Assessing dynamic energy efficiency in the organization for economic Co-operation and development (OECD) countries and China during COVID-19

According to the October 2021 Glasgow Climate Agreement reaffirming the cooling goals of the Paris Agreement and the Glasgow Leaders Declaration on Forests and Land Use, this research applies the Super-D-DDF model to non-oriented variable returns to scale to evaluate the Organization for Economic Cooperation and Development (OECD) and China (38 countries in total), collect important production and energy variables from 2016 to 2020, and measure the total efficiency of energy dynamics and its changes during COVID-19. The empirical results are as follows. (1) Comparing energy efficiency from 2016 to 2018 and 2019 to 2020 (during COVID-19), we find that most countries (22 countries) changed from high efficiency to low efficiency, showing a decrease in energy efficiency. (2) The emissions of carbon dioxide in China in 2020 are close to the sum of OECD carbon dioxide emissions, highlighting that the energy policy in China should be adjusted appropriately. (3) From 2016 to 2020, the forest area of various countries has a significant impact on overall energy efficiency performance. In line with the United Nations’ policy goals, countries should adjust forest protection policies to effectively reduce carbon emissions.


Introduction
The COVID-19 disease that broke out at the end of 2019 turned into a global pandemic after rapidly spreading in early 2020.As of July 2022, the fatality rate is about 1.12%, making it one of the largest pandemics in history.According to the statistics of BP Group World Energy [1], the various measurements taken to alleviate its impact in 2020 resulted in a 4.5% drop in primary energy consumption.Oil still accounts for the largest proportion (31.2%) within the energy structure, and coal is the second most used fuel, accounting for 27.2% of total primary energy consumption.GDP losses have declined by more than 3.5% globally.However, in 2021, as economic activity resumed, energy demand rebounded to pre-pandemic levels.
Burning fossil fuels, such as coal and oil, leads to an elevation in the levels of carbon dioxide (CO2) in the atmosphere.Moreover, extensive deforestation, agricultural expansion, and industrial development contribute to the accumulation of greenhouse gases, causing a rise in the Earth's temperature and giving rise to significant climate variations.These changes have far-reaching consequences on the natural environment, impacting both living organisms and human economic activities .Data from the Goddard Institute for Space Studies of NASA [2] present global surface temperatures in which 2016 and 2020 are the warmest years on record (figure 1).With the global warming, woodlands around the world are ravaged by wildfires.According to Curtis et al (2018) [3], a study pointed out that between 2001 and 2015, the global forest loss caused by fires accounted for approximately 21%-25%.However, the latest research survey shows that between 2001 and 2019, the global forest loss caused by fires has reached as high as 26%-29%, and the global forest loss caused by fires is showing a continuous increasing trend (Tyukavina et al 2022) [4].Due to climate change leading to an increase in the frequency of wildfires and the exchange of forest resources with carbon dioxide in the atmosphere, climate change and global warming can be slowed down (Mansoor et al 2022) [5].To slow down higher global temperatures, the United Nations passed the Paris climate agreement at the COP21 meeting in 2015.The goal is to control global average temperatures rising within 2 Celsius of pre-industrial temperatures (year 1880).COP26 [6] in 2021 also emphasizes a commitment to work together and preserve forests until net-zero emissions are reached around 2050.Therefore, we believe that when exploring energy efficiency, attention should be paid to the relationship between wildfires, forests, and carbon emissions.However, the difficulty in collecting wildfire data has become a limitation of this study, and this factor should be excluded.On the other hand, considering the United Nations' call for forest injection and emission reduction, this study considers it as an output that means more is better, and includes it in the analysis of energy efficiency.
Based on the changes affecting the global economy during COVID-19, this research takes the members of the Organization for Economic Cooperation and Development (OECD) (table 1) as the research sample to understand the dynamic total efficiency of energy and its changes during this period and to analyze the impact of forest areas on carbon emissions.The 38 members of the OECD sample account for 17.4% [7] of the earth's population and more than 60% [8] of the world's GDP.OECD collaborates across countries at a regional level, notably through regional initiatives, spanning Africa, Eurasia, the Middle East and North Africa, Latin America, the Caribbean, Southeast Asia, and Southeast Europe.OECD countries and key partners represent about 80% [9] of world trade and investment.As China is the world's most populous country, the second largest economy in the world, and the world's third largest country by total land area, this study utilizes a merger assessment in order to be more objective.Since Costa Rica joined the OECD in 2021 and some data are missing, it is not included in the scope of this study.
This research gathers data spanning from 2016 to 2020 and incorporates various variables, such as labor, fossil fuel energy consumption, gross domestic product (GDP), carbon dioxide emissions (CO2), forest area, and other factors.It utilizes fixed capital formation as a temporal variable, accounting for carry-over effects.The study employs the Super Efficiency dynamic directional distance function (Super-D-DDF) model to assess overall efficiency, considering non-oriented variable returns to scale.Additionally, it examines the policy implications of energy efficiency for the Paris Agreement.
Many studies in the literature have examined the energy efficiency of China and OECD countries, but few have pointed out the impact of COVID-19 on said efficiency.To fill this gap, this study applies Super-D-DDF to measure overall efficiency during the pandemic.The empirical analysis results offer a reference for countries to initiate effective energy policies.
The rest of this paper runs as follows/ section 2 reviews the literature.Section 3 introduces the research methodology.Section 4 describes the variables' data and discusses the empirical research.Section 5 analyzes energy efficiency and policy implications based on the empirical results.Section 6 provides some conclusions and policy implications for OECD countries and China (38 countries in total).

