The driving factors of corporate carbon emissions: an application of the LASSO model with survey data

Corporate carbon performance is a key driver of achieving corporate sustainability. The identification of factors that influence corporate carbon emissions is fundamental to promoting carbon performance. Based on the carbon disclosure project (CDP) database, we integrate the least absolute shrinkage and selection operator (LASSO) regression model and the fixed effects model to identify the determinants of carbon emissions. Furthermore, we rank determining factors according to their importance. We find that Capx enters the models under all carbon contexts. For Scope 1 and Scope 2, financial-level factors play a greater role. For Scope 3, corporate internal incentive policies and emission reduction behaviors are important. Different from absolute carbon emissions, for relative carbon emissions, the financial-level factors’ debt-paying ability is a vital reference indicator for the impact of corporate carbon emissions.


Introduction
Reducing greenhouse gas (GHG) emissions is now the target of global efforts, as increased carbon emissions are the main cause of environmental deterioration. Under this context, how to decrease carbon emissions has become a topic of research that is incredibly significant at both the international and domestic levels. To achieve the emission reduction target, scholars began to study the factors affecting carbon emissions (Jiang et al. 2021). Druckman and Jackson (2016) find that household consumption accounts for about 72% of global carbon emissions. Thus, they studied the drivers of carbon emissions at the household level. Lamb et al. (2014) and Karasoy (2019) explore the driving factors affecting carbon emissions at the national level. Azizalrahman and Hasyimi (2019) dissect urbanization into sectors: residential, commercial, and industrial to explore urban sector drivers of carbon emissions.  use the structural decomposition analysis to uncover the driving forces of urban CO 2 emission change in China. The existing research analyzes the drivers of carbon reduction at the national, city, and household levels from a macroperspective. As one of the main carriers affecting global warming, corporations improving the performance of carbon emissions can effectively alleviate environmental stress. However, few studies explore the factors that affect carbon emissions at the micro-firm level.
Prior studies have found that the impact of factors such as corporate inherent characteristics, the external environment, and corporate climate strategy behavior on carbon emission reduction has mixed results. Firm size (Lee 2012), political connection (Jiang et al. 2021), the carbon reporting decision (Córdova et al. 2018), industry category, sustainability reporting (Córdova et al. 2018), existence of a sustainability committee (Córdova et al. 2018), international experience of CEO and board of directors (Amran et al. 2016), organizational slack (Amran et al. 2016), emission trading policy , and social culture (Liu et al. 2018) have significant positive impacts on carbon emission reduction, whereas countries  (Córdova et al. 2018), state ownership (Yang et al. 2019), and energy prices ) have significant negative impacts on carbon emission reduction. Most previous studies have used panel regression models, which cannot shed light on the relative importance of impact factors. Thus, it is necessary to choose LASSO regression models that can be prioritized to explore the determinants of corporate carbon emissions.
In recent years, a series of legally binding climate change treaties, such as the United Nations Framework Convention on Climate Change (UNFCCC), the Kyoto Protocol, and the Paris Agreement, have been developed internationally to better assume environmental responsibility and jointly tackle climate change. However, as a major world power in the USA, the attitude toward acceding to international treaties is vague because of greater emission responsibilities and economic burdens. Matsumura et al. (2014) argue that firms may be penalized by capital markets for higher emission levels, leading to a decreased firm value. Thus, exploring the relationship between corporate costs of reducing emissions and financial performance is critical for improving the environment, achieving corporate sustainability, and allowing policymakers to mitigate carbon emissions.
This study makes the following contributions to the extant literature. Firstly, in terms of methods, we introduce the LASSO regression model to investigate the driving factors influencing corporate carbon emissions. LASSO provides an objective and comprehensive data-driven approach to capture the most important drivers of corporate carbon emissions. Secondly, we extend the findings of Jiang et al. (2021) to broaden the range of drivers that impact carbon emission reduction. Jiang et al.'s (2021) paper only discusses the driving factors of corporate emission reduction from the five aspects of political ties, corporate scale, industry category, regional disparity, and environmental regulation. We use the LASSO regression model to contain more internal and external factors. Compared with existing research which only explores the positive and negative impacts of driving factors on carbon emission reduction, LASSO regression is not restricted to the verification of whether each variable exerts an impact on corporate carbon emissions but to decide the priority of the driving factors and ranking them. This affords policymakers more flexibility in determining policy interventions, not only provide both a more accurate quantitative basis for policymakers and a theoretical basis, but also make contributions to the existing literature and corporate decision-making. Thirdly, we combine corporate carbon performance and financial performance indicators and discuss the importance of the impacting factors from the perspective of corporate environmental responsibility and profit development, which supplements the literature on corporate performance and provides theoretical guidance for managers to achieve corporate performance.
The rest of the paper is organized as follows: the "Literature review" section provides the literature review, the "Methodology and data" section describes the methodology and the data collection, the "Results" section shows the results, and the "Discussion and policy implications" section presents the discussion, policy implications, and future research directions.

