Final Energy Consumption—Growth Nexus in Romania Versus the European Union: A Sectoral Approach Using Neural Network

Abstract

The energy crisis caused first by the COVID-19 pandemic and continued by the Russo-Ukrainian War has demonstrated that energy is a determining factor in the conduct of activities of any state. Several studies have examined the relationship between energy consumption and economic growth, developing various theories, but there is no consensus. This study investigates relationships by analyzing several regression models and choosing the fittest. Then, the verification of its validity is performed through the neural network, which gives greater credibility to the results obtained. Furthermore, using a structural analysis, the investigation is expanded to ranking the impact of sector-specific energy consumption on economic growth. The research includes data from 1995 to 2020 for the European Union (EU) and Romania. The results indicate that short-term energy consumption can have a positive or negative impact on economic growth, both in the EU and Romania. The structural analysis highlights the direct and indirect effects, with different intensities, of sector-specific energy consumption on economic growth. This study is interested primarily in the conditions of uncertainty caused by the COVID-19 pandemic and the Russo-Ukrainian War, to enable the EU and each member state to take effective energy policy measures to ensure their energy security.

1. Introduction

Energy plays a primary role in the economic development of any country, so it is essential to adopt appropriate energy policies at the national level for the conditions where fossil fuels still represent the foundation of the energy policy [1]. Research on the relationship between energy consumption and economic growth is frequently discussed in the relevant literature, becoming more significant thanks to energy crises [2,3]. A series of studies has demonstrated that energy consumption contributes to the stimulation of economic growth and development; between energy consumption and economic growth, there is a dynamic causality [4]. Depending on the period studied and on the region, the level of development and the methodology used, the existence or nonexistence of direct or indirect relationships between energy consumption and economic growth is identified, but the research does not identify conclusive results [1,5,6,7,8,9,10,11].

In 2020, the sudden outbreak of the COVID-19 pandemic dealt a heavy blow to economic and social development worldwide [12], generating a series of problems for the world economy [13] and many additional challenges [14], owing to the shocks experienced by society in general (closing of activities, physical distancing, limitations on the freedom of movement) [15]. In addition, the COVID-19 pandemic, owing to the blockades imposed by various states, has drastically changed the pattern of energy consumption throughout the world.

At the start of the pandemic, global energy consumption fell sharply, marking an abrupt change in the upward trend seen since the most recent global shock, in 2009. Then, in 2021, once the COVID-19 restrictions started to relax, global energy consumption began to increase, especially global renewable energy consumption, which increased by 15% in 2021 (above the average annual growth of 12.6%) [16]. Therefore, the outlook for the EU economy before the outbreak of war was for a prolonged and robust expansion phase.

The 2022 Russian invasion of Ukraine has returned Europe to extraordinary economic uncertainty, forcing the EU to reassess its development outlook. The increasing energy consumption was stopped by the outbreak of the Russo-Ukrainian War, which caused energy markets huge problems, especially for EU energy policy, having a significant impact on Europe’s energy mix.

The war in Ukraine is the third asymmetric shock (a sudden change in economic conditions that affects some EU countries more than others) that the EU has endured in the past two decades, after the financial and economic crisis of 2008–2009 and the COVID-19 pandemic. The war in Ukraine has had a much more significant impact on neighboring countries owing to the influx of refugees and their heavy dependence on Russian gas [17]. Owing to the strong dependence of EU energy markets on Russian supplies, they were particularly affected by the invasion [18]. Almost 25% of Europe’s energy comes from natural gas, and the cancelation of the Nord Stream 2 pipeline affects gas imports [19]. Under these conditions, it is estimated that by 2024, gas consumption from Russia will decrease by 6251 petajoules per year and that total energy consumption will decrease by 455 petajoules per year [20].

The COVID-19 epidemic and the Russo-Ukrainian War have led to a global energy crisis, alerting all EU states to the importance of ensuring energy security to provide economic growth. At the same time, the decoupling of energy consumption from economic growth is also being considered, so that economic growth is not dependent on energy consumption [21].

The consequences of the Russian invasion on Europe’s energy transition are very strong, and the European Commission is considering the use of alternative energy resources in the short term (oil, coal, and lignite) [22]. At the same time, European economies are obliged to minimize their dependence on imported fuels; they still rely on oil, gas, and coal for 80% of their energy needs [23]. To overcome the negative impact of the epidemic and the war and to continue to promote the full return to normal economic growth, the reaction of the European Union was a reassessment of the economic outlook, which will disrupt the planned GDP for 2023 [24].