Literature review
Many countries have used data envelopment analysis (DEA) to examine the efficiency between multiple inputs and outputs to make dynamic evaluations when engaging in different activities with other countries of different backgrounds.We can analyze the efficiency of a basic measurement period over time in the case of a carry-over variable connecting consecutive time periods.DEA has the characteristics of processing multiple inputs and outputs at the same time to solve uncertainty and non-productivity in the data.This section collects the literature and journals related to this research topic, analyzes and organizes them, and summarizes them as follows.
Examples of applications of DEA analysis run as follows.Lu and Lu (2019) [11] used DEA to investigate and analyze data of 28 selected European countries from 2009 to 2013 to study their intertemporal efficiency and implementation efficiency based on fossil fuel carbon dioxide emissions.The research results show from 2009 to 2013 that the overall efficiency score of each country was 0.743 on average, the average carbon dioxide emissions of each country increased year by year, and the average real GDP of the overall country did not fluctuate significantly.Lu et al (2019) [12] applied dynamic DEA to explore environmental energy efficiency and its negative impact on the environment in 48 high-income economies (including China) from 2010 to 2014.The results showed that European economies are more efficient in energy consumption than other economies, while Asian economies are the least efficient.To pursue GDP growth, economies need to consider reducing energy consumption and carbon dioxide emissions and improving energy efficiency.
Yang and Wei (2019) [13] employed DEA to explore urban total factor energy efficiency (UTFEE) under environmental constraints in 26 cities in China from 2005 to 2015.The results showed that economic development and city size promote urban energy efficiency.However, government spending, industrial structure, energy prices, foreign investment, research investment, and production endowments harm urban energy efficiency.Fidanoski et al (2021) [14] utilized DEA to explore the efficiency scores of 30 OECD member samples in minimizing energy use and losses and environmental emissions from 2001 to 2018.The results presented that the average inefficiency margin of primary energy in each country was 16.1% and ranged from 10.8% to 13.5% for electricity.Results from the extended model showed that focusing on the environment generally does not affect efficiency, while reliance on energy generated from renewable sources does reduce efficiency slightly.
Hao et al (2021) [15] explored carbon dioxide emissions from environmentally adjusted multifactor productivity growth (i.e., green growth) in the G7 countries from 1991 to 2017.Using the DEA (CS-ARDL) model, the results showed that the linear and non-linear terms of green growth reduce carbon dioxide emissions and that environmental taxes, renewable energy, and human capital improve the environment.Simeonovski et al (2021) [16] used DEA to explore the efficiency scores of energy efficiency management in a sample of 28 EU member states from 2010 to 2018.The results showed that average inefficiency in the EU was 16.0%, and the efficiency of the old member states (4.2%) was significantly higher than the new member states (29.5%).However, new member states could improve energy efficiency by opening energy markets, supporting energyefficient and technologically advanced industries, and taking measures aimed at raising the level of economic productivity.Wu et al (2021) [17] used DEA data on energy efficiency in APEC economies from 2010 to 2014 to measure energy efficiency and studied the impact of poor output and energy efficiency rankings.By reducing fossil fuel consumption and carbon dioxide emissions, economies are expected to see increased GDP.
