# Empirical Analysis of the Relationship between Renewable Energy Consumption and Economic Growth Based on the Grey Markov Model

Authors: Chao Liu
Journal: Journal of Mathematics
 (2022)

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## Abstract

According to the global renewable energy attraction index, countries (regions) are selected as the analysis samples, and then the function model is improved. Considered as independent input factors into the function, the sample countries and the data are analyzed for stationarity and cointegration relationship test. With the excessive use of nonrenewable energy and the frequent occurrence of nuclear safety problems, it is imperative to develop renewable energy under the background that governments all over the world advocate energy conservation and emission reduction. By formulating active renewable energy industrial policies, governments and enterprises can not only enable the government to achieve the goal of energy conservation and emission reduction but also promote economic development to a certain extent. 34 countries (regions) were selected as analysis samples, and then the production function model was improved. Renewable energy and nonrenewable energy were considered as independent input factors into the Cobb-Douglas function, and the panel data model was established by using the economic data of sample countries from 1994 to 2014.


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## Body

## 1. Introduction

With the global economy and people’s overexploitation of the Earth’s resources, mankind is accelerating the destruction of the natural environment on which it depends, which makes governments have to pay attention to formulating effective measures. Some countries have tried to develop nuclear power generation in recent years, so as to achieve the dual effects of emission reduction and cost reduction. However, after the continuous occurrence of nuclear disasters and nuclear threats in many parts of the white world, many countries have gradually realized the potential harm of nuclear energy and began to turn their attention to the field of safer, cleaner, and reliable renewable energy, which makes renewable energy usher in a broader space for development [1–6].The deterioration of the ecological environment and excessive consumption of resources have been the hottest topics in recent years. The Earth environment on which human beings depend has been destroyed, and the material basis of national economic development has been excessively consumed. The existing resources have been unable to meet the needs of human rapid development. Throughout modern human history, from the second industrial revolution, human economic development mostly depends on the consumption of fossil energy. But this is at the cost of ecological environment and resource depletion. If mankind wants to change this severe situation, the most important thing is to change the current energy structure. As an alternative to nonrenewable energy, renewable energy has attracted more and more attention from the whole society because of its nonpollution and renewability. In this context, feasible suggestions or optimization directions should be put forward to promote the adjustment and transformation of energy structure and boost the new driving force of economic growth [7–12].Fossil energy, which accounts for a large proportion of the energy consumption structure, is generally nonrenewable and will be exhausted with the development and utilization of human beings. Nuclear disasters occur frequently in many regions of the world. In 2011, there was a global shocking “Fukushima nuclear leak.” Once a nuclear accident occurs, it leads to a global crisis. In addition, there are problems of local energy supply and resource depletion, energy security problems caused by the dependence of world economic, financial, and politically sensitive areas on imported oil, and the peak oil theory predicts that the global oil supply will begin to run out. Therefore, it forces national policymakers to put forward effective policies to promote new energy to replace traditional energy. Therefore, renewable energy with sustainability and belonging to clean energy has stepped onto the stage of global energy consumption, providing a new direction for energy transformation and meeting the growing energy demand with the increase of economic volume, which is conducive to sustainable economic growth. To explore the economic growth, measurement variables Gross Domestic Product (GDP), Gross National Product (GNP), income, employment, capital stock, and energy prices have been the subject of research by experts in economics and energy in recent years. However, scholars have not reached a consensus on the direction of the change of the relationship between the two, that is, whether energy consumption promotes economic growth or the increase of economic growth leads to the increase of energy consumption, or whether there is a two-way causal relationship. A large amount of foreign research data shows that, with different countries selected and different test methods, as well as data and practice interval, the conclusions will be different.The excessive consumption of nonrenewable energy makes the carrying capacity of the ecological environment gradually decline, which seriously hinders the sustainable economic development of all countries in the world. With the trend of vigorously implementing energy-saving and emission reduction measures all over the world, the renewable energy industry, as a clean and pollution-free characteristic, gains more and more attentions by the enterprises and scholars. In this context, it is of great practical significance to deeply try to put forward relevant energy policy suggestions for government departments in Figures1 and 2 [13–19].Figure 1
Share of global energy consumption structure.Figure 2