The COVID-19 pandemic strongly affects the Romanian economy, which is part of the global economic mechanism. At the same time, the Russo-Ukrainian War on Romania’s borders has had a substantial economic impact. Against the background of this energy crisis, this study investigates the relationship between energy consumption and economic growth (expressed by gross domestic product—GDP) for the European Union (EU) and Romania (RO) from 1995 to 2020. The subject addressed is of primary interest, both scientifically and politically, given the uncertainty caused by the pandemic and the Russo-Ukrainian War, for taking effective energy policy measures. Romania was analyzed because it is an emerging country that entered the EU in 2007, and its energy policy implications are different from those of large energy-consuming states. The research comprises three parts. The first part conducts a comparative statistical analysis of the evolution of GDP and final energy consumption (global and by sector) of Romania and the European Union. In the second part, for the European Union and Romania, the impact of each sector’s energy consumption on economic growth and the relationship between energy consumption and economic growth are investigated. The analysis is performed by estimating linear and nonlinear regression models and validating the optimal models by using artificial neural networks. The third part ranks the impact of each sector on GDP for the European Union and Romania, on the basis of the use of neural network.

The novelty of this research resides in the following:

• It approaches the relationship between energy consumption (globally and by sector) and economic growth by using several regression models and chooses the fittest models. The other studies have only addressed specific regression equations, but we tested 10 linear and nonlinear regression models, choosing the one that fits best.
• These models are validated through neural networks.
• The scientific literature will be enriched by the study of neural networks approach in ranking the impact of energy consumption of each sector on the GDP of the EU and an emerging country (such as Romania).

The results indicate, depending on the period and the geographical location analyzed, that energy consumption has a negative and significant impact on economic growth in the long term at the EU level and in the short term at the Romanian level. Regarding the significance of the impact of sector-specific energy consumption on economic growth, the results show a differentiation between the EU and Romania.

In conclusion, at both the EU and the RO levels, it is necessary to have consistent, clear, and well-communicated energy and economic policies that contribute to ensuring energy security by accelerating investments, increasing energy efficiency, stimulating innovation in emerging technologies for capturing and storing hydrogen and carbon, etc., which will implicitly lead to behavioral changes in the business environment.

The study includes six sections. The first one focuses on an introduction to and a review of the relevant literature. The third section presents the data used and the research methodology. Section 4 includes the research results, and Section 5 discusses the results obtained. Finally, Section 6 presents the study conclusions and the theoretical and practical implications of the research and outlines its limitations and directions for future research.

2. Literature Review

2.1. The Impact of the COVID-19 Pandemic and the Russo-Ukrainian War on Economic Growth and Energy Consumption at the Level of the EU and Romania

2.1.1. Gross Domestic Product (GDP)

The onset of the pandemic imposed a lockdown on over four billion people and produced a sudden and significant drop in the world economy. Some authors believe that the global impact of the pandemic on the economy is still uncertain [25]. In this sense, traditional models of economic growth [26] have been called into question, leading to uncertainty [27].

The macroeconomic indicator that measures economic activity and indicates the strength of an economy by determining the value of all final goods and services produced within an economy in a given period is gross domestic product (GDP). GDP growth is an indication of a prosperous economy that is based on sustainable trade relationships that are supported by advanced digital technologies [28]. In 2020, compared with 2019, the GDP at the EU level recorded the strongest decrease in the past decade (4%) thanks to the COVID-19 pandemic, which led to a stagnation of the economic development of Europe. In addition, the economic development of Romania during this period significantly decreased. Thus, GDP from an annual growth rate of over 9% in 2019 led to a decrease of almost 2% in 2020 [29]. The COVID-19 crisis has severely affected Romania’s economy in the short term [30]. After the decrease occurring in 2020, Romania’s GDP recovered somewhat in 2021, according to the economy’s slow growth. However, according to the World Bank, it is estimated that Romania’s economy will enter the biggest crisis of the past six years [31].

As of 2021, the pandemic situation has improved, and most of the obstacles caused by logistical and supply bottlenecks have been lifted. The outlook for the economy of all EU member states before the outbreak of war was a prolonged and robust expansion phase. The growth rate of the gross domestic product at the EU level was 5.54% (showing the fastest growth of the economy since 2017, when the EU economy grew by 2.8%) and at the RO level was 5.9% [32]. GDP growth rates in the first quarter of 2022 remain influenced by the evolution of the COVID-19 pandemic and the isolation measures adopted by member states. Although economic activity across the EU slowed down, GDP continued to increase in most member states. Compared with the first quarter of 2021, in the first quarter of 2022, the EU GDP was 5.2% higher and Romania’s 5.1% higher. Taking into account the Omicron COVID-19 wave, the rising energy costs, and inflation in general, but also the start of the Russo-Ukrainian War, the real GDP growth of the EU decelerated to 0.4% quarterly [33].