Examples of applications of the SBM model are as follows.Lu et al (2020) [18] used dynamic SBM to discuss and analyze the annual and overall energy efficiencies of 13 ASEAN plus three cooperation (abbreviated as APT) countries from 2011 to 2015 and to assess forest areas for 2 intertemporal stages and health efficiency.The research results showed in APT economies from 2011 to 2015 that there are 3 countries with the best average efficiency performance, BRN (1), SGP (0.9996), and CHN (0.9994), while the 3 worst efficient countries are THA (0.0626), PHL (0.0237), and VNM (0.0117).For the 5-year carry-over or average maximum adjustment score of the forest area, KHM is 950.01%and KOR is 387.71%, which means that these two countries should greatly expand afforestation and reduce reclamation.
Lu et al (2021) [19] used SBM to assess the impact of forest areas on annual and overall energy efficiencies in 28 EU countries between 2009 and 2016, and the results showed that including forest area leads to annual and overall energy efficiencies growth of.Although overall energy consumption has gradually declined, carbon dioxide emissions remain problematic.Lu et al (2021) [20] employed dynamic SBM to explore changes in energy, health efficiency, and DN-TFP productivity in OECD member countries from 2011 to 2015.The results showed that Estonia, Finland, Hungary, Iceland, Mexico, New Zealand, Portugal, Slovenia, Sweden, and Turkey were the best performers in overall efficiency, while Ireland, Israel, and the Netherlands were the three worst.A total of 29 economies improved in productivity, although Chile, Mexico, the Slovak Republic, Turkey, and the UK fell slightly.Twenty 20 countries had an above-average overall efficiency score and an upward trend in productivity, of which only the UK had an overall efficiency value below the overall average while productivity showed a decline.
Examples of applications of other models run as follows.Sun et al (2019) [21] used Bootstrap DEA and the systematic GMM method to explore vertical and horizontal data of 29 provinces in China from 2000 to 2015 and to study the impact of market fragmentation on ecological efficiency.Fragmentation harms eco-efficiency, indicating that market fragmentation significantly inhibits the improvement of eco-efficiency.
Liu et al (2020) [22] utilized DEA Tobit regression to explore the impact of income inequality on energy efficiency from 2000 to 2016, which is of great significance for the sustainable development of countries along the Belt and Road.The overall energy efficiency of the 33 Belt and Road countries is low at 0.38.Specifically, in high-income Belt and Road countries, income inequality has a U-shape effect on energy efficiency, while in the Belt and Road countries, income inequality and energy efficiency have an inverted U-shape relationship.Economic growth has a positive impact on energy efficiency, while industrialization and energy structure harms energy efficiency.
Matsumoto et al (2020) [23] applied the DEA Malmquist-Luenberger technique to explore the environmental performance of 27 EU countries with vertical and horizontal data and time-varying data from 2000 to 2017.Studying different types of non-performing outputs and using EU country's long-term crosssectional data, the findings show that economic and environmental variables significantly affect performance.Baloch et al (2021) [24] used a DEA-SBM hybrid model to explore the best efficiency scores for 15 regions in the Asia-Pacific region surveyed from 2015 to 2018.Analyzing both over-efficiency-based and over-balance-based measures in a non-parametric DEA model (SBM) data, the results showed that Bangladesh, Pakistan, China, Singapore, New Zealand, Philippines, Japan, India, Indonesia, Malaysia, Thailand, and Vietnam achieved the most effective results in both DEA models throughout the study period 1, Australia and Sri Lanka had low scores for the whole study period, while Hong Kong had no data for all study years.
In summary, we found that many literatures use variables such as labor force, capital energy, GDP, carbon dioxide emissions, or pollutants to examine the energy efficiency of a single industry, organization, or economy, but rarely consider the carbon neutrality of forests.Measuring efficiency during COVID-19.In response to the goals of the Paris Agreement, this study chooses forest area as an output variable, expecting more output, the better, and analyzes the efficiency of China and OECD countries during COVID-19 to fill in the gaps in previous studies.

