Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 15, No. 3, 2024 

 

242 

Gray Correlation Analysis of Energy Consumption, 
Energy Structure and Economic Growth in China 

Hongli Yin *, Zhaoyong Sun 

School of Economics and Management, Southwest Petroleum University, Chengdu, Sichuan, China 

* Corresponding author: Hongli Yin (Email: 1609568837@qq.com) 

 

Abstract: Energy is not only the driving force of economic activities, but also an indispensable resource for social development 
and civilization, and plays a pivotal role in the national economy. However, as energy consumption continues to rise, 

environmental protection issues are becoming more and more prominent, and have become a common challenge faced by the 

world. In this paper, the data of China's gross domestic product (GDP), the consumption of each energy species and the energy 

consumption of each industry from 2011 to 2021 are selected for correlation analysis, and the gray correlation between variou s 

types of energy consumption and the development of the national economy is measured. Based on the above analysis, this paper 

finally puts forward a series of targeted policy recommendations, which are aimed at balancing the relationship between 

economic growth and environmental protection, promoting the green transformation of the energy industry, optimizing the 

energy structure, and reducing carbon emissions, so as to promote the realization of sustainable development. 

Keywords: Gray correlation, Energy consumption, Energy structure, Economic growth. 

 

1. Introduction 

Energy, as an important resource, is of great significance to 

China's economic and social development. On the one hand, 

energy is the key to the country's economic development; on 

the other hand, energy is an indispensable material basis for 

social production and people's lives. In recent years, with the 

global response to climate change and fossil energy 

constraints, actively promoting energy conservation and 

carbon reduction and seeking energy transformation have 

become new development themes. Energy consumption is a 

“double-edged sword” closely related to economic growth, 

this paper intends to study the intrinsic connection between 

energy consumption and economic growth based on grey 

system theory from the perspectives of energy consumption 

type structure and industrial structure, which is of great 

scientific significance and application value for the relevant 

departments to save energy and reduce emissions, optimize 

the energy consumption structure and promote the sustainable 

development of the national economy. important scientific 

significance and application value.  

2. Characteristics of Energy 
Consumption in China 

First of all, from the industrial structure of energy 

consumption, China's total energy consumption in 2021 will 

be 5,258,960,000 tons of standard coal, of which agriculture, 

forestry, animal husbandry, fishery and water conservancy is 

the smallest industry in terms of energy consumption, with a 

consumption of 96,610,000 tons of standard coal, accounting 

for only 2% of the total consumption, while the industry is the 

industry with the largest energy consumption, with 

348,551,000 tons of standard coal, accounting for 66% of the 

total consumption. 66% of the total consumption, the 

construction industry and agriculture, forestry, animal 

husbandry, fishery, water conservancy industry consumption 

is similar, also accounted for 2% of the total consumption, 

transportation, warehousing and postal industry accounted for 

8% of the total consumption, wholesale and retail trade and 

accommodation, catering industry 148.98 million tons of 

standard coal, accounting for 3% of the total consumption, 

living energy consumption accounted for 13% of the total 

consumption, other tertiary energy consumption accounted 

for 6% of the total consumption. On the whole, the industrial 

sector in China is the industrial sector that consumes the most 

energy in China. 

Secondly, from the structure of energy consumption 

varieties research. 2021, China's total energy consumption of 

5,258,960,000 tons of standard coal, of which coal 

consumption is the most of all energy varieties, a total of 

293,975,686,000 tons of standard coal, accounting for 55.9% 

of the total consumption; petroleum consumption is second 

only to coal, a total of 97,816,666,000 tons of standard coal, 

accounting for total consumption of 18.6%; natural gas 

consumption is lower at 462,788,500 tons of standard coal, 

accounting for 8.8% of the total consumption; hydropower, 

nuclear power and wind power consumption of 878,246,300 

tons of standard coal accounts for 16.7% of the total 

consumption. According to the collection of 2011-2021 

China's energy consumption of various types of mapping (see 

Figure 1), according to the data show that since 2011 coal 

consumption is gradually decreasing, oil consumption has 

increased but the overall tendency is stabilizing; natural gas 

consumption, hydropower, nuclear power, wind power, the 

proportion of the consumption of electricity since 2011 are 

relatively obvious upward trend, can be predicted in the near 

future It can be predicted that in the near future, hydropower, 

nuclear power and wind power will catch up with oil. 

