A Study of Factors Affecting National Energy Efficiency

Abstract

National energy efficiency is a key driver for the sustainable development of society. However, the conditions for increasing energy efficiency vary widely around the world and depend on numerous controllable and uncontrollable factors. Existing indicators for assessing energy efficiency typically focus on individual factors, neglecting the complex interplay of socioeconomic, environmental, technological, and other factors that influence energy efficiency. This limitation hampers the quality of assessments. The goal of this study is to develop and apply a comprehensive methodological approach for assessing the influence of key factors on energy efficiency across different countries. The approach utilizes factor analysis methods to identify correlations between indicators and energy-efficiency factors. The study’s findings offer a model for assessing energy efficiency that enables a more profound and comprehensive analysis of the multifactorial impact experienced by national economies in various energy-efficiency domains and areas.

1. Introduction

Increasing energy efficiency is considered a necessary condition for achieving energy and environmental goals. It plays a crucial role in ensuring the development of economies, sectors, and industries. It also helps to reduce the energy intensity of industries while increasing energy security and independence.

Energy-efficiency assessment at the national level serves several purposes. It helps to identify areas of improvement and the main ways to reduce energy losses, save and rationally use limited energy sources [1,2], reduce greenhouse gas emissions and carbon emissions [3], etc.

Given the global efforts to combat climate change and move towards a more sustainable future, evaluating energy efficiency has become increasingly relevant [4]. According to the International Energy Agency (IEA), energy-efficiency measures can deliver nearly 40% of the energy-related greenhouse gas emission reductions needed to meet global climate goals [4]. In addition, energy efficiency can increase the competitiveness of businesses, reduce energy costs for consumers, and create jobs in the clean energy sector [5].

Emerging market and developing countries (EMDEs) collectively account for approximately 260 EJ, or 60%, of final energy consumption. Despite declining energy demand in many countries, final energy consumption is projected to rise by nearly 20% to around 305 EJ by 2030 under current conditions [6]. This growth will increase the global share of EMDEs by 5%, as energy demand in advanced economies is expected to remain relatively stable [7].

As developing countries account for a growing share of energy demand, the greatest opportunities for energy-efficiency improvements will be found in countries such as Brazil, China, India, Indonesia, Mexico, and South Africa. Given their importance to global energy security and climate goals, the IEA is partnering with these and other countries in Africa, Latin America, and the ASEAN region [8] to support energy efficiency through its Energy Efficiency in Emerging Economies (E4) program [9].

Reaching energy efficiency necessitates implementing one of the fastest and most cost-effective CO₂ emission reduction scenarios. In the Net Zero Emissions by 2050 scenario, the energy intensity of the global economy is projected to decrease by 35% by 2030 relative to the current level. This will be driven by energy-efficiency improvements along with complementary measures such as electrification and changes in consumer behavior [10,11]. This would allow for an increased use of clean energy sources such as wind and solar, outpacing the overall demand for energy services. Despite an expected 40% growth in the world economy by 2030 due to population and income level increases, the scenario predicts a 7% reduction in the consumption of traditional energy sources compared to today’s figures [9]. In this context, a comprehensive assessment of the impact of energy efficiency not only on economic growth but also on the values of the human development index is very promising.

A lot of attention is paid to energy-efficiency issues in studies on economy and energy trends [12,13]. This research focus stems from the relevance of interrelated energy and environmental problems of economic growth. Also, there is an increasing recognition of the importance of optimizing energy consumption, along with the necessity of selecting effective measures to manage this process.

In this context, the quality of information for analysis largely depends on the objectivity of the energy-efficiency assessment indicators used. This concerns both private companies [14] and government agencies and other bodies involved in the development of an energy policy [15] that best meets national and international interests while addressing the Sustainable Development Goals [16,17,18].

Energy efficiency is influenced by various complex factors, including energy savings, the use of alternative energy sources, and the flexibility of the energy system [19].

