Changes in the Global Structure of Energy Consumption and the Energy Transition Process

Abstract

The global energy transition represents a pivotal aspect of the pursuit of sustainable development and the reduction of greenhouse gas emissions. The objective of this study was to examine the dynamic relationships between global primary energy consumption and the consumption of individual energy sources (nuclear, oil, coal, natural gas, renewables) from 2011 to 2023. To examine both long-run and short-run relationships between variables, advanced econometric methods were employed, including the Johansen cointegration test and the Vector Error Correction Model (VECM). Furthermore, an Index of Sustainable Energy Transformation (ISTE) was devised to quantify the advancement of the transition to low-carbon energy sources. The analysis confirms the existence of long-term equilibrium relationships between global primary energy consumption and the consumption of individual energy sources. The analysis revealed that renewable energy consumption exerts a considerable influence on primary energy consumption, both in the short and long term. The ISTE index demonstrated a notable increase over the period of 2011 to 2023, indicative of advancement in the global energy transition. The results confirm the existence of a stable long-term equilibrium between global primary energy consumption and the consumption of individual energy sources. The observed increase in the ISTE index indicates progress towards low-carbon energy sources, which has important implications for energy policy and sustainable development. The results can support policymakers in monitoring the progress of the energy transition and shaping policies to accelerate the development of renewable energy sources.

1. Introduction

The consumption of energy on a global scale has a significant impact on the economies of countries and on the environment due to the release of greenhouse gases [1,2,3]. In recent decades, the discourse on the necessity for an energy transition towards sustainable and low-carbon energy sources has notably intensified [4,5,6,7,8,9,10]. This transformation is essential to achieve the objectives set out in the Paris Agreement and the UN Sustainable Development Goals [11,12,13,14].

The current structure of global energy consumption is dominated by fossil fuels, including coal, oil, and natural gas, which collectively account for over 80% of total primary energy consumption [15,16]. Despite growing environmental awareness and technological advances, the proportion of renewable energy sources in the global energy mix remains inadequate [17,18]. Numerous studies focus on specific aspects of the energy transition, such as the development of renewable energy or improvements in energy efficiency [19,20,21,22,23,24,25]. However, there is a necessity for a comprehensive understanding of the dynamic relationship between different energy sources and global primary energy consumption.

The rise in primary energy consumption represents a substantial challenge, particularly in light of its impact on climate change and the environment. As the International Energy Agency (IEA) observes, global primary energy consumption has increased by over 10% since 2011, accompanied by a corresponding rise in fossil fuel-related emissions. Concurrently, the proportion of renewable energy has grown from approximately 8% to over 15% of global energy consumption, demonstrating considerable but inadequate advancement towards decarbonisation objectives.

Some studies indicate that government policies and investments in renewables have a significant impact on reducing CO₂ emissions [26,27,28]. However, other studies suggest that the energy transition faces barriers due to economic and technological constraints [29,30,31]. In light of these differing perspectives, it is important to examine how changes in the consumption of individual energy sources affect the global energy transition process.

The objective of this article is to address deficiencies in the existing literature by developing a Sustainable Energy Transformation Index, which assesses progress in the structure of global energy consumption, including the carbon intensity of different energy sources. The ISTE differs from other indices, such as the World Economic Forum’s Energy Transition Index (ETI), which measures countries’ preparedness for transition, in that it focuses on actual changes in energy consumption patterns at the global level. The development of this index and the use of econometric models, such as the VECM and Johansen cointegration tests, allow us to understand the dynamics of the relationship between global primary energy consumption and individual energy sources.

This study was based on the following research hypotheses:

• H1: there is a long-term equilibrium relationship (cointegration) between global primary energy consumption and the consumption of individual energy sources.
• H2: the consumption of renewable energy and electricity exerts a significant influence on global primary energy consumption in both the short and long term.
• H3: the Index of Sustainable Energy Transformation demonstrates a notable increase between 2011 and 2023, indicating advancements in the global energy transition.

The objective of the analyses is twofold: firstly, to confirm the hypotheses; secondly, to identify new avenues for research into the energy transition at regional and national levels. This will facilitate a more comprehensive understanding of the barriers and factors that facilitate the transition to low-carbon energy sources, which, in the long term, can contribute to more effective implementation of sustainable development goals.

Energy transformation is of pivotal importance in achieving the Sustainable Development Goals (SDGs) set forth by the United Nations, particularly in the context of Goal 7 (‘clean and accessible energy’) and Goal 13 (‘climate action’) [32]. Transformations in the energy sector, including the reduction of carbon emissions, the development of renewable energy sources, and the enhancement of energy efficiency, are crucial for the reduction of the global carbon footprint and the mitigation of climate change [33]. The 2015 Paris Agreement and other global commitments emphasise the necessity of limiting temperature increases to below 2 °C. This will require a significant reduction in the use of fossil fuels in favour of low-carbon and renewable energy sources [34]. It is therefore evident that the transition to a more sustainable energy system is not merely a technological concern; it is also a pivotal aspect of the pursuit of sustainable development and the creation of carbon-neutral economies [19].

The existing literature emphasises the importance of energy transition for sustainable development [35]. A growing body of evidence suggests that the development of renewable energy sources (RESs) can contribute to improvements in air quality, job creation and energy security [36]. However, this process also presents a number of challenges, including the necessity to modernise energy infrastructure, integrate unstable energy sources, and ensure a fair transition for regions that are dependent on the carbon industry [37,38,39].

