Sustainable Development in the Export Trade from a Symbiotic Perspective on Carbon Emissions, Exempliﬁed by the Case of Guangdong, China

: CO 2 emissions are increasing with the expansion of export trade. Against the backdrop of the prominent trend of decarbonization in the global economy, the question of how to rise to the occasion to maintain the advantages of international trade, as well as achieving sustainable growth in export trade, has become an urgent issue for us to consider. This paper uses empirical analysis to propose and establish an econometric model of the symbiosis between carbon emissions and export trade dependence, economic structural changes and clean technology changes, based on the environmental Kuznets curve and using time series data for Guangdong Province from 2000 to 2021. The study found that there is a long-term, stable equilibrium relationship between the scale effect and technology effect on carbon emissions, and a positive relationship between the structural effect and carbon emissions. The study then constructed a symbiotic system of exports and carbon emissions from a symbiotic perspective. The Lotka–Volterra MCGP model was used to measure the evolution of the export and carbon emission symbiosis system from the optimization of three perspectives: the scale and structure of energy consumption under the dual constraints of export trade and carbon emissions, the scale of export trade under the carbon emission constraints, and the scale of carbon emissions under the export trade constraints. The results show that there is considerable room for improvement in the structure of energy consumption and carbon emissions in the current Guangdong export trade process. At the same time, this improvement can be achieved by adjusting the energy consumption structure and improving the efﬁciency of the system without changing the scale effect, technology effect or structural effect.


Introduction
China's economic success since its reform and opening up can be considered a miracle in the history of the world's economic development, with its economy rising to the second largest in the world.Its development of foreign trade has also taken a leap forward since joining the World Trade Organization, helping China's economy to boom.China has also become the world's largest exporter by virtue of its unique advantages.Since the beginning of the 21st century, "greenhouse gases" have become a major concern for people all over the world, with climate disasters and accidents occurring frequently and having a huge impact on the ecological environment.China's economic take-off has been accompanied by the highest carbon emissions in the world.As a major manufacturing country, China's economy and trade are still growing in a sloppy manner and are facing serious problems of energy loss and pollution.
With the awakening of public awareness regarding environmental protection and the increasing demand for an ecological living environment, countries around the world are starting to pay attention to the control of carbon emissions.Some countries are trying to strike a balance between economic development and environmental protection, but the international community has different views on the sharing of responsibility for emissions reduction, especially between developed and developing countries, where conflicts are more prominent.Developed countries have a good economic foundation, relatively better-established environmental regulations, and stricter constraints on import and export enterprises, regulating products that do not meet environmental requirements by imposing high tax rates, such as a carbon tax.At the same time, the shift of high-emission industries to countries with relatively weaker environmental regulations due to resource endowments, production technologies and other reasons has led to a shift in carbon emissions from developed to developing countries.At COP15, China made it clear that its future energy consumption would continue to grow in line with its economic development and that an increase in carbon emissions was inevitable, but that it would do its part to contribute to the global carbon reduction by taking real-time measures to reduce emissions and effectively combat global warming.The carbon shift caused by the production of a large number of high-emission products in developing countries for export to high-income countries should be borne by the consumer countries, not the exporting countries that produce carbon-intensive products.