Energy technologies are rapidly evolving towards resource-saving and environmentally efficient systems, with a particular emphasis on renewable energy sources (RES) [20,21,22,23]. This trend is expected to continue, as evidenced by the commitments made by many countries participating in the 2015 Paris Climate Agreement.

However, the use of energy sources, the availability of alternative energy, and the flexibility of energy systems vary greatly across countries. These variations depend on factors such as natural and climatic conditions, access to energy sources, economic structure, technological development, and energy consumption patterns [24].

The energy intensity of an economy is strongly influenced by the structure of its gross domestic product (GDP). In Russia, for example, the resource specialization of the economy and the low level of innovation in production have resulted in an energy intensity that is twice as high as that of the U.S. economy and three times higher than that of developed European countries [25].

When fixed assets demonstrate obsolescence and a high degree of wear and tear, it increases energy intensity in all sectors of the real economy, not only in the energy sector.

Tax incentives and government programs aimed at increasing energy efficiency foster the achievement of energy-efficiency goals. Developed European countries such as Great Britain, Germany, France, and Italy are notable for the important role that their governments play in making their economies energy efficient.

Energy savings, which are crucial for achieving energy efficiency, are largely determined by the individual characteristics of production activities in different industries. Improving these characteristics and indicators is possible in various areas, such as material production, service, and household sectors. In the last decade, the importance of energy management and energy audits has significantly increased in achieving energy-efficiency goals.

At present, it is generally recognized that in the current environmental, social, and economic conditions, achieving energy-efficiency goals is possible only when governmental bodies, business, and society cooperate.

Research hypothesis: the quality and structure of energy sources and their environmental friendliness have a significant impact on energy efficiency in modern conditions.

Research goal: to develop a comprehensive model for assessing the impact of various factors on national energy efficiency by analyzing existing methods for energy-efficiency assessment.

The study’s scientific novelty lies in the authors’ exploration of the role of energy resources in creating new value within the context of GDP. The creation of almost all tangible and intangible products requires energy. The value of energy intensity varies greatly depending on the type of production and end products. When considering the industrial context, the energy intensity of GDP reveals structural shifts towards industries that rely on extensive development. This should be accounted for in macroeconomic analysis and forecasting.

2. Literature Review

Based on the experiences of different countries, two major approaches can be distinguished in energy-efficiency assessment [7].

The first approach measures energy efficiency by its results or effects, such as energy savings or a decrease in electricity consumption [26,27]. However, this approach is not considered economically accurate since the costs incurred in achieving the result are not taken into account.

The second approach involves correlating economic results, including output volumes and GDP, with energy costs, such as energy consumption and electricity generation costs. Energy efficiency is calculated as the ratio of GDP to energy consumed in units of oil equivalent, according to UN and World Bank statistics [28,29]. These energy-efficiency indicators can be adapted to a wide range of problems connected with national sustainable development.

The American Council for an Energy-Efficient Economy (ACEEE) has developed the Energy Efficiency Index (EEI), which ranks countries based on their energy-efficiency policies and performance in various sectors, such as construction, industry, and transportation. The index helps policymakers identify areas for improvement and learn from best practices in other countries, ultimately contributing to global energy efficiency and sustainability. The country’s ranking is determined by the sum of points earned in each of the four categories: buildings, industry, transportation, and national efforts [30].

In Russia, the energy intensity indicator has become widely used as a measure of energy efficiency. It is considered the most universal for comparison and shows the ratio of primary energy consumption to GDP. This indicator is also popular worldwide and is used, for example, by the U.S. Department of Energy [31].

The energy intensity of GDP can be assessed by comparing TPES (total primary energy supply) or TES (total energy supply) and TFC (total final consumption), which factors in energy losses, to GDP (Figure 1).

Primary energy accounting is a way of looking at energy use in terms of natural resources. This is the energy used to produce secondary fuels and generate electricity. This type of accounting is useful for determining a country’s total energy supply (TES) and focuses on where the energy comes from.