Literature review
With the intensification of global warming, carbon emissions have become a key concern for corporations. Countries are beginning to work together to reduce GHG emissions, and indeed, this has become a required goal for corporations in terms of environmental performance. However, the pursuit of corporate environmental performance has a mixed impact on corporate development (Dixon-Fowler et al. 2013). Earlier scholars put forward two markedly different views. The traditional economic trade-off argument posits that corporations incur large costs to improve environmental performance, and these additional financial burdens reduce corporate profits and value (Walley and Whitehead 1994). In contrast, the revisionist view argues that corporations can improve their economic performance by exploiting environmental opportunities as a first mover (Esty and Porter, 1998;Reinhardt, 1999). A visualization of the impact factors in corporate carbon emissions is shown in Fig. 1. Corporate carbon emissions are affected by a combination of factors, which we divide into three categories.
Firm-level factors are one category that affects corporate carbon emissions. If corporations are to address climate change, it cannot be viewed as an isolated environmental issue. It is important to integrate climate change into corporate business strategies (Amran et al. 2016). McKinsey (2008) found that more than 30% of the executives admitted to seldom or never including climate change in business strategies. In corporate emission reduction strategies, executive (especially CEO) attitudes and characteristics play a very important role, such as CEO compensation, CEO power, and CEO duality (Raghunandan and Rajgopal 2022;Hossain et al. 2022). Under the complex operating activities, not only the CEO but also the board of directors plays an important role in corporate emission reduction. The relationship between board characteristics and carbon emissions, such as foreign directors, board gender diversity, outside directors, and the number of directors, is widely studied by scholars (Mardini and Lahyani 2021;Nuber and Velte 2021;Kurnia et al. 2020). Liao et al. (2015) argue that independent directors are more willing to pursue environmental opportunities to acquire more reputation and honor. Nuber and Velte (2021) find that women directors exhibit a strong orientation toward environmental responsibility and are more concerned with environmental issues. Mardini and Lahyani (2021) find that foreign directors are more engaged in sustainability and influence the board's decisions toward supporting climate change activities. These board characteristics all have positive impacts on decreasing carbon emissions. Corporations use different reporting boundaries and accounting methodologies when calculating amounts of carbon emissions (Stanny 2018). If energy expenses relative to total expenses are higher, the corporations invest more in environmental energy projects and so achieve lower emissions (Mahapatra et al. 2021).
Carbon action-level factors are a category that affects corporate carbon emissions. Good corporate awareness of environmental issues promotes pro-environmental activities (Sharma 2000). Awareness of the environment can be divided into carbon-risk awareness and carbon opportunity awareness. Compared to carbon opportunity awareness, corporations with a greater awareness of carbon risk not only exhibit a greater willingness to develop mutually beneficial relationships with stakeholders to enhance corporate capacity to generate sustainable development but also will adopt a variety of governance mechanisms to promote corporate emission reduction, such as setting carbon targets, providing carbon reduction incentives, and linking compensation to carbon reduction (Luo and Tang 2021;Jung et al. 2018). Researchers find that incentives are adopted by firms to reduce carbon emissions from their operations. Eccles et al. (2012) argue that monetary incentives lead to higher carbon emissions, while non-monetary incentives lead to lower carbon emissions. A growing number of global initiatives are supporting corporate non-financial target-setting efforts. Different types of corporate climate change targets exhibit different behaviors regarding trading corporate carbon. Compared to absolute targets, intensity targets reflect ambitions to reduce GHG emissions at a more relative level (Slawinski et al. 2017;Dahlmann et al. 2019). To achieve lower carbon emissions, corporations participate in the carbon emission trading system (ETS) to achieve carbon credit purchases, implement internal carbon pricing (ICP) mechanisms within corporations, and actively promote investment in emission reduction activities. Firms find that voluntarily reducing carbon emissions often brings economic benefits (Hart 1997).
Financial-level factors are a category that affects corporate carbon emissions. The relationship between corporate environmental performance and profitability is extensively studied in the existing literature (Larasati et al. 2020;Dixon-Fowler et al. 2013;Guenther and Hoppe 2014). R&D is often considered a financial-level impact factor. Under regulatory pressure from carbon emissions, corporations are trying to "offset" the additional costs of regulatory compliance through innovation. As an effective means to promote corporation innovation, R&D can effectively affect corporate carbon emissions (Lanoie et al. 2011). Corporate capital expenditures are associated with a larger carbon footprint and will lead to more carbon emissions (Karim et al. 2021). Trade-off theory suggests that firms with a high leverage There is a negative relationship between market-tobook ratios and carbon emissions because the carbon premium is unlikely to be driven by cash flow effects related to productivity (Bolton et al. 2022).