Literature Review 2.1. Carbon Emissions Hypothesis in Foreign Trade
The existence of comparative advantage has shaped the international division of labor, and the pollution haven hypothesis suggests that international trade, under the premise of free trade, will lead to carbon shifting from developed to developing countries [1].This hypothesis also suggests that industries with high carbon emissions will move from countries with strict environmental regulations to countries with relatively lax environmental regulations.Environmental factors can also be used as production inputs for enterprises.If a country has low environmental standards, it has a comparative advantage in producing resource-and pollution-intensive products because of its relative abundance of environmental resources, and the lower environmental costs make the prices of products competitive in international markets.Under conditions of complete free trade, the prices of products in the international market will converge and enterprises seeking to maximize profits will move to countries or regions with lower environmental standards in order to save costs, including environmental costs.Differences in environmental standards lead to differences in the cost of products, which will attract investment from foreign enterprises, and more and more highly polluting and high-consumption multinational enterprises will move to countries or regions with lax environmental policies; these countries or regions become "pollution refuges" or "pollution havens" [2].Strict environmental regulations are not a decisive factor, though they may have an impact on the relocation of highly polluting industries [3].
In the case of the environmental impact of NAFTA, it was found that as per capita income increased, environmental pollutants tended to rise and then fall, and that there was an inverted U-shaped relationship between the two [4], which was defined as the Environmental Kuznets Curve (EKC) [5].Later, some scholars explained the hypothesis from the perspective of international trade, i.e., that trade liberalization and foreign direct investment would make developing countries "pollution havens" for developed countries, so that developing countries are in the upward side of the Environmental Kuznets Curve, while developed countries are in the downward side of the curve [6].The relationship between trade openness, economic growth and the environment is consistent with the law of the Environmental Kuznets Curve [7].The results of a study based on a north-south trade model suggest that trade liberalization causes an increase in global pollution [8].General equilibrium pollution-trade models have been constructed to analyze pollution transfer, known as the "ACT theory" [9], which models scale, structural and technological effects and provides a theoretical basis for analyzing the environmental impact of trade [10].
The scale effect is the effect of foreign trade on carbon emissions by increasing the size of the economy and the level of domestic output of the trading country, while keeping the structure and technology of the economy constant.Foreign trade is one of the three driving forces of economic growth, and the expansion of the economy is driven by foreign trade activities, which in turn leads to the extraction and consumption of energy and therefore to a gradual increase in carbon emissions.In addition, in the course of trade, trade and transport activities also become a major source of pollution emissions.The burning of fossil fuels in the process of transporting goods by sea and air, which is largely powered by fossil fuels, results in significant carbon emissions.It is thus concluded that the expansion of foreign trade would increase carbon emissions, i.e., the effect of scale on carbon emissions would be positive.
The technology effect refers to the impact of foreign trade on the environment through the upgrading of technologies such as cleanliness, while the scale and structure of the economy remains unchanged.From a domestic perspective, trade activities stimulate economic growth and increase people's income levels, resulting in a stronger demand for a cleaner environment, which leads to a reduction in pollutant emissions through the introduction of relevant environmental policies and the improvement of low-carbon technologies.From an international perspective, on the one hand, foreign trade makes international markets more competitive, and in order to occupy a favorable position in the market, enterprises will take the initiative to accelerate technological innovation and improve production technology in order to improve production efficiency and reduce pollution and production costs.On the other hand, international trade activities generate technological spillover effects, i.e., technologically advanced countries spread clean technologies to technologically backward countries through international trade and reduce their pollutant emissions and improve energy efficiency.It is therefore generally accepted that the technological effects of trade openness will improve the environment and reduce carbon emissions, i.e., the effect of technological effects on carbon emissions will be negative.
The structural effect is the indirect impact that trading countries have on the environment through changes in industrial structure, while the scale of the economy and the level of clean technology remain constant.The international division of labor resulting from trade between countries around the world leads to the emergence of structural effects.According to Ricardo's theory of comparative advantage, when countries engage in international trade they take advantage of their factor endowments and concentrate on producing and exporting products in which they have a comparative advantage, while importing products in which they have a comparative disadvantage, so factor endowments influence the division of labor in each country, and the industrial structure of each country changes accordingly.For countries with relatively high environmental standards, carbon emissions can be seen as a relatively scarce factor.Conversely, in countries with lower environmental standards, carbon emissions are a relatively abundant factor, so that the carbon-intensive products they produce have a relative comparative advantage internationally, and the proportion of highly polluting industries in these countries increases accordingly, with higher levels of carbon emissions.In other words, if the carbon intensity of a country's comparative advantage product is higher than that of its comparative disadvantage product, the country's participation in international trade will have a negative effect on its own carbon emissions, and the structural effect will be negative.Otherwise, the structural effect will be positive.

The Relationship between Foreign Trade and Carbon Emissions
Research on the relationship between foreign trade and carbon emissions has attracted much attention from scholars at home and abroad, with most scholars using the scale of imports and exports to quantify the level of foreign trade.Some studies have found that the relationship between import and export trade and carbon emissions is positively boosted.The non-competitive input-output model analyzed the factors that contribute to changes in carbon emissions in international trade and concluded that both the trade structure and total volume of international trade contributed to the increase in carbon emissions [11]; the autoregressive model examined the drivers of per capita carbon emissions, such as the scale of China's imports and exports, and found that the increase in the scale of China's imports and exports positively contributed to the increase in per capita carbon emissions [12].Some analyses have suggested that foreign trade contributes to the reduction of carbon emissions [13,14].Some scholars have also examined the relationship between carbon emissions and foreign trade from the perspective of the scale, structure and technology of export and import trade development based on the object of export and import, and have tested the "pollution haven hypothesis" [15,16].The relationship between national trade and carbon emissions is positive in the long run in developing countries, but negative in developed countries, confirming the "pollution haven hypothesis".The development of foreign trade in middle-and high-income countries is conducive to reducing their carbon emissions, while increasing those in low-income countries [17]; the increase in the scale of imports and exports is not conducive to the improvement of environmental quality in developing countries [18].