For example, transportation energy makes up a much smaller share of primary energy than end-use energy. This is because very little energy is wasted when converting crude oil into transportation fuels (gasoline, diesel, and kerosene). Conversely, electricity accounts for about three times as much primary energy as end-use energy because most power plants are about 33% efficient. This means they have to burn 3000 MW of fuel to generate 1000 MW. This considerably (by a factor of 3) changes the amount of energy that goes into electricity [33].

End-use energy accounting refers to all energy that is directly consumed in a country.

Along with the energy intensity indicator, the energy consumption indicator is widely used in global practice, reflecting the amount of energy that was used for industrial and domestic needs [34]. Different institutions around the world evaluate energy consumption [28,29,31,35].

Energy intensity can serve as a benchmark to compare individual countries. The change in energy consumption required to increase a country’s GDP over time can be described as its energy elasticity, which measures the percentage change in energy consumption needed to achieve a one percent change in national GDP.

It is important to note that with both approaches, the indicators used to assess energy efficiency provide for making general conclusions without identifying the influence of various factors, primarily environmental, technological, and climatic ones, among others.

In the 1990s, the UN, the World Bank, the International Monetary Fund, the OECD, and the European Commission made attempts to develop the necessary indicators. In 2012, the Central Framework for the System of Environmental-Economic Accounting (SEEA) was published, which was intended to be the first international statistical standard for environmental accounting. This system considered the relationship between a country’s economy (which is reflected in the system of national accounts), environmental factors and natural resources [36].

From an energy-efficiency assessment perspective, it is crucial to consider the energy factor in indicators by adjusting gross savings to factor in the depletion of energy sources. The social and environmental aspects of energy efficiency are accounted for through indicators reflecting CO₂ and particulate emissions. The World Bank proposed a formula (1) to calculate the true, or genuine, savings (GS) [37]:

$$\mathrm{GS}=\left(\mathrm{GDS}-\mathrm{CFC}\right)+\mathrm{EDE}-\mathrm{DPNR}-\mathrm{DMGE}$$

(1)

where GDS is gross domestic savings, CFC is the depreciation of production assets, EDE is education expenditure, DPNR is the depletion of natural resources, and DMGE is damage from environmental pollution. Accounting for human capital, energy, and environmental factors, which are integral to the national wealth of each country, provides for an adjusted indicator.

The indicator is based on a comprehensive approach to assessing the sustainability of a system. Its calculation takes into account not only natural resources but also other components necessary to ensure that future generations have the same ability to meet their needs as we do.

The indicator described above can serve as an aggregate energy-efficiency assessment index [38]. One of its advantages is its versatility: it can be calculated using different methodologies, providing for both global and national assessments. This enables making comparisons between different countries. It is worth noting that many countries worldwide have already adopted GS as an official macro-level indicator [38].

GS is a useful tool for considering and evaluating energy efficiency as a critical factor in sustainable development. It serves as a general indicator for energy-efficiency assessment. However, a more in-depth evaluation of the economy requires a qualitative analysis of the adjustment components based on each country’s unique characteristics and the most influential component. This approach is necessary to identify the primary sources of the problem. Also, making GDP adjustments poses certain challenges such as the valuation of environmental data and the lack of essential statistical information [39]. Thus, while GS is an excellent tool, it is too general for assessing the sustainable development of economies.

GS and the energy intensity of GDP are calculated based on statistical data from countries, international agencies, and the World Bank. They are primarily used for comparative macroanalysis and can serve as a foundation for developing collaborative decisions between governments in areas such as energy efficiency and environmental safety.

The experience of developed countries demonstrates that energy efficiency comprises important components. They include energy savings, decrease in energy intensity, decrease in the country’s dependence on energy imports, fuel diversification, curbing CO₂ emissions, increase in the share of renewable energy sources in the country’s energy mix, and better quality of life [40].