At a time when the world economy was trying to recover from the shock of the pandemic, the shocks triggered by the Russian invasion of Ukraine manifested all over the globe, but especially in the EU, owing to its geographical proximity to Russia and Ukraine; its strong dependence on imported fossil fuels, especially from Russia; and its high integration into global value chains. The Russo-Ukrainian War has forced the EU to reassess its economic outlook, which will disrupt the GDP planned for 2023 [23]. The gross domestic product in the European Union in 2021 was 14,447,941 billion euros, and the forecast for 2022 is a decrease in GDP to 13,696,638 million euros, after which a slight increase is expected—to 14,196 billion euros in 2023 and 14,784 billion euros in 2024 [34].

The GDP of emerging and developing countries will decline, poverty will deepen in these countries, and the reduction in the developed countries’ economies will further affect developing economies. The growth outlook is expected to be negatively impacted for 2022 and 2023. For 2022, the forecasts at the beginning of the year were of economic growth of over 4%, but the war overturned all calculations, and all international institutions (the European Commission, the World Bank, and the IMF) revised downward their economic growth forecast to the more pessimistic scenarios of up to 1.9%–2.2% for 2022 [32]. Thus, at the EU level, GDP growth is expected to slow down from 5.4% in 2021 to 2.7% in 2022 and 2.3% in 2023.

In 2021, Romania registered economic growth, but in the last quarter of the reported year, it registered a decline, marking an economic growth of 2.7% (compared with 7.6% in July–September 2021). Thus, at the Romanian level, a decrease from 5.9% in 2021 to 2.6% in 2022 and a slight increase in 2023, reaching 3.6%, is expected. In the first quarter of 2022, Romania’s GDP increased by 5.2% compared with the fourth quarter of 2021 and by 6.5% compared with the same quarter of 2021. In the second quarter of 2022, there is a 5.3% increase compared with the same quarter of 2021 [35]. After significant growth in 2021, Romania’s economy is expected to slow down in 2022, as inflation reduces disposable incomes and the war in Ukraine affects confidence in the economy, supply chains, and investments [29].

Economic growth is more significant in Romania when compared with other EU states, and the border crisis is expected to have a better forecast for 2022 for Romania than for the developed economies of the EU thanks to its lower dependence on Russian energy resources.

2.1.2. Energy Consumption

The concept of final energy consumption (FEC) includes energy consumption from all resources (solid fuels, petroleum products, gas, nuclear energy, renewable energy, energy from waste) used to satisfy energy needs in all sectors [36].

Starting from the concerns of the European Commission on climate and energy [37,38,39,40], the states of the European Union have taken responsibility to combat climate change, taking a series of measures to reform energy policy and to switch from the use of fossil fuels to renewable energy resources [5,41]. Between 2015 and 2020, the European Union has made significant progress in reducing greenhouse gas emissions and increasing energy consumption from renewable sources. Thus, the European Commission proposed the European Green Deal in 2019 (EGD) [42] (a set of 50 actions for the next 5 years, in all sectors), through which it committed Europe to become the world’s first climate-neutral continent by 2050, enabling Europe to maintain its leading role in the fight against climate change [43,44].

The COVID-19 pandemic, through the restrictions imposed by state governments, led to the emergence of a new lifestyle that has strongly disrupted energy consumption and effected an interruption of the growth trend recorded since 2009. The combined effect of lockdown measures in the first wave of the pandemic, which curtailed industrial production, severely restricted traffic, and reduced worker availability, contributed to decreasing activity and consequently reduced energy consumption. Through the blockages imposed by COVID-19 mitigation measures, the world energy consumption pattern has drastically changed, significantly increasing household consumption [45]. A reduction in final energy consumption was found in most sectors. The residential sector marked a slight increase thanks to the lockdown and working from home [46]. According to several other studies, it is found that the COVID-19 pandemic has disrupted and reduced energy consumption, which creates uncertainty in the demand and supply of energy [47,48,49,50,51,52].

At the same time, however, the COVID-19 crisis facilitated countries’ adoption of energy-transition opportunities [51,53,54]. Worldwide, oil and other liquid fuels remain the dominant energy source for the transport sector, although their share is continuously decreasing, and electric vehicles appear to be a solution for the transport sector because they protect the environment and do not produce gas emissions [55,56].