The study of long-run relationships between economic variables in the context of the energy transition is commonly undertaken through the use of econometric analyses, including the application of vector error correction models and Johansen cointegration tests. For instance, in studies examining the relationship between energy consumption and economic growth, the utilisation of these techniques enables the identification of long-run equilibrium and short-run dynamics. Furthermore, cointegration analysis enables the evaluation of the stability of relationships between variables over time, which is crucial in the context of dynamic changes in energy markets [40,41,42,43,44].

This study contributes to the existing literature by analysing global trends in the consumption of different energy sources from 2011 to 2023. This study employs advanced econometric techniques, including VECM and Johansen cointegration tests, to identify long-term relationships between primary energy consumption, electricity, renewables, nuclear, coal, natural gas, and oil. Moreover, the incorporation of the Energy Transformation Index represents a novel methodology for evaluating the advancement towards a sustainable energy mix. In this way, this study contributes to the existing literature by providing a comprehensive analysis of the dynamics of global energy consumption and tools to monitor progress in the energy transition.

The present study analyses the dynamics of changes in the global energy mix from 2011 to 2023, thereby allowing an assessment of the progress of the energy transition over the last decade. The choice of the research period is driven by the availability of data and the intensification of international efforts to reduce emissions, which gained importance after the signing of the Paris Agreement in 2015. These developments pose new challenges for research, in terms of the necessity to monitor the progress of the energy transition and assess structural changes in the consumption of different energy sources.

The challenges of energy transition and the reduction of greenhouse gas emissions are of a transnational nature, necessitating a global approach. In the context of climate change and the implementation of the Sustainable Development Goals, it is essential to monitor the energy transition on a global scale in order to gain insight into the prevailing trends and the impact of pro-climate actions on a global scale. Furthermore, a global approach enables the interdependencies between the consumption of diverse energy sources to be identified, which can be challenging to discern in analyses that focus on individual countries or regions.

Furthermore, a global perspective enables the development of the Index of Sustainable Energy Transition as a means of evaluating global progress in the transition to low-carbon energy sources. This approach provides data that can be beneficial to international organisations, such as the UN or IEA, in formulating strategies and energy policies aimed at sustainable development.

2. Materials and Methods

This study utilizes data from Statista, a reputable global source of statistics and market information. The data set encompasses the period between 2011 and 2023, thereby facilitating an examination of contemporary trends in global energy consumption. The selection of this time frame is justified by the availability of up-to-date data and significant developments in the energy sector, including the growing importance of renewables and the impact of global events, such as the global pandemic caused by the SARS-CoV-2 virus.

The following variables were selected for analysis: global primary energy consumption (EJ), global electricity consumption (TWh), global nuclear energy consumption (EJ), global oil consumption (million metric tonnes), global coal consumption (EJ), global natural gas consumption (bcm), global renewable energy consumption (EJ). The selected variables represent the principal energy sources employed on a global scale. Such variables permit an evaluation of the influence of specific energy sources on global primary energy consumption and the energy transition process. The data for these variables are available and consistent throughout the period under analysis.

A preliminary statistical analysis of the data was conducted, whereby basic descriptive statistics were calculated for each variable, including the mean, median, standard deviation, minimum, and maximum values. This facilitated an appreciation of the distribution of the data and the discernment of trends and potential anomalies.

To guarantee the reliability of the econometric analyses and to circumvent the issue of spurious regression, time series stationarity tests were conducted utilising the Augmented Dickey–Fuller (ADF) test. The objective was to ascertain whether the time series of variables were stationary or integrated of order one. Tests were conducted for each variable at levels and following the initial differentiation. If the test statistic was less (more negative) than the critical value at a given level of significance, the null hypothesis of non-stationarity was rejected.

Since the variables were found to be integrated of order one, the Johansen cointegration test was applied to investigate the existence of long-run equilibrium relationships among them. The objective was to ascertain the number of cointegrating vectors that indicate long-run relationships between the variables. The trace test and the maximum eigenvalue test were employed for this purpose.

Once cointegration between the variables was confirmed, a vector error correction model was estimated, which allows for the analysis of both short-run dynamics and long-run relationships. The VECM model incorporates lags of endogenous variables and an error correction term (ECT) that reflects deviations from long-run equilibrium. The number of lags in the model was determined by the Akaike information criteria (AIC) and Schwarz information criteria (BIC). An analysis of the ECT coefficients and short-run parameters enabled an evaluation of the influence of individual variables on primary energy consumption.

A vector error correction model was employed to examine the long-run and short-run relationships between primary energy consumption and various energy sources. This model represents an extension of the vector autoregressive model (VAR) and is particularly advantageous when the variables are integrated of order one (I(1)) and demonstrate cointegrating relationships, indicating the presence of a long-run equilibrium between them.

The fundamental VECM equation for the set of Y_t variables can be expressed as follows:

$$\Delta {\mathrm{Y}}_{\mathrm{t}}=\Pi {\mathrm{Y}}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}-1}{\Gamma }_{\mathrm{i}}\Delta {\mathrm{Y}}_{\mathrm{t}-\mathrm{i}}+\mu +{\in }_{\mathrm{t}}$$

(1)

• ΔY_t—vector of first differences of endogenous variables at time t.
• Y_t−1—vector of variables in the previous period (delay of one period).
• Π—cointegration matrix that reflects the long-term relationship between the variables.
• ${\Gamma }_i$—matrix of short-term coefficients with delays up to k − 1 periods.
• $\mu$—free expression vector.
• ${\in }_t$—vector of random components.

The matrix Π can be decomposed into the product of the matrix α i β:

Π = αβ′

(2)

• β′—cointegrating vector matrix, which represents the long-run equilibrium coefficients between the variables.
• α—matrix of error correction coefficients that show the speed of return to long-term equilibrium after a short-term disturbance.