Pathways for Carbon Reduction in Foreign Trade
One way for a country to reduce its carbon emissions is through industrial relocation.With the globalization of trade, countries are participating in the international division of labor based on their factor endowments and comparative advantages, playing different roles in the global value chain; the overall efficiency of the global economy has increased significantly [19].The development of international trade and the verticalized professional division of labor has led to a geographical separation of production and consumption.International trade has led to a shift in carbon emissions without addressing the issue of pollution [20].It has also led to deindustrialization in the countries of origin.Industrial shifts, employment shifts and carbon shifts are at the forefront of international trade research and are equally important for countries at different stages of development.
The global value chain perspective gives a deeper explanation of industrial shifts [21].Combining the method of calculating trade implied emissions in value added trade accounting with global value chains, a new environmental accounting system can be established.This accounting system allows value added and carbon emissions to be measured in different global value chain pathways.The distinction between simple and complex value chains provides an applicable method for carbon transfer analysis in the framework of global value chains [22,23].Continuous innovation in research methods for trade-embedded carbon emissions has driven the development of studies in emission balance and net trade emission shift [24,25].
If global value chains are restructured, with some degree of manufacturing repatriation from developed countries, will carbon emissions be affected?One study found a significant reduction in global CO 2 emissions if the return of multinational corporations led to anti-globalization [26].As international trade deepens, a geographical division of labor in production can be achieved, which in turn leads to a regional shift in global carbon emissions [27].In summary, developed economies in the upstream of the global value chain outsource high-emissions production to countries with lax environmental standards, which has the potential to increased global emissions, though it can reduce carbon emissions at home.
The impact of globalization, international trade and global value chains on carbon emissions is widespread and particularly strong in certain regions.Research findings confirm that the link between energy consumption and carbon pollution in East Asia is significantly influenced by the international division of labor [28].Of course, it is possible to reduce the total carbon emissions of trading countries if export trade is well utilized.For example, when trade between Japan and South Korea is conducted through simple global value chains, it not only helps to reduce carbon emissions in the two countries, but also effectively promotes employment [29].It is the ideal trade route.There is also something that can be achieved in the area of energy saving and emissions reduction from the national and industrial levels.For example, China should adjust its export trade structure according to the characteristics of implied carbon emissions in export trade to achieve low-carbon development [30].China's agricultural carbon emissions are growing slowly [31], and there is still room to improve low-carbon agricultural productivity.This also brings enlightenment for energy saving and emission reduction in other industries.
Existing studies have analyzed the carbon emissions of export trade based on the ACT theory and global value chain theory.These studies assume that variables such as export industry scale, industry structure, industry technological efficiency and export industry innovation chain location can be changed in the short term.This is theoretically feasible, but in practice it is difficult for most developing countries' export industries to upgrade their industrial structure, technological innovation and value chains in the short term.Therefore, this paper attempts to analyze the issue of carbon emissions in export trade from a different perspective.Export trade and carbon emissions are viewed as a symbiotic system, in which they affect each other.Export trade is analyzed from the perspective of the equilibrium of the symbiotic system of export trade and carbon emissions under certain carbon emission constraints.
The research objectives of this paper are set to break through the assumptions of classical studies that scale effects, technology effects and structural effects are all variable in the short term, in order to understand the relationship between exports and carbon emissions from a symbiotic perspective, and to find a path to sustainable development.The research in this paper is as follows: (1) Using time series data of Guangdong Province from 2000 to 2021, an econometric model of the symbiosis between carbon emissions and export trade dependence, economic structural changes and clean technology changes is proposed and developed based on the environmental Kuznets curve.(2) A symbiotic system of carbon emissions and export trade is constructed based on a population dynamics symbiotic relationship model (Lotka-Volterra model).( 3) The Lotka-Volterra MCGP model is used to measure the evolution of the symbiotic system of exports and carbon emissions from the optimization of three perspectives: the scale and structure of energy consumption under the dual constraint of export trade and carbon emissions, the scale of export trade under the carbon emissions constraint, and the scale of carbon emissions under export trade constraints.The research highlights of this paper include the construction of the Lotka-Volterra model of the symbiotic system of exports and carbon emissions and the optimization of the MCGP.

Methods and Data
The technical roadmap for this paper is shown in Figure 1, and the study used a combination of econometric and population symbiosis models to compare and analyze the relationship between export trade and carbon emissions.

Research Samples
As a pioneer of China's reform and opening up, Guangdong Province has been the number one province for foreign trade for the 36th year due to its superior geographical location and policy advantages.Over the past decade, the scale of Guangdong's foreign trade imports and exports has reached record highs, growing by 33.1% from CNY 6.21

Research Samples
As a pioneer of China's reform and opening up, Guangdong Province has been the number one province for foreign trade for the 36th year due to its superior geographical location and policy advantages.Over the past decade, the scale of Guangdong's foreign trade imports and exports has reached record highs, growing by 33.1% from CNY 6.21 trillion in 2012 to CNY 8.27 trillion in 2021, with an average annual growth rate of 3.2%, contributing 14% to the growth of China's foreign trade, according to data from the Guangdong Sub-Administration of the General Administration of Customs, China.Among these data, the total value of exports increased from CNY 3.62 trillion in 2012 to CNY 5.05 trillion in 2021, with an average annual growth rate of 3.8%.Shenzhen, Dongguan and Guangzhou have exceeded the threshold of CNY 1 trillion in export trade, and Guangdong contains three of the seven cities that have exceeded CNY 1 trillion in China [32].However, with the expansion of export trade, energy consumption in Guangdong Province has increased, and environmental pollution has become an increasingly serious problem, with carbon dioxide emissions increasing, which has become a major obstacle to the development of export trade in Guangdong Province.
In the face of the requirements of energy conservation and emission reduction in China, the trend of low carbonization in the global economy, the threat of carbon tariff barriers in developed countries in Europe and the United States, the pressure of upgrading the industrial structure of Guangdong and the increasing importance of foreign trade, Guangdong Province is facing many challenges, and how to maintain the advantages of international trade as well as achieve sustainable growth in export trade has become an urgent issue for us to consider.
This paper examines the relationship between export trade and carbon emissions in Guangdong Province for a total of 22 years, from 2000 to 2021, in order to provide suggestions for export trade policies, energy conservation and emission reduction.
As shown in Table 1, this article provides export data for Guangdong.In recent years, Guangdong's exports have struggled to achieve their previous high growth; however, in 2021 they still experienced high growth.
Table 1.Total import and export, export value and export growth rate of Guangdong Province in previous years.

Year Total Imports and Exports (CNY Billion)
Exports (CNY Billion) Export Growth Rate

Carbon Emission Measurement Methods
In the specific data on carbon emissions in Guangdong Province, there are no statistics on the level of carbon emissions, so the level of carbon emissions in Guangdong Province can only be measured through mathematical modelling.There are a number of estimation methods available in academia, and this paper uses energy consumption data for Guangdong Province to develop the following model to measure the emissions of direct carbon dioxide in Guangdong Province: where E i refers to consumption of energy i, and β i is the carbon emission factor of energy i.The carbon emission factor is the amount of carbon emissions per unit of energy produced during the combustion or use of a certain energy source.When measuring carbon emissions, each energy consumption unit must be converted to the standard statistic for energy metrics in China, i.e., standard coal.The carbon emission factors are based on the emission factors for each energy source published by the United Nations Intergovernmental Panel on Climate Change (IPCC), as shown in the table below.
As shown in Table 2, this article provides carbon emission coefficients for different energy sources.

