The Impact of Environmental Protection Investment on Provincial Carbon Emissions in China: Empirical Analysis Based on Two-way Fixed Effects Model

: In confront of global climate change, promoting carbon emission reduction and sustainable development has come to be acknowledged internationally. On the basis of panel data from 30 Chinese provinces from 2009 to 2020, this paper undertakes an empirical investigation into the connection between carbon emission intensity and investment in environmental protection. The findings demonstrate that investment in environmental protection has a nonlinear inverted U-shaped relationship with carbon emission intensity, that is, with the increase of environmental protection investment, its effect on carbon emission has changed from promoting to inhibiting. And the influence degree varied in different regions, with the influence in western and central regions being significantly stronger than that in eastern regions. The government should take full account of local conditions and formulate policies of environmental protection investment in accordance with local conditions.


Introduction
On September 22, 2020, China proposed a two-stage carbon emission goal, indicating that it will make all efforts to attain "Carbon Peak" and "Carbon Neutrality" by 2030 and 2060, respectively. Since then, promoting carbon emission reduction has emerged as a key objective for China in its efforts to advance a green economy and ecological preservation. Environmental protection investment has gained increasing attention as China's economy shifts from rapid growth to high-quality development. As a new mode of investment, environmental protection investment plays an essential role in transforming the economic growth pattern of each country and achieving the sustainable development of human society.
Against the background, this paper explores whether environmental protection investment can effectively curve carbon emissions, which is of great research value. At present, the academic circle has conducted a profound discussion on the relationship between environmental protection investment and carbon emissions. However, most scholars discuss the relationship from the perspective of green finance, and there is little literature directly studying the relationship between environmental protection investment and carbon emissions. Moreover, the discussion of the relationship is only from the national level, lacking the focused discussion and horizontal comparison of different regions in the east, middle and west. Therefore, based on the previous studies, this paper discusses the impact of environmental protection investment on carbon emissions based on provincial panel data. Combined with regional differences, this paper further discusses the different manifestations of the effect of environmental protection investment on carbon emissions in the eastern, middle and western provinces of China, so as to put forward more targeted policy suggestions and provide effective policy programs for promoting green development and achieving "carbon peaking and carbon neutrality" goals.

Review of Related Research
At the macro level, environmental protection investment refers to the investment of the state or government in environmental pollution control, which has both economic and environmental effects. Relevant studies have initially explored the relationship between environmental protection investment and carbon emission reduction, and formed the following two views: one opinion is that environmental protection investment has a linear relationship with carbon emissions, and environmental protection investment helps to reduce carbon emissions. According to Jiang et al. (2020), carbon emissions can be decreased through both green venture capital and green financing [1]. You et al. (2022) took green credit, green industrial investment and green bonds as examples, and believed that all green financial businesses could significantly reduce carbon emissions [2]. Ren Yayun et al. (2023) found that pilot policies of green finance could indirectly reduce industrial and agricultural carbon emission intensity through the increase of green fixed asset investment [3]. Another view holds that green investment has a nonlinear relationship with carbon dioxide emissions. Cheng Sijin and Ren Xiaocong (2022) analyzed the relationship between green investment and carbon emissions from the static and dynamic perspectives by using the system-GMM model, and found that green investment presents an inverted U-shaped curve relationship to carbon emissions [4]. Zeng Sheng and Zhang Minglong (2021) use Spatial Durbin Model (SDM) and semi-parametric panel spatial lag model to analyze and show that green investment has an "inverted U-shaped" or "inverted N-shaped" nonlinear effect on carbon emission intensity [5]. Regional variability may also affect how green finance affects carbon emissions, according to some academics. Lin Lefen and Yang Qianwen (2022) found that the investment in green infrastructure and carbon emissions showed an inverted U-shaped relationship, and there is regional heterogeneity between the two. The inverted U-shaped impact of green infrastructure investment in carbon emissions in the eastern and middle regions is more obvious [6]. According to Wang Lian and Wu Zhaoxuan (2022), the growth of regional green finance can effectively encourage the improvement of carbon emission efficiency, with this effect being more pronounced in the eastern region and in regions with high carbon emission efficiency [7].