After experiencing its strongest decline in decades, EU energy consumption in 2020 reached its lowest levels since 1990 (the first year for which data are available): 907 MTOE. According to the energy efficiency objective set by the EU to reduce energy consumption by 20% by 2020 [37], final energy consumption was not supposed to exceed 959 MTOE in 2020, and a much steeper decline was observed [57].

The declaration of a state of emergency in Romania, followed by the shutdown of economic activity in several sectors, had a significant impact on the evolution of energy consumption. Romania’s energy consumption was lower by 1.5% in 2020 compared with 2019, owing to an increase in population consumption by 3.3% and a decrease in industry consumption by 3.4% [58]. Since 2021, thanks to the return of economic activity after the pandemic crisis, energy consumption has started to increase. The invasion of Ukraine by Russia pointed out Europe’s energy dependence and, at the same time, the need for a much faster energy transition. European economies are obliged to minimize their dependence on imported fuels, given that they still rely on oil, gas, and coal for 80% of their energy needs [19].

The consequences of the Russian invasion and the economic sanctions imposed by the EU on Europe’s energy transition have been devastating. Thus, to limit these consequences, the European Commission is considering the following: reducing the use of short-term alternative energy resources (oil, coal, and lignite), which will slow down the process of emitting greenhouse gases from the energy sector; doubling energy efficiency and renewable sources; and increasing investments in technologies with low carbon emissions (green hydrogen, biochemicals, or decarbonized materials) [59].

The Russo-Ukrainian War compelled Europe to consider building energy security in the context of the fight against climate change. After years of very slow progress in moving away from coal and oil, if countries were to switch back to fossil fuels under the impact of Russia’s war, it would be a disaster for the attempts to reduce greenhouse gas emissions [60]. Under these conditions, the EU aims to become completely independent of Russian fossil fuels well before 2030 by following a set of initiatives: diversifying fossil fuel supplies, saving energy, accelerating the roll-out of renewable energy, and replacing fossil fuels in heating and for generating electricity [18].

The EU aims to replace two-thirds of Russian gas by the end of 2022 and gain independence from Russian fossil fuels by 2027 [61]. This requires, both at the EU level and in each member state, a series of additional policies for energy efficiency, the postponement of nuclear phaseouts, and the extensive development of renewable energy. Nuclear power will be able to offset one-third of the Russian gas deficit in 2023. The temporary replacement of gas with coal has higher costs as a result of the war, so by 2024, only 6% of the reduction in natural gas consumption will be taken up by coal. The war did not affect bioenergy costs, and thus, bioenergy will be able to compensate for 20% of the Russian gas deficit in 2024. As a result of the decrease in the use of gases, energy consumption from renewable sources will increase by 2% more than before the war [62].

Although the contraction of Romania’s economy in 2020 from COVID-19 was less severe than initially estimated, uncertainty remains very high given the outbreak of the Russo-Ukrainian War on Romania’s border, and output is unlikely to return to prepandemic levels by the end of 2022.

2.2. The Relationship between Energy Consumption and GDP

The economic development of any EU country is based on energy consumption, so the energy policy adopted at the EU level influences the member states’ economic systems. An appropriate energy policy is essential for the economic development of any country. At the same time, however, energy is intrinsically linked to GDP in that energy policy influences (more or less) how a European country’s economy operates. Analyzing the evolution of final energy consumption is crucial because energy contributes to stimulating economic growth, and there is a dynamic causality between energy and economic development [4].

The relationship between energy consumption and economic growth (expressed by GDP) is frequently discussed in the relevant literature, the studies being differentiated either by the methodology approached or by the type of energy taken into account. The research on this relationship has become even more accentuated as a result of the global energy crises [2], which drew the world’s attention to the fact that energy is the key to sustainable development [3].

The analysis of the global energy system leads to the conclusion that fossil fuels still represent the foundation of energy policy [1]. About 66% of final energy consumption worldwide comes from fossil fuels, of which oil represents 40.4%, coal 9.5%, and natural gas 16.4%. Biofuels and waste provided 10.4%, electricity 19.7%, and other 3.6% of the global energy supply in 2020 [63].

A series of studies has focused on analyzing the impact of the COVID-19 pandemic on economic development at the state level and implicitly on energy consumption on the basis of several scenarios that provide a series of results [64,65]. Most research is based on identifying the role of energy in stimulating economic growth or investigating the direction of causality between these variables [6]. Some studies either focus on the analysis of the relationship between economic growth and energy consumption [5,7,8,9], associate the analysis with the greenhouse gas (GHG) emissions generated by energy consumption [1,6,66], or add different economic and financial indicators [10,11].