Carbon Emission Measurement and Descriptive Analysis
According to the Guangdong Provincial Statistical Yearbook, the energy consumption data required for the calculations from 1990 to 2021 were selected, and the CO 2 emissions of three major energy sources, namely coal, oil and natural gas, were calculated using Equation (1), and the data and trend graphs of CO 2 emission levels in Guangdong Province were measured as follows.
As shown in Table 3, Guangdong has a large scale of carbon emissions, with annual carbon emissions accounting for about 11% of the country's total.The overall performance of Guangdong's carbon dioxide emission levels over the period 2000-2021 is on an upward trend.The year 2001 saw China's accession to the WTO and the rapid expansion of Guangdong's foreign trade, which led to a significant increase in carbon dioxide emissions, which grew by approximately 2.7 times over the decade 2001-2011.In 2011, since the "11th Five-Year Plan" put forward the policy of energy conservation and emission reduction, China has continuously issued relevant policies to actively comply with the low-carbon development of the world.Guangdong Province is one of the first low-carbon pilot provinces in the country, and from the "12th Five-Year Plan" to the "13th Five-Year Plan", and especially since the "13th Five-Year Plan", Guangdong has continued to solidly promote the work of addressing climate change.A number of plans and work programs in the area of greenhouse gas emission control, including "The 13th Five-Year Plan for Energy Conservation and Emission Reduction in Guangdong Province" and "Implementation Plan for the 13th Five-Year Plan for the Control of Greenhouse Gas Emissions in Guangdong Province", have been released, and significant results have been achieved in low-carbon emission reduction, with the growth rate of carbon emission levels slowing down.However, CO 2 emissions show a steep increase from 2019 to 2021, from 160,051,100 tons in 2019 to 200,476,600 tons in 2021, with a growth rate of about 25%.In order to investigate the relationship between export trade and carbon emissions in Guangdong Province, the following carbon emission analysis model is constructed in this paper: where Y denotes the historical carbon emissions of Guangdong Province, calculated according to the carbon emission measurement function.
EX indicates the export trade dependence of Guangdong Province, which is obtained by dividing the total export trade by GDP.
S represents the change in the structure of the economy, derived using the share of the secondary sector in GDP.
T denotes clean technology change, i.e., energy consumption intensity, derived using total energy consumption divided by GDP.α 1 , α 2 and α 3 denote the influence weight of each economic factor on carbon emissions, respectively; all data are obtained from Guangdong Statistical Yearbook.
As mentioned in the previous section on the mechanism of influence, the scale effect refers to the impact on carbon emissions by increasing the size of the economy and the level of domestic output of the trading country, so it is more appropriate to use export trade dependence as an explanatory variable than simply the volume of export trade or gross product, denoted by EX.The structural effect refers to the indirect impact of exports on the environment through changes in the structure of the economy, hence the use of S as the explanatory variable for changes in economic structure.The technology effect refers to the impact on carbon emissions through human demand, the international division of labor, increased competitiveness and technological spillovers.Considering the availability of data, this paper uses total energy consumption divided by GDP as a proxy for technological change in energy, denoted by T. Due to the possibility of heteroskedasticity in the data, in order to eliminate the effect of heteroskedasticity, all data in this paper are taken as natural logarithms, and therefore the logarithm of each variable is used in the analysis process.
where α 0 is the constant term, α 1 , α 2 and α 3 are the parameters to be estimated, δ is the residual term and i is the period 2000-2021.