Theoretical Analysis and Hypothesis
The effect of environmental protection investment on carbon emission is mainly related to scale effect, technology effect and structure effect. From the perspective of scale effect, environmental protection investment will promote economic growth, while the expansion of economic scale will also increase the demand for energy consumption, thus affecting carbon emissions. At the same time, investment in environmental protection can make idle funds flow into the environmental protection industry, foster green innovation industries, and accelerate the green transformation of polluting enterprises, thereby helping to reduce carbon emissions. The studies show that when the level of economic development is low, environmental protection investment will drive economic growth, which will increase the total market demand, increase resource consumption, and increase carbon emissions; When the economic level grows to a certain extent, policies related to environmental protection investment can make funds flow into green industries such as new energy and promote green transformation. At the time, environmental protection investment will bring high-quality economic growth and help reduce carbon dioxide.
From the perspective of technical effect, the scale of environmental protection investment is small in the initial stage, which makes it difficult to provide sufficient funds for improvement of enterprises' productive technology or innovation of green technology, and has a limited role in promoting industrial transformation and upgrading. Meanwhile, regional economic development gives rise to the increasing demand for energy consumption, leading to rapid growth of carbon emissions and offsetting the effect of carbon emission reduction brought by environmental protection investment, forming an energy rebound effect. With the expansion of the scale of environmental protection investment, enterprises have sufficient funds for technological innovation, the production technology is increasingly perfect, and the production efficiency and energy utilization efficiency of enterprises are significantly improved, which can effectively reduce carbon emissions in the production process.
From the perspective of structural effect, when the level of economic development is low, the supporting effect of environmental protection investment on the R&D innovation of green enterprises is limited, resulting in the lack of scale effect of green industry and slow transformation of economic structure, and the impact of environmental protection investments on reducing carbon emissions is constrained at the same time. After economic development reaches a certain stage, with the expanding scale of investment in environmental protection, policy loans related to environmental protection investment can provide a stable source of funds for more enterprises to support green technology innovation, and provide start-up funds for green industries, guiding the transfer of funds from highly polluting and energy-consuming industries to green and environmental protection industries, to realize the greening of investment structure and promote the upgrading of industrial structure, thus helping to reduce carbon emissions. Therefore, affected by scale effect, technology effect and structure effect, investments in environmental preservation may have a positive or negative effect on carbon emission. Based on this, the following hypothesis is proposed: the impact of environmental protection investment on carbon emission shows a nonlinear relationship.

Data Sources
This paper is mainly selected from the panel data of 30 provinces in China from 2009 to 2020 (Xizang, Hong Kong, Macao and Taiwan were excluded due to missing data). The China Statistical Yearbook, China Energy Statistical Yearbook, and so on are the primary sources of the original data for this paper. At the same time, because the China Energy Statistical Yearbook is currently updated to 2021, and the data disclosed is in 2020, which has a certain time lag, the data of this paper is only selected to 2020. All panel data were collated and statistically analyzed through Excel2019, Stata16.0 software.

Explained Variable: carbon emission intensity (CE).
This paper only selects the ratio of the total carbon emission to GDP of each province as the carbon emission intensity (ton/ten thousand yuan). At present, the provincial data on carbon emissions is not comprehensive enough, and most scholars have a unified measurement method for carbon emissions. Thus, this article draws lessons from the IPCC's standard coal method and considers the terminal consumption of coal, coke, crude oil, gasoline, kerosene, diesel, natural gas, and fuel oil in each province, and multiplies the 8 kinds of energy consumption with their respective carbon emission coefficient, we can estimate the carbon dioxide emissions of Chinese provinces. This paper, the method of Du Limin (2010), calculates the provincial carbon emissions by using the standard coal method provided by IPCC [8]. 8 8 t represents year, i represents province, j represents energy; 2ti CO represents the emissions of the i province in the t year; tij E represents the consumption of the j energy of the i province in the t year; j F represents the low heating value of the j energy; j C represents the carbon emission factor of the j energy; j q represents the carbon oxidation rate of the j energy; Fraction indicates the oxidation of carbon to 2 CO molecular weight changed from 12 to 44, the corresponding calculation of the 2 CO emissions needs to be multiplied by 44 and divided by 12.
The carbon emission coefficients j  of coal, coke, crude oil, gasoline, kerosene, diesel, natural gas and fuel oil are shown in Table 1. Core Explanatory Variable: Environmental investment (GI). It refers to Liu Zhixiong (2011) who used China's fiscal expenditure in environmental protection to measure the level of environmental investment in each province [9].
Control Variables: The specific definition of each variable is shown in Table 2. Terms and Definitions Of Variables Table 2. Ma Xiaojun et al. (2018) believe that the principal influential factors of carbon emissions are development level of economy, population scale, industrial structure and others [10]. On the one hand, economic growth will spur technical advancement and improve environmental quality for people; on the other hand, the development will inevitably lead to an increase in carbon dioxide emissions. The continuous growth of the population size will also bring great pressure on the consumption of resources and the environment, thus continuously increasing the amount of carbon dioxide. Therefore, this paper chooses the control variables as follows: ①Per capita disposable income (PCDI): This paper uses per capita disposable income to represent the level of economic development. ②Resident population number (POP): This paper uses the resident population to represent the population size. ③Industrial structure (IS): This article measures the proportion of the output value of the secondary industry in the GDP.   According to the descriptive statistics in Table 3, the mean value of carbon emission intensity is 2.169, the maximum value is 8.486, and the minimum value is 0.241. And the standard deviation of carbon emission is large, indicating that there are large differences in carbon emission intensity of various provinces in our country. In addition, the standard deviation of environmental protection investment, economic level, population scale, and energy consumption is also large, mainly due to the unbalanced environmental protection investment of different provincial governments, the great difference in economic development level, and the uneven distribution of population. Therefore, in the following empirical analysis, this paper calculates the logarithm of environmental protection investment, economic level, population scale, and energy consumption. Besides, the standard deviation of the industrial structure is 0.089, which is relatively small.