LASSO regression model
We chose to integrate the LASSO and the fixed effects model into identifying determinants of corporate carbon emissions. Firstly, we take the absolute carbon emissions of total, Scope 1, Scope 2, and Scope 3 and the relative carbon emissions of per revenues and per full-time equivalent employees as dependent variables, respectively. Then, we applied the LASSO regression model to rank the importance of factors affecting carbon emissions and capture the important preferences of influencing factors on the different corporate carbon emission scopes through the fixed effects model. By integration of the models, we can consider the factors affecting carbon emissions from more dimensions. Figure 2 shows the framework of our methodology.
Proposed by Tibshirani (1996), LASSO is a regression variable selection method that automates model selection. As a selection procedure, it combines the least squares method with a constraint on the sum of the absolute values of the coefficients to improve prediction accuracy and interpretability. Considering ordinary linear models, supposing y i = y 1 , y 2 , y 3 , … , y d T is t he response var iable and i s t h e c ova r i a t e fo r e a ch where ε i is an error term. (1) When X is a full rank design matrix, the regression coefficient β can be obtained by the ordinary least squares estimation method: where d is the number of the covariates.
When the design matrix X does not meet the full rank, the penalty method is introduced to achieve the effect of variable selection by compressing some parameters to zero. The penalty method is to take the minimum value of the penalty likelihood function as the estimated value of the regression coefficient; this is shown below: , m ≥ 0 is the penalty term (is also named as the tuning parameter). When m = 1, � is the L 1 norm of the parameter vector. λ is a nonnegative regularization parameter. β j are the other parameters.
By adding the L 1 norm to the ordinary linear model, the LASSO estimate is shown below: where t ≥ 0 is a pre-specified free parameter that is chosen to determine the amount of regularization through cross- � , when t < t 0 , a part of the coefficient will be compressed to zero, thereby reducing the dimension of X and reducing the complexity of the model. N is the total number of observations.
The LASSO estimator ̂ can be equivalently written in Lagrangian form as where t corresponds to λ one-to-one and is the adjustment coefficient. λ is the regularization parameter and the higher the value of λ, the lower the number of non-zero β and vice versa.
According to the above equations, we can derive a sparse regression model which regularizes the parameters β under sparse assumption. When λ is exceptionally large, the value of all the parameters of the independent variables is zero. By adjusting the value of λ, the parameters will gradually increase and turn from zero to non-zero one by one. Then, based on the sequence of the appearance of the parameters, the degree of importance of the different independent variables can be known for prediction.
Least absolute shrinkage and selection operator (LASSO) Ranking of impacts of factors selected under mean squared prediction error constraints (MSPE) Carbon actionslevel Step 1: Identifying importance Step 2 We introduced K-fold cross-validation to estimate the best regularization parameters or t. Firstly, the data set was randomly split into K approximately equal-sized sets. The first subsample was left as the "validation set" and the remaining K-1 subsamples were used as the "training set" to estimate the model. We then predicted the first subsample and calculated the mean squared prediction error (MSPE) for the first subsample. Secondly, the second subsample was used as the validation set, while the remaining K-1 subsamples were used as the training set to predict the second subsample and calculate the MSPE of the second subsample. By analogy, we performed k training runs in turn in K sets for validation. Then, we added up the MSPE of all the sub-samples and took the average test error over the K runs, which was regarded as the test error for the regression model. Finally, the regularization parameters λ were selected so that they corresponded to the lowest estimated generalization error, which consequently gives the best predictive power.
To estimate the regression coefficient vector β, we repeated it multiple times on different values of (Shi et al. 2020). Specifically, the optimized λ was set for all coefficients except the intercept that was forced to zero and was computed according to a geometric sequence. We computed the largest λ and the smallest λ, while making the largest value of λ 10,000 times the smallest value. The 100 specifications sets of regressions were run with different values of λ, denoted as SP (Shum et al. 2021). Specification 1 and specification 100 are the specifications with the smallest value of λ and the largest value of λ. When the corresponding λ or SP values increase, the coefficient of an independent variable increases from zero. The first independent variable with a non-zero coefficient has the most influence on corporate carbon emissions. The earlier the variable appears, the more important it is for prediction. Thus, using multiple iterations of the LASSO method, we could observe changes in the importance of independent variables. To identify independent variables that are important enough, we selected the value at the MSPE. Then, we included those variables in a fixed model to explore the significance of corporate carbon emission factors.