OLS Model Estimation and Significance Test
This paper used regression analysis and the OLS estimation of Equation (3) using Eviews12, and the regression results are as follows.
According to the estimation results of the model, the model fit relatively well, with R 2 close to 1.The T and F values of each variable passed the significance test, which indicates the significant influence of export trade dependence, economic structure and clean technology changes on carbon emissions in Guangdong Province.
As this paper selected time series, which are mostly unsteady and have unit roots, unit root tests were carried out to select smooth variables for regression to avoid pseudoregression in the regression equation.In this paper, Eviews12 was used to select the ADF test to determine whether each series was smooth.The results of the ADF test are shown in Table 4 below.From the ADF test results in Table 4, it can be seen that the original series was only stationary for LNEX, i.e., the ADFs of the three variables, carbon emissions, economic structure and clean technology change, were all greater than their critical values, all contained unit roots, and the series was non-stationary, except for foreign trade dependence.The results of the first difference unit root test on each variable showed that the first difference series of LNY was stationary at the 10% significance level, and the ADF test values of LNEX, LNS and LNT were less than the 5% critical value, and their first difference series were stationary at the 5% significance level, i.e., the null hypothesis that the series had unit roots was rejected at the 5% significance level.This leads to the conclusion that all four variables are integrated of order 1.
To ensure that the causality of the regression models constructed from the individual variables was not a pseudo-regression, this paper conducted a cointegration test.Cointegration can be interpreted as a stable equilibrium relationship between variables over time.The main methods of a cointegration test are the Johansen test and the E-G two-step approach.As the E-G two-step approach is only applicable to the estimation and testing of cointegration between two variables, the Johansen test was selected since this paper studies the cointegration of four variables, namely carbon emissions, export trade dependence, economic structure and clean technology change.In the unit root test above, the four variables were integrated of same order, satisfying the conditions of the cointegration test.The table below shows the results of the Johansen test using Eviews12.
From the results of the Johansen test in Table 5, it can be concluded that both the maximum eigenvalue test and the trace test had two cointegration equations at the 5% significance level, indicating the existence of a cointegration between carbon emissions and export trade in Guangdong Province from 2000 to 2021.Meanwhile, the standardized coefficient cointegration function for each variable can be derived from the results generated by Eviews12, as shown in the following table.As shown in Table 6, from this cointegration function it was concluded that there was a stable long-term equilibrium relationship between carbon emissions and changes in export trade dependence, economic structure and clean technology in Guangdong Province.The Johansen test for standardized coefficients showed that the coefficient of influence of export trade dependence on carbon emissions in Guangdong Province was 0.53, indicating that there was a positive relationship between export trade dependence and carbon emissions in Guangdong Province; i.e., for each percentage point increase in export trade dependence, carbon emissions in Guangdong Province increased by 0.53 percentage points, with no change in economic structure and clean technology.This shows that export trade in Guangdong Province increases carbon emissions.As mentioned above, the effect of export trade dependence on carbon emissions represents a scale effect, so the scale effect of Guangdong's export trade is negative.Guangdong's carbon emissions showed a negative correlation with economic structure, indicating that the economic structure has been conducive to a reduction in carbon emissions over the period 2000-2021, and that changes in the economic structure have had a greater impact on carbon emissions, with an impact coefficient of 3.79.This indicates that the economic structure of Guangdong Province has been optimized and adjusted, the downsizing of highly polluting production sectors reduces carbon emissions, and participation in international trade has a positive impact on carbon emissions, i.e., the structural effect of export trade in Guangdong Province is positive.
Clean technology change and carbon emissions in Guangdong Province show a negative correlation, with the coefficient of influence of clean technology change being −1.66 and the two changing in opposite directions, indicating that for every unit increase in clean technology change, carbon emissions will subsequently decrease by 1.66 units, with no change in export trade dependence and economic structure.Therefore, the energy technology optimization of Guangdong enterprises reduces pollutant emissions and lowers carbon emission levels, and the technology effect has a negative impact on carbon emissions.

Management Insights
Guangdong's export trade is growing rapidly and its high dependency on export trade has played an important role in driving Guangdong's economic development, but the resulting environmental pollution is becoming increasingly serious, with carbon emissions rising every year.Under the pressure of the global trend towards low carbon emissions, it has become an inevitable path for Guangdong Province to maintain its advantages in international trade and to achieve sustainable growth in export trade in harmony with environmental development.The ways to achieve low-carbon sustainable development of Guangdong's export trade include: (1) optimizing the export structure, (2) improving energy-saving and emission reduction technologies, and (3) introducing strong environmental protection measures.
The economic structure of Guangdong's exports has a positive impact on carbon emissions with a high coefficient of influence, so optimizing the export structure plays an important role in reducing energy consumption and carbon emissions.As a major economic province, Guangdong should actively make use of its economic achievements to optimize its economic structure, achieve a gradual shift from labor-intensive industries to capital-intensive industries, especially knowledge-and technology-intensive industries, and vigorously develop the tertiary industry, especially the high-productivity and lowpollution high-tech production sector.It should also take advantage of capital, talents and policies to carry out green trade and strive to master the high-end of the green industry chain at an early date.In the structure of export commodities, the exports of high carbon emission production sectors such as the chemical industry and the metal smelting and processing industry should be strictly controlled, and the proportion of exports of highly polluting production sectors such as paper and textile should be gradually reduced, and the environmental supervision of them should be increased.Therefore, encouraging the export of tertiary industries and appropriately reducing the proportion of exports of secondary industries can optimize the export structure, eliminate backward production capacity and accelerate the upgrading of industrial structures, which can reduce energy consumption and lower carbon dioxide emissions.
The innovation of energy-saving and emission-reducing technologies is the key to achieving lower carbon emissions in export trade, actively developing high-yield, lowpollution knowledge and technology-intensive products and mastering the upper reaches of the industrial chain.Firstly, we should attach importance to the development of lowcarbon technologies, take advantage of Guangdong Province as a large foreign trade province, actively utilize foreign investment and allow technological spillovers while carrying out import trade activities.In addition, we should encourage enterprises to acquire energy-saving and emission reduction technologies and intellectual property rights through investment and cross-border mergers and acquisitions, and vigorously introduce and absorb technologies from developed countries.Furthermore, we should attach importance to the cultivation of high-end technical talents, create conditions for the introduction of talents and optimize the environment and mechanism for the introduction of talents.Finally, we should encourage export enterprises to create their own brands, drive exports of their own branded high-tech products, improve the conversion rate of scientific and technological achievements, and build industrial incubators.
In view of the irreversible globalization of the economy, Guangdong Province should actively participate in international cooperation for low-carbon economy and take the initiative to study the low-carbon technical norms and standards of trading countries to ensure that the products exported meet the norms of partner countries in order to circumvent their green barriers and trade protectionism.The Guangdong government should also give full play to its governmental functions and give policy preferences to environmentally friendly enterprises to guide them towards low-carbon production.They can also make clever use of the tariff system to leverage its differentiated export tax rebate policy for different product exports.The government should raise export tariffs on carbonintensive products and reduce or even abolish export rebates to a certain extent, lower export tariffs on low-carbon products and raise export rebates appropriately.In addition, tariff systems such as carbon tariffs and energy taxes can be implemented following the example of the European Union.Moreover, the government should also introduce strong environmental protection measures, step up the enforcement of environmental protection, raise environmental standards in Guangdong Province to prevent it from becoming a "pollution haven" for other countries or regions, and improve laws and regulations on carbon dioxide emissions reduction to provide legal protection for the development of a low-carbon economy.