Unit Root Test
There may be pseudo-regression in panel data.   In this paper, the variance inflation factor is used to test the multicollinearity. The results, shown in Table 5, demonstrate that related coefficients among the variables are no more than 0.8, and the VIF values of all the variables are far less than the prescribed critical value of 10, demonstrating that the explanatory variables are not multicollinear. Model (1) is constructed to test the impact of environmental protection investment on carbon emissions at the national level. It can be figured out from Table 6, whose regression results demonstrate the coefficient of the primary term of environmental protection investment is 0.573, while the coefficient of the square term is -0.094, which is significant at the 5% level, verifying the hypothesis that environmental protection investment has an inverted U-shaped influence on carbon emissions. The inflection point of the inverted "U" type effect is 4.2 by calculation. That is, when 0 <lnGI <4.2, the effective coefficient of lnGI on CE is positive; when lnGI≥4.2, the effective coefficient of lnGI on CE is negative. The results show that when environmental investment break through the inflection point, it can well inhibit carbon emissions, and carbon emissions can be reduced by 0.094 units when environmental protection investment increases by 1 unit. The possible reason is there is a scale economies effect and scale populations effect, and the inhibition of environmental investment on carbon emissions has not yet emerged in the early stage. As environmental protection investment rises gradually, the inhibition of carbon emissions also could be well shown. The coefficient of per capita disposable income among the control variables is significantly positive at the level of 1%. It indicates that economic growth has a favorable effect on carbon dioxide emissions. With the rapid development of the economy, the social demand for energy consumption and production is constantly expanding, which leads to an increase in carbon emissions. The effect of industrial structure on carbon emissions is significantly negative, which might be attributed to the fact that the majority of secondary industrial businesses have high levels of energy consumption and emissions. Along with the adjustment and upgrade of industrial structure, which has a favorable impact on lowering carbon emissions, the proportion of the secondary industry has decreased, and the social economy has developed towards a more low-carbon, environmental protection, and clean direction. Therefore, in order to effectively support the reduction of carbon emissions and achieve sustainable economic development, the government should scale up its investments in environmental protection. On the one hand, the government should effectively carry out its duties to ensure that relevant funds can be effectively implemented in the field of environmental protection investment and make pertinent information available to the general public. On the other hand, the government should actively broaden the channels for environmental protection investment, promote the diversification of environmental protection investment modes, encourage more private capital into the field of green investment, better meet the demand for funds for the development of green industries, improve the level of green investment generally, and thus effectively reduce carbon emissions.