Data
We identified a range of potential factors that affect corporate carbon emissions from both the Carbon Disclosure Project (CDP) database and the Compustat database. The CDP was established in 2000 as a non-governmental organization (NGO) in the UK. The CDP asks firms to describe climate change management strategies, to identify climate change and its risks and opportunities and to disclose GHG emissions. Many of the world's largest firms responded to the CDP survey requests; by 2015, more than 5500 firms had responded (CDP, 2018). The BoardEx database has compiled the full list of their directors, senior managers, and disclosed moneymakers for over 18,000 corporations worldwide and has built complete profiles on each individual. Firm-level and carbon action-level information were obtained from the CDP database and BoardEx database in 2009-2019. Firmlevel information included business strategy, GHG inventory boundary, individual positions, CEO duality, the number of directors serving on the board, energy consumption, energy consumption intensity, total compensation, nationality mix proportion, the proportion of male directors, and the number of directors. The carbon action-level includes carbon awareness, identity climate change risks, identity climate change opportunities, incentive for climate change issues, benefit from incentive, incentive type, emission reduction target, emission reduction activities, internal carbon price, emission reduction initiatives, third party, carbon credits, emission trading schemes, public policy, voluntarily published information, and value chain. Only CEO duality, the number of directors serving on the board, total compensation, nationality mix proportion, the proportion of male directors, and the number of directors were obtained from the BoardEx database; the others were all obtained from the CDP database. The Compustat database provides nearly 20 years of historical data on financial indicators for North American publicly traded corporations. Therefore, financial-level information was obtained from Compustat for 2009-2019. Such information included debt-paying ability, operation capability, profitability, growth ability, R&D, total assets turnover, capital expenditure, asset intensity, firm leverage, market-to-book ratio, debt-to-asset ratio, and return on assets. We employed unbalanced panel data estimate approaches and controlled for the year fixed effects in our model. After matching the data with the CDP database, the BoardEx database, and the Compustat database and deleting observations with missing values, we were left with 4013 observations. Tables 1 and 2 present the variable definitions and the descriptive statistics for our sample. Table 3 reports the regression of whole impact factors to carbon emissions. From columns (1) to (6), we report the regression results of carbon emissions in different measurement methods. In columns (1), (2), (3) and (4), we report the regression of absolute carbon emissions. In columns (5) and (6), we report the regression of relative carbon emissions. All the models are controlled for the year fixed effects. Firstly, we analyzed the effects of firm-level information on corporate carbon emissions. Operate has a positive Energy consumption intensity. Energy percentage of total operational spend more than 0% but less than or equal to 5%

Opexpense510
Energy consumption intensity. Energy percentage of total operational spend more than 5% but less than or equal to 10%

Opexpense1015
Energy consumption intensity. Energy percentage of total operational spend more than 10% but less than or equal to 15% (2) Absolute targets (Absolute)

Regulatory
Emissions reduction activities: 1 if corporations use compliance with regulatory requirements/standards to drive investment in emissions reduction activities CDP effect on the corporate carbon emissions of Scope 1, Rin, and Ein. Greenhouse gas, measured in both operate control and financial control, has a positive impact on the reduction of corporate carbon emissions. The aggregate effect of Scope 1, Rin, and Ein decreases by 6.3%, 13%, and 9.5% respectively for a one-standard-deviation increase in Operate. The aggregate effects of Scope 1, Scope 3, Rin, and Ein decrease by 4.5%, 9.4%, 8.5%, and 6.7% respectively for

Mtbt
Market-to-book ratio. The ratio of market-to-book value of equity Compustat Lev Debt-to-asset ratio. Total assets divided by total liabilities Compustat ROA Return of assets. Profit after taxes divided by total assets Compustat a one-standard-deviation increase in Finance. The operate boundary has a greater impact on decreasing carbon emissions than that of the finance boundary. When the CEO is also the founder of firms, it contributes to reducing the carbon emissions of Scope 1 and Scope 2 by 2.8% and 5.3% respectively for a one-standard-deviation increase in CEO. However, Dual is not conducive to the reduction of corporate carbon emissions. Corporations should moderately decrease CEO's discretion to ensure better implementation of emission reduction strategies. Boardamount can decrease 3.7% of the aggregate effect for both Rin and Ein, but it will increase the aggregate effect of Scope 1 by 2.3% for a one-standard-deviation increase in Boardamount. Energy consumption intensity of Opexpense05, Opexpense510, and Opexpense1015 has a positive influence on reducing carbon emissions. Opexpense05 decreases the aggregate effect of Total, Scope 1, Rin, and Ein by 4.9%, 11.8%, 18.7%, and 14.9% respectively for a one-standard-deviation increase.
Opexpense510 decreases the aggregate effect of Scope 1, Rin, and Ein by 2.5%, 4.4%, and 3.1% respectively for a one-standard-deviation increase. Opexpense1015 decreases the aggregate effect of Rin and Ein by 155.5% and 154.1% respectively for a one-standard-deviation increase. For Scope 2 and Scope 3, the higher energy consumption intensity is less conducive to reducing carbon emissions. Although energy consumption intensity can decrease corporate carbon emissions, the role of Opexpense is not efficient. The corporations with energy consumption cannot be effective for emission reduction, which is insignificant because of energy consumption intensity that is too high. TDC decreases the aggregate effect of Total, Scope 1, Scope 3, Rin, and Ein by 0.1% for a one-standard-deviation increase. Genderratio has an efficiency on Scope 3, which decreases the aggregate effect of Scope 3 by 135.1%. Numberdirectors has an efficiency on relative carbon emissions, which decreases    Secondly, we analyze the effects of carbon action-level information on corporate carbon emissions. Oppo has a positive effect on decreasing Scope 2 carbon emissions by 4.9%. Managerexe has a positive effect on decreasing Scope 1 carbon emissions by 5.1%. Target has a positive effect on decreasing Scope 3 carbon emissions by 7.1%. Compared to intensity targets, absolute targets decrease the aggregate effect of Scope 1, Rin, and Ein by 3.9%, 4.8%, and 4.3% respectively for a one-standard-deviation increase. In the emission reduction activities, Incentiveemp decreases the aggregate effect of Total, Scope 1, Rin, and Ein by 3.3%, 4.7%, 5.4%, and 5.5% respectively for a one-standard-deviation increase. Other emission reduction activities do less to reduce corporate carbon emissions. Voluntary has a positive effect on decreasing the aggregate effect of Total and Scope 3 by 4.3% and 6.2% respectively for a one-standarddeviation increase. Energy, Icp, Carbonmes, Thirty, Credit, Ets, Touch, and Value have significant effects on corporate carbon emissions, but the role is the opposite.
Thirdly, we analyze the effects of financial-level information on corporate carbon emissions. Currentratio decreases the aggregate effect of Scope 1, Rin, and Ein by 9.5%, 10%, and 5% respectively for a one-standard-deviation increase. Quickratio decreases the aggregate effect of Scope 3 by 11.7% for a one-standard-deviation increase. Operprotio decreases the aggregate effect of Total, Scope 1, Scope 2, Scope 3, Rin, and Ein by 20.6%, 22.7%, 31.5%, 16%, 9.4%, and 18.1% respectively for a one-standard-deviation increase. Inventurn decreases the aggregate effect of Total, Scope 1, Scope 2, Rin, and Ein by 4%, 3.2%, 8.3%, 4.3%, and 4.6% respectively for a one-standard-deviation increase. Capitalstock decreases the aggregate effect of Total and Scope 3 by 13% and 19.6% respectively for a one-standarddeviation increase. R&D decreases the aggregate effect of Scope 1, Rin, and Ein by 7.1%, 9.8%, and 9.9% respectively for a one-standard-deviation increase. Totassover decreases the aggregate effect of Rin by 8.4% for a one-standard-deviation increase. Mtbt has an effect on relative carbon emissions, which decreases the aggregate effect of Rin and Ein by 17.6% and 13.2% respectively. Asset and Lev decrease the aggregate effect of Scope 2 by 17.5% and 14% respectively. ROA decreases the aggregate effect of Scope 1 and Rin by 6.1% and 7.3% respectively for a one-standard-deviation increase. Operprotio and Capx have a significant impact on carbon emissions across all ranges (Table 3).