Research methods
3.1.DEA DEA is a method for measuring efficiency that uses linear programming to evaluate the relative efficiency of a decision-making unit (DMU) according to the concept of Pareto optimality in economics.It originated from Farrell's research in 1957, in which all data are enveloped under the production function.Subsequent models appeared, such as the fixed-scale CCR (1978) [25], the variable-scale BCC (1984) [26], and that of Tone (2001) [27] who based on CCR and BBC proposed Slacks-Based Measure (SBM) to solve the problem that input or output cannot be adjusted in equal proportions to achieve the best efficiency.Here, CCR and BCC are radial measurements, while SBM is a form of non-oriented DEA.
Traditional DEA focuses on static comparisons and does not consider evaluation and analysis across different time periods.Eventually, Tone and Tsutsui (2010) [28] extended SBM to include a carry-cover variable between two consecutive periods as a form of cross-periodic dynamic analysis of links.

Super-efficiency dynamic direction distance function
The directional distance function (DDF) is often used to measure the efficiency of unintended output.The general directional distance function is a ray measurement mode.Since a non-zero difference and all sources of inefficiency cannot be considered when calculating efficiency, the efficiency value is overestimated.To solve the problem that the efficiency value is overestimated, Fare & Grosskopf (2010) [29] established a non-oriented directional distance function based on the Tone (2001) SBM model, which provides a more reasonable and accurate calculation for efficiency measurement result.The traditional DEA model also cannot rank DMUs with an efficiency (>1), and in the case where most efficiency scores are 1, DEA has the problem of insufficient judgment, Chambers et al (1996) [30] thus proposed a directional distance function (DDF) to evaluate whether a DMU is super-efficient under the condition that input can be increased while output can be reduced.
As DEA can quantify efficiency, quickly compare the gap between a single DMU and the best DMU, and measure the need for improvements, this research selects DEA to quantitatively investigate the improvement status in each DMU.Traditional DEA is regarded as a single process when measuring the efficiency of DMUs and is mainly based on the static comparison of cross-sectional data.It cannot evaluate the efficiency of individual departments and different periods and does not reflect changes in efficiency over time.Because the dynamic model can obtain the only optimal solution, the result is more convergent.
This study considers exogenous variables and super efficiency, and applies the Fare&Grosskopf (2010) [29] directional distance function model and the concept of Tone and Tsutsui (2010) [28] dynamic model to propose a super efficient dynamic directed distance function (SDDDF) with super efficiency and unexpected output.We use six variables: input is labor and energy consumption, two ideal outputs are GDP and forest area, and bad outputs are carbon dioxide emissions, carry-over is fixed capital.We apply Max DEA Ultra 8 software to obtain solutions with variable returns to scale and non-directional models, and further explore the energy efficiency of OECD countries and China from 2016 to 2020.The structure of this research appears as figure 2.
Suppose N countries use two inputs, labor (TLF) and energy consumption (ENG), producing two desirable outputs, gross domestic product (GDP) and forest area (FSA), and one unintended output, carbon dioxide emissions (COE), along with a carry-over factor of fixed capital formation (Zt).In group R h at time t, referring to the research of Li et al (2021) [31], the relevant definitions are as follows.

Set of possible productions
T C = {(TLF t , ENG t , GDP t , FSA , COE t ): (TLF t , ENG t ) can produce (GDP t , FSA t , COE t )}, Z t is carryover, where t = 1, ¼, T.    From the changes in the variables from 2016 to 2020 (see table 4), labor force is on the rise (0.18%), fixed capital formation is on the rise (10.58%), and overall gross domestic product is on the rise (6.28%).This shows that as investment capital per capita increases, the average income per person also increases.Energy consumption presents a downward trend (−2.68%), and carbon dioxide emissions also show a downward trend (−4.56%).

