The European energy crisis has been a pressing issue in recent years, with a significant impact on the region’s economy and daily life. This crisis has been primarily driven by a combination of factors such as the increasing demand for energy, supply disruptions, and the transition towards renewable sources (Eurostat, 2023h). Additionally, geopolitical tensions and changing weather patterns have further exacerbated the situation, making it important for European countries to implement sustainable and diversified energy strategies to mitigate the effects of this crisis. The EU has set targets to reduce greenhouse gas emissions and increase the share of renewable energy in the overall energy mix, ensuring a more sustainable and secure energy future for Europe (M. Yu et al., 2021). European measures to reduce the energy crisis include promoting renewable energy sources, such as wind and solar power, and increasing energy efficiency through stricter regulations on energy consumption (IEA, 2022). The European Union has implemented policies to encourage energy conservation and the development of innovative technologies to address the energy crisis. Some of the specific regulations implemented include setting energy efficiency standards for appliances and buildings, promoting the use of renewable energy sources, and implementing carbon pricing mechanisms to incentivize the reduction of greenhouse gas emissions. These measures not only help combat climate change, but also stimulate economic growth and job creation in the clean energy sector (IRENA, 2023). The EU’s commitment to renewable energy sources has already resulted in the creation of thousands of jobs in the green energy sector. As solar panels and wind turbines become more affordable and efficient, the demand for skilled workers in these industries continues to rise (IEA, 2022). Moreover, the development of energy interconnections between countries opens up new avenues for collaboration and trade, fostering a sense of shared responsibility and mutual benefit.

In this context, we aim to define a new model of energy consumption and the function of energy sustainability at the European level, aspects that will lead to highlighting the position of the 27 European member states in the period 2005–2022 in terms of their energy sustainability.

Given the above context, we consider it important to assess the effectiveness of energy sustainability measures by means of a dynamic energy consumption model and propose to achieve this goal through the following specific objectives:

O1: Identifying a typology of sustainable energy measures found in the literature.

O2: Enhancing the accuracy and reducing the duplication of data by applying dedicated statistical methods to the panel databases.

O3: Developing a new dynamic energy consumption model using panels data regression with fixed effects.

O4: Defining the energy sustainability function based on the new dynamic energy consumption model.

The novelty of the study lies, on the one hand, in the critical analysis of the dynamics of energy consumption, but also in the design of the energy sustainability function that can be used by European decision-makers to develop future energy development strategies in the European Union, thus underlining its importance in ensuring an efficient and sustainable energy transition capable of meeting the current challenges of climate change, energy security and sustainable economic growth. This study provides a robust framework for energy policies that not only optimise resource use, but also promote innovation and resilience in the face of global energy market fluctuations. This being absolutely new at the level of literature. The study continues with the presentation of the extensive study of the literature, the presentation of the methodological approaches, the results and the discussions regarding the level of energy sustainability in Europe, and its conclusions will be presented at the end of the research.

Research interest in the sustainable development of the energy sector has increased significantly in recent times especially in areas such as political, economic and social energy security (Luty et al., 2023); green energy transition strategies (Wang et al., 2023); increasing renewable energy sources (Cristea et al., 2022; Kemec and Altinay, 2023; Raza et al., 2023); reducing carbon emissions (Wang et al., 2023; Streimikiene, 2023); the impact of social responsibility on energy poverty reduction (Batool et al., 2023; Shkura and Fedulova, 2023); combating climate change and developing renewable energy sources (Tang and Solangi, 2023; Trojanowski and Kozak, 2023; Tweneboah-Koduah et al., 2023).

According to the Web of Science database, in 2023, 7,343 Open Access articles were published by the phrase “sustainable energy” used in the titles, abstracts or keywords of the articles included in this database (Figure 1). Analysing the 7,343 published articles we find that the Hirsch index was 15 points while the citation rate was 3.97 on an article with no author citations.

We used Vosviewer software to perform a bibliometric analysis grouping the 7,343 articles into areas of research interest such as sustainable development, renewable energy, carbon emissions, performance, optimization, economic growth, green innovations, energy transition, green energy, energy policy, climate change (Figure 1).