In 2011, I. A. Danilov proposed using the level of technological development as an integral indicator of energy efficiency, which is expressed as a percentage. It is defined as the share of useful electrical energy in the final consumption of primary energy taking into account energy losses and energy consumption for the energy sector’s own needs [41]. The level of technological development is included in tables of energy efficiency indicators and is calculated based on data from the U.S. Energy Information Administration (EIA), with useful electricity recalculated according to the so-called theoretical (coal) equivalent of approximately 123 g/kWh. The level of technological development is considered to be a more adequate reflection of the scale of progress in countries with a high GDP per capita. This is because it simultaneously reflects both the energy intensity and electricity intensity of GDP [41].

The application of this indicator is complicated by the fundamental difference between the final consumption (energy use) as presented in energy mixes and the consumption of primary energy sources in the data provided by the IEA (International Energy Agency). According to the EIA (Energy Information Administration), primary energy consumption includes not only the consumption of petroleum products, dry natural gas, coal, and output from nuclear power plants and hydroelectric power plants but also other renewable electricity sources, as well as net electricity imports, which are calculated as the ratio of imports to exports. The inclusion of net imports may be necessary to adjust for net production as reported in the International—U.S. Energy Information Administration, which excludes net imports of electricity and therefore only accounts for electricity consumption for own and production needs. In contrast, energy mixes indicate final electricity consumption, which is calculated including net imports of electricity.

At the end of the 20th century, the EROI (energy return on investment) indicator was proposed by C. Hall to determine the ratio between the energy generated and the energy consumed in the generation process [42].

Despite the simplicity of its calculation, EROI can vary greatly for the same energy source due to different conditions regardless of the energy source used. In addition, EROI can be calculated both for a specific object (power plant, mining facility, etc.) and for energy industries as a whole, which can lead to significant variations in the final values of the indicator [23].

In international practice, other methods for assessing energy efficiency are also used, as shown in Table 1.

Table 1. Other international indicators of energy efficiency.

Name	Content
LROE (levelized revenue of electricity)	which is calculated as the ratio of the total income from electricity generation to the total energy produced over the entire life of the power plant;
LCOE (levelized cost of electricity)	which is the ratio of the total cost of creating a power plant to the total energy produced during the entire service life of the power plant;
EPBT (energy payback time)	which is the ratio of all energy used to all energy generated [24].

The indicators that are used at the industry level are presented in Table 2.

Table 1. Other international indicators of energy efficiency.

Name	Content
LROE (levelized revenue of electricity)	which is calculated as the ratio of the total income from electricity generation to the total energy produced over the entire life of the power plant;
LCOE (levelized cost of electricity)	which is the ratio of the total cost of creating a power plant to the total energy produced during the entire service life of the power plant;
EPBT (energy payback time)	which is the ratio of all energy used to all energy generated [24].

The indicators that are used at the industry level are presented in Table 2.

Table 2. Industry energy-efficiency indicators.

Name	Content
EOI (energy-efficiency operating indicator)	which is used as a practical method for assessing the energy efficiency of ships and CO2 emissions [43].
EEOI (energy-efficiency operational indicators)	which is the total volume of CO2 emissions over a period of time per unit of revenue in ton miles.
EEDI (energy-efficiency design index)	which reflects the amount of CO2 emissions by the ship in relation to the volume of cargo carried (in grams per ton-mile).
NER (net energy ratio)	which is calculated as the ratio of the amount of useful energy generated from a certain energy source to the amount of energy used to obtain this energy source.
EER (energy-efficiency ratio)	which is the ratio of the cooling capacity (Qx) at the highest load to the power used (Ncons). It is determined by the following formula: EER = Qx/Ncons [8,10,11] and many others.

Table 2. Industry energy-efficiency indicators.