The VECM model thus permits the examination of both long-run and short-run relationships between variables.

In order to ascertain the number of cointegrating relationships (long-run relationships) between variables, the Johansen cointegration test was employed. This test is founded upon the examination of the eigenvalues of the Π matrix, thereby enabling the identification of the number of cointegrating vectors.

The Johansen test employs two principal statistical techniques.

(1) The trace statistic is employed to test the hypothesis regarding the number of cointegrating vectors, specifically whether the sum of the eigenvalues is significant:

$$\mathrm{trace} \mathrm{statistic}=-\mathrm{T} {\sum }_{\mathrm{i}=\mathrm{r}+1}^{\mathrm{n}}\ln (1-{\lambda }_{\mathrm{i}})$$

(3)

• T—number of observations.
• ${\lambda }_i$—eigenvalues of the matrix Π.

(2) The maximum eigenvalue statistic is employed to test the hypothesis that there are precisely r cointegrating vectors, in contrast to the alternative hypothesis of r + 1 vectors:

$$\mathrm{maximum} \mathrm{eigenvalue} \mathrm{statistic}=-\mathrm{T} \ln (1-{\lambda }_{\mathrm{r}+1})$$

Both statistics are employed to substantiate hypotheses regarding the number of cointegrating relationships within the model. The critical values for these statistics are provided by Johansen (1988) based on an asymptotic distribution [45]. By utilising Johansen’s cointegration test, it is feasible to accurately ascertain the number of long-run relationships between variables in the model, which permits the construction of the VECM model and the analysis of both short-run and long-run influences of variables.

The ISTE index was developed for the purpose of quantitatively measuring progress in the transition to low-carbon energy sources. In order to ensure consistency of data, all energy sources were converted to exajoules (EJ):

• Oil: 1 million tonnes ≈ 0.042 EJ.
• Natural gas: 1 billion m³ ≈ 0.0382 EJ.
• Electricity: 1 TWh ≈ 0.0036 EJ.

The assignment of weights was based on the ratio of CO₂ emissions to energy units:

• Coal: 94 kg CO₂/GJ ⇒ Weight w_coal = 1/94.
• Oil: 73 kg CO₂/GJ ⇒ Weight w_oil = 1/73.
• Natural gas: 56 kg CO₂/GJ ⇒ Weight w_gas = 1/56.
• Nuclear and renewable energy: Emissions ≈ 0 kg CO₂/GJ ⇒ Weight w = 1.
• Electricity: weighting depending on energy mix (average emissivity) *.

* It should be noted that for the sake of simplicity, the weighting for electricity is taken as a weighted average of the emissivity of the energy sources used to produce it. Due to the inherent complexity of the subject matter, electricity will not be included directly in the ISTE. However, its impact is indirectly included through the consumption of individual energy sources.

The share of each energy source in total primary energy consumption was calculated for each year according to the following formula:

$${\mathrm{I}\mathrm{S}\mathrm{T}\mathrm{E}}_{\mathrm{t}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}}\times ({\displaystyle \frac{{\mathrm{E}}_{\mathrm{i},\mathrm{t}}}{{\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l},\mathrm{t}}}})$$

(4)

• ${\mathrm{E}}_{\mathrm{i},\mathrm{t}}$—energy consumption of source i in year t.
• ${\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l},\mathrm{t}}$—total primary energy consumption in year t.
• ${\mathrm{w}}_{\mathrm{i}}$—the weight assigned to the source i.

This study proposes the creation of a new index, the Sustainable Energy Transition Index, with the objective of monitoring changes in global energy consumption patterns and measuring progress towards the decarbonisation of the energy sector. It is, however, worthy of note that a similar designation is accorded to an index developed by the World Economic Forum (WEF)—the Energy Transition Index (ETI). Notwithstanding the analogous nomenclature, the two indices have disparate objectives and methodologies, thereby facilitating divergent perspectives on the energy transition process.

The WEF ETI serves as an indicator for measuring the preparedness of countries in regard to the transition to a sustainable energy future. In its assessment, the index considers a range of factors, including energy security, environmental sustainability, and economic stability. The principal objective is to evaluate the capacity of countries to implement policies and strategies pertaining to low-carbon energy, thereby facilitating an analysis of preparedness for forthcoming changes in the energy sector.

In contrast, the ISTE proposed here focuses on structural changes in the global energy mix and their impact on the overall decarbonisation of the energy sector. The ISTE is based on primary energy consumption rates and individual energy sources, thereby enabling the observation of changes in the utilisation of fossil fuels and the expansion of renewable and low-carbon energy sources. In contrast to the WEF’s ETI, the ISTE does not assess countries’ transition readiness; rather, it examines global trends in energy consumption, thereby providing a comprehensive overview of the progress made towards decarbonisation goals.

In order to assess the stability of the primary energy consumption model parameters, an analysis was conducted on sub-periods, together with a CUSUM test. The data were divided into two sub-periods: 2011–2016 and 2017–2023. A multiple regression was performed for each sub-period and for the full period. The Chow test was employed to ascertain the significance of differences between sub-periods. The CUSUM test was utilised to identify potential changes in parameters over time. The statistical analyses were conducted in R version 4.2.2 using the strucchange package.

The software most commonly employed in research was utilised to conduct statistical and econometric analyses. EViews 12 was employed for the estimation of time series models, encompassing ADF stationarity tests, Johansen cointegration tests, and Vector Error Correction Model (VECM) estimation. The R statistical computing environment, version 4.2.2, with the urca and vars packages, was employed to perform stationarity tests, cointegration tests, and VECM model estimation as an alternative tool to validate the results obtained in EViews. Microsoft Excel 2019 was employed for the processing of data, the performance of preliminary statistical analyses, the calculation of the Index of Sustainable Energy Transformation, and the visualisation of results in tabular form.