This study aims to identify and analyse the determinants of final energy consumption (FEC) in European Union (EU) Member States over the period 2005–2022 using information from the Eurostat platform (Eurostat, 2023a) to design a panel data model with fixed effects. The theoretical framework aims to investigate the determinants of final energy consumption (FEC) in the European Union, focusing in particular on the role of energy import dependence, the share of renewable energy, primary energy consumption, greenhouse gas emissions, GDP per capita and energy productivity. The study provides new insights and fills gaps in the existing literature, contributing to the development of more efficient and sustainable energy policies. Unlike many studies in the literature that focus on a single factor, this research integrates multiple variables, including the share of renewable energy and energy productivity, to provide a holistic understanding of FEC. From a renewable energy share perspective this research investigates the direct impact of renewable energy share on the FEC, providing empirical evidence on how increasing renewable energy use influences overall energy consumption patterns. With respect to energy import dependency the study examines how energy import dependency directly affects the FEC, contributing to the energy security and sustainability discussions by showing the quantitative impact of import dependency. By linking PEC to FEC, the study provides a nuanced view of how total energy demand translates into end-user consumption, highlighting the importance of reducing primary energy consumption to lower FEC. Through empirical analysis of the impact of energy productivity on FEC, the research highlights its role in decoupling economic growth from energy consumption. The methodology used takes into account the estimation of the power of the model with fixed or random effects using the Hausman test, the independence of the residuals using the Breusch-Pagan test, the application of the Pesaran’s test for cross-sectional independence and the modified Wald test for heteroscedasticity. The Hadri LM test was also applied to test for deviations from stationarity. The proposed model is based on the use of the multiple linear regression method with fixed effects (according to the Hausman test results) whose validity was tested by calculating the statistical representativeness of the model and testing the error distributions at the chosen representativeness threshold of 5%.

In order to quantify the dynamics of final energy consumption as a dependent variable, in the fixed-effects panel regression model we designed the model equation with reference to sustainability indicators expressed by the dynamics of energy import dependency, the dynamics of the transition to green energy, primary energy consumption, greenhouse gas emission limitation, sustainable development and energy productivity dynamics at the level of each European Member State. Based on the consolidated data, we designed the model Equation 1 as shown below: F E C i t = β 0 + β 1 ∗ SRNWEN i t + β 2 ∗ EIMPD i t + β 3 ∗ PEC i t + β 4 ∗ NGRNHE i t + β 5 ∗ GDPCAP i t + β 6 ∗ ENPROD i t + u i + ε i t (1)

Where:

F E C i t , dependent variable final energy consumption for unit i at time t; β 0 , is the intercept; β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , are the coefficients of the independent variables; SRNWEN i t , is the share of renewable energy in gross final energy consumption; EIMPD i t , is dependence on imported energy; PEC i t , is primary energy consumption; NGRNHE i t , are net greenhouse gas emissions; GDPCAP i t , is real GDP per capita; ENPROD i t , is the energy productivity

u i , represents the fixed effects specific to each DMU

ε i t , is the error term

The indicators selected for the econometric model are presented in Table 1.

From the literature review, we have observed an increased interest in energy efficiency. In this respect, some authors (Yumashev et al., 2020; Qasim Alabed et al., 2021; Zhen et al., 2022; Hafez et al., 2023; Anser et al., 2024) have observed the link between sustainable development and efficient management of energy consumption. Using various regression models, the authors find that (Shafique et al., 2020; Aboul-Atta and Rashed, 2021; Maaouane et al., 2021; Tahmasebinia et al., 2022; Bouznit et al., 2023; Guamán et al., 2023; Soava and Mehedintu, 2023) there is a direct link between final energy consumption and sustainable development. The current study aims to identify and analyse the determinants of final energy consumption (FEC) in European Union (EU) Member States over the period 2005–2022. Although, this is an area that has been researched in the last period, we have noticed that no study investigates comprehensively the link between final energy consumption and sustainable development and the current European geopolitical context makes this topic even more important as global interests converge towards the EU area during this period. The proposed model uses in a new and innovative way the linear regression of panel data to determine the variations of energy import dependency, share of renewable energy in gross final energy consumption, primary energy consumption, net greenhouse gas emissions, real GDP per capita and energy productivity on final energy consumption from a sustainable perspective.