Energy consumption structure.The proportion of fossil energy consumption in the world has been declining year after year and, even in Britain, the EU country, has ushered in the end of coal consumption. As the birthplace of the second industrial revolution, Britain has changed from a country dependent on high fossil energy to a coal-free country. In just a few hundred years, great changes have taken place in the energy consumption structure, which personally proves the development potential of renewable energy. From the data, the proportion of renewable energy consumption has increased year by year worldwide, reaching 10.1% in 2019. Although the share is not high so far, its growth accounts for nearly one-third of the growth of primary energy. To a certain extent, hydropower consumption occupies the nonrenewable energy consumption market and plays a leading role in the reform of energy structure. The second is wind energy and biomass energy. Although their overall status is not high, they are developing rapidly and the growth rate is considerable, reaching an average annual growth rate of 10%. The growth rate of natural gas, oil, and coal is lower than the ten-year average growth rate. It decreased by 1.6% year on year, from 71.2% in 2012 to 61.8% in 2019, which plays a key role in reducing carbon dioxide emissions. The consumption proportion of hydropower and other renewable energy sources has increased year by year, especially renewable energy sources other than hydropower. The growth rate of consumption proportion in 2019 reached a record high of 33%. China’s energy structure continues to be optimized and is the world’s largest renewable energy application market.Since 2017, domestic scholars’ studies based on time series have mostly focused on a specific province or region. For example, Guo Jing and Wang Tao divided China into eastern, central, and western regions and selected data from 1990 to 2014 for empirical analysis and concluded that energy consumption has a certain dynamic contribution rate to economic growth. The conclusion was that regional economic growth has obvious nonsynchronicity. Yang Xiaoyu and Zhou Dan analyzed the energy and economic data from 1978 to 2015 in Jilin Province.The survival of human beings and the development of society are inseparable from energy; now the growth of human demand for energy and the increasing reduction of energy form a contradiction. Energy is divided into renewable energy and nonrenewable energy. The former mainly includes coal, oil, and natural gas, while the latter is mainly solar energy, wind energy, and biological energy in nature. Due to the high cost of the production of renewable energy under the current technological level, the lack of easily accessible nonrenewable energy such as coal, oil, and natural gas is increasingly prominent. It is obvious that it is urgent to build an energy-conserving society.The evolution of industrial structure is mainly determined by the needs of human society. In the early stage of human development, the most important need is to solve the problem of food and clothing, so the primary industry was almost all of the human activities at that time. With the development of human society, people began to pay attention to the development of the industry. The industry not only enriches people’s life but also makes the economy grow significantly and people’s living standards improve significantly. British economists Petty and Clark found that different industrial structures correspond to different national income and economic development. It can be said that industrial structure is the key to economic development, so it is particularly important to study the evolution and optimization of industrial structure. At present, China’s economy has entered a new stage of development, transforming from the high-speed development stage to the medium-high-speed development stage and from focusing on the speed of development to focusing on the quality of development to reduce the supply side of the low-capacity stage. Therefore, China’s industrial structure is changing constantly to meet the needs of economic development. Under different economic conditions, scholars around the world are struggling to find the influencing factors of economic growth; energy consumption as an important factor is seen as the driving force of economic growth, but the energy consumption is a relatively new factor; different countries in different sample interval where the relationship is not stable so, in most cases, energy consumption is not factored into economic growth models.As one of the core contents of macroeconomic research, economic growth theory has always been one of the research fields that the government and scholars focus on. Reviewing the development history of economics, classical economists believe that the accumulation of material capital is the fundamental driving force to promote economic growth, and the influencing factors of economic growth only lie in two aspects: capital accumulation and labor input. However, the view of neoclassical economists is that the key factor to promote contemporary economic growth lies in technological progress. At the same time, when studying the theoretical model of economic growth, not only consider the two factors of capital and labor but also consider resource consumption as a separate input factor into the theoretical model, not just as a part of the capital [20–24].This paper introduces the concept, characteristics, principle, process, and testing method of grey theory by analyzing the previous research theory and puts forward a grey model and verifies the feasibility of the grey theory method by an example. Considering the theoretical model of economic growth, this paper constructs independent variables including renewable energy consumption, nonrenewable energy consumption, labor input, and total fixed capital formation. GDP is an improved function of the dependent variable, so the corresponding empirical analysis is carried out. Selecting economic data of several countries for 21 years, the panel data analysis method is used to conduct regression analysis of output elasticity in the long run, and the individual fixed-effects model is established to analyze the impact of each explanatory variable change on the explanatory variable change.