Sorting the importance of impact factors
To identify the factors affecting carbon emissions, we selected the LASSO regression model and adopted the linear regression method of L 1 regularization to make the eigenvalues of some influencing factors as 0 so as to achieve the purpose of sparsification and feature selection. SP is a sparse constraint that reflects the importance of each impact factor on carbon emissions. SP is in the range of 0-100 and gradually decreases from 100 to 0. At this time, the coefficients of impact factors also start to change from zero to non-zero. The variables with non-zero coefficients that enter the model first have the greatest impact on carbon emissions. We classified carbon emissions into absolute and relative quantities and tested the importance of impact factors from the absolute quantities of different ranges and the relative quantities of per revenues and per full-time equivalent employees. The results are shown in Fig. 3a-f. We list only the variables that entered the model the first ten times in the legend. To present a complete and more intuitive result, we give the LASSO path for all the variables that entered the model in Tables 5,  6, 7, 8, and 9. The results are presented in the Appendix. Figure 2 shows that of all the impact factors, except the influence on Ein, Capx is the first variable to enter the model. Corporate capital expenditures are associated with more value-relevant activity and lead to more carbon emissions (Karim et al. 2021). Corporations with higher capital expenditure not only communicate more environmental impact information with the stakeholders, but also promote environmental activity to convey a positive image to their stakeholder (Zheng et al. 2020 Fig. 3 a-f The trend of coefficients with the decrease of SP influence factor. As corporate liquidity, the current ratio reflects the corporate short-term debt solvency. The greater the amount of corporate liquidity, the more it can assist in the reduction of carbon emissions (Chen et al. 2022). For the absolute carbon emissions, Ets is the second variable to enter the model. Ets is a cap-and-trade program that allows corporations regulated by the Ets to choose the most cost-effective way to manage their emissions through the purchase and sale of carbon allowances. Corporate adoption of this regulatory policy demonstrates its willingness to formulate strategies on carbon emissions that help corporations reduce emissions (Hossain and Farooque 2019). Scope 1 and Scope 2 are the corporate direct carbon emissions and indirect carbon emissions respectively associated with the purchase of electricity and energy, so Opexpense seems to be important and enters the model earlier.
For the relative carbon emissions, Fig. 3e, f shows that Opexpense is critical. Energy consumption reflects the corporate operational efficiency. In the production of energy, corporations need to reduce carbon emissions significantly. Corporations may incur higher energy expenses by greater investments in environmental energy projects, which reflect lower emissions (Mahapatra et al. 2021). Furthermore, Operate is also an important impact factor. A firm's boundary choice determines which emissions are under its control. We found that the operate boundary has a greater impact on carbon emissions than the finance boundary (Stanny 2018). Scope 3 emissions include indirect emissions that occur in the upstream and downstream of a company's supply chain. Thus, in Fig. 3d, Value is the third variable to enter the model supply chain when corporations integrate climate-related issues into their business strategy. Carbon emissions in the supply chain are closely tied to business strategies, so Strategy is the fourth variable to enter the model. Only R&D does not enter the model of Total and Scope 3. Compared to other carbon emission ranges, R&D enters the model earlier. It can be seen that R&D is a key factor in corporate carbon emissions. Thirty tends to measure goods and services. Compared to the direct carbon emissions in Scope 1, the importance of Scope 2 and Scope 3 and relative quantities is higher. Risk is also included in the model, but Oppo does not enter any model. This is because companies focus more on risks than on opportunities when considering climate-related risks and opportunities (Gasbarro et al., 2017). Icp enters all the models. The implementation of the internal carbon price (ICP) contributes to enhancing the ability to implement and transform corporate environmental strategies and promotes the improvement of corporate carbon performance (Zhu et al. 2022). In Fig. 3a, b, c, f, Touch enters the model. We find that corporations' participation in public policy is also an important factor influencing carbon emissions. When firms reach out to decision makers on taxation, regulation, and carbon regulation, they are the first to understand policy trends and engage in favorable emission reduction activities that cater to policies. Incentive can greatly affect corporate activities. In Fig. 3a     For Scope 2, Finance, CEO, Founder, Opexpense05, and Nationalitymix enter the model as firm-level impact factors. Finance, Founder, Opexpense05, and Nationalitymix affect Scope 2 at a significant level of 5%. Founder and Opexpense05 decrease the aggregate effect by 4.6% and 2.1% respectively. Awareness, Risk, Incentive, Managerexe, Incentiveemp, Icp, Carbonmes, Thirty, and Ets enter the model as carbon action-level impact factors. Incentive, Carbonmes, Thirty, and Ets affect Scope 2 at a significant level of 5%, but these factors have an opposite role in decreasing carbon emissions. Currentratio, Netprosales, Operprotio, Receiturntio, Inventurn, Totassgrate, R&D, Capx, Asset, Leverage, and Mtbt enter the model as financial-level impact factors. Currentratio, Operprotio, Receiturntio, Inventurn, R&D, Capx, Asset, Leverage, and Mtbt affect Scope 2 at a significant level of 5%. Operprotio, Inventurn, and Asset decrease the aggregate effect by 26.7%, 7.6%, and 20% respectively.