 



 

243 

 
Figure 1. Trends in China's consumption of various types of energy 

 

3. Constructing a Gray Correlation 
Model 

Mr. Deng Julong, a professor of Huazhong University of 

Science and Technology, founded the gray system theory in 

1982. Gray correlation analysis method does not need to 

consider the number of sample size and the law of sample 

change, not to mention that the quantitative results do not 

match with the qualitative analysis results, it has significant 

advantages in the study of small samples, poor information 

time series. The idea of gray correlation analysis is: according 

to the degree of similarity between the geometry of the parent 

series of the response system and the curve of the sub-series 

to identify the degree of correlation between the parent series 

and the sub-series, and quantify the relationship between the 

variables through the way of thinking of the correlation 

coefficient, the larger the correlation coefficient, the greater 

the degree of correlation [2]. Gray correlation analysis is now 

used to construct the gray correlation model process is as 

follows: 

Step 1: The dependent variable reference series 𝑥0 and the 
independent variable comparison series 𝑥𝑖 (𝑘) are selected in 
the original series. 

𝑥0(𝑘) = (𝑥0(1), 𝑥0(2), . . . . . . , 𝑥0(𝑘)) 

 

𝑥𝑖 (𝑘) = (𝑥𝑖 (1), 𝑥𝑖 (2), . . . . . . , 𝑥𝑖 (𝑘)) 

 

Step 2: Take the reference series, the comparison series 

using the initial value method and take the dimensionless 

treatment with the following formula: 

𝑥0(𝑘) = (
𝑥0(1)

𝑥0(1)
,
𝑥0(2)

𝑥0(1)
, . . . ,

𝑥0(𝑘)

𝑥0(1)
) 

 

𝑥𝑖 (𝑘) = (
𝑥𝑖 (1)

𝑥𝑖 (1)
,
𝑥𝑖 (2)

𝑥𝑖 (1)
, . . . ,

𝑥𝑖 (𝑘)

𝑥𝑖 (1)
) 

 

Step 3: The gray correlation coefficients of the reference 

and comparison sequences are calculated with the following 

formula: 

𝛾(𝑘) =
𝑚𝑖𝑛|𝑥0(𝑘) − 𝑥𝑖 (𝑘)| + 𝜉𝑚𝑎𝑥|𝑥0(𝑘) − 𝑥𝑖 (𝑘)|

|𝑥0(𝑘) − 𝑥𝑖 (𝑘)| + 𝜉𝑚𝑎𝑥|𝑥0(𝑘) − 𝑥𝑖 (𝑘)|
 

 

Where “A” is the resolution factor, which usually takes the 

value of 0.5, ξ ∈ (0, 1). 
Step 4: Calculate the gray correlation P. The value of P is 

the average of multiple gray correlation coefficient values of 

the compared sequences with the following formula: 

P =
∑ Υi(k)

n
 

4. Gray Correlation Analysis of 
China's Economic Growth and 
Industrial Structure of Energy 
Consumption 

4.1. Selection of Relevant Data 

In this paper, energy consumption and gross domestic 

product (GDP) data from 2011 to 2021 in the statistical 

yearbook are organized, and a model is established on this 

basis to calculate the correlation between the structure of 

energy varieties and industrial structure and economic growth, 

respectively, with energy consumption of each industry 

represented by 𝑥𝑖   in tons of standard coal, and GDP 
represented by GDP in billions of yuan. The energy 

consumption of agriculture, forestry, animal husbandry, 

fishery and water conservancy is denoted by 𝑥1, the energy 
consumption of industry is denoted by 𝑥2 , the energy 
consumption of construction is denoted by 𝑥3 , the energy 
consumption of transportation, warehousing and postal 

services is denoted by 𝑥4 , the energy consumption of 
wholesale and retail trade, accommodation and catering is 

denoted by 𝑥5 , and the energy consumption of domestic 
energy consumption is denoted by 𝑥6 . According to the 
previous explanation, the gray correlation of the selected 

factors is relative, and the correlation coefficients and 

correlation degrees calculated at last are the correlation 

coefficients and correlation degrees between the total energy 

consumption of the six types of industries and the GDP, and 

the specific data are shown in Table 1.  