The choice of these indicators is based on their theoretical and empirical relevance in explaining final energy consumption (Figure 2). By using a fixed effects model, we can control for unobservable characteristics specific to each entity, thus obtaining more robust and informative results.

To achieve the proposed goal the working hypotheses H1- H4 will be tested during the modelling.

The proposed dynamic energy consumption model is based on the application of the least squares method and multiple linear regression to the panel data using STATA program vs. 18. The Hausman test is used to compare fixed and random effects models. The null hypothesis (H0) of the Hausman test states that the differences between the coefficients are not systematic, which means that the random effects model is appropriate. If the null hypothesis is rejected, it suggests that the fixed effects model is more appropriate (see Table 2).

Analyzing the data and the Hausman test results, we can conclude that the fixed effects model is preferred over the random effects model for this data set. The variables show systematic differences between the coefficients obtained from the two models, suggesting that the fixed effects better capture the variation in the data.

The regression model was run on a dataset consisting of 504 observations, grouped into 28 decision units (DMUs), and revealed an impressive R-squared coefficient of determination of 0.8972 within groups, 0.9983 between groups and 0.9976 overall, with an F-test for the whole model (6, 470) resulting in a value of 683.84 and an associated probability (Prob > F) of 0.0000, indicating the extremely high statistical significance of the model, all complemented by a very strong correlation between individual effects and prediction values (u_i, Xb) of 0.9912 (see Table 3).

The coefficient for EIMPD (Energy Import Dependence) indicates a positive relationship between energy import dependence and final energy consumption. The level of significance (p < 0.001) indicates that the coefficient is statistically significant, allowing us to state with a high degree of confidence that energy import dependence influences final energy consumption. This validates Hypothesis 1 that dependence on energy imports exerts a significant positive effect on final energy consumption is well supported by the data from the fixed effects regression model. Comparing these results with those in the literature, we observe significant consistency. For example, studies by Wu and Chen (Wu and Chen, 2017), Dey et al. (Dey et al., 2022), Shahbaz et al. (Shahbaz et al., 2024) and Dogan et al. (Doğan et al., 2022) also found a positive relationship between energy import dependence and final energy consumption. This research suggests that countries with a high dependence on energy imports tend to have higher final energy consumption, which is attributed to the need to supplement the lack of domestic production with imports. Thus, we can conclude that countries with a higher dependence on energy imports tend to have higher levels of final energy consumption, which can be attributed to the need to supplement insufficient domestic demand with external purchases.

The coefficient for the SRNWEN indicator (Share of renewable energy in final energy consumption) indicates a positive relationship between the share of renewable energy and final energy consumption. The level of significance (p < 0.015) indicates that the coefficient is statistically significant, which allows us to state with a high degree of confidence that the percentage of renewable energy influences final energy consumption. These confirmed factors indicate that hypothesis 3 that the share of renewable energy in final energy consumption has a significant positive impact on final energy consumption is well supported by the data from the fixed effects regression model. The positive relationship between the share of renewable energy and final energy consumption is well documented and supported by previous studies, a higher share of renewable energy in the national energy mix is associated with higher final energy consumption (Shahbaz et al., 2020; Tutak and Brodny, 2022b; Nibedita and Irfan, 2024). Other studies (Arbolino et al., 2024; Liu and Feng, 2023; Zhao et al., 2022) suggest that policies that promote renewable energy sources boost overall energy use. Thus, it can be concluded that an increase in the share of renewable energy in the national energy mix is associated with increased end-use energy use. This phenomenon can be attributed, in part, to government policies promoting renewable energy sources and the infrastructure needed to integrate these sources into the national energy system.

The value of the coefficient of primary energy consumption indicates a positive relationship between primary energy consumption and final energy consumption. The p-value associated with the PEC coefficient is less than 0.001 (p < 0.001), having a statistically significant level which allows us to state with a high degree of confidence that primary energy consumption influences final energy consumption. An increase in primary energy consumption is associated with a proportional increase in final energy consumption, reflecting the interdependence between these two variables and highlighting the importance of monitoring and managing primary energy resources efficiently to ensure energy sustainability. These results are also supported by the literature which stresses the importance of implementing efficient energy policies and careful management of primary energy resources to ensure energy sustainability and economic growth (Economidou et al., 2022; Su et al., 2023; Yu et al., 2023).