The regression of filtered impact factors to carbon emissions
For Scope 3, Strategy, Finance, Dual, Nationalitymix, Genderratio, and Numberdirectors enter the model as firm-level impact factors. Strategy, Dual, and Genderratio affect Scope 3 at a significant level of 5%. Genderratio decreases the aggregate effect by 128.3%. Incentive, Employees, Managerexe, Target, Intensity, Absolute, Regulatory, Energy, Icp, Thirty, Credit, Ets, Touch, Voluntary, and 11%,and 0.2% respectively. Risk,Incentive,Employees,Target,Intensity,Regulatory,Incentiveemp,Icp,Carbonmes,Thirty,Ets, and Touch enter the model as carbon action-level impact factors. Risk, Intensity, Incentiveemp, Icp, Thirty, and Touch affect Ein at a significant level of 1%. Only Incentiveemp decreases the aggregate effect by 4.5%. Currentratio, Quickratio, Operprotio, Inventurn, Totassgrate, R&D, Capx, Asset, Leverage, Mtbt, and Lev enter the model as financial-level impact factors. Except for Currentratio, all the factors affect Rin at a significant level of 5%. Operprotio, Inventurn, R&D, and Mtbt decrease the aggregate effect by 16.5%, 5.4%, 11.2%, and 15.3% respectively. Table 5 reports the estimated results of the regression of impact factors in different sectors. The impact factors affecting different sectors vary widely. Corporations from the carbon-intensive sector are subject to higher climate change-related risks, and therefore, we may expect these corporations to provide more information about climate change-related strategies than corporations from the low-carbon sector. Inspired by Zhou et al. (2018), we define chemicals, gas and electrical utilities, oil and gas, coal mining, pipelines, steel, and transportation as belonging to the carbon-intensive sector. Others belong to the non-carbon-intensive sector.

Subsample analysis for the carbon-intensive sector
For the carbon-intensive sector, financial-level impact factors are of high importance. Capx is the impact factor with the highest importance. Higher capital expenditures are not conducive to reducing carbon emissions. Karim et al. (2021) show that capital expenditure leads to more carbon emissions. It is punishable by the market because non-green investments in capital expenditures may increase carbon emissions. Green investments may not offer any benefits in the short term, leading to a more negative market reaction (Lee et al. 2015). This is followed by operation capability. The coefficient of Operprotio is − 1.674 and is significant at the level of 1%. Operprotio decreases the aggregate effect of Total by 14%. Ets is the third important factor. It is easier for corporations to carbon trade after participating in the ETS. A variety of corporate carbon actions also have a significant impact on corporate carbon emissions, including Icp, Touch, Thirty, Energy, Target, and Intensity. Voluntary can reflect that corporations with voluntary emission reduction awareness are more conducive to carbon emission reduction, and it decreases the aggregate effect of Total by 3%. In the impact factors of firm level, although Numberdirector, Strategy, and Dual affect corporate carbon emissions, they cannot promote a reduction in the number of carbon emissions. The coefficient of Opexpense05 is − 0.287 and is significant at the level of 1%. Opexpense05 decreases the aggregate effect of Total by 3.4%.
For the non-carbon-intensive sector, Capx first enters the model. The greatest impact is also by financiallevel factors. Corporate carbon actions have a significant impact on corporate carbon emissions. Ets, Value, Thirty, Touch, Risk, Target, Regulatory, Employees, Icp, Intensity, and Energy all have a significant influence on carbon emissions. In addition, the impact factors of financial level, debt-paying ability, operation capability, and profitability deserve attention from corporations. Currentratio, Operprotio, and Inventurn can decrease the aggregate effect of Total by 3.5%, 12.9%, and 3.4% respectively. In the impact factors of firm level, the coefficient of TDC is − 0.016 and is significant at the level of 1%. TDC decreases the aggregate effect of Total by 0.1%.