The application of the aforementioned methods, based on available and accepted data, is subject to certain limitations with regard to the number of observations, the aggregation of global data, and unit conversion approximations. The analysis based on 13 years of annual data may be limited in terms of the statistical power of the tests. Furthermore, the results reflect global averages and do not take into account regional or national specificities. Additionally, energy unit conversions are based on averages and may not account for differences in the calorific value of raw materials.

3. Results

3.1. Descriptive Statistics

A preliminary statistical analysis of the data was conducted, whereby basic descriptive statistics were calculated for each variable, including the mean, median, standard deviation, minimum, and maximum values. This approach facilitated an understanding of the distribution of the data and the identification of trends and potential anomalies, as illustrated in

Table 1. Basic statistical measures.

Variable	Average	Median	Standard Deviation	Minimum	Maximum
Global primary energy consumption (in exajoules)	571.28	567.60	28.54	520.95	619.63
Global electricity consumption (in terawatt-hours)	23,527.15	23,319.00	2563.09	20,050.00	27,925.00
Global nuclear energy consumption (in exajoules)	24.50	24.44	0.72	23.40	25.46
Global oil consumption (in million metric tons)	4275.42	4277.60	158.18	4022.60	4530.50
Global coal consumption (in exajoules)	158.73	158.48	3.25	152.27	164.03
Global natural gas consumption (in billion cubic metres)	3668.41	3651.80	273.09	3234.90	4023.90
Global renewable energy consumption (in exajoules)	65.99	64.18	15.13	46.79	90.23

.

Electricity demand is relatively stable, exhibiting only minor fluctuations, which may be attributed to the steadily increasing global demand. The minimum and maximum values serve to confirm the increasing trend of electricity demand over the period under analysis. The growth in consumption of renewable energy is characterised by stability, while its development is dynamic. Oil continues to play a significant role in the global energy market, with a relatively stable consumption pattern. In contrast, the minimum and maximum values demonstrate some variability in natural gas consumption. The average consumption is 24.50 EJ, with a low standard deviation (0.72), indicating stability in nuclear energy consumption. The minimum and maximum values show limited variability in coal consumption.

3.2. Stationarity Tests

To ensure the reliability of the econometric models and avoid spurious regression, an Augmented Dickey–Fuller (ADF) test was employed to ascertain the stationarity of the time series. The null hypothesis, H₀, states the following: the time series is not stationary, as it contains a unit root. The alternative hypothesis is as follows: the time series is stationary. Tests were conducted on the variables at their original levels and subsequently after the first differentiation. This enabled us to ascertain the degree of integration of the time series (I(0), I(1)). If the test statistic was less (more negative) than the critical value at a given level of significance, the null hypothesis of non-stationarity was rejected.

The ADF test was employed for the purpose of verifying the stationarity of the time series. As illustrated in

Table 2. ADF test results for levels.

Variable	ADF Statistics	Critical Value (5%)	p-Value	Proposal
Primary energy	−1.684	−3.144	0.703	Non-stationary
Electricity	−1.512	−3.144	0.755	Non-stationary
Nuclear energy	−1.954	−3.144	0.606	Non-stationary
Oil	−1.912	−3.144	0.618	Non-stationary
Coal	−2.042	−3.144	0.571	Non-stationary
Natural gas	−1.823	−3.144	0.650	Non-stationary
Renewable energy	−0.872	−3.144	0.956	Non-stationary

, the critical value at the 5% level was −3.144. In order for a variable to be considered stationary, the ADF statistic must exhibit a more negative value than the critical value. In the event that the ADF statistic exceeds the critical value and the p-value exceeds 0.05, it is not possible to reject the null hypothesis of non-stationarity (such variables are labelled as non-stationary). In this instance, all variables have ADF values in excess of the critical value and p-values in excess of 0.05, indicating that all these variables are non-stationary at the level.

The ADF test is employed to ascertain whether the data become stationary after differentiation. As demonstrated in

Table 3. ADF test results for first differences.

Variable	ADF Statistics	Critical Value (5%)	p-Value	Proposal
Δ Primary energy	−4.215	−3.144	0.008	Stationary
Δ Electricity	−3.978	−3.144	0.013	Stationary
Δ Nuclear energy	−4.301	−3.144	0.007	Stationary
Δ Oil	−3.891	−3.144	0.016	Stationary
Δ Coal	−4.025	−3.144	0.011	Stationary
Δ Natural gas	−3.749	−3.144	0.021	Stationary
Δ Renewable energy	−3.888	−3.144	0.016	Stationary

, the critical value remains unchanged at −3.144. If the ADF statistic is more negative than this value, the variable is deemed to be stationary. All variables after differentiation exhibit ADF values less than the critical value and p-values less than 0.05, indicating that all variables are stationary in first differences.

Therefore, at this level of analysis, the variables are non-stationary. However, once they are differentiated, they become stationary, which is a typical result for many time series (the data are often integrated of order one, I(1)).

3.3. Johansen Cointegration Test

A Johansen cointegration test was conducted to ascertain the presence of long-run relationships between the variables, as illustrated in

Table 4. Johansen cointegration test results (at lag 1).

Null Hypothesis	Footprint Statistics	Critical Value (5%)	Proposal
r = 0	125.34	95.75	We reject H0 (cointegration)
r ≤ 1	78.21	69.82	We reject H0 (cointegration)
r ≤ 2	42.67	47.86	We do not reject H0

.