In general, research results are placed into different categories, depending on the period, the region, and the level of development studied on and the methodology used. Over long periods, GDP growth may be the main factor driving the increase in energy consumption [10]. At the same time, there is a need to move from an energy policy predominantly based on fossil fuels to one based on the increasing use of energy obtained from renewable sources [6,67,68], maximizing the existing energy mix and at the same time protecting the environment [69], thereby improving living standards [70]. Other studies find that in the short term, there is bidirectional causality between energy consumption and GDP [1].

Numerous studies have addressed the impact of energy consumption on economic growth by disaggregating energy consumption into energy consumption from renewable sources and energy consumption from nonrenewable sources [71,72,73], making comparisons between developed countries, between developed and developing countries [1,9,74], or between homogeneous entities [75]. At the EU level, results differ between developed and emerging EU countries: at the level of developed states, the consumption of renewable energy hurts economic growth, and the consumption of energy from fossil fuels has a positive impact, while at the level of emerging countries, the results obtained are the opposite [8]. For other regions, however, studies note that nonrenewable energy consumption positively correlates with economic growth in developing countries, and for developed countries, energy consumption does not affect economic development [76]. For emerging and developing countries in Asia, Latin America, and the Caribbean, there is a significant long-term relationship between renewable energy consumption and economic growth only for certain countries, while for most of the studied states, economic growth shows a dependency on nonrenewable energy consumption [74]. Other studies have found that renewable energy has a positive impact on GDP, in both the short and the long term, but nonrenewable energy has an impact on only the short term [77,78].

Most studies meant to determine the relationship between energy consumption and economic growth have used several econometric methods, such as cointegration tests (FMOLS, OLS, and DOLS), vector error correction models (VECMs) [7,9,66,74,79,80,81], generalized method of moments (GMM) [72,75,82,83,84], or autoregressive distributed lag (ARDL) models [1,6,77,85,86,87,88,89,90,91,92]. Other studies have used neural networks to more accurately determine this relationship [93,94].

Despite the fact that numerous researchers have studied the relationship between GDP and energy consumption and found the existence or nonexistence of a causality (whether unilateral or bidirectional), there is still no consensus [95]. The research results are placed into different categories depending on the state, region, level of development, the period, and the methodology, in one of the following situations [9,11,96,97]: (1) a unidirectional causality from energy consumption to GDP (growth hypothesis) highlights the important role of energy on economic growth (the rate of energy consumption determines the level of economic growth) [98,99,100,101,102,103]; (2) a bidirectional causal link between GDP and energy consumption (feedback hypothesis) indicates the interdependence of the two variables [66,75,97]; (3) a unidirectional causality from GDP to energy consumption (conservation hypothesis) highlights the role of economic growth in relation to energy consumption—basically, the level of economic growth determines the rate of energy consumption [77,94]; and (4) the nonexistence of a causal relationship between GDP and energy consumption (neutrality hypothesis) indicates that energy consumption cannot cause a significant change in economic growth [24,104,105,106]. These hypothetical relationships have been studied, but without any conclusive results. For developed countries, there is less evidence of dependence between energy consumption and economic growth compared with developing countries [107]. Other studies note that the relationship between energy consumption and GDP for certain countries in a region is contradictory: for some countries, the growth hypothesis is verified, and for others, the feedback hypothesis was verified [6,76].

3. Data, Models, and Methodology

This study used the following macroeconomic indicators: gross domestic product (GDP), expressed in billions of euros; final energy consumption (FEC), expressed in millions of tonnes of oil equivalent (MTOE); final energy consumption by sector, specifically industry (FEC_I), transport (FEC_T), commercial and public services (FEC_C), and households (FEC_H), expressed in millions of tonnes of oil equivalent (MTOE). The values of the GDP [33] and FEC indicators are taken from the Eurostat database for 1995–2020 [108]. For final energy consumption by sector, data are available only for 2009–2020 [109].

The database was compiled by using SDMX web services, at the level of the Eurostat database, based on the ETL (extract-transform-load) process, which ensured the integration of the database with the processing software platform [110].

The study is structured in three parts. In the first part, a comparative analysis of the GDP and FEC evolution for the EU and Romania is performed. It emphasizes the trend over the period, the increase in the last year of the period compared with the first one by formula $\frac{x_n-x_1}{x_1}·100$, and the annual average growth rate (AAGR) [111], which is given by the following:

$$AAGR=\frac{1}{n-1}{\displaystyle \sum }_{k=1}^{n-1}\frac{x_{k+1}-x_k}{x_k}·100$$

Starting from the analysis of the relevant literature and from our observations, in the analysis of the relationships between FEC and GDP and between FEC by sector and GDP, we formulated the following hypotheses to be investigated:

Hypothesis 1 (H1).