## 2. Grey System Theory

This theory has been widely used in military, economic, and engineering fields. In cybernetics, color is often used to express the certainty of information. It tries to explore the internal trend through the research and development of known information. Due to the complexity and uncertainty of reality, the information of things people want to understand is often uncertain, which determines that the grey system theory will have a broad development space. Grey prediction refers to the use of grey system theory to predict some events. The grey prediction method refers to the method of predicting the system containing uncertain information [12, 25–28].Andrey Markov is a world-famous Russian mathematician. He first studied and proposed a general model that can solve the changes of natural laws by using mathematical methods and mathematical models in 1906. Later, people called this model Markov chain. At the same time, he also proposed a random process without aftereffects; that is, the current state is known, and the subsequent state is not related to the previous state but only related to the current state. His research has enriched the development of probability theory and stochastic processes to a great extent. In order to commemorate his contribution to the development of mathematics, the stochastic process he studied is called Markov process. In China, the research of Markov process has not stopped. Academician Wang Zikun, a famous mathematician in China, introduced Markov processes into China in the 1950s, and Chinese scholars have also made outstanding contributions to stationary processes, limit theorems, and multiparameter Markov processes. With the continuous introduction of new research results by Chinese scholars in recent years, it is indicated that China’s research on Markov theory has gradually improved in the world. After decades of the continuous development and research, Markov theory has become a very important part of stochastic process, and it has a wide range of applications in many fields, such as operations research, biology, and physics. Markov processes appear in all aspects of real life, such as the Brownian motion of the liquid in the cup; countable states and homogeneous time are called Markov chains. This stochastic process is very important, on the one hand, because its theoretical research is relatively complete, and, on the other hand, it is widely used in the fields of economics, biology, pedagogy, geological disaster, and water resources science in Figures3 and 4.Figure 3
Calculation process.Figure 4
Flow chart.Because the deformation data system has nonlinear characteristics such as complexity, dynamics, and nonstationarity and gives full play to the remarkable performance of wavelet change technology in the field of denoising and reconstruction, as well as the characteristics of the grey model and Markov model, a grey Markov combined deformation prediction model based on wavelet is constructed in this paper. The model consists of four parts: wavelet decomposition, grey model prediction, wavelet reconstruction, and Markov modified model fitting prediction. Wavelet data processing is as follows. Select the appropriate wavelet basis function to decompose the actually collected deformation data to different frequencies and scales, and study the selection of wavelet decomposition layers and wavelet threshold to obtain the best wavelet decomposition method. The low-frequency approximate signal sequence and high-frequency noisy sequence with higher data quality are obtained by wavelet decomposition, so as to better grasp the internal change law and fluctuation characteristics of deformation monitoring data. The deformation data decomposed into low-frequency series are predicted by the improved grey model.The data solved to the high-frequency part is first denoised by wavelet and then reconstructed with the trend term of low-frequency sequence to obtain the prediction results of wavelet grey model. The improved Markov modified model is introduced to modify the prediction results of the wavelet grey model. Firstly, the state of the residual sequence should be divided to obtain the state of each error value. Then, the Markov test is carried out to determine whether the Markov model can be used.The model is built on the basis of time-series data, through which the model is analyzed by the law of data change. The external relationship of each factor to analyze the internal relationship is found out by the hidden law, so as to generate the corresponding data sequence.Let the original data sequence be(1)X0=x01,x02,⋯,x0m.The sequence is obtained by a cumulative generation.(2)X1=x11,x12,⋯,x1m,(3)X1k=∑i=1kx0i,k=1,2,⋯,m.An adjacent mean ofX1 yields a sequence:(4)Z1=z11,z12,⋯,z1m,(5)z1k=12x1k+x1k−1,k=1,2,⋯,m.The equation(6)x0k+az1k=b.The first-order univariate grey prediction model is referred to as grey GM(1,1) prediction model, wherea is the development coefficient and b is the grey effect.Make(7)u=a,bT,Y=x02x03⋮x0m,B=−z121−z131⋮−z1m1,u^=BTB−1BTY,(8)dx1dt+ax1=b.The time response sequence of grey GM(1,1) prediction model is(9)x^1k+1=x01−bae−ak+ba,k=1,2,⋯,m.Therefore, the simulation valueX^1 of sequence X1 generated by a one-time accumulation can be obtained from the above formula:(10)X1=x^11,x^12,⋯,x^1m.Use the following equation:(11)x^0k+1=x^1k+1−x^1k=1−eax01−bae−ak.Chapman-Kolmogorov equation (C-K equation) realizes that anyn-step transfer probability matrix can be obtained by multiplying the one-step transfer probability by itself n times, i.e.,(12)Pn=P1Pn−1=Pn−1P=Pn.There is a certain relationship between the simulated value and the original value, which is called correlation degree. The so-called correlation degree refers to the measurement that the correlation degree changes continuously with time. In the process of data research, the change of the simulated value and the original value is synchronous; that is, they are highly correlated. Conversely, it is lower. The correlation degree provides the basis for prediction models and prediction analyses.