Energy efficiency analysis during COVID-19 4.2.1. Overall efficiency
The average efficiency of each year from 2016 to 2020 is 1.1857, 1.2146, 1.2351, 1.1851 and 1.1309, respectively, and the overall average efficiency is 1.1843.The top three super-efficiency countries are the United States at

Efficiency before and during the pandemic
The outbreak of the novel coronavirus (COVID-19) at the end of 2019 affected the global economy.Hence, this study divides the analysis period into pre-pandemic (2016-2018) and during the pandemic (2019-2020) to examine the changes in energy efficiency under the pandemic.

Pre-pandemic efficiency
The average energy efficiency of OECD countries and China is reported to be 1.2118.Notably, the United States, Latvia, and Canada stand out with super-efficiency scores of 4.7934, 4.3240, and 4.1111, respectively.On the

Efficiency impact analysis
After measuring the efficiency of OECD countries and China from 2016 to 2018 (before the pandemic) and from 2019 to 2020 (during the pandemic), we note that the average efficiency fell from 1.2118 to 1.1580.
(1) The countries that have changed from high efficiency to low efficiency include the United States, Latvia, and Canada.The top three countries with a decreasing rate are Hungary from 0.6646 to 0.4314, Poland from 0.8510 to 0.6153, and Latvia from 4.3240 to 3.2657.Hungary is the country with the largest decline after the efficiency comparison.
(2) Iceland is flat as its efficiency always remains at 1.
(3) The countries that have changed from low efficiency to high efficiency include Switzerland, the United Kingdom, and Colombia.The top three countries with an increasing rate are Turkey from 0.6088 to 1 , Switzerland from 1.7117 to 1.8273 , and China from 0.4843 to 0.5110 .Turkey was the country with the largest change higher after efficiency comparison (As figure 3).

Analysis of the impact of carbon dioxide and forest area on efficiency
This study further explores the impact of CO 2 emissions and forest area on overall efficiency.After aggregation (see table 7), the results are explained as follows.

Efficiency without CO 2 emissions
From 2016 to 2020, the annual efficiencies were 1.   (1) After excluding the measurement of carbon dioxide emissions, the overall average energy efficiency of OECD countries and China experienced a slight decrease from 1.1843 to 1.1740.Among the twenty countries analyzed, including Australia, Canada, and Chile, their energy efficiency levels remained unchanged.However, some countries, such as Austria, Belgium, and France, transitioned from high efficiency to low efficiency.Notably, Latvia witnessed a significant drop in efficiency from 3.8254 to 3.6625, indicating the largest change in the overall energy efficiency gap.Conversely, there were no substantial changes observed in the overall energy efficiency shifting from low to high levels.
(2) After excluding the measurement of forest area, the overall average energy efficiency of OECD countries and China decreased from 1.1843 to 0.9344.Ten countries, including Belgium, Germany, and Iceland, were flat.28 countries including Australia, Austria, and Canada are the ones that have turned from high efficiency to low efficiency.Among them, Canada's efficiency dropped from 4.1108 to 0.7435, a drop as high as 81.9%.This is the country with the largest change in the overall energy efficiency gap.In addition, there is no significant change in overall energy efficiency from low to high (As figure 4).