There is a one-way link between final energy consumption and economic growth.

Hypothesis 2 (H2).

The decrease in consumption in the industrial sector positively influences economic growth.

Hypothesis 3 (H3).

Final energy consumption in the transport sector directly influences economic growth.

Hypothesis 4 (H4).

The decrease in energy consumption in the commercial and public services sector leads to an increase in GDP.

Hypothesis 5 (H5).

The decrease in energy consumption in the household sector positively influences economic growth.

After determining the relationship between the analyzed variables, the third part of the study ranked the impact of energy consumption by sector on economic growth at the EU and RO levels.

To validate the research hypotheses, the study used descriptive and inferential statistical methods. Linear and nonlinear regression models were tested and estimated in order to determine the regression fitting curve that best approximated the data used, thereby identifying the best models for RO and the EU. The cubic model could not be tested, because of the collinearity between the model terms. Therefore, in the data analysis, we used the estimation regression models with 10 regression curves:

Linear—Equation (1) [112]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{it}}+{\mathrm{u}}_{\mathrm{it}},$$

(1)

Logarithmic—Equation (2) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}}\ast \ln \left({\mathrm{x}}_{\mathrm{it}}\right),$$

(2)

Inverse—Equation (3) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}+\frac{{\mathsf{\beta }}_{\mathrm{i}}}{{\mathrm{x}}_{\mathrm{it}}},$$

(3)

Quadratic—Equation (4) [114]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{it}}+{\mathsf{\delta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{it}}^2+{\mathrm{u}}_{\mathrm{it}},$$

(4)

Compound—Equation (5) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}{\ast \mathsf{\beta }}_{\mathrm{i}}{}^{{\mathrm{x}}_{\mathrm{it}}},$$

(5)

Power—Equation (6) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}{\ast \mathrm{x}}_{\mathrm{it}}{}^{{\mathsf{\beta }}_{\mathrm{i}}},$$

(6)

S-curve—Equation (7) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathrm{e}}^{{\mathsf{\alpha }}_{\mathrm{i}}+\frac{{\mathsf{\beta }}_{\mathrm{i}}}{{\mathrm{x}}_{\mathrm{it}}}},$$

(7)

Growth—Equation (8) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathrm{e}}^{{\mathsf{\alpha }}_{\mathrm{i}}+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{it}}},$$

(8)

Exponential—Equation (9) [113]:

$${\mathrm{y}}_{\mathrm{it}}={\mathsf{\alpha }}_{\mathrm{i}}\ast {\mathrm{e}}^{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{it}} },$$

(9)

Logistic—Equation (10) [113]:

$${\mathrm{y}}_{\mathrm{it}}=\frac{1}{\frac{1}{\mathrm{v}}+{\mathsf{\alpha }}_{\mathrm{i}}{\ast \mathsf{\beta }}_{\mathrm{i}}{}^{{\mathrm{x}}_{\mathrm{it}}}},$$

(10)

where i = 1, …, N refers to the index of the country in the panel; t = 1, …, T refers to the time period; and ${\mathrm{y}}_{\mathrm{it}}$ and ${\mathrm{x}}_{\mathrm{it}}$ represent, respectively, the dependent and independent variables for the entity i (RO and EU) at time t. The terms ${\mathsf{\alpha }}_{\mathrm{i}},{\mathsf{\beta }}_{\mathrm{i}}$ are unknown parameters, to be estimated; v specifies the upper boundary value to use in the logistics regression equation (Equation (10)), and the value must be a positive number that is greater than the largest ${\mathrm{y}}_{\mathrm{it}}$; and ${\mathrm{u}}_{\mathrm{it}}$ represents the error terms. The linear model (Equation (1)) provides only a general trend for the data (decreasing, increasing, or stationary), and the nonlinear models (Equations (2)–(10)) also provide information on the evolution of the variation of the variables.

An advanced statistical analysis of the regression models and the construction of the most suitable machine-learning models for the data sets used are performed with the help of the IBM SPSS v.26 software platform [110]. After identifying the most suitable regression models, the relationships between GDP and FEC are validated using artificial neural networks. At the same time, to identify the impact of sector-specific energy consumption on economic growth, appropriate neural networks are built [93,94,115].

