(6)
Tctrade	−46.565 (1432.082)	1.996 ** (0.802)	−400.216 (1399.706)	1.437 ** (0.641)	−0.312 (1.443)	0.370 *** (0.072)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes
Sample Size	1004	1004	1004	1004	389	389

Note: ** and *** denote statistical significance at the 5%, and 1% levels, respectively. Standard errors are in parentheses.

. As indicated in the table, when controlling for the interaction terms and quadratic terms of control variables, the coefficients of Tctrade are all significantly positive. This demonstrates that the CETP’s significant promotion effect on the HQDM in the western region is robust.

(2)

Firm Ownership

The impact of carbon regulation varies across enterprises with different ownership types. In this paper, the regression is conducted according to the ownership of enterprises, and the results are presented in

Table 11. Estimation results of firm ownership heterogeneity.

Variable	TFP
	SOEs		non-SOEs
	(1)	(2)	(3)	(4)
Tctrade	0.073 ** (0.034)	0.087 ** (0.037)	0.085 * (0.046)	0.071 (0.046)
Control Variable First-order Term	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes
Sample Size	4842	4842	1929	1929

Note: * and ** denote statistical significance at the 10% and 5% levels, respectively. Standard errors are in parentheses.

. Columns (1) and (2) of the table show that the coefficient of Tctrade is all significantly positive. This indicates that the CETP significantly promotes the HQDM of state-owned enterprises. In Column (4), the coefficient of Tctrade can not pass the significance test, which means that this policy exerts no significant impact on the HQDM of non-state-owned enterprises. The possible reasons for the above heterogeneous effects lie in the following aspects: In comparison to non-state-owned enterprises, state-owned enterprises (SOEs) exhibit higher enthusiasm for policy response, stronger social responsibility, and greater emphasis on corporate image and reputation. They also more effectively carry out national policy decisions and arrangements. Thus, the CETP has a significant effect on improving the HQDM, which aligns with the results of the benchmark regression. In contrast, non-state-owned enterprises prioritize corporate profits, have a weaker capacity to implement carbon regulation policies, and even engage in illegal carbon emission behaviors, leading to an insignificant policy effect.

(3)

Factor Intensity

Carbon regulation may exert different impacts across manufacturing sectors with varying factor intensities. In line with the 2012 Industry Classification Standard issued by the China Securities Regulatory Commission, manufacturing industries are categorized into technology-intensive, capital-intensive, and labor-intensive sectors based on the degree of product factor intensity.

When controlling for the interaction terms and quadratic terms of control variables, as shown in Column (2) of

Table 12. Estimation results of factor intensity heterogeneity.

Variable	TFP
	Technology-Intensive		Capital-Intensive		Labor-Intensive
	(1)	(2)	(3)	(4)	(5)	(6)
Tctrade	0.132 *** (0.046)	0.169 *** (0.049)	0.082 ** (0.041)	0.054 (0.046)	−0.193 *** (0.070)	−0.118 ** (0.053)
Control Variable First-order Term	Yes	Yes	Yes	Yes	Yes	Yes
Control Variables Interaction and Quadratic Terms	No	Yes	No	Yes	No	Yes
Sample Size	3725	3725	2248	2248	798	798

Note: ** and *** denote statistical significance at the 5%, and 1% levels, respectively. Standard errors are in parentheses.

, the coefficient of Tctrade is notably positive. This indicates that the CETP has promoted the HQDM of technology-intensive manufacturing. As shown in Column (4) of Table 12, the coefficient of Tctrade is positive yet insignificant, meaning the CETP fails to generate a significant promotional impact on the HQDM of capital-intensive manufacturing. Conversely, Column (6) of Table 12 demonstrates that the coefficient of Tctrade is notably negative, which suggests the CETP has imposed a notable inhibitory effect on the HQDM of labor-intensive manufacturing. A plausible explanation for this lies in the fact that labor-intensive manufacturing relies heavily on labor input while exhibiting low reliance on technology and equipment. Their profitability is relatively weak, thereby making it difficult for them to enhance TFP through technological innovation.

6. Conclusions, Policy Implications, and Discussion

6.1. Conclusions

As a typical market-oriented carbon regulation, the CETP serves as an important initiative for cities’ low-carbon transition and sustainable development. This paper evaluates its impact on the HQDM and the underlying mechanism using the double machine learning method, based on micro-level data of listed manufacturing firms spanning 2003 to 2021. The research results of this paper are as follows: ① The CETP significantly promotes the HQDM, and this conclusion is still valid after undergoing a series of robustness tests. ② Through mechanism analysis, it is found that the policy significantly advances manufacturing technological innovation, while its impact on resource allocation efficiency is not significant. ③ Heterogeneity analysis indicates that the policy exerts a promotional effect on manufacturing in eastern and western regions, state-owned manufacturing, and technology-intensive manufacturing, while its effect on central regions and labor-intensive manufacturing’s HQDM is inhibitory.

6.2. Policy Implications

(1)

Efforts should be made to accelerate the market-oriented transformation of carbon regulation. Given that the study findings of this paper indicate that the CETP significantly promotes the HQDM, it is necessary to make efforts to accelerate carbon regulation’s transformation from a purely “command-driven” model to a dual model with both “command-driven” and “market-oriented” characteristics, thereby enabling the market to fully exert its decisive role in carbon emission reduction, and lay a more solid institutional foundation for promoting sustainable development.

(2)

Carbon markets should be improved and perfected to achieve the optimal allocation of resources. Analysis of the impact mechanism reveals that the resource allocation effect of carbon markets has not yet emerged. This may be because the mechanisms of carbon markets in pilot regions are not yet well-established and have limited coverage, which in turn leads to insufficient liquidity in carbon markets and inadequate trading of carbon allowances. Thus, efforts should be made to further establish and improve carbon market trading mechanisms and supporting systems, and expand the carbon market’s coverage to include more industries and participants, while at the same time providing institutional support to promote the full flow of resources, thereby facilitating the optimal allocation of resources.

(3)

Differentiated policies for carbon emission rights trading should be formulated based on enterprise attributes and in light of local conditions. Heterogeneity analysis indicates that the impact of these policies is constrained by enterprise heterogeneity. The efficiency of carbon emission reduction is closely associated with the economic capacity required for low-carbon transformation and the technological characteristics of enterprises. Therefore, it is necessary to formulate differentiated carbon allowance standards for enterprises in different regions and with different attributes. For instance, for the central regions, efforts should be made to strike a balance between the carbon constraints brought by carbon trading policies and the local economic development level, with an appropriate increase in carbon allowances.

6.3. Discussion

This study focuses exclusively on listed firms, which generally possess advantages in scale, resources, and risk resilience compared to small and medium-sized enterprises (SMEs). After sample screening, the analysis is limited to 404 listed enterprises. The inclusion of SME data and an expansion of the firm scope to encompass such entities would likely enhance the representativeness of the research findings. Subsequent studies may incorporate SME data to broaden the sample scope and improve representativeness.