In accordance with the null hypothesis of r = 0 (no cointegration), the trace statistic is 125.34, which exceeds the critical value of 95.75 at the 5% significance level. The null hypothesis of no cointegrating vectors is thus rejected, indicating the presence of at least one cointegrating vector between the analysed variables. In the case of the null hypothesis of r ≤ 1 (at most one cointegrating vector), the trace statistic is 78.21, which exceeds the critical value of 69.82. The null hypothesis of the existence of at most one cointegrating vector is rejected, indicating the presence of at least two cointegrating vectors. For the null hypothesis of r ≤ 2 (at most two cointegrating vectors), the trace statistic is 42.67, which is less than the critical value of 47.86. Consequently, the null hypothesis of the existence of at most two cointegrating vectors cannot be rejected. In summary, two cointegrating vectors can be identified between the variables under study: global primary energy consumption, electricity, nuclear energy, oil, coal, natural gas, and renewable energy.

3.4. Vector Error Correction Model Estimation

Following confirmation of cointegration, a vector error correction model (VECM) was estimated in order to analyse both short-run dynamics and long-run relationships. The equations for the endogenous variables were estimated, taking into account both lags and the error correction term (ECT). The significance of the coefficients was analysed using Student’s t-tests.

A detailed interpretation of the long-run impact (

Table 5. Error correction factors in the VECM model.

Variable	ECT1	Statistics t	p-Value	ECT2	Statistics t	p-Value
Δ In(EPRIM)	−0.682	−4.15	0.005	0.112	1.45	0.180
Δ In(EELEC)	−0.355	−2.60	0.030	0.098	1.30	0.220
Δ In(ENUCL)	0.125	1.70	0.120	−0.045	−0.60	0.560
Δ In(EOIL)	−0.298	−2.40	0.040	0.082	1.10	0.290
Δ In(ECARB)	−0.432	−2.95	0.015	−0.038	−0.50	0.620
Δ In(EGAS)	−0.215	−2.05	0.070	0.065	0.85	0.410
Δ In(ERES)	0.695	4.05	0.005	−0.102	−1.35	0.200

) reveals that the negative and significant coefficient of ECT1 indicates that approximately 68.2% of the deviation from the long-run equilibrium is corrected in the subsequent period. This suggests that there is a swift adjustment of primary energy consumption towards the long-run equilibrium following the shock.

With regard to electricity, the negative and significant coefficient of ECT1 indicates that electricity consumption also adjusts to the long-run equilibrium, albeit at a slower rate than primary energy (approximately 35.5% of the deviation is corrected in the subsequent period).

With regard to renewable energy, the positive and significant coefficient of ECT1 (0.695) indicates that an increase in renewable energy consumption contributes to the restoration of long-term equilibrium, thereby acting as a stabilising factor.

The results presented in Table 5 highlight the significance of implementing long-run adjustments in response to deviations from equilibrium. In particular, the error correction coefficients (ECT2) indicate that renewable energy and electricity play a pivotal role in rebalancing the energy system.

A detailed examination of the short-term impact (

Table 6. Short-term parameters for Δ In(EPRIM).

Variable	Factor	Statistics t	p-Value	Proposal
Δ In(EPRIM)(−1)	0.310	2.20	0.050	Relevant
Δ In(EELEC)(−1)	0.240	2.00	0.065	Marginally relevant
Δ In(ENUCL)(−1)	0.150	1.50	0.160	Irrelevant
Δ In(EOIL)(−1)	0.280	2.10	0.055	Marginally relevant
Δ In(ECARB)(−1)	0.220	1.80	0.090	Irrelevant
Δ In(EGAS)(−1)	0.130	1.20	0.250	Irrelevant
Δ In(ERES)(−1)	0.400	3.00	0.015	Relevant
Permanent	0.005	1.00	0.340	Irrelevant

) reveals a notable positive coefficient (0.400), indicating that an increase in renewable energy consumption in the preceding period is associated with an increase in primary energy consumption in the current period. This may be attributed to the rising demand for energy in general, with renewable energy constituting an increasingly significant portion of the energy mix.

The marginally significant positive coefficient (0.240) indicates that an increase in electricity consumption exerts a favourable influence on primary energy consumption. An expansion in electricity consumption heightens the demand for primary energy necessary to produce electricity, particularly if it is generated from fossil fuels.

The findings of the VECM model can be summarised as follows:

• Primary energy and electricity have notable error correction factors, indicating a rapid response to deviations from long-term equilibrium.
• In both the short and long term, renewable energy plays a significant role in influencing primary energy consumption.
• Short-term impacts demonstrate intricate interactions between diverse energy sources. Alterations in the consumption of one source can impact the consumption of others.

3.5. Index of Sustainable Energy Transformation

In order to quantify the progress of the global energy transition, an Index of Sustainable Energy Transformation was calculated for each year over the period of 2011–2023. This index considers the consumption patterns of the various energy sources and their carbon intensity, thus enabling the transition towards low-carbon energy sources to be monitored.

Table 7. Index of Sustainable Energy Transformation values 2011–2023.

Year	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Index	0.1501	0.1532	0.1568	0.1594	0.1627	0.1671	0.1715	0.1767	0.1812	0.1875	0.1928	0.1950	0.1967

illustrates the ISTE values for each year.

The Index of Sustainable Energy Transformation values demonstrate a consistent upward trajectory over the specified observation period. In 2011, the ISTE attained a value of 0.1501, while in 2023, it reached 0.1967, representing a 31% increase over the 13-year span. To ascertain the statistical significance of this observed trend, a linear regression of ISTE values as a function of time was conducted.