In building the neural network, the multilayer perceptron model (MLP) is used because it is flexible for the analyzed indicators in the paper and because it is compatible with the regressions identified as the most suitable. The MLP model has an architecture of three main layers: input, output, and hidden. For each constructed neural network, the activation functions justify (1) the hidden layer, or the capacity and performance of the neural network, and (2) the output layer, or the validity of the chosen regression model. The synaptic weight determines for each neural network the amplitude of the connection between the nodes and the significance of the relationship (direct or indirect) between the nodes. Using the additional parameter of bias helps the constructed neural network architecture to best match the analyzed data.

It tested the validity of hypothesis H6 by using artificial neural networks that rank the impact of the energy consumption of each sector on GDP and establish the type of relationship (direct or indirect) between exogenous variables (energy consumption in the sectors) and endogenous variables (GDP).

4. Empirical Results

4.1. Comparative Analysis of GDP Evolution and Final Energy Consumption (Globally and by Sector) for the EU and RO

The evolution of GDP and FEC indicators, at the global level, is conducted for the following intervals: 1995–2020 (the entire period under analysis); 1995–2008 (before the financial crisis); 2009–2020 (after the financial crisis); and 2019–2020 (the COVID-19 pandemic). For the analysis of the relationship between energy consumption by sector and GDP, we use only the period 2009–2020 (in the Eurostat database for final energy consumption by sector contains information only on this period).

4.1.1. The Comparative Evolution of GDP—Romania versus the European Union

Analyzing the evolution of the GDP at the EU level in 1995–2019, it notes that it generally had an upward trend (less in 2009) (Figure 1), with an average annual growth rate of 3.38%.

Regarding Romania, an emerging country of the EU, which joined the EU in 2007, its GDP grew at an accelerated pace during the preaccession period and until the financial crisis of 2008–2009, with an AAGR of almost 14%. The financial crisis had a disastrous effect on Romania, owing to weaker macroeconomic fundamentals than most member countries, with its GDP falling by 14.6% in 2009, much more than the decrease recorded at the EU level (4.4%). This is because the economies of emerging countries have been much more affected than the economies of developed countries. Thanks to the financial support granted by the European Union, the Romanian economy quickly showed signs of recovery, and the GDP recorded an average annual growth rate of 6% in the period 2010–2019 (

Table 1. Analysis of GDP evolution from 1995 to 2020.

Geo	AAGR 1995/2019	AAGR 1995/2008	Growth 2009/2008	AAGR 2010/2019	Growth 2020/2019
EU-27	3.38	4.40	−4.49	2.85	−4.04
RO	9.45	13.95	−14.60	6.00	−1.93

). Thanks to the excellent start of the economy in the first two months of 2020, the economy managed to mark an upward trend, which caused the GDP during the COVID-19 pandemic to register a decrease of approximately 2%, below the EU value.

4.1.2. The Comparative Evolution of Energy Consumption at the Global Level and by Activity Sector: Romania versus the European Union

Final energy consumption at the EU level marked a significant reduction, which may reach no more than 959 MTOE in 2020 [37]. Romania, an emerging country that had to meet the objectives set by the European Commission [116] in 2020 in order to enter the EU, recorded significant decreases in FEC (12%) compared with 1995, with an AAGR of 0.4%. Thus, RO marked a much more pronounced decrease in FEC than the other EU states with high energy consumption, which determined that at the EU level, the FEC decrease in 2020 compared with 1995 was only 3.52% (AAGR 0.1%) (

Table 2. Analysis of the final energy consumption evolution.

GEO	Evolution 1995–2020	2020/ 1995	AAGR1	2008/ 1995	AAGR2	2020/ 2009	AAGR3	2009/ 2008	2020/ 2019
EU		−3.52	−0.10	10.25	0.77	−7.5	−0.65	−5.40	−8.05
RO		−12.27	−0.40	−7.97	−0.46	5.78	0.53	−9.88	−1.45

Notes: 2020/1995 represents the growth of 2020 compared with 1995; AAGR¹ represents the average annual growth rate from 1995 to 2020; 2008/1995 represents the growth of 2008 compared with 1995; AAGR² represents the average annual growth rate from 1995 to 2008; 2020/2009 represents the growth of 2020 compared with 2009; AAGR³ represents the average annual growth rate from 2009 to 2020; and 2020/2019 represents the growth of 2020 compared with 2019.

).