Discussion
The 2021 COP26 Glasgow Climate Pact reaffirms the Paris Agreement goals approved in 2015, which are to limit the global temperature rise in the 21st century to less than 1.5 Celsius, gradually reduce the use of coal, and promise to end deforestation and land loss by 2030.The BP World Energy Statistical Yearbook pointed out that due to the impact of COVID-19 in 2020, various measures taken by countries to mitigate the impact of the pandemic affected economic activities and led to a decline in the world's primary energy consumption and carbon emissions.This study incorporates carbon dioxide emissions and forest areas into the analysis to explore changes and differences in the energy efficiency of OECD countries and China.This research uses the super-efficiency dynamic directional distance function (Super-D-DDF) to analyze the model structure of non-oriented variable returns to scale and selects statistical data from 2016 to 2020.The input variables are labor force and energy consumption, output variables are gross domestic product, carbon dioxide emissions, and forest area, and fixed capital formation is a carry-over factor.We investigate the data before the pandemic (2016-2018) and during the pandemic (2019-2020) for changes in energy efficiency and then discuss three different combinations of carbon dioxide emissions and forest area exclusions.The cross-comparison of the impact of carbon dioxide emissions and forest area on energy efficiency in OECD countries and China is summarized as follows.
(1) After comparing the efficiency before the pandemic (2016-2018) and during the pandemic (2019-2020), the average efficiency decreased from 1.2118 to 1.1580.Most countries (22) turned from high efficiency to low efficiency, and the percentage increase and decrease in efficiency and amplitude showed a downward trend of 4.44%.This shows that various measures taken by various countries to mitigate the impact of the pandemic have indeed led to a decline in energy efficiency.
(2) Before the pandemic and during the pandemic, energy efficiency changed from high to low in 22 countries including Austria, Belgium, and Canada.Hungary dropped from 0.6646 to 0.4314 (−35.09%) and was the country with the largest change after the efficiency comparison.Iceland is flat as its efficiency always remains at 1. Conversely, 15 countries including Australia, China, and Colombia have turned from low to high.Turkey increased from 0.6088 to 1 (64.26%) and has the largest change after efficiency comparison.
(3) For the range of changes in the variables from 2016 to 2020, labor force, fixed capital, and gross domestic product all showed an upward trend.This means that capital investment per person increased, and the average income per person also increased.In addition, energy consumption and carbon dioxide emissions showed a downward trend.(4) From 2016 to 2020, 14 countries including Australia, Canada, and Colombia were the most energy efficient, while China (0.4943), South Korea (0.4678), and the Czech Republic (0.3658) were the three countries with relatively poor performance in energy efficiency.
(5) After excluding carbon dioxide emissions, the overall energy efficiency dropped from 1.1843 to 1.1740 (−0.87%), indicating that carbon dioxide affects the overall energy efficiency performance.Among them, the countries with overall energy efficiency have not increased or decreased.China (0.4943), South Korea (0.4621), and the Czech Republic (0.3658) were still the three countries with the worst efficiency.Latvia dropped from 3.8254 to 3.6625.After excluding carbon dioxide emissions, the overall energy efficiency has dropped the most.
(6) After excluding the assessment of forest area, the overall energy efficiency decreased from 1.1843 to 0.9344.Countries with high efficiency were France, Greece, Iceland, Ireland, Luxembourg, Switzerland, the United Kingdom, and the United States.South Korea (0.4678), Chile (0.4250), and the Czech Republic (0.3600) had the worst efficiency.Canada's forest area accounts for 35% of the country's land area.After excluding the forest area, its efficiency fell 4.1108 to 0.7435 (−81.9%), or the largest change in energy efficiency slippage.In Latvia, the forest area accounts for 52.82% of its land.After excluding the forest area, its efficiency fell from 3.8254 to 0.8397 (−78%), or the second greatest percentage drop.The results show that the forest area of each country significantly affects the overall energy efficiency performance, and so increasing forest coverage is an important policy.

Conclusions
This study collects important production and energy variables from 2016 to 2020, taking the OECD and China as the research samples and employing Super-D-DDF).It analyzes statistical data from 2016 to 2020 and uses labor force and energy consumption as input variables, gross domestic production, carbon dioxide emissions, and forest area as output variables, and fixed capital formation as a carry-over factor.The study compares energy dynamic total efficiency changes before and during the COVID-19 pandemic and analyzes carbon dioxide emissions and forests and their impacts on energy efficiency.The conclusions are as follows.
(1) Looking at energy efficiency before the pandemic (2016-2018) and during the pandemic (2019-2020), we find that the average efficiency decreased from 1.2118 to 1.1580 (−4.44%), 22 countries have changed from high efficiency to low efficiency.showing that the various measures taken in response to the impact of the pandemic did indeed lead to a decline in energy efficiency.
(2) Compared before and during the pandemic , the primary energy consumption dropped from 191,250 Ktoe of oil equivalent before the pandemic to 188,567 Ktoe of oil equivalent during the pandemic.In addition, carbon dioxide emissions dropped from 576 million tons before the pandemic to 561 million tons during the pandemic .It shows that production activities are affected by the pandemic.Due to the decrease in energy demand caused by the pandemic, global carbon emissions have seen a decline during the COVID-19 period.The reduction in air travel and transportation has had a significant impact on lowering global greenhouse gas emissions.This has provided a temporary opportunity to work towards global climate goals and highlighted the importance of renewable and clean energy sources.
(3) Chinas carbon dioxide emissions in 2020 (9.899 billion tons) were close to the total carbon dioxide emissions of OECD countries (10.778 billion tons).This highlights that China should adjust its energy policy appropriately.
(4) After excluding the assessment of forest area in this study, the overall energy efficiency dropped from 1.1843 to 0.9344, and the efficiency weakened by 21.1%.The results show that the forest area of each country significantly affects the overall energy efficiency performance from 2016 to 2020.In line with the United Nations policy goals, countries should adjust forest conservation and forest protection policies to effectively reduce carbon emissions.