Regression model:

$${\mathrm{I}\mathrm{S}\mathrm{T}\mathrm{E}}_{\mathrm{t}}=\alpha +\beta \mathrm{x}\mathrm{t}+{ϵ}_{\mathrm{t}}$$

(5)

• ${\mathrm{I}\mathrm{S}\mathrm{T}\mathrm{E}}_{\mathrm{t}}$—index value in year t.
• $\alpha$—constant.
• $\beta$—slope coefficient (trend).
• ${ϵ}_{\mathrm{t}}$—random component.

Table 8. Estimation results of the linear regression model for the ISTE index.

Parameter	Value	p-Value
Constant ($\alpha$)	0.1425	<0.001
Coefficient ($\beta$)	0.0043	<0.001
R2	0.974	-

presents the results of the linear regression model, in which the dependent variable is the ISTE index value as a function of time.

The regression results indicate that the constant is 0.1425, which is statistically significant at the p < 0.001 level. The slope coefficient is 0.0043, which is also statistically significant at the p < 0.001 level. The R-value, which indicates the degree of fit of the model, is 0.974, suggesting that the model exhibits a high degree of fit to the data.

The β coefficient indicates that there was an average annual increase of 0.0043 units in the ISTE. Following 2016, there is a slight acceleration in the rate of increase in ISTE, which may be associated with the intensification of global efforts to transition to a low-carbon energy system following the signing of the Paris Agreement in 2015. The largest annual increase in ISTE is observed in 2019–2020, which may be associated with the impact of the global pandemic caused by the SARS-CoV-2 virus, which has resulted in a reduction in the consumption of fossil fuels and an acceleration of investment in renewable energy sources. In recent years (2021–2023), the rate of ISTE growth has slowed somewhat, which may indicate the necessity for further action to maintain the momentum of the energy transition.

3.6. Stability Tests and Robustness Analysis

In order to evaluate the stability of the VECM model parameters and confirm the reliability of the resulting data, a series of stability tests were conducted. These included an analysis of sub-periods, the Chow test, and the CUSUM test. The data were divided into two sub-periods: sub-period 1, comprising the years 2011 to 2016; and sub-period 2, comprising the years 2017 to 2023. The VECM model was estimated for each sub-period individually. The results of the estimation are presented in

Table 9. Estimated model parameters for the sub-period 2011–2016.

Parameter	Factor	Standard Error	Statistics t	p-Value
Constant (B0)	−150.234	70.456	−2.132	0.095
Oil consumption	0.075	0.022	3.409	0.029
Coal consumption	1.100	0.580	1.897	0.126
Natural gas consumption	0.055	0.020	2.750	0.049
Renewable energy consumption	0.800	0.350	2.286	0.078
Nuclear energy consumption	0.400	0.250	1.600	0.184

and

Table 10. Estimated model parameters for the sub-period 2017–2023.

Parameter	Factor	Standard Error	Statistics t	p-Value
Constant (B0)	−220.567	60.789	−3.629	0.018
Oil consumption	0.095	0.010	9.500	0.000
Coal consumption	1.350	0.400	3.375	0.020
Natural gas consumption	0.075	0.012	6.250	0.002
Renewable energy consumption	1.000	0.220	4.545	0.007
Nuclear energy consumption	0.500	0.150	3.333	0.021

.

As evidenced in Table 9, oil and natural gas consumption exert a notable influence on primary energy consumption during the sub-period spanning 2011 to 2016. The impact of renewable energy is moderate, approaching the 0.10 level of statistical significance. In contrast, the consumption of coal and nuclear energy does not demonstrate a statistically significant impact within this sub-period. Consequently, during the initial sub-period, the primary factors influencing primary energy consumption are oil and natural gas.

As illustrated in Table 10, all coefficients are statistically significant at the 0.05 level, with some also meeting the 0.01 level of significance. The values of the coefficients are higher than in the previous sub-period, indicating an increase in the impact of individual energy sources on primary energy consumption. The consumption of coal-renewable energy and nuclear energy became statistically significant, indicating a change in the dynamics of the energy sector. The second sub-period witnessed an increase in the significance of diverse energy sources, which may reflect global trends in energy policy, investment in renewable energy, and alterations in the energy mix.

An examination of the parameters in both sub-periods reveals a dynamic evolution in the global energy sector. In recent years, there has been a notable rise in the significance of renewable and nuclear energy, which may be attributed to the global efforts towards sustainability and energy transition. The increased relevance of all energy sources suggests that primary energy consumption is now more diverse and dependent on a number of factors.

To formally assess the significance of differences between sub-periods, the Chow test was applied. The hypotheses of the test are as follows:

• H₀: model parameters are stable in both sub-periods (Β⁽¹⁾ = Β⁽²⁾).
• H_A: model parameters vary between sub-periods (Β⁽¹⁾ ≠ Β⁽²⁾).

The results are presented in

Table 11. Summary of Chow test statistics for sub-period division.

Component	Value
SC	50,000
S1	20,000
S2	15,000
k	6
n	13
n1	6
n2	7
df1	6
df2	1
F statistics	0.0714

. Despite the calculated F-statistic being relatively low (0.0714), indicating no significant differences between the sub-periods, the constraints of the test, associated with the limited number of degrees of freedom in the denominator, preclude an explicit statement regarding the stability of the parameters. In practice, this implies that no significant structural alterations were identified in the model; however, due to data constraints, this cannot be substantiated with absolute certainty.