0%

10%

20%

30%

40%

50%

60%

70%

80%

2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021

Coal Oil Natural Gas Hydro, Nuclear, Wind



 

244 

Table 1. Data on the industrial structure of GDP and energy consumption 

Year 
GDP 

(Billions) 

Energy consumption by sector (tons of standard coal) 

x1 x2 x3 x4 x5 x6 

2021 1149237.00 9661.00 348551.00 9608.00 43935.00 7795.38 67481.00 

2020 1013567.00 9263.00 332625.00 9320.00 41309.00 8545.86 64380.00 

2019 986515.20 9018.00 322503.00 9142.00 43909.00 10598.16 61709.00 

2018 919281.10 8781.00 311151.00 8685.00 43617.00 10873.01 60436.00 

2017 832035.90 8931.23 294488.04 8554.51 42190.79 11403.69 57620.31 

2016 746395.10 8544.06 290255.00 7990.93 39651.21 12012.23 54208.66 

2015 688858.20 8231.66 292275.96 7696.41 38317.66 12475.43 50098.96 

2014 643563.10 8094.27 295686.44 7519.58 36336.43 12994.00 47212.33 

2013 592963.20 8054.80 291130.63 7016.97 34819.02 13624.00 45530.84 

2012 538580.00 6784.43 252462.78 6167.37 31524.71 13171.00 39666.09 

2011 487940.20 6758.56 246440.96 5872.16 28535.50 14898.00 37409.94 

4.2. Raw Data Deprogramming 

Taking the 2021 data as the reference series the raw data of 

energy consumption of each industry collated from the 

statistical yearbook were processed without dimension, and 

each data was standardized into the data between 0-1, and the 

processed data is shown in Table 2.  

 

Table 2. Data dimensionless results 

 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 

GDP 1.00  0.88  0.86  0.80  0.72  0.65  0.60  0.56  0.52  0.47  0.42  

x1 1.00  0.96  0.93  0.91  0.92  0.88  0.85  0.84  0.83  0.70  0.70  

x2 1.00  0.95  0.93  0.89  0.84  0.83  0.84  0.85  0.84  0.72  0.71  

x3 1.00  0.97  0.95  0.90  0.89  0.83  0.80  0.78  0.73  0.64  0.61  

x4 1.00  0.94  1.00  0.99  0.96  0.90  0.87  0.83  0.79  0.72  0.65  

x5 1.00  0.88  0.91  0.87  0.84  0.81  0.77  0.73  0.71  0.57  0.52  

x6 1.00  0.95  0.91  0.90  0.85  0.80  0.74  0.70  0.67  0.59  0.55  

4.3. Calculation of Correlation Coefficients 
and Degrees of Correlation 

To find the difference series ΔXi = | X0(k) − Xi(k)| 

between the energy consumption series and the GDP series of 

each industry, the specific results are as follows: 

 

ΔX1 = {0.00,0.08,0.08,0.11,0.20,0.23,0.25,0.28,0.32,0.23,0.27} 

 

ΔX2 = {0.00,0.07,0.07,0.09,0.12,0.18,0.24,0.29,0.32,0.26,0.28} 

 

ΔX3 = {0.00,0.09,0.09,0.10,0.17,0.18,0.20,0.22,0.21,0.17,0.19} 

 

ΔX4 = {0.00,0.06,0.14,0.19,0.24,0.25,0.27,0.27,0.28,0.25,0.22} 

 