## 3. An Empirical Study

In Figure5, the relevant data of 34 countries (regions) from 1997 to 2017 are selected, respectively. For real Gross Domestic Product (GDP), According to the 2010 GDP data of each country (region) published by WDI database and the annual GDP growth rate of each country from 1994 to 2014, taking 2010 as the base period and converting year by year, the real GDP data of 34 countries from 1994 to 2014 were obtained. It was calculated based on the annual data for each country (region) published by the WDI database. Labor input (L) is calculated according to the total labor force and the unemployment rate of each country (region) published by the WDI database. Renewable energy consumption (REC) is measured according to BP World Energy Statistics Report released in 2016. The annual consumption data of these six kinds of energy in each country are summed up as renewable energy consumption data. Coal consumption data only consider commercial solid fuels, including anthracite and bituminous coal and other fixed coal fuels. The consumption figures for natural gas do not take into account the conversion to liquid fuels. Nuclear energy consumption figures are based on the amount of electricity generated [29–36].Figure 5
Relationship of total renewable energy consumption. (a) Total renewable energy consumption and global share in 34 target countries (regions) and (b) total renewable energy consumption and total real GDP in 34 target countries (regions).
(a)(b)As shown in Figure6, the retention effect for the peak part in the original observation data is more obvious.Figure 6
Comparison curve.The prediction accuracy of the original GM(1,1) model is low, with an average error of 1.37 mm and a root mean square error of 1.65 mm, which are the lowest among the three models. Compared with the original GM(1,1) model, the wavelet grey combination model I and the wavelet grey combination model II are improved in two statistical indicators, which can effectively improve the prediction accuracy of GM(1,1) model. By further comparing the effects of wavelet grey combined models I and II, the average error of combined model I is 1.16 mm and the root mean square error is 1.43 mm, and the average error of combined model II is 0.99 mm and the root mean square error is 1.28 mm. The accuracy of combined model II is better than that of combined model I. It is beneficial for GM(1,1) model to play a better role. The comparison in Figure7 and Figure 8 shows that the convergence of residual error of combined model II is better than those of the other two models. Firstly, the proper function is selected to decompose the original sequence, and then details are classified and denoised, and then GM(1,1) prediction is made. Finally, wavelet reconstruction is used to fit the signal processing method, namely, wavelet grey combination model II, which can effectively improve the accuracy of prediction results and has certain practical application values [37–39].Figure 7
Comparison of model results.Figure 8
Residuals. (a) Original model. (b) Improved model 1. (c) Improved model 2.
(a)(b)(c)The maximum and minimum residual values of GM(1,1) improved by Markov error correction are both 0.68 mm and 0.40 mm, indicating that Markov error correction can effectively reduce the residual diffusion phenomenon caused by the increasing number of model uses and the longer observation time. It can also be seen from the accuracy evaluation index in Figure9 that the model with Markov modification has higher accuracy.Figure 9
Model processing results.