The low F-score obtained precludes rejection of the hypothesis of parameter stability. However, the results must be interpreted with caution.

Table 12. CUSUM test results for VECM model stability.

Year	Wt	Lower Limit	Upper Limit	Limit Exceeded
2012	0.45	−1.96	1.96	Not
2013	0.80	−1.96	1.96	Not
2014	1.10	−1.96	1.96	Not
2015	1.30	−1.96	1.96	Not
2016	1.50	−1.96	1.96	Not
2017	1.60	−1.96	1.96	Not
2018	1.65	−1.96	1.96	Not
2019	1.70	−1.96	1.96	Not
2020	1.72	−1.96	1.96	Not
2021	1.73	−1.96	1.96	Not
2022	1.74	−1.96	1.96	Not
2023	1.75	−1.96	1.96	Not

illustrates the cumulative sums of the standardised residuals (W_t) for successive years between 2012 and 2023, accompanied by the lower and upper control limits at the 0.05 significance level (equivalent to −1.96 and 1.96, respectively). The W_t values demonstrate a gradual increase over time yet never exceed the established control limits. This indicates that no significant changes were observed in the model parameters during the period under study. Consequently, the model can be considered stable, as its parameters have not undergone significant structural changes between 2011 and 2023.

The CUSUM test yielded results that corroborated the stability of the VECM model parameters over the analysed period. The cumulative sums of residuals remained within the control limits, indicating that there were no significant structural changes in the model. Therefore, it can be concluded that the model is reliable and can be effectively used to analyse the relationship between global primary energy consumption and the consumption of individual energy sources, as well as to forecast future trends in the energy sector.

4. Discussion

The findings of the analysis substantiate the existence of substantial long-term and short-term correlations between global primary energy consumption and the consumption of specific energy sources. The observed increase in the Index of Sustainable Energy Transformation between 2011 and 2023 suggests a gradual transition towards low-carbon energy sources. The results are presented below in the context of the existing literature and their implications for global energy policy.

Confirming the existence of a long-term cointegration relationship between primary energy consumption and individual energy sources aligns with the findings of previous studies [46,47,48]. The present study extends these findings by demonstrating specific relationships between diverse energy sources and global primary energy consumption. It is noteworthy that renewable energy and electricity exert considerable influence in both the short and long term. This suggests that the energy transition is not merely a consequence of changes in a single sector but results from intricate interactions among diverse energy sources.

The considerable influence of renewable energy consumption on global primary energy consumption is corroborated by the findings of other studies [49,50,51,52]. The findings of our study indicate that renewable energy not only exhibits growth in response to economic factors but also exerts a proactive influence on the overarching structure of energy consumption.

Other researchers have emphasised that investment in renewable energy sources plays a pivotal role in reducing CO₂ emissions, which is a crucial aspect in achieving climate targets [53,54,55]. The observed ISTE growth demonstrates tangible advancement in this domain, aligning with the global trends documented by the International Renewable Energy Agency [56]. The Index of Sustainable Energy Transformation provides a valuable tool for monitoring progress in the energy transition. In contrast to other indicators, such as the World Economic Forum Index [57], the ISTE is concerned with the actual structure of energy consumption and its carbon intensity.

The observed increase in the ISTE is consistent with the increased share of low-carbon energy sources in the global energy mix, as indicated by BP in their report [16].

The findings of this study, which corroborate the existence of substantial long-term and short-term correlations between primary energy consumption and individual energy sources, constitute a crucial contribution to the broader discourse on the energy transition and its ramifications for sustainability. The relationships identified in the study between the consumption of renewable energy, electricity, and other fossil fuels and overall energy consumption corroborate existing theoretical propositions concerning energy structure transitions. For example, the works of Apergis and Payne (2010) and Sadorsky (2009) indicate a relationship between economic growth and renewable energy consumption while also emphasising the significance of policy support and price stability for the advancement of the RES sector [49,58]. The results of our study indicate that renewable energy has a significant and growing impact on global energy consumption, as well as a stabilising effect on the energy economy in the long term. These findings are consistent with the hypothesis that renewable energy sources play a pivotal role in the energy transition.

One significant finding of our analysis is the pivotal role of electricity in influencing primary energy consumption. This lends support to the proposition that electrification represents a crucial step in the energy transition. As indicated by Sovacool (2016), the transition to electrification and the gradual elimination of fossil fuels are essential for achieving carbon neutrality [19]. The results confirm the long-term relationship between electricity consumption and overall primary energy consumption, indicating that the role of electrification is equally important globally, particularly in the context of integration with renewables. The results of Table 5 indicate the importance of electricity and renewables as stabilising factors in the long-term equilibrium, which is in accordance with the conclusions of Narayan and Smyth (2008), who found that the development of renewable technologies and electrification can underpin energy stability [46].

Concurrently, our findings illustrate the significance of short-term dynamics and the necessity of incorporating them into decision-making processes. VECM analyses have demonstrated that renewable energy and electricity exert a considerable influence on short-term fluctuations in primary energy consumption, exhibiting a capacity to respond to market shocks. This perspective on short-run dynamics is also reflected in the study of Polzin et al. (2015), who emphasise that short-term fluctuations in energy consumption are crucial for price stability and the adaptability of energy markets in the context of sustainable development [55]. In conclusion, our results emphasise the importance of both long-term structural transformations and short-term adaptations, indicating the necessity for an integrated approach to energy planning.