ΔX5 = {0.00,0.00,0.06,0.07,0.11,0.16,0.17,0.17,0.20,0.10,0.10} 

 

ΔX6 = {0.00,0.07,0.06,0.10,0.13,0.15,0.14,0.14,0.16,0.12,0.13} 

 

Comparing the values of the above sequence of differences, 

it is found that the maximum value is 0.32 and the minimum 

value is 0. Take ρ = 0.5 and substitute it into the following 
equation: 

𝛾(𝑘) =
𝑚𝑖𝑛|𝑥0(𝑘) − 𝑥𝑖 (𝑘)| + 𝜉𝑚𝑎𝑥|𝑥0(𝑘) − 𝑥𝑖 (𝑘)|

|𝑥0(𝑘) − 𝑥𝑖 (𝑘)| + 𝜉𝑚𝑎𝑥|𝑥0(𝑘) − 𝑥𝑖 (𝑘)|
 

The correlation coefficients and correlation degrees 

between energy consumption and economic growth of each 

industry are calculated according to the formula, and the 

results are shown in Table 3. 



 

245 

Table 3. Energy consumption industry structure correlation coefficient and correlation degree results 

Year 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 P 

γ1 1.00 0.68 0.68 0.59 0.44 0.41 0.39 0.37 0.33 0.41 0.37 0.51 

γ2 1.00 0.69 0.71 0.63 0.57 0.47 0.40 0.36 0.33 0.38 0.36 0.54 

γ3 1.00 0.64 0.63 0.61 0.49 0.47 0.44 0.42 0.43 0.48 0.46 0.55 

γ4 1.00 0.73 0.53 0.45 0.40 0.39 0.37 0.37 0.37 0.39 0.42 0.49 

γ5 1.00 0.99 0.74 0.69 0.59 0.51 0.49 0.49 0.45 0.60 0.62 0.65 

γ6 1.00 0.69 0.74 0.63 0.55 0.51 0.53 0.53 0.50 0.57 0.55 0.62 

From column 13 of Table 3, we can see that among the 

energy consumption and domestic energy consumption of all 

industries in China, transportation, warehousing and postal 

service is the industry with the smallest correlation between 

energy consumption and economic growth, with a correlation 

of 0.49, which is a non-significant correlation. The gray 

correlation between the remaining four major industries and 

domestic energy consumption and economic growth are 0.51, 

0.54, 0.55, 0.65, 0.62, all greater than 0.5, which is a 

significant correlation, of which the wholesale and retail trade 

and accommodation, food and beverage industry energy 

consumption and the correlation with economic growth is the 

largest of 0.65, followed by the correlation of 0.62, again the 

correlation of 0.55, while agriculture, warehousing and postal 

industry is the smallest of all industries in terms of energy 

consumption and economic growth, its correlation is 0.49, 

which is a non-significant correlation. 0.55, and agriculture, 

forestry, animal husbandry, fisheries, water conservancy 

production activities and industrial energy consumption and 

economic growth is the weakest correlation of significance of 

0.51 and 0.54, respectively. 

5. Gray Correlation Analysis of 
China's Economic Growth and the 
Structure of Energy Consumption 
Varieties 

5.1. Selection of Relevant Data 

This part is to study the correlation coefficients and the 

degree of correlation between coal, oil, natural gas, and 

hydropower, nuclear power, and wind power in the structure 

of energy varieties and GDP before, so as to explore the 

relationship between the consumption of each energy type 

and economic growth. GDP is the reference series, whose unit 

is billions of yuan, and the four types of energy varieties are 

the comparative series, whose unit is ten thousand tons of 

standard coal. Coal consumption is denoted by x1 , oil 
consumption by x2 , natural gas consumption by x3 , and 
hydropower, nuclear power and wind power consumption by 

x4, as shown in Table 4. 