Symbiotic Systems for Export Trade and Carbon Emissions
Export trade and carbon emissions form a symbiotic system.The development of export trade increases carbon emissions, and increased carbon emissions influence the attitudes of stakeholders from all sectors of society (governments, communities and businesses) towards trade policies.When carbon emissions are within a relatively small threshold, stakeholders are more tolerant of carbon emissions and will be more inclined to promote export trade to increase economic benefits.When carbon emissions exceed a certain threshold, stakeholders are less tolerant of carbon emissions and are more inclined to promote energy efficiency and emission reduction to increase socio-ecological benefits.Export trade and carbon emissions form a complex interactive and symbiotic system.This symbiotic system can be explained by the Lotka-Volterra (LV) system in ecology.
The Lotka-Volterra (LV) power system, consisting of the scale of export trade (P1) and the scale of carbon emissions (P2), is as follows: Equation ( 4) is known as the Lotka-Volterra (LV) system.β 12 is the impact factor of carbon emissions on export trade.When β 12 > 0, carbon emissions have a synergistic effect on export trade, and the increase in carbon emissions is within the limits of the socio-economic system.When β 12 < 0, carbon emissions have a competitive, disincentive effect on export trade.The growth of carbon emissions is beyond the socio-economic system's capacity.
β 21 is the influence of export trade on carbon emissions.When β 21 > 0, the effect of export trade on carbon emissions is synergistic and the growth of export trade accelerates carbon emissions.When β 21 < 0, the effect of export trade on carbon emissions is a competitive disincentive effect.The development of export trade influences the industrial and product structure, and this restructuring is conducive to the reduction of carbon emissions.
LV models are based on logistic models of individual species that take into account the dynamic growth of two or more entities competing and co-occurring simultaneously in an ecosystem [33], and can accurately describe competition and co-occurrence between populations.LV systems can determine the influence of populations in the evolution of the whole ecosystem [34], and therefore have better data-fitting and predictive expressions [35].
The classical Lotka-Volterra model is a differential dynamics system used to model the dynamics of relationships between populations in ecology.Later, economists introduced it to fluctuations in macroeconomic growth and to market competition of moderate size and scope.According to biological principles, there are multiple functional relationships, facilitating or inhibiting, between populations of organisms.There is also a relationship between export trade and carbon emissions for their own survival and development, facilitating or inhibiting the diffusion process of another subject.LV models for the growth of two or more populations are differential dynamical systems that simulate the dynamic relationships between populations.
Based on β value, the type of interaction between variables can be determined [36] as follows.
The Lotka-Volterra system econometric model is shown below.
Assume that γ 1 = α 1 .In general, γ 1 > 0, representing the synergy within a group referred to as the internal synergy coefficient.When γ 1 > 1, the synergistic effect is significant.Assume that γ 11 = − α 1 K 1 , and generally γ 11 < 0, representing the competitive effect within a population, which is known as the internal competition coefficient or the population density inhibition coefficient.Assume that γ 12 = α 1 β 12 K 2 , denoting the effect of population 2 on population 1.The sign properties are the same as for β 12 .
By the same token, we can obtain the following: Assume that γ 2 = α 2 .In general, γ 2 > 0, representing the synergy within a group referred to as the internal synergy coefficient.When γ 2 > 1, the synergistic effect is significant.Assume that γ 22 = − α 2 K 2 , and generally γ 22 < 0, representing the competitive effect within a population, which is known as the internal competition coefficient or the population density inhibition coefficient.Assume that γ 21 = α 2 β 21 K 1 , denoting the effect of population 1 on population 2. The sign properties are the same as for β 21 .
An equilibrium point in the evolution of a population means that the output of both sides has reached a maximum and remains stable.The following stability analysis is presented.In the steady state, the equation is: The equilibrium point is: Because of the interdependence between these two populations, the population size should not be zero.Point (P4) corresponds to the size of population 1 (P1) and population 2 , respectively.Additionally, the conditions for a meaningful (P4) are: By solving the above equation, a unique non-negative solution can be obtained.The equilibrium solution is: This equilibrium solution indicates the equilibrium state of a stable system.The equilibrium state in a natural ecosystem predicts the harmonious co-existence of two populations, with sufficient system resources to support the development of both populations and a mutually beneficial co-existence between the populations.The equilibrium state in a socio-economic system means that the two enterprise populations effectively support the development of the related populations while developing themselves, and that a lasting symbiotic relationship can be achieved within a certain range of development and innovation.This symbiotic relationship is well documented in the study of industrial chains, innovation chains and value chains.
Table 7 shows that the intrinsic growth rate of total carbon emissions (0.125) was higher than that of export trade (0.093).The growth rate of total carbon emissions was higher than the growth rate of export trade in the same period, which indicates that export growth in Guangdong Province is accompanied by high energy consumption and high carbon emissions, which is not in line with the green growth concept.The negative internal disincentive coefficient for export trade indicates that the export trade industry is highly competitive internally.Carbon emissions have a positive contribution towards export trade, and total carbon emissions are converted using total energy consumption, which indicates that energy consumption has a positive effect on exports.Based on the comparative relationship between the number of existing system equilibrium points we can find that: Based on the above equilibrium value proportional relationship, the equilibrium value of export trade was measured using the actual observed data of carbon emissions for all years, and the equilibrium value of export trade is shown in the table below.
As shown in Table 8, the equilibrium value of export trade shows an increasing trend from year to year.Although there is a difference between the equilibrium and actual values, the difference is within a more reasonable range and the trend between the two can be shown in the graph below.As shown in Figure 2, the trend in the equilibrium point of export trade is essentially the same as the trend in the actual value of export trade.There is a difference between the equilibrium point and the actual value, but this difference gradually decreases.The equilibrium values of export trade basically reproduce the symbiotic relationship of the system.As shown in Figure 2, the trend in the equilibrium point of export trade is essentially the same as the trend in the actual value of export trade.There is a difference between the equilibrium point and the actual value, but this difference gradually decreases.The equilibrium values of export trade basically reproduce the symbiotic relationship of the system.