Recommendations
(1) This study uses the World Bank (WB) and BP World Energy Statistical Yearbook (2021 edition) as the main sources to evaluate the efficiency of research and development activities using publicly available objective data.For input items, output items, and related variables, there are also some difficulties and omissions in data collection, which limit the selection and observation period of variables.It is recommended to consider other factors in future research, such as increasing wildfire factors, for more extensive consideration in order to conduct more in-depth research.
(2) This study adopts an ultra-high efficiency dynamic wind direction distance function, and it is recommended that future scholars can use other research methods to evaluate efficiency.And this study takes the period from 2016 to 2020 as the research period, and it is recommended to extend it to a longer period to improve the empirical analysis.

Figure 1 .
Figure 1.This graph illustrates the change in global surface temperatures relative to 1951-1980 average temperatures, with 2020 and 2016 tying for the hottest on record.Source: NASA/JPL-CalTech.
2. Dynamic unguided DDF objective formula å b b b b b

Figure 2 .
Figure 2. Model structure of this research source: self-organized.

Table 1 .
Summary of OECD countries and China's background (38 countries in total).
Source: Organization for Economic Cooperation and Development (OECD) [10], self-organized by this study.
To evaluate the impact of carbon dioxide emissions and forest area on energy efficiency, the research scope encompasses the 38 economies that have joined the OECD member countries and China before 2020.
Five consecutive annual statistical datapoints from 2016 to 2020 are selected.Input variables are labor and energy consumption, output variables are gross domestic production, carbon dioxide emissions, and forest area, and carry-over variable is use fixed capital formation.To distinguish different combinations of excluding carbon dioxide emissions, containing carbon dioxide emissions, excluding forest area, and including forest area, we apply Super-D-DDF to analyze the energy efficiency of all countries in the sample.The research variables are sourced from the World Bank (WB) and the BP World Energy Statistical Yearbook (2021 edition).Table 2 lists the source descriptions of input, output, and intertemporal variables.

Table 2 .
5efinitions of inputs, outputs, and intertemporal variables.The average labor force is 38.5million, the maximum is 800.02 million in China in 2019, and the minimum is 208,270 in Iceland in 2016.The standard deviation is 128.44 million.The average value of energy consumption is 190,176 Ktoe.The maximum is 2,929,937 Ktoe in China in 2020, and the minimum is 832 Ktoe in Iceland in 2020.The standard deviation is 525,422 Ktoe.The average value of GDP is US$1,663 billion.The maximum value is US$19,974 billion in the United States in 2019, and the minimum value is US$18 billion in Iceland in 2016.The standard deviation is US$3,683 billion.The average value of CO2 emissions is 569.97 million tons.The maximum value is 9.899 billion tons in China in 2020, and the minimum value is 2.59 million tons in Iceland in 2020.The standard deviation is 1.693 billion tons.The average forest area is 362,188 square kilometers.The maximum is 3,470,760 square kilometers in Canada in 2016, and the minimum is 486 square kilometers in Iceland in 2016.The standard deviation is 802,144 square kilometers.The average value of fixed capital formation is US$423 billion.The maximum value is US$5,663 billion in China in 2020, and the minimum value is US$4.142 billion in Iceland in 2020.The standard deviation is US $1,040 billion.
Labor force comprises people ages 15 and older who supply labor to produce goods and services during a specified period.WBLu et al (2019) Energy consumption (kiloton of oil equivalent; Ktoe) Statistics on the final consumption of local oil, liquefied natural gas, and coal in each country.BP Wu et al (2021) Output Gross domestic product (US$ million) (constant 2015 US$) Total value added from all producers in an economy over a time period.WB Lu et al (2020) CO 2 emissions (million tons) Carbon dioxide emissions come from the burning of fossil fuels.BP Lu et al (2021) Forest area (km 2 ) Forest area refers to trees that are at least 5 m under natural forest or planted forest, whether productive or not.WB Lu et al (2021) Carry-over Gross fixed capital formation (US$ million) (constant 2015 US$) Gross fixed capital formation includes land improvements (fences, ditches, drains, etc); purchases of plant, machinery, and equipment; construction of roads, railways, etc, including schools, offices, hospitals, private residences, and commercial and industrial buildings.WB Hsieh et al (2019) Source: Self-organized.The overall narrative statistics are as follows (as in table3).