Subsample analysis for region
According to the geographic distribution of the United States Census Bureau, we divided the 50 US states into the Northeast region, South region, Mid-west region, and West region. Then, we explored the factors affecting corporate carbon emissions in these four regions. The results are reported in Table 6  The factors of Currentratio, Capx, and Asset at the financial level have a significant impact on corporate carbon emissions. Currentratio decreases the aggregate effect of Total by 8.1%.

Discussion and conclusion
Corporations are gradually becoming major actors in the fight against climate change. Governments, investors, and stakeholders are also beginning to value the environmental responsibilities of corporations. Therefore, it is necessary to identify the key drivers affecting corporate carbon reduction to implement effective emission reduction measures. The existing literature mostly involves research into the drivers of carbon emission reduction based on specific assumptions (Mahapatra et al. 2021). This method can only explore the degree of importance of the drivers and cannot distinguish the relative importance of the drivers. The LASSO regression differs from the general regression model in that not only can it empirically test the impact of firmlevel, carbon action-level, and financial-level information on corporate carbon emissions, but it also ranks their importance and thus identifies the most influential driving factors of corporate carbon emissions.   This paper used CDP database questionnaire data, BoardEx data, and Compustat data to select a sample of 4016 US-listed corporations from 2009-2019. The LASSO regression model was then used to prioritize the most important factors affecting absolute carbon intensity (Total, Scope 1, Scope 2, and Scope 3) and relative carbon intensity (Rin and Ein). There is a further significant analysis of the important factors which are screened out. The results show that Capx is the most important factor affecting corporate carbon emissions. Although Capx does not enter the model first for Ein, it is the second variable to enter the model, which indicates that the impact is also very high. However, Capx has a negative impact on decreasing corporate carbon emissions. The result is consistent with Karim et al. (2021), who find that capital expenditure leads to more carbon emissions. Capital expenditures reflect more value-relevant activity, which causes an increase in corporate carbon emissions. While corporations with higher carbon emissions will provide more information on carbon emissions to reduce negative market reactions, these corporations are still punished by the market. Even green capital expenditures do not pay off in the market (Lee et al. 2015). Thus, we argue that corporations should reduce carbon emissions by reasonably reducing capital expenditures. For absolute carbon emissions, Ets is the most important impact factor, but we find that ETS is not conducive to reducing carbon emissions. Unlike the EU ETS, which is a mandatory program, the USA is a contracted-based and voluntary market for trading carbon allowances. It is a dynamic market, and the determinant of carbon allowance trading is energy prices, particularly influenced by the price of coal (Kim and Koo 2010). The USA implements many other strategies for reducing carbon emissions (Villoria-Sáez et al. 2016); only the ETS does not play a great role. Scope 1 and Scope 2 are direct and indirect emissions associated with corporations, so financial-level factors play a greater role. For Scope 1, corporate debt-paying ability is more important. Highly indebted corporations struggle with onerous debt responsibilities, which limit the implementation of management strategies to reduce carbon emissions (Sun et al. 2022). Thus, we argue that the higher corporate debt-paying ability, the more focus is on carbon emission reduction activities. For Scope 2, corporate operation capability is more important. Operprotio is the third factor that enters the model and has a negative relationship with carbon emissions. This finding is consistent with Ganda and Milondzo (2018). Furthermore, research and development (R&D) is also a factor worth paying attention to. Corporations with R&D are more likely to be associated with improved environmental performance . Many studies find that R&D contributes to a reduction of carbon emissions Petrović and Lobanov 2020;Koçak and Ulucak 2019). We also have consistent results that R&D can reduce both Scope 1 emissions and relative carbon emissions. However, we find R&D cannot reduce Scope 2 and Scope 3 emissions. Scope 2 emissions are the indirect emissions from electricity, which are sources from corporate purchases and consumption. Scope 3 emissions are not corporate owned or controlled. Thus, R&D activities that are applied to reduce Scope 1 emissions can contribute to reducing emissions. For Scope 3, corporate internal incentive policies and emission reduction behaviors are important. Thirty, Value, Strategy, Employees, Icp, and Incentive are all among the top ten variables that enter the model. For relative carbon emissions, the financial-level factors' debt-paying ability can be used as a reference indicator for the impact of corporate carbon emissions. Energy consumption intensity also enters the model earlier. Especially, when the energy percentage of the total operational spend is more than 0% but less than or equal to 5%, corporate carbon emissions can be most affected. Mahapatra et al. (2021) have also studied the impact of energy consumption intensity on corporate carbon emissions. Our finding is consistent that corporations concerned about carbon emissions have lower energy consumption intensity. In the analysis of the impact on Total, Scope 1, Rin, and Ein, Risk enters the model. It can be seen that carbon-risk awareness has a greater impact on the corporate total emission amount and the relative emission amount. Further, in the firms with carbon-intensive sector and non-carbon-intensive sector, the most important factor is still Capx. Ets is the second factor entering the model. However, firms with carbon-intensive sector are mainly influenced by the factors of financial level. Firms with non-carbon-intensive sector are mainly influenced by the factors of carbon action level. In the partial sample analysis of the region, we find that for corporations in the Northeast and Midwest, the factors of carbon action level have a greater impact. For corporations in the South, impact factors are the most. Firm level, carbon action level, and financial level all have an influence. For corporations in the West, the impact factors are mainly focused on carbon action level and financial level. Only Strategy plays an influential role at the firm level.