Optimization of the Symbiotic System of Export Trade and Carbon Emissions Based on LV MCGP Model
In order to analyze in more detail the energy consumption structure of export trade and its optimization under carbon emission constraints, this paper constructed a Lotka-Volterra model of the export trade and energy symbiosis system, with the model parameters shown in the table below.
Table 9 gives the regression results of the Lotka-Volterra model of the export trade and energy symbiosis, based on which the following equations for the symbiosis can be obtained.

Optimization of the Symbiotic System of Export Trade and Carbon Emissions Based on LV MCGP Model
In order to analyze in more detail the energy consumption structure of export trade and its optimization under carbon emission constraints, this paper constructed a Lotka-Volterra model of the export trade and energy symbiosis system, with the model parameters shown in the table below.
Table 9 gives the regression results of the Lotka-Volterra model of the export trade and energy symbiosis, based on which the following equations for the symbiosis can be obtained.
where N 1 is the total export trade (in CNY billion), N 2 is coal consumption (in 10,000 tons of SCE), N 3 is oil consumption (in 10,000 tons of SCE) and N 4 is natural gas consumption (in 10,000 tons of SCE).The Lotka-Volterra model describes the operation mechanism of export and carbon emission symbiotic systems.The preferences and evolutionary paths of the existing system's operation can reveal the possibilities for energy saving and emission reduction under existing conditions.In this paper, the Lotka-Volterra MCGP model was used for system optimization, which can embed the export and carbon symbiosis expressed by Lotka-Volterra into the MCGP model, effectively combining the advantages of the Lotka-Volterra and MCGP models [37][38][39][40].
In this section, the Lotka-Volterra MCGP model was used to measure the evolution of the export and carbon emission co-generation system from the optimization of three perspectives: (1) the scale and structure of energy consumption under the dual export trade and carbon emission constraints, (2) the scale of export trade under the carbon emission constraints, and (3) the scale of carbon emissions under the export trade constraints.The problem of optimizing the scale and structure of energy consumption under the dual constraints of export trade and carbon emissions was examined.The results of the systematic evolution of the energy consumption structure were first assumed under the condition that the scale of export trade and total carbon emissions of the symbiotic system remained constant in value.In this scenario, the focus was on the inherent energy consumption preferences of the symbiotic system.The Lotka-Volterra MCGP model with the dual export trade and carbon emission constraints is shown below: Constraints : The results of the model calculations are shown in the following table.
As shown in Table 10, the Lotka-Volterra MCGP model was relatively well adapted, and the results of the system evolution were successfully calculated.The most significant change in the evolutionary results was the "optimization" of gas consumption.This is not to say that natural gas is not a good energy source, but that coal and oil consumption are sufficient to meet the energy consumption of the symbiotic system without any change in exports or carbon emissions.It follows that the current energy consumption structure of China's export trade in Guangdong is essentially dependent on high carbon emitting energy sources such as coal and oil products.This high-emission energy consumption structure is not conducive to green and sustainable development.

Optimization of Export Trade Scale under Carbon Emission Constraints
The problem of optimizing the export trade scale under carbon emission constraints was examined.The results of the systematic optimization of the export trade scale were first assumed under the condition that the value of total carbon emissions in the symbiotic system remains unchanged.In this scenario, the focus was on the space for export trade enhancement under the carbon emission constraint in the symbiotic system.The Lotka-Volterra MCGP model under the carbon emission constraint is shown as: The results of the model calculations are shown in the following table.
As shown in Table 11, under the condition of limiting total carbon emissions, the share of natural gas consumption increased significantly, and the consumption of oil products occupied the major share of energy consumption.At the same time, the share of energy consumption accounted for by coal, a high carbon-emitting energy source, decreased significantly.Under the carbon emission constraint, coal is the main target for energy substitution.Another interesting result of the model optimization is that coal remained the main source of energy consumption in the 2000 and 2001 optimization results.This suggests that coal can still meet the energy consumption and carbon emission requirements Under the existing carbon emission constraint, the optimized value of exports showed a substantial increase, which indicated that there was still room for Guangdong's export trade to improve.Although in the real world there is not as much room for export improvement as in the model optimization results, this result is still relevant.It also shows that Guangdong's carbon emissions are still relatively inefficient, and that exports and economic growth are still rough.

Optimization of the Carbon Emissions Scale under Export Trade Constraints
The problem of optimizing the carbon emissions scale under export trade constraints was explored.Firstly, the results of the systematic optimization of the carbon emissions scale were assumed under the condition that the value of total export trade in the symbiotic system remained unchanged.In this scenario, the focus was on the scope for reducing carbon emissions in the symbiotic system.The Lotka-Volterra MCGP model with export trade constraints is shown below.