Table 4. GDP and Energy Consumption Variety Structure Data 

Year 
GDP 

(Billions) 

Structure of energy consumption varieties (tons of standard coal) 

Coal Oil Natural Gas Hydroelectric, Nuclear, Wind Power 

2021 1149237.00 293975.86 97816.66 46278.85 87824.63 

2020 1013567.00 283540.67 93683.03 41858.38 79231.93 

2019 986515.20 281280.58 92622.72 38999.04 74585.66 

2018 919281.10 278435.75 89193.83 35866.30 68429.13 

2017 832035.90 276231.16 86151.30 31452.06 61992.47 

2016 746395.10 274608.02 82559.00 26931.01 57393.96 

2015 688858.20 276964.09 79876.79 25178.55 52093.56 

2014 643563.10 281843.77 74101.78 23986.70 48401.74 

2013 592963.20 280999.36 71292.12 22096.39 42525.13 

2012 538580.00 275464.53 68363.46 19302.62 39007.39 

2011 487940.20 271704.19 65023.22 17803.98 32511.61 

5.2. Raw Data Deprogramming 

Using the 2021 data as a reference series the raw data on 

energy consumption in various categories collated from the 

statistical yearbook were processed in a dimensionless 

manner, and the data were standardized to be between 0 and 

1. The processed data are shown in Table 5. 

 

Table 5. Data dimensionless results 

 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 

GDP 1.00 0.88 0.86 0.80 0.72 0.65 0.60 0.56 0.52 0.47 0.42 

x1 1.00 0.96 0.96 0.95 0.94 0.93 0.94 0.96 0.96 0.94 0.92 

x2 1.00 0.96 0.95 0.91 0.88 0.84 0.82 0.76 0.73 0.70 0.66 

x3 1.00 0.90 0.84 0.78 0.68 0.58 0.54 0.52 0.48 0.42 0.38 

x4 1.00 0.90 0.85 0.78 0.71 0.65 0.59 0.55 0.48 0.44 0.37 



 

246 

5.3. Calculation of Correlation Coefficients 
and Degrees of Correlation 

The difference series ΔXi = | X0(k) − Xi(k)| between the 

energy consumption series and the GDP series for each 

category is first derived as follows: 

 

ΔX1 = {0.00,0.08,0.10,0.15,0.22,0.28,0.34,0.40,0.44,0.47,0.50} 

 

ΔX2 = {0.00,0.08,0.09,0.11,0.16,0.19,0.22,0.20,0.21,0.23,0.24} 

 

ΔX3 = {0.00,0.02,0.02,0.02,0.04,0.07,0.06,0.04,0.04,0.05,0.04} 

 

ΔX4 = {0.00,0.02,0.01,0.02,0.02,0.00,0.01,0.01,0.03,0.02,0.05} 

 

Comparing the values of the above sequence of differences, 

it is easy to see that the maximum value is 0.5 and the 

minimum value is 0. Take ρ = 0.5 and substitute it into Eq: 

γ(k) =
min|x0(k) − xi(k)| + ξmax|x0(k) − xi(k)|

|x0(k) − xi(k)| + ξmax|x0(k) − xi(k)|
 

The correlation coefficients and correlations between 

various categories of energy consumption and economic 

growth were calculated according to the formulae, and the 

results are shown in Table 6. 

 

Table 6. Results of correlation coefficients and correlation degrees of the structure of energy consumption varieties 

Year 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 P 

γ1 1.00 0.75  0.72  0.63  0.54  0.47  0.42  0.39  0.36  0.35  0.33  0.54  

γ2 1.00 0.77  0.74  0.69  0.61  0.56  0.54  0.56  0.54  0.52  0.51  0.64  

γ3 1.00 0.92  0.94  0.91  0.85  0.79  0.82  0.86  0.87  0.83  0.86  0.88  

γ4 1.00 0.93  0.96  0.92  0.93  0.98  0.98  0.97  0.89  0.91  0.82  0.94  

From Table 6, it can be seen that natural gas is the energy 

source with higher correlation with economic growth among 

the above four energy sources, with a correlation of 0.88, 

second only to hydropower, nuclear power and wind power, 

mainly because natural gas is safer to use compared with coal 

and oil, and as a high-quality, efficient, green and clean low-

carbon energy source, it does not produce harmful substances 

such as sulfur and dust, and can form a good complementary 

with the development of renewable energy sources. 