Name	Content
EOI (energy-efficiency operating indicator)	which is used as a practical method for assessing the energy efficiency of ships and CO2 emissions [43].
EEOI (energy-efficiency operational indicators)	which is the total volume of CO2 emissions over a period of time per unit of revenue in ton miles.
EEDI (energy-efficiency design index)	which reflects the amount of CO2 emissions by the ship in relation to the volume of cargo carried (in grams per ton-mile).
NER (net energy ratio)	which is calculated as the ratio of the amount of useful energy generated from a certain energy source to the amount of energy used to obtain this energy source.
EER (energy-efficiency ratio)	which is the ratio of the cooling capacity (Qx) at the highest load to the power used (Ncons). It is determined by the following formula: EER = Qx/Ncons [8,10,11] and many others.

In general, it can be stated that no universal energy-efficiency methodology has yet been developed that could comprehensively serve as a basis for sustainable and green development. The aforementioned are the most developed and studied metrics that can be statistically compared.

3. Research Materials and Methods

The methodology of this research focuses on identifying the statistical relationship between the macro-level indicator that characterizes the energy efficiency of the economy and various factors. Correlation and regression analyses are used to study and interpret the data.

The secondary information sources used for this research included data from the International Energy Agency [44] and the World Bank [45].

In this study, the energy intensity of GDP is used as an energy-efficiency indicator. It is defined as the ratio of TFC to GDP calculated at purchasing power parity. The study investigates the relationship between this indicator and several factors, including the volume of GDP, energy intensity, and carbon intensity of GDP (at purchasing power parity) [39], total energy supply (TES), population, gross CO₂ emissions, GDP per capita [45], primary energy losses per unit volume of GDP, and the share of carbon-containing sources in the primary energy mix. The specific indicator of energy losses was computed independently due to the absence of available data. Additionally, based on primary energy consumption data, the proportion of carbon-containing sources such as gas, oil and coal was determined.

The choice of these indicators for analysis is based on the following reasons. Absolute indicators reflect the scale of the economy and the associated volumes of energy use, energy consumption, GDP generation, and CO₂ emissions. On the other hand, specific indicators allow for making comparisons between countries with different conditions. The resulting indicator of the GDP’s energy intensity makes it possible to compare different countries; the indicator of energy losses is, in our opinion, one of the main indicators that affect energy intensity and reflect the level of energy savings. To take into account economies of scale, the value of energy losses calculated per unit of GDP produced was taken as an indicator of losses. The indicator of GDP per capita reflects the level of economic activity and, to a first approximation, the standard of living of the population. The carbon intensity of GDP compares the volume of emissions generated and the product, while the share of carbon-containing energy sources measures the quality of energy sources used from an environmental standpoint. The calculations used data from 2018, prior to the onset of the COVID-19 pandemic.

The study analyzed 21 countries with the highest indicators of installed net capacity [46]. They vary in their economic development, average per capita income, sources and volumes of energy produced and consumed, and CO₂ emissions.

The initial data used for the calculations is presented in

Table 3. Initial data.