Table 3 .
Statistical scale of overall input-output variables from 2016 to 2020.

Table 4 .
Average yearly values of variables and energy efficiency from 2016 to 2020.Canada at 4.1108, and Latvia at 3.8254, which fall on the efficiency boundary.Iceland has energy efficiency of 1, followed by China at 0.4943, South Korea at 0.4678, and Czech Republic at 0.3658.In terms of overall energy efficiency, the top three countries are the United States, Canada, and Latvia.Australia, Austria, Belgium, and other 29 countries have not reached the overall average energy efficiency level.The best overall efficiency performance is the United States, and the worst is the Czech Republic (see table5).

Table 5 .
Year-by-year and overall energy efficiency rankings for 2016-2020.
4.2.2.2.Efficiency during the pandemicThe average energy efficiency of OECD countries and China is 1.1580.Super-efficiency has a score of 4.5722 in the United States, 4.1103 in Canada, and 3.2657 in Latvia.Three countries with energy efficiency reaching 1 are Finland, Iceland, and Turkey.22 countries with energy efficiency below 1 are South Korea 0.4764, Hungary 0.4314, and the Czech Republic 0.3764.The United States has the best average efficiency performance during the pandemic, and the Czech Republic has the worst performance (see table6).

Table 6 .
Summary of dynamic energy efficiency comparison and rankings.
1745, 1.1911, 1.2029, 1.1897, and 1.1303, respectively, the overall average efficiency was 1.1740, and the super-efficiency was 4.7019 in the United States, 4.1108 in Canada, and 3.6625 in Latvia.Energy Efficiency reached 1 for Iceland.Those whose energy efficiency is less than 1 are China 0.4943, South Korea 0.4621, the Czech Republic 0.3658, and other 24 countries.In terms of overall energy efficiency, Australia, Austria, Belgium, and other 29 countries have not reached the overall average energy efficiency level.The overall energy efficiency performance was best in the United States and worst in the Czech Republic.
4.3.2.Efficiency without forest areaThe annual efficiencies from 2016 to 2020 were 0.9319, 0.9647, 0.9533, 0.9406, and 0.9040, respectively, and the overall average efficiency was 0.9344.The super-efficiency is 4.5447 in the United States, 1.8635 in Luxembourg, and 1.7554 in Switzerland.On the efficiency boundary, Iceland has energy efficiency of 1.The 30 countries whose energy efficiency is less than 1 are South Korea 0.4678, Chile 0.4250, and the Czech Republic 0.3600.Austria, Belgium, Canada, and other 27 countries have not reached the overall average energy efficiency.The overall energy efficiency performance was best in the United States and worst in the Czech Republic.The United States had the best overall efficiency, and the Czech Republic had the worst.

Table 7 .
Overall energy efficiency comparison and ranking for 2016-2020.
It is observed that China's carbon dioxide emissions in 2020 (9.899 billion tons) are close to the total carbon dioxide emissions of OECD countries (10.778 billion tons).Therefore, while pursuing economic growth, China should focus on an appropriate allocation of energy structure and actively develop alternative energy sources to effectively reduce carbon emissions.Forest areas have expanded from 361,222.63 square kilometers in 2016 to 363,214.13 square kilometers in 2020, showing an upward trend (0.55%).This implies that OECD countries and China exhibit sustained maintenance of forest areas.