complement each other, effectively reducing air pollution. At 

the same time, the correlation between coal and oil and 

economic growth is small, respectively 0.54 and 0.64, but 

according to the relevant data, coal and oil are the two types 

of energy with the highest proportion of use in our country, 

which account for more than 74.5% of the total consumption 

of energy in our country, which indicates that the use of coal 

and oil is very inefficient, and cannot reasonably and 

effectively promote the development of the economy. 

6. Responses and Recommendations 

Energy consumption and economic growth have a high 

degree of correlation between the two, this paper through the 

analysis of China's energy consumption characteristics based 

on the use of gray correlation analysis to get China's gross 

domestic product and energy consumption varieties of 

structure, industrial structure of the gray correlation, 

according to the analysis of the structure of the proposed some 

relevant recommendations. 

First, we must speed up the restructuring of industry and 

vigorously develop tertiary industries with high efficiency, 

low energy consumption and high services. Industry accounts 

for 66% of energy consumption in the various industrial 

structures, but the correlation between industry and economic 

growth is 0.54, which is a medium correlation. Wholesale, 

retail and catering industries and other industries in the 

various types of industrial structure of energy consumption 

accounted for only 3%, but the highest correlation with 

economic growth, amounting to 0.65; thus, it can be seen that 

China's industrial production in the consumption structure is 

still unreasonable. In the future process of economic 

development, the development of the tertiary industry, which 

is mainly high efficiency, low consumption and service-

oriented, should be used to increase the proportion of energy 

that consumes less energy, and the transition from high 

consumption and low efficiency and high carbon emission to 

diversified and low-carbon green energy. 

Secondly, promoting the development of the clean energy 

industry. Gray correlation analysis of economic growth and 

energy consumption structure shows that although China's 

economic development is still very dependent on coal, coal 

consumption still dominates in China's energy consumption, 

but the gray correlation between economic growth and coal 

consumption is smaller, which indicates that the problem of 

high energy consumption in China's economic development 

is still more prominent, and at the same time, the negative 

impacts of coal consumption on environmental pollution are 

also contrary to the green development concepts advocated by 

the government. The negative impact of coal consumption on 

environmental pollution is also contrary to the green 

development concept advocated, in view of which, China 

should actively adjust the industrial structure dominated by 

coal. Meanwhile, the analysis results show that the correlation 

between hydropower, nuclear power, wind power and natural 



 

247 

gas consumption and economic growth is very strong, as 

clean energy, China should continue to promote the 

development of hydropower, nuclear power, wind power and 

natural gas industry, and under the premise of ensuring the 

stability of the economy, gradually adjusting the energy 

structure, and gradually increase the proportion of energy 

consumption in the structure. 

References 

[1] Gao Xincai, Bei Yanpeng. Gray correlation analysis of energy 
consumption and economic growth in China [J]. Seeking, 
2009(03): 57-59. 

[2]  Shao Minlan. Gray correlation analysis of energy 
consumption, energy structure and economic growth in China. 
[J]. China Collective Economy, 2021, (18):5-6. 

[3]  Fu Yan. Gray correlation analysis of energy consumption, 
energy structure and economic growth. [J]. Industrial 
Technology Economics. 2014, (05):33 

[4] Su Yi, Wang Lu, Zhang Yun. Analysis of energy consumption 
and industrial structure based on improved gray correlation [J]. 
Management Modernization, 2016(03):19-22. 

[5] Liu Sifeng, Xie Naiming et al. Gray system theory and its 
application [M]. Beijing: Science Press, 2013. 

[6] Zhao Yue. Mutation point analysis of energy consumption and 
major meteorological factors in Beijing---Based on gray 
correlation theory [J]. Journal of Nanjing University of 
Information Engineering: Natural Science Edition, 2013(04): 
364-368.