NameFull	Name	Energo_1	Energo	TES	TFC	Losses	Gdp	Losses_gdp	CO2_Gdp	CO2_Gdp_10_3	Gdp_pers	CO2_pers	CO2 Part	CO2	Popul
Australia	Aus	2.4	2.80	5,389,961	35,12,305	1,877,656	1,253,150	1.50	0.00031	0.31	0.050	0.0000157	0.93	391.4	24,966,643
Brazil	Bra	5.2	3.00	11,936,318	94,29,873	2,506,445	3,145,953	0.80	0.00013	0.13	0.015	0.0000020	0.53	411.4	210,166,592
Canada	Can	4.2	3.75	13,021,934	6,939,939	6,081,995	1,852,986	3.28	0.00031	0.31	0.050	0.0000154	0.75	570.0	37,065,084
China	Chi	6.5	4.01	135,747,020	87,152,137	48,594,883	21,736,536	2.24	0.00045	0.45	0.015	0.0000070	0.88	9777.1	1,402,760,000
France	Franc	2.5	2.03	10,522,519	6,334,853	4,187,666	3,125,380	1.34	0.00010	0.1	0.047	0.0000045	0.46	300.2	67,158,348
Germany	Ger	2.6	2.04	12,876,998	9,326,833	3,550,165	4,579,331	0.78	0.00015	0.15	0.055	0.0000084	0.78	694.5	82,905,782
India	Indi	10	8.29	38,808,108	25,833,423	12,974,685	3,116,595	4.16	0.00074	0.74	0.002	0.0000017	0.76	2316.5	1,369,003,306
Indonesia	Indon	6.5	0.72	9,846,631	6,529,350	3,317,281	9,021,614	0.37	0.00006	0.06	0.034	0.0000020	0.74	533.0	267,066,843
Iran	Ira	16.8	5.84	11,457,984	7,483,659	3,974,325	1,282,417	3.10	0.00046	0.46	0.015	0.0000068	0.99	586.2	85,617,562
Italy	Ita	2.6	1.91	6,146,162	4,977,698	1,168,464	2,600,326	0.45	0.00012	0.12	0.043	0.0000052	0.81	317.1	60,421,760
Japan	Jap	2.6	2.23	17,770,515	11,924,928	5,845,587	5,340,832	1.09	0.00020	0.2	0.042	0.0000086	0.89	1084.9	126,811,000
Korea	Kor	4.8	3.44	11,802,989	7,630,296	4,172,693	2,220,442	1.88	0.00027	0.27	0.087	0.0000236	0.85	605.5	25,638,149
Mexico	Mex	3.8	1.90	7,241,674	4,810,220	2,431,454	2,535,950	0.96	0.00016	0.16	0.020	0.0000034	0.89	416.2	124,013,861
Russian Federation	Rus	15.1	5.09	32,347,519	21,538,849	10,808,670	4,231,842	2.55	0.00038	0.38	0.029	0.0000111	0.90	1601.5	144,477,859
Saudi Arabia	Sau	9.8	4.04	9,707,198	6,646,845	3,060,353	1,643,611	1.86	0.00030	0.3	0.047	0.0000142	1.00	498.1	35,018,133
South Africa	Safr	8	3.47	5,432,087	2,850,008	2,582,079	821,364	3.14	0.00053	0.53	0.014	0.0000076	0.92	434.1	57,339,635
Spain	Spa	2.8	1.89	5,182,354	3,593,785	1,588,569	1,904,500	0.83	0.00013	0.13	0.041	0.0000053	0.74	248.7	46,797,754
Turkiye	Tur	4.4	1.87	6,039,636	4,314,189	1,725,447	2,302,310	0.75	0.00016	0.16	0.028	0.0000045	0.86	374.7	82,809,304
United Kingdom	UK	1.7	1.68	7,200,474	5,322,753	1,877,721	3,161,750	0.59	0.00011	0.11	0.048	0.0000053	0.79	353.8	66,460,344
United States	USA	3.4	3.25	92,629,207	66,680,893	25,948,314	20,527,156	1.26	0.00024	0.24	0.063	0.0000150	0.82	4910.0	326,838,199
Vietnam	Vie	8.5	2.67	2,500,641	1,062,052	936,445.46	936,445	1.13	0.00025	0.25	0.010	0.0000025	0.80	235.1	94,914,330

Designations and units of measurement: Energo—energy intensity of GDP, J/$; TES—total energy supply, 10⁶ J, TFC—total final consumption, 10⁶ J; losses—total primary energy losses, 10⁶ J; gdp—GDP volume, 10⁶ $; Losses_gdp—energy losses per unit of GDP; CO₂_gdp—CO₂ emissions per unit of GDP; gdp_pers—GDP per capita; CO₂_part—share of carbon-containing energy sources in total primary sources, %; CO₂—total CO₂ emissions, 10⁹ kg.

.

The R Project tools were used to make calculations [47], which provide a modern toolkit for statistical data processing [48].

The program’s general algorithm follows a procedure similar to building a multiple regression model. It involves selecting the form of connection (regression equations), choosing factor features, evaluating model parameters, and verifying model adequacy.

Specific operations include normalizing the data, constructing a correlation matrix, correlating pairs of variables, forming the final set of independent variables, building a correlation model, ranking factors, and validating the model.