Discussion
In contrast to classic papers in the field of international trade and carbon emissions, this paper offers a fresh perspective.At the theoretical level, this paper constructed a symbiotic system of exports and carbon emissions based on the symbiotic system theory in ecology and the population dynamics approach.In this symbiotic system, exports and carbon emissions were not simply opposite to each other, but had an interactive symbiotic relationship.The development of exports inevitably leads to carbon emissions, and higher carbon emissions will inhibit export development.It is important to find a path for the harmonious development of both.At a practical level, it is difficult for many developing countries and economies to achieve industrial upgrading, structural adjustment and energy technology improvements in the short term without mastering the advantages of innovation.The classical theoretical vision of energy efficiency and emission reduction may not be achievable in developing countries.Therefore, it makes sense to explore sustainable development based on the realities of science, technology and industry.
There is a wealth of detailed analysis in existing research on the non-linear characteristics of EKC models.For example, some papers consider whether the relationship between variables in the EKC model is inverse U-shaped or N-shaped.It is therefore necessary to consider whether these characteristics affect the Lotka-Volterra model.In scientific practice, the graphs of the Lotka-Volterra model, depending on the parameter coefficients, take on different shapes, including the inverse U-shape and the N-shape.Therefore, the shape of the EKC model is not contradictory to the graph of the Lotka-Volterra model.As this paper focuses on the analysis of the symbiotic relationship between foreign trade and carbon emission systems and the optimization of emission reductions, the graphical characteristics of the model were not analyzed.

Results
This paper proposed and developed an econometric model of the correlation between carbon emissions and export trade dependence, economic structural change and clean technology change based on the Environmental Kuznets Curve using the time series data of Guangdong Province from 2000 to 2021, and found that they had a long-term stable equilibrium relationship, with the scale effect and the technology effect having a negative impact on carbon emissions, and the structural effect showing a positive correlation with carbon emissions.The study then constructed a symbiotic system of exports and carbon emissions from a symbiotic perspective.The Lotka-Volterra MCGP model was used to measure the evolution of the export-carbon symbiotic system from the optimization of three perspectives: the scale and structure of energy consumption under the dual constraints of export trade and carbon emissions, the scale of export trade under the constraints of carbon emissions, and the scale of carbon emissions under the constraints of export trade.The results showed that there was considerable room for improvement in the structure of energy consumption and carbon emissions in the current Guangdong export trade process.At the same time, this improvement could be achieved by adjusting the energy consumption structure and improving the efficiency of the system without changing the scale effect, technology effect and structural effect.

Management Inspiration
Government also plays a very important role in this research area.The government can guide industry towards green development by strengthening environmental regulation and through the use of legal and economic instruments.Due to the externalities of environmental costs and a certain degree of market failure, it is essential for the government to strengthen supervision and management.It is important to continuously improve the construction of environmental regulations and to strengthen their enforcement.The relevant market access requirements should be raised, the development of pollution-intensive industries should be strictly restricted, and enterprises that do not meet environmental protection standards should be urged to rectify or even be shut down.Corresponding incentives should be developed for environmental industries.The implementation of economic instruments such as a carbon tax should be studied urgently, and the price mechanism should be brought into play to reduce pollution emissions.The establishment of a carbon emissions trading market should be accelerated, and the establishment of a carbon financial system should be studied, including carbon funds, carbon insurance and carbon securities.Active participation in relevant international cooperation should be continued.As a major world economic and trade power, China should continue to actively participate in international environmental cooperation, in the development of international environmental and trade standards, and in the United Nations Framework Convention on Climate Change.

Research Limitations
In this study, Guangdong Province was used as the main research sample, which meant the study was a bit insufficient and lacking a comparative study with other provinces in China.As with the existing studies, due to the availability of data, the research in this paper was limited to the area of trade-induced carbon emissions, and failed to address the relationship between industrial structure, consumption structure, foreign trade structure and carbon pollution.Given the reality of developed countries shifting part of their production to developing countries so as to maintain their consumption structure, it is important to explore consumption-based measures of trade-induced pollution emissions, and thus to study the environmental impact of trade across borders, for a more comprehensive understanding of the environmental impact of trade.This should be a feasible direction for future research when conditions allow.In future research, comparative studies of different provincial regions will be included to expand the research sample and increase the practical value of the study.

Figure 2 .
Figure 2. Trends in export trade equilibrium points.

Figure 2 .
Figure 2. Trends in export trade equilibrium points.

3. 4 . 1 .
Energy Consumption Scale and Structure Optimization under the Dual Constraints of Export Trade and Carbon Emissions

Table 2 .
Energy carbon emission factor table.
Data source: IPCC Carbon Emissions Measurement Guidelines.

Table 3 .
Coal, Oil and Natural Gas Consumption and Total Carbon Emissions in Guangdong Province, 2000-2021.
3.2.An Empirical Study on the Relationship between Export Trade and Carbon Emissions3.2.1.Econometric Model Construction and Description of Variables
Note: (1) D denotes variable first order difference.(2) ** indicates rejection of the null hypothesis at the 5% level of significance, *** indicates rejection of the null hypothesis at the 10% level of significance.(3) (C T K) where C denotes the constant term (C for yes NC for no), T denotes the time trend (T for yes NT for no) and K denotes the optimal lagged order determined by the AIC criterion.
Note: * indicates rejection of the null hypothesis at the 5% level of significance.

Table 6 .
Johansen test for the standardized coefficient cointegration function.

Table 8 .
Export trade equilibrium point measurement over the years.

Table 9 .
Export trade and energy coexistence system parameters.

Table 10 .
Symbiotic system parameters under the dual constraints of export trade and carbon emissions.