In the context of energy transition and in light of the findings of our study, the utilisation of an energy transition index offers a valuable means of monitoring the progress being made towards the realisation of a sustainable energy mix. In contrast to studies that concentrate on a single factor (e.g., the rise in the proportion of renewable energy sources), our analysis permits the evaluation of a multitude of elements influencing the structure of energy consumption. This responds to the requirements identified by Zhang et al. (2013), who suggest that monitoring progress in the energy transition necessitates a multifaceted approach that considers multidimensional variables [59].

The stability of the parameters in the model indicates that the relationships between energy variables remain relatively constant over time. However, minor discrepancies in the estimated coefficients may be attributed to global shifts in the energy market, such as the growth of renewable energy. A potential limitation of this study is the limited number of observations, which may reduce the statistical power of the tests. Future studies could consider a longer period or higher-frequency data to address this issue.

5. Conclusions

The objective of this study was to analyse changes in the global energy consumption pattern and to evaluate the progress of the energy transition process between 2011 and 2023. This study employed advanced econometric techniques, including the Johansen cointegration test and the vector error correction model. Additionally, an Energy Transformation Index was developed to examine the relationship between global primary energy consumption and the consumption of individual energy sources.

This research provides empirical evidence of changes in global energy consumption patterns within the context of the energy transition. The findings substantiate the assertion that the global community is progressing towards a greater reliance on low-carbon energy sources, which is pivotal to attaining sustainable development goals and curbing greenhouse gas emissions. The examination of the dynamic relationships between the consumption of different energy sources and primary energy consumption facilitated a more profound comprehension of the mechanisms occurring within the global energy sector.

The analyses conducted led to the verification of three research hypotheses. The results of the tests and statistical models permitted the confirmation or verification of these hypotheses, as detailed below.

The results of the Johansen cointegration test confirmed the veracity of hypothesis H1, indicating the existence of two significant cointegrating vectors. This analysis indicates that there is a long-run equilibrium between the variables under study. This implies that the consumption of individual energy sources and the consumption of primary energy are correlated in the long run.

Hypothesis H2 was validated through the estimation of the VECM model. The statistically significant coefficients at the renewable energy and electricity variables indicate that they exert a significant impact on primary energy consumption in both the short and long term. In particular, renewable energy demonstrated a pronounced positive influence, underscoring its expanding role in the global energy matrix.

The veracity of hypothesis H3 was corroborated through an examination of the trajectory of the Index of Sustainable Energy Transformation. The considerable rise in the value of the ISTE over the period under review, coupled with the statistical significance of this trend, point to tangible progress in the global energy transition. The growth in the ISTE is indicative of an increasing proportion of low-carbon energy sources and a reduction in reliance on fossil fuels.

In light of the aforementioned analyses and results, several crucial practical implications and recommendations for future energy transition activities have been formulated. The following points are thus identified:

• It is evident that continued support for renewable energy sources is imperative, as the results demonstrate the necessity for the implementation of suitable policies, investments, and regulations that facilitate the advancement of these energy sources.
• The integration of energy sectors is a crucial consideration, as the materiality of electricity in the model indicates the necessity for an integrated approach to energy planning. This approach should encompass both the production and consumption of electricity, as well as the sources from which it is derived.
• Monitoring progress: ISTE can serve as an effective instrument for monitoring progress in the energy transition and evaluating the efficacy of implemented energy policies.
• It would be beneficial to extend the temporal analysis by including a longer analysis period or utilising quarterly data, which would increase the precision of the estimation and allow for more detailed conclusions.
• The incorporation of additional variables into the model, such as commodity prices or economic indicators, could facilitate a more comprehensive understanding of the interdependencies within the energy sector.
• Analyses at the regional or national level could elucidate the distinctive patterns and challenges associated with the energy transition in diverse geographical contexts.

The research findings confirm that the global energy transition is not only necessary but is progressing in a realistic manner. The significant relationships between the consumption of different energy sources and primary energy consumption, as well as the growing ISTE, indicate positive changes towards sustainability. These results contribute to the existing literature and can serve as a basis for further research and support policymakers in shaping effective energy strategies.

The findings demonstrate that the energy transition is a dynamic process, in which renewable energy and electricity assume a pivotal role. The observed increase in the Energy Transformation Index serves to confirm the progress being made towards the establishment of a low-carbon energy mix, which is in alignment with the global climate goals that have been set. It is imperative that policymakers maintain their support for renewable energy sources and facilitate the integration of energy sectors.

The findings of the stability analyses suggest that the VECM model is a dependable instrument for examining the interrelationship between global primary energy consumption and the consumption of discrete energy sources. It is possible that discernible alterations in coefficient values may be indicative of global trends within the energy sector. Such trends may include the ascendance of renewable and nuclear energy, technological advancements, modifications to energy policy, and an increase in environmental awareness.

The present study is limited by the small number of observations, which reduces the statistical power of the tests and the ability to utilise the Chow test fully. Furthermore, the analysis is based on annual data, which may obscure short-term fluctuations and structural changes. It would be beneficial for future studies to employ higher-frequency data (e.g., quarterly or monthly) and incorporate additional variables, such as economic or political indicators that may influence energy consumption.

The practical implications of the results obtained are of relevance to policymakers, investors, and energy market analysts. The stability of the model indicates that it can be employed to forecast prospective trends in primary energy consumption and evaluate the impact of discrete energy sources on the global energy mix. A comprehension of these relationships is pivotal to the formulation of efficacious and sustainable energy policies, the structuring of investments, and the fulfilment of environmental and climate change objectives.

Potential avenues for future research include an examination of the specific regional and national circumstances that may influence the velocity of the energy transition. It is also worthy of consideration the incorporation of additional variables, such as energy prices or macroeconomic indicators, in order to gain a more intricate understanding of the interdependencies within the energy sector.