The final set of independent variables was formed using the stepwise elimination method, which utilized the stepAIC() function from the MASS package [49].

At the first step, all combinations of variables were sorted, and the least informative feature was excluded based on the given criterion. This process was repeated until the best value was obtained according to the stopping criterion.

To rank the factors based on their influence on the result, the factors were standardized to have a zero mean and a standard deviation of one.

4. Results and Discussion

Table 4. Factors influencing energy intensity: pairwise correlation.

Indicator (Factor)	Denomination	Pairwise Correlation Coefficient
Energy losses per unit of GDP	losses_gdp	0.884
CO2 emissions per unit of GDP	CO2_gdp_103	0.904
GDP per capita	gdp_pers	−0.367
The share of carbon energy sources in the primary energy mix	CO2_part	0.254
Total CO2 emissions	CO2	0.278
Losses per unit of popul	lossesMln	0.314
TFC per unit of popul	TFCMln	0.291
Popul	PopulMln	0.554
CO2 per unit of popul	CO2_Mln	0.123
GDP per unit of popul	gdpMln	−0.001
TES per unit of popul	TESMln	0.300

shows the values of the pairwise correlation coefficients between energy intensity and several factors. The results reveal a notable correlation between energy intensity and energy losses, as well as a correlation with GDP’s carbon intensity. Although the level of correlation is considerably lower in all other instances, it is not advisable to dismiss the influence of these factors at this stage, as they can be filtered out during model development.

The selection of factors for the energy-efficiency assessment model was based on a qualitative theoretical and economic analysis. Further analysis confirmed their quantitative relationship and the feasibility of including them in the model. The direct correlation between primary energy losses and CO₂ emissions can be explained as follows: as transportation distances and the scale of primary energy resource processing increase, CO₂ emissions also grow. This correlation is supported by statistical data on the two factors across countries (see Table 1). Similarly, the correlation between the population size (Popul) and total final energy consumption (TFCMln) can be easily explained. As the population grows, there is an increase in both energy consumption per unit of GDP and the number of energy consumers, including large ones. The correlation between CO₂ emissions and GDP (gdpMln) is also explicable. As a country’s GDP expands, domestic consumption and the generation of industrial and domestic waste increase. Unfortunately, the processing of such waste still leads to significant emissions.

A fragment of the correlation table is shown in Figure 2.

The regression model was developed using the stepwise inclusion method, employing the stepAIC function from the MASS package in the R Project system. This method follows a step-by-step approach to select factors that demonstrate the strongest influence on the response variable. During each step, the algorithm identifies the factor that provides the most optimal solution in combination with the previously selected factors. This process continues until the criterion reaches an extremum, and only significant variables are included in the final model. To evaluate the model’s performance, the Akaike information criterion is utilized within the stepAIC function.

Figure 3 shows the resulting indicators and the multiple regression model.

The multiple regression equation has the following mathematical form:

$$Y_{energo}=0.57x_{looses\_gdp}+2.8x_{CO2part}-0.02x_{CO2}+0.002x_{Popul}-0.29x_{gdp}+0.17x_{TES}-0.4$$

The significance of the model’s coefficients was evaluated using a t-test. All p-values were found to be smaller than the generally accepted significance level of 0.05. This indicates that all coefficients are significantly different from zero and have a significant impact on the response.

Residuals are the differences between the observed (given) values and the theoretical values of energy intensity. A smaller value indicates a better-fitting model. Our model has small residuals ranging from −0.6930 to 1.0690. The values of the first quartile, median, and third quartile of the residuals are −0.1918, −0.0711, and 0.1651, respectively.

As a result, among the factors identified, the model assessing their impact on energy intensity incorporates energy losses, the share of carbon energy sources in the primary energy mix, CO₂ emissions, population, GDP, and primary energy consumption.