For the NGRNHE indicator (Net Greenhouse Gas Emissions) the coefficient value was 0.0249, which indicated a positive relationship between net greenhouse gas emissions and final energy consumption. The p-value associated with the NGRNHE coefficient is less than 0.048, signifying a statistically significant level which allows us to state with reasonable confidence that net greenhouse gas emissions influence final energy consumption. This validates hypothesis 4 of the study. Thus, we can conclude that countries with higher greenhouse gas emissions also tend to have higher final energy consumption, reflecting both the reliance on fossil energy sources and the energy efficiency of the economy. This underlines the importance of policies to reduce emissions and increase energy efficiency in order to control final energy consumption and reduce environmental impacts. Ensuring comparability with the literature, the results highlight the need to implement effective policies to reduce emissions and increase energy efficiency in order to ensure energy sustainability and reduce environmental impacts, which is supported by previous studies (Khan et al., 2022; Paramati et al., 2022; Xu and Xu, 2022; Xue et al., 2022).

In the case of the GDPCAP indicator, the coefficient value showed a positive relationship between real GDP per capita and final energy consumption. The p-value associated with the GDPCAP coefficient (p < 0.001) is highly statistically significant, allowing us to state with a very high degree of confidence that real GDP per capita influences final energy consumption. Thus, we can conclude that an increase in real GDP per capita is associated with an increase in final energy consumption, reflecting the economic capacity and living standards of the population. It underlines the importance of considering economic growth and sustainable development in energy policy making to ensure a balance between economic progress and efficient use of energy resources. Previous studies in the literature have shown a positive relationship between per capita GDP growth and final energy consumption. This research (Su et al., 2022; Tran et al., 2022; Wang et al., 2024) suggests that as economies grow and per capita incomes rise, so does the demand for energy to support economic activities and the standard of living of the population.

The coefficient value for the ENPROD indicator is showing a negative relationship between energy productivity and final energy consumption. The p-value associated with the ENPROD coefficient (p < 0.033), allows us to state with a reasonable degree of confidence that energy productivity influences final energy consumption. Energy productivity, defined as the ratio of GDP to energy consumption, is an indicator of the efficiency of the use of energy resources in the production of economic value. A negative and significant relationship between ENPROD and FEC reflects the fact that economies that use energy more efficiently have lower final energy consumption, which is essential for sustainability and reducing environmental impacts. This validates hypothesis 2 of the study. Thus, we can conclude that an increase in energy productivity is associated with a reduction in final energy consumption, reflecting a more efficient and sustainable use of energy resources. This underlines the importance of policies and technologies that improve energy efficiency to control energy consumption and promote sustainable development. Energy productivity has a significant negative impact on final energy consumption, a point well supported by the literature (Ding et al., 2021; Sun et al., 2024; Wang et al., 2024; Zhen et al., 2022) results highlight the need to implement policies and technologies to improve energy efficiency in order to control energy consumption and promote sustainable development (Chen et al., 2021; Zakari et al., 2022; Anser et al., 2024; Song et al., 2024).

The Breusch-Pagan LM test for independence is used to test for the presence of serial dependence between the residuals of the regression model. In the context of a panel regression model, the test checks for correlation between the residuals of different time units. The value of 1211.799 is calculated for 378 degrees of freedom. The probability of 0.0000 indicates that the observed chi-square value is extremely unlikely under the null hypothesis.

Pesaran’s test for cross-sectional independence is used to assess the presence of correlation between time units in a panel regression model. The results of the test are: Pesaran’s test of cross sectional independence = 4.643, Pr = 0.0000, Average absolute value of the off-diagonal elements = 0.352. This is a significant test statistic indicating the degree of cross-sectional independence between residuals from different units. A Pr value of 0.0000 suggests that the observed test value is highly unlikely under the null hypothesis. The mean absolute value of the off-diagonal items indicates that there is a moderate correlation between residuals in different units.

The results of the modified Wald test for heteroscedasticity (chi2 (28) = 1.6*10⁵, Prob > chi2 = 0.0000) indicate that the null hypothesis can be rejected.

The Hadri LM test (Table 4) is used to check whether data panels are stationary or contain unit roots. The null hypothesis (H0) of the Hadri test is that all panels are stationary, while the alternative hypothesis (Ha) is that some panels contain unit roots, i.e. are not stationary.