Regression Analysis
Model (2) is built to test the impact of environmental protection investment on carbon emissions in eastern China. As shown by the regression results in Table 6, investment in environmental protection has a primary term coefficient of 0.162. the coefficient of the primary term of environmental protection investment is 0.162, while the coefficient of the secondary term is -0.038, which is significant at the 10% level, indicating that under the high level of environmental investment, carbon emissions will reduce by 0.038 units for each unit increase in environmental protection investment. The coefficient of per capita disposable income in the control variables is significantly positive at the 5% level. However, compared with the national level, the coefficient is small, indicating that the improvement of the economy in eastern China has a minor positive impact on carbon emissions. It probably accounts to east China's strong economic growth and the gradual shift from high-speed to high-quality. Therefore, energy consumption and pollution emissions caused by economic growth are reducing gradually.
Model (3) is designed to test the impact of environmental protection investment on carbon emissions in central China. According to the regression results, investment in environmental protection has a primary term coefficient of 3.833, which is significant at the 5% level. The coefficient of the secondary term is -0.450, and it is significant at the 1% level, indicating that when the level of environmental protection investment is low in the central region, each unit increase in environmental protection investment will increase carbon emissions by 3.833 units. At this time environmental protection investment will promote carbon emissions. At a high level of environmental protection investment, carbon emissions will reduce by 0.450 units for every unit increase in environmental protection investment. In this case, environmental investment inhibits carbon emissions vigorously. The influence coefficient of population-scale on carbon emissions is notably negative among the control variables, indicating that as population increases, carbon emissions in central region will relatively decline. The reason may be that economy in central China is relatively developed, and the concentration of resources, especially human resources, is more likely to bring technological progress, thereby improving energy efficiency and fundamentally alleviating global warming.
Model (4) is aimed to test the impact of environmental protection investment on carbon emissions in western China. According to the regression results, the primary term coefficient of environmental protection investment is 3.851, and the secondary term coefficient is -0.463, both of which are significant at the 1% level, indicating that with the increase in environmental investment in western China, the impact of environmental protection investment on carbon emissions changes from promoting to inhibiting. The coefficient of per capita disposable income among the control variables, which is 4.381 and is significantly positive at the 1% level, is higher than the influence coefficient of the national and eastern regions. These findings suggest that the economic growth in the western region has a stronger positive influence on carbon emissions than the national average and the east region. The lower level of economic growth in the western region and the relatively extensive economic development mode could be the cause. Therefore, economic growth will bring more energy consumption and pollution emissions, causing a significant rise in carbon emissions. Meanwhile, the coefficient of industrial structure's effect on carbon emission in western China is significantly negative at the 1% level, and the absolute value of the coefficient is much higher than the national level, indicating that the adjustment and upgrade of industrial structure in western China has a greater impact on environmental improvement and can promote carbon emission reduction.
By comparing model (2), model (3) and model (4), it demonstrates that the absolute value of the secondary term coefficient of environmental protection investment in the western region is the largest, followed by the central region and the eastern region. It indicates that while environmental protection investment has a relatively little impact on carbon emissions in east China, it has a more pronounced inverted U-shaped effect on emissions in the middle and west of China. The reason could be that the level of environmental protection investment in the east is higher than that in the central and western regions. Therefore, the increase of one unit of environmental investment in the center and west is more effective in inhibiting carbon emissions, which means environmental protection investment in the middle and western regions is more efficient. In view of this, the government should take into full account the industrial structure and economic development stages of various regions when formulating environmental protection investment policies, so as to effectively play the role of environmental protection investment on carbon emission suppression. From the central government's point of view, the central government should allocate resources in favor of the west and increase financial allocations for the environment in the western region, thus being able to more effectively improve the role played by environmental protection investment on carbon emission reduction. From the perspective of local governments, the central and western regions should adopt a high level of environmental investment policy, strengthen policy support for environmental investment, maximize the contribution of environmental investment to the development of green technologies and industrial transformation, and improve the efficiency of carbon emission reduction in the central and western regions; the eastern regions should adopt a more flexible and lenient environmental investment policy, focusing environmental policy on changing the mode of economic development, improving science and technology level, and fully utilize the leadership role that economically developed regions play in the effort to meet the "double carbon" target.

Conclusion
Based on the data of 30 provinces (excluding Tibet, Hong Kong, Macao and Taiwan) in China from 2009 to 2020, this paper empirically analyzes the impact of environmental protection investment on carbon emissions in different provinces by using the two-way fixed effect model, and draws the following research results:

Environmental protection investment has an inverted U-shaped impact on carbon emission intensity
The empirical research shows that environmental protection investment has a nonlinear inverted "U" effect on carbon emission intensity. When environmental protection investment is low, it contributes to the growth of carbon emissions; however, as investment in environmental protection increases and reaches a certain level, it can effectively inhibit carbon emissions. It demonstrates that the impact of environmental protection investment on reducing carbon emissions is closely related to the magnitude of that investment, and that only significant environmental protection investment can successfully encourage a reduction in carbon emissions.

There are regional differences in the impact of environmental protection investment on carbon emissions
The findings indicate that carbon emissions in eastern, central, and western China are affected differently by investments in environmental protection. The inverted "U" effect of environmental investment on carbon emissions is more pronounced in the central and western regions. This is reflected in the fact that the initial environmental investment in the central and western regions has a stronger effect on carbon emissions, while as the scale of environmental investment expands, the high level of environmental investment has a more significant inhibitory effect on carbon emissions compared to the east. It shows that there is regional variability in the effect of environmental investment on carbon emissions, and therefore the focus of environmental investment policies in different regions should be tailored to local conditions. Low carbon economy is a hot issue in China's current economic development. This paper empirically examines the impact of environmental protection investment on China's provincial carbon emissions, and obtains some useful conclusions, which provide guidelines for subsequent related studies and theoretical references for the formulation of China's environmental protection policies and help promote the practice of carbon emission reduction in China. However, given the availability of data, this paper only considers the environmental investment at the government level, but the actual environmental investment includes not only the government level, but also enterprises and private entities, which needs to be further explored by subsequent studies using a more comprehensive measure.