The coefficients in the model indicate how energy intensity changes with a unit change in the factor. For instance, an increase in energy losses by 1 J/$ leads to an increase in energy intensity by 0.57 10⁶ J/$, while an increase in the share of carbon-containing sources leads to an increase in energy intensity by 2.8 10⁶ J/$.

The p-value, which indicates that the confidence intervals in the coefficient estimation do not contain zero, is also shown in parentheses. It indicates the significance of the coefficients at various levels of significance. The coefficient of determination (0.9461) and the p-value level demonstrate the significance of the equation as a whole.

The standardized coefficients of the regression model, which allow for ranking the factors based on their level of influence on energy intensity, are displayed in

Table 5. Regression model coefficients on a standardized scale.

	Est.	S.E.	t Val.	p Value
TESMln	3.35795	0.62862	5.34178	0.00010
CO2	2.66024	0.50850	−5.23157	0.00013
gdpMln	1.01362	0.26754	−3.78862	0.00200
PopulMln	0.54487	0.12257	4.44533	0.00055
losses_gdp	0.36495	0.10914	3.34388	0.00482
CO2 part	0.21412	0.07441	2.87740	0.01217

.

The selected fragment presents the coefficients for the variables, which indicate that the extensive factors are the most significant in the model. These include the amount of primary energy used, gross CO₂ emissions, GDP, and population. This corresponds to the current situation for countries with the largest generating capacities. The ranks of energy losses and the share of carbon-containing energy sources are lower.

Model test results show that the coefficient of determination R², which reflects the quality of the equation as a whole, has a value of 0.95, meaning that 95% of the response variation is explained by the factors included in the model. The p-value is of the order of 10⁻⁸, indicating the significance of the equation as a whole.

The absolute deviation of the model data from the actual data is shown in Figure 4.

Fitted values are theoretical response values produced by the model.

Residuals are the discrepancies between the observed (given) values and the theoretical values of energy intensity. The red line in the plot represents the average values of the residuals corresponding to each fitted value. As they are close to zero, it indicates that the model errors are minimal, suggesting a high-quality model.

The largest deviations of the model data from the actual data are observed for the economies of Iran, Mexico, and Brazil. This suggests that the model does not fully capture the factors that affect their energy efficiency. They may include the structure of the economy (the share of industrial production and those of non-industrial sectors), GDP components, climatic conditions, peculiarities of energy logistics, etc. However, for all other countries, including Russia, the model appears to be applicable regardless of their level of economic development.

Future studies may consider incorporating additional factors that affect energy efficiency and conducting panel studies.

Further studies should focus on specifying the relationship between the considered indicators. The following aspects require attention:

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Identifying all potential indicators and factors that contribute to changes in the energy-efficiency indicator of a national economy. This entails establishing an extensive database of factors.

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Determining the factors that cause real changes in the energy-efficiency indicator;

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Assessing how strongly each factor affects energy efficiency;

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Classifying the factors as strong or weak;

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Establishing the factor or factors that produce the biggest changes in the energy-efficiency indicator.

The objective of conducting factor analysis is to gather the necessary information for effectively managing these factors in strategic planning and forecasting the energy efficiency of the national economy.

5. Conclusions

The study has revealed that currently, there is no single indicator that can reflect energy efficiency at the national level. However, the energy intensity of GDP (i.e., the ratio of energy consumed to GDP determined at purchasing power parity) is the most well-known and generally accepted indicator. It is based on international statistics and provides for utilizing the indicators used within the national statistical system.

The study utilized the R Project tools to develop a multiple regression model that can be employed to analyze and predict the impact of several factors on the national energy intensity of both economically developed and developing countries. These factors include energy losses, the share of energy produced from carbon-containing sources, CO₂ emissions, population size, GDP, and the volume of primary energy used. However, the model may not be suitable for Brazil, India, and Mexico.

The study also found that extensive factors, such as the use of primary energy, CO₂ emissions, and GDP, contribute the most to energy intensity. Energy losses and the energy generation mix have a lower impact on energy intensity, which confirms the research hypothesis.