From the point of view of the distribution of errors it can be observed that they tend to flatten out towards the end of the period with the largest magnitudes of errors being observed graphically in the period 2005–2010 (Figures 3–5).

Energy consumption in the European Union experienced a slight increase between 2005 and 2010. This can be attributed to the growing population and economic development in some member states. Additionally, advancements in technology and industrial processes also contributed to the rise in energy consumption. However, efforts were made during this period to promote energy efficiency and renewable energy sources, which helped mitigate the overall impact on the environment. These efforts included the implementation of energy-saving policies and regulations, such as the Energy Efficiency Directive and the Renewable Energy Directive. Many member states also invested in renewable energy infrastructure, such as wind farms and solar power plants, to reduce their dependence on fossil fuels. Furthermore, public awareness campaigns and incentives were introduced to encourage individuals and businesses to adopt energy-saving practices and technologies. As a result of these combined efforts, the European Union was able to achieve a more sustainable energy future despite the increase in consumption.

Energy consumption in the European Union has seen a gradual decline from 2011 to 2019. This can be attributed to the region’s increased focus on renewable energy sources and energy efficiency measures. The implementation of stricter regulations and policies has resulted in significant improvements in energy conservation, leading to a more sustainable and environmentally-friendly energy landscape in the European Union. Furthermore, advancements in technology have played a crucial role in reducing energy consumption. The adoption of smart grids and energy-efficient appliances has allowed for better energy management and reduced wastage. Additionally, the shift towards cleaner and greener modes of transportation, such as electric vehicles, has also contributed to the overall decrease in energy consumption. These efforts have not only helped the European Union achieve its climate goals but have also created new opportunities for the development of a green economy.

Energy consumption in the European Union experienced a significant decline in 2020–2021 due to the impact of the COVID-19 pandemic. Lockdown measures and travel restrictions led to a decrease in industrial activity, transportation, and overall energy demand. Additionally, the shift towards remote working and online activities further contributed to the reduction in energy consumption. As a result, the European Union made significant progress towards achieving its clean energy goals and reducing carbon emissions during this period. Furthermore, the decrease in energy consumption also led to a decrease in the use of fossil fuels, such as coal and oil, which are major sources of carbon emissions. This reduction in carbon emissions not only helped the European Union meet its climate targets but also contributed to improved air quality and reduced pollution levels. The pandemic served as a catalyst for the adoption of renewable energy sources and the implementation of energy-efficient practices, setting the stage for a more sustainable and resilient energy sector in the future. Despite the challenges faced during this time, the decline in energy consumption brought about positive environmental outcomes, demonstrating the potential for a greener and more sustainable future.

In the year 2022 it can be seen from the Normal P-P Plot of the standardised residuals (Figure 6) for final energy consumption that countries with energy sustainability such as Italy and Malta have improved their position towards the new model due to energy reforms by reducing the value of the standardised residuals compared to the right of the trend while for countries with lower energy sustainability such as Romania and Slovakia the position compared to the right of the trend indicates a move away from the proposed sustainability model.

In Italy, for example, progress has been made on the back of major investments in wind farms and the continued optimisation of the use of hydropower resources, with the country managing to maximise energy production from these sources. At the same time, Italy has adopted measures to reduce its dependence on fossil fuel imports through the use of biofuels and diversification of energy sources, in which case it has increased its gas storage infrastructure as part of its energy security measures. Malta, for its part, has made progress in developing infrastructure for renewable energy sources, with the government implementing subsidy programmes for the installation of photovoltaic panels in 2022. Malta has also offered subsidies for the purchase of energy efficient household appliances and has been pushing for the diversification of energy sources by encouraging the adoption of new technologies and innovations to support the energy transition such as smart grid technologies and investments in energy storage technologies. At the other end of the spectrum, Romania and Slovakia’s energy sustainability model has experienced difficulties and challenges that have led to a worsening energy situation in both countries. Romania has shown a high dependence on fossil fuels and delays in the adoption of renewable energy based on insufficient investment and lack of adequate government incentives. Romania’s outdated energy infrastructure and rising energy prices amid the geopolitical conflict in Ukraine have contributed to Romania’s energy sustainability. As in the case of Romania, Slovakia is a country that relies significantly on the use of fossil fuels and is lagging behind in the adoption of renewable energy due to legislative instability and the lack of a clear and coherent strategy to support the transition to more sustainable energy.