Policy implications
Based on our study, we offer important suggestions for managers and policymakers. First of all, Capx has a positive effect on the absolute carbon emissions of Total, Scope 1, Scope 2, and Scope 3 emissions. Thus, it is essential to appropriately reduce corporate capital expenditure. Corporate capital expenditure increases the carbon footprint of activities related to increased value. Corporations with greater capital expenditure can improve the transparency of their corporate carbon information by providing more carbon disclosures; more carbon emission information minimizes market penalties for corporate emissions (Matsumura et al. 2014). For policymakers, it means that they can increase the level of corporate carbon disclosure in the annual reports. Meanwhile, managers need to enhance internal governance to ensure that any carbon emissions caused by capital expenditure are fully communicated to the stakeholders and to improve the relationship between capital expenditure and carbon emission disclosures to promote lower corporate carbon emissions.
Secondly, for Scope 1 and Scope 2 emissions, the factors of Currentratio and R&D have important effects. Managers should pay more attention to corporate debtpaying ability to ensure a reduction in corporate carbon emissions. Tackling climate change challenges will impose additional costs and constraints on corporations. Thus, to ensure competitiveness, corporations should have an innovative ability. R&D is unlikely to make a decent profit in the short term, but investing in green technology, R&D can reduce carbon emissions and lead to positive financial outcomes (Lee et al. 2015). Regarding policymakers, they can not only develop fiscal incentives to encourage corporate R&D but can also cooperate with corporations to alleviate corporate pressure. Managers should comprehensively measure corporate environmental responsibility and financial performance to avoid missing business and profit opportunities as a result of insufficient information. They should also focus on investing in environmental technologies and green R&D.
Thirdly, for Scope 3 emissions, ETS, Thirty, Value, and Employees all have a significant impact on Scope 3 emissions. However, although Scope 3 emissions are affected by more corporate carbon actions, these impacts have not contributed to the reduction of Scope 3 emissions. Efforts to reduce carbon emissions are always incompatible with substantial environmental responsibility and economic outcomes. Chowdhury et al. (2018) argue that passive or symbolic carbon reduction actions are not effective and cannot reduce carbon emissions. For policymakers, they can strengthen the substantive role of emission reduction actions by changing the direction of policy supervision and distributing policy benefits. For managers, they should reduce these symbolic emission reduction actions and strive to integrate emission reduction actions into their business strategies and achieve them.
Fourthly, for the relative carbon emissions of Rin and Ein, energy consumption intensity is another impact factor we are concerned with. We compare the different proportions of energy consumption intensity and find that only when the energy percentage of the total operational spend is less than or equal to 10% does it have an impact on corporate carbon emissions. Opexpense05 and Opexpense510 all enter the model, but Opexpense1015 is excluded. Opexpense only enters one model of Rin, which indicates that having a higher proportion of energy consumption is not always better. For policymakers, they can require corporations to disclose proportions of energy consumption intensity in annual reports to play a monitoring role, while managers can try to maintain the corporate energy percentage of the total operational spend of more than 5% but less than or equal to 10% to promote lower carbon emissions.
For corporations, carbon emission reduction as a corporate strategy is affected by a combination of factors. Although the LASSO regression used in this paper explores the factors affecting corporate carbon emissions in multiple dimensions, it is still limited by the linear regression model. Therefore, future research can consider incorporating nonlinear analysis techniques into studies to complement existing studies. Secondly, this study is limited by micro-data and does not include macro-level data, such as the economic development capacity of each region, which we argue is also an effective impact factor affecting corporate carbon emissions. Tables 7,8,9,10,11,and 12.

Declarations
Ethical approval This research does not involve human participants and/or animals.

Consent for publication
We consent to publish the manuscript according to journal policy.

Competing interests
The authors declare no competing interests.
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