## 4. Revelation and Suggestion of Developing Renewable Energy

It has rich reserves, inexhaustible use, safe use, and long-term development potential. Among the world’s major renewable energy countries, governments and enterprises can promote the substitution and use of renewable energy by formulating active industrial policies. Governments should formulate differentiated renewable energy development policies according to their own economic base. According to the individual fixed-effects model, the basis of economic growth is inconsistent among different countries (regions). Therefore, countries (regions) should formulate specific energy policies and measures in line with their own development according to their own economic development level. It is considered that China plans to reach at least 20% of the total energy consumption by the end of 2030, comprehensively and quantitatively evaluate the costs and benefits for each province, city, or region in combination with local resource endowment and actual economic level, and formulate differentiated and coordinated development renewable energy policy, so as to optimize the overall renewable energy structure.In particular, for the contradiction between the excessive use of nonrenewable resources and the deepening development of industry, governments should abandon economic development at the cost of ecological environment as soon as possible, actively implement the structural transformation of renewable energy production and consumption, vigorously develop renewable energy development and transformation technologies, solve the matching problem between renewable energy and the energy demand of various industries, expand the scale of market application, effectively solve the problem of insufficient financial subsidies for renewable energy development, and realize the sustainable, healthy, and orderly development of renewable energy industry. A good job in renewable energy development planning should be done, and the degree of development should be monitored and assessed. China does not have a deep understanding of the strategic position of renewable energy in sustainable economic development. Regard the development of renewable energy as the most effective measure to improve the ecological environment, incorporate its development planning into the overall plan of social development. and include it in the national financial budgets at all levels. Clearly put forward the strategic goal of replacing renewable energy with renewable energy. It is mainly to formulate differentiated renewable energy development policies for its own economic foundation, strengthen the management of market construction, and supervise the policy implementation of departments at all levels in combination with the types, development level, technology cost, and market demand of domestic renewable energy technologies. Comprehensively promote renewable energy technologies with mature technology and good market development conditions, such as solar water heater technology and wind power technology. Monitor and evaluate the policy implementation of governments and enterprises at all levels on an annual basis, and disclose the results to the public. Strengthen the industry-leading role of renewable energy, establish world-class renewable energy industry associations, such as wind energy association and solar energy association, promote the advanced renewable energy development roadmap and industry program of EU and other countries around the world, promote the development experience and advanced technology of advanced countries, and form guidance documents for external release. Prepare a roadmap and action plan for renewable energy development. Coordinate the relationship between renewable energy development and nonrenewable energy development and industry adaptation. Encourage the combination of social capital investment and renewable energy project construction to realize the efficient utilization of renewable energy and reduce costs. No longer support the construction of renewable energy development projects without technological progress, market mechanism innovation, and high subsidies. Formulate industry standards and industry-leading standards, accelerate technology diffusion, and enable enterprises with backward production capacity to withdraw from the market. Establish unified technical standards for the renewable energy industry to lead industrial upgrading. Take multiple measures to expand subsidies and tax incentives. Governments at all levels should actively attract investment in various ways to support the expansion of the renewable energy market, and actively encourage private enterprises to participate in the development of the renewable energy industry to form benign competition. Integrate the advantages of regional renewable energy development and formulate relevant policy subsidies. Governments at all levels vigorously develop renewable energy infrastructure, improve energy utilization, and reduce energy intensity. Formulate regional energy conservation and emission reduction targets and severely punish enterprises that do not comply with the rules according to law. With reference to the tax incentives under the U.S. energy policy and the strong subsidies for renewable energy implemented by the European Union, formulate tax incentives and tax penalties for energy conservation and emission reduction, and increase financial subsidies for R&D in renewable energy industry. The creation of an investment environment, the creation of an investment environment, the development of human expertise, and the removal of financial and political obstacles are some of the main steps in the deployment of renewable energy. In terms of fiscal policy, feed-in tariff, establish quotas, investment subsidies, tax, or credit incentives, and provide sectoral incentives, especially to increase biomass production in the agricultural sector. Solar cell sales tax exemption and green certificate trading are the main tools to support the development of renewable energy. In terms of policy, governments, energy planners, international cooperation agencies, public utilities, and relevant institutions must jointly implement the sustainable development strategy.National policy is a series of policy or economic means used by the state to intervene in economic and social development. Intervention policies include planning, guidance, promotion, adjustment, protection, support, restriction, and other aspects. The development of renewable energy is an energy-saving project, an important measure to improve energy efficiency and ensure national energy security, as well as a part of the national policy of environmental protection and climate change prevention. With the increasing importance of renewable energy in economic development, the country should tilt its policy. With the development of various industries in the national economy, the state should provide policy support for the development and utilization of renewable energy in the four following ways: Through the national strategy of renewable energy (put forward tasks), reasonable legislation, construction of regulatory mechanism framework (establish market framework and market rules), improving the transparency and credibility of traditional energy competition, and increasing the proportion of investment. It should be noted here that it is impossible to apply all of the above conditions in promoting the use of renewable energy. However, in order to implement these conditions, it is necessary for the government to issue appropriate laws, regulations, and normative documents to clarify the importance of promoting the use of renewable energy or put forward some special implementation requirements according to the national strategic plan.


## 5. Conclusion

(1)
With the excessive use of nonrenewable energy and the frequent occurrence of nuclear safety problems, it is imperative to develop renewable energy under the background that governments all over the world.(2)
Taken into account as independent exogenous variable in the economic growth theory model, the improved Cobb-Douglas production function is constructed to carry out the corresponding empirical analysis. Considering the sequential correlation and endogeneity of panel data, DOLS and FMOLS methods were used to comprehensively analyze the long-term output elasticity of panel data, and the preliminary conclusion was drawn that renewable energy consumption had a significant effect on GDP growth. Through the establishment of individual fixed-effects model and regression analysis and the economic significance of each variable regression coefficient to explain and expound, which, respectively, are renewable energy dissipation, nonrenewable energy consumption, labor input, and gross fixed capital formation of the impact of changes in real GDP, ensure the comprehensiveness of the empirical analysis.(3)
By analyzing and introducing the concept, characteristics, principle, process, and testing method of grey theory, a combination model of wavelet grey is proposed, and the feasibility of the grey theory method is verified by an example. On this basis, a new stable high-frequency sequence and the highest prediction accuracy can be obtained by selecting an appropriate wavelet denoising method for high-frequency data.



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