We define the energy sustainability function based on the dynamic energy consumption model Equation 2 as follows: S E N y e a r i = 0.101 ∗ E I M P D y e a r i + 0.129 ∗ S R N W E N y e a r i + 0.739 ∗ P E C y e a r   i −   0.033 ∗ N G R N H E y e a r   i −   0.00002 ∗ G D P C A P y e a r i + 0.171 ∗ E N P R O D y e a r   i −   6.987 ∗ E N P R O D y e a r i E N P R O D y e a r E U 27 (2) S E N y e a r i > 1   → e c o n o m y   w i t h   a   g o o d   e n e g e r g e t i c   s u s t a i n a b i l i t y S E N y e a r i = 1   → e c o n o m y   w i t h   a   m i n i m u m   e n e g e r g e t i c   s u s t a i n a b i l i t y S E N y e a r i < 1   → e c o n o m y   w i t h   a   p o o r   e n e g e r g e t i c   s u s t a i n a b i l i t y

Where, SENyeari-energy sustainability of state i based on changes in dynamic model regression indicators and member state energy productivity index compared to the European average.

For the year 2022 the equation becomes Equation 3: S E N 2022 i = 0.101 ∗ E I M P D 2022 i + 0.129 ∗ S R N W E N 2022 i + 0.739 ∗ P E C 2022   i −   0.033 ∗ N G R N H E 2022   i −   0.00002 ∗ G D P C A P 2022 i + 0.171 ∗ E N P R O D 2022   i −   6.987 ∗ E N P R O D 2022 i E N P R O D 2022 E U 27 (3)

The graphical representation of energy sustainability in 2022 is shown in Figures 5, 7.

It can be seen from the graph that countries such as Belgium, Germany, Ireland, France, Italy, Luxembourg and Malta have a high level of energy sustainability while at the opposite pole Romania, Slovakia, Bulgaria, Czech Republic are in the position of energy unsustainability.

Based on the research results, we propose the following implementable public policies to improve energy sustainability in European states (Table 5).

We appreciated that well formulated and implemented energy policies can make a significant contribution to creating a sustainable and efficient energy system in Europe.

We set out to study the sustainability of the energy sector by means of the newly designed dynamic econometric model, whose importance as a methodological tool for the correlative statistical investigation of sustainability from the perspective of SDG 7, exceeds the European reference space of the analysis, and can be used with favorable results at the global level. The study achieved all the research objectives by conducting an extensive literature search that substantiated the working hypotheses, the authors showing that at the European level, the degree of final energy consumption is directly influenced by the growing reliance on imports. The sustainability of energy is indicated by the increasing dependence of final energy consumption on the proportion of renewable energy in the overall energy consumption across different sectors. The reduction of greenhouse gas emissions is a key aspect of energy sustainability in Europe and has an inverse relationship with final energy consumption. Additionally, energy productivity plays a significant role in determining final energy consumption, as it is sensitive to the impacts of energy crises.

The new dynamic model showed the link between consumption and the sustainable dimension, the results were statistically significant, and the model was homogeneous and well determined. The energy sustainability function has been defined and the energy sustainability ranking of the Member States in 2022 has been prepared. The results of the study are useful for energy policymakers to adjust their energy strategies for the coming years in order to achieve the targets proposed by Agenda 2030 and 2050. As we showed in the paper, economic policies should encourage sustainable growth by integrating energy efficiency measures and promoting technologies and economic practices that reduce energy consumption. The fixed effects regression model clearly shows that different economic and policy factors influence final energy consumption in Europe. To ensure a more sustainable and efficient energy system, energy policies should focus on reducing import dependency, promoting renewable energy, improving energy efficiency and reducing greenhouse gas emissions.

The dynamics of the energy sector in the context of the transition to climate neutrality is a very important aspect that makes it necessary to complete the database and other indicators on the transition to the green economy, this is a limitation of this study, the authors propose to carry out new research in which to quantitatively expand the research area by completing the database and to refine the conclusions of the present research based on new relevant observations.