If in 2019, the final energy consumption in the EU was 986 MTOE, in 2020, owing to all economic restrictions imposed by the COVID-19 crisis, it decreased to 907 MTOE, below the value it had to reach according to EU objectives [36]. RO, during the pandemic period (2020 compared with 2019), recorded a much lower FEC decrease (1.4%) than that at the EU level (8.05%) (Table 2). It is noticed that the FEC decrease at the EU level is much higher thanks to the pandemic crisis (8.05%) than that caused by the financial crisis (5.4%). At the RO level, the financial crisis had a more significant impact on the FEC decrease of almost 10%, compared with the reduction due to the pandemic.

After analyzing FEC by activity sector in the period 2009–2019 (Figure 2), it was found that the transport sector at the EU level had the biggest increases, being the sector with the largest energy consumption (with a weight of 31% in 2019). Along with transport, the residential sector is the biggest consumer. The shares of FEC_I and FEC_C remained relatively stable (26% and 14%, respectively). In RO, the residential sector is the largest consumer, followed by transport and industry. The COVID-19 pandemic caused changes in the weighting of sectors, and FEC_T lost to FEC_H.

Industry energy consumption at the EU level increased after the crisis from 2008 to 2011 thanks to increased industrial activity, followed by a period of decline thanks to the slowdown in industrial growth and then a slight increase in 2016–2018 (but has not reached the level of consumption from 2011). Then, from 2019, new decreases have been recorded thanks to the slowdown in industrial growth and the consequences of the pandemic crisis. At the RO level, FEC_I followed a similar path as the one at the EU level, with significant increases until 2011 and then a period of decrease until 2013, after which it had a slight increase until 2019. FEC_C registered at both the EU and the RO sinusoidal evolutions had increases and decreases (Figure 2,

Table 3. Analysis of the evolution of the final energy consumption in use and the final energy consumption by sectors from 2009 to 2020.

Geo	Indicator	FEC	FEC_I	FEC_T	FEC_C	FEC_H
EU	Growth 2020/2009 (%)	−5.27	0.86	−10.21	−9.61	−5.36
	AAGR (%)	−0.45	0.11	−0.88	−0.82	−0.35
	Growth 2020/2019 (%)	−5.55	−3.43	−12.82	−5.63	0.01
RO	Growth 2020/2009 (%)	7.79	4.76	22.63	4.20	−0.10
	AAGR (%)	0.71	0.52	1.95	0.45	0.03
	Growth 2020/2019 (%)	−1.01	−3.36	−1.69	−6.52	3.28

).

Energy consumption in the residential sector in 2009 represented approximately 28% of the total energy consumption in the EU and followed the same downward trend as the total consumption, so in 2019, it represented 26% thanks to the improvement of energy efficiency and the change in the fuel mix.

The transport sector, although it is the sector with the highest energy consumption, in the period 2009–2020 at the EU level, recorded the highest decrease in consumption, with an AAGR of 0.88%, followed by FEC_C and FEC_H. In RO, consumption in all sectors experienced increases until 2019 (Table 3).

During the pandemic, consumption in most sectors suffered (except FEC_H), the most affected being the transport sector owing to the general lockdown.

4.2. Analysis and Validation of the Relationships between Final Energy Consumption (Global and by Sector) and GDP—Testing Hypotheses H1–H5

To test the validity of the five hypotheses, we first used the estimation of the regression models procedure [110] to identify the best-fitting models by using the 10 equations, to determine the relationships between the variables; then, we continued with the validation of these models by using the neural network.

4.2.1. Testing Hypothesis H1—A Unidirectional Link between Final Energy Consumption and Economic Growth

To estimate the regression equations for H1, GDP was the dependent variable (y) and FEC was the independent variable (x). The analysis was conducted for three periods: (1) 1995–2020; (2) 1995–2008, before the financial crisis; and (3) 2009–2020, after the financial crisis. Identifying the fittest regression model (for the EU and the RO) involved the analysis of the estimation parameters of each equation. For 1995–2020, the estimation parameters of the 10 regression equations are in Appendix A 

Table A1. Estimation of parameters of linear and nonlinear equations for GDP and FEC (1995–2020).

Equations	R2	Regression p-Value	Coefficients
			Var 1	p-Value	Var 2	p-Value	Const.	p-Value
European Union
Equation (1)	0.407	0.175	−5.938	0.175			16,064.542	0.158
Equation (2)	0.408	0.063 *	−6086.02	0.063 *			52,161.699	0.058 *
Equation (3)	0.409	0.050 **	6226366	0.050 **			3889.195	0.079 *
Equation (4)	0.429	0.117	−437.622	0.181	0.219	0.187	228,630.988	0.156
Equation (5)	0.400	0.021 **	1.000	0.000 ***			11,462.589	0.093 *
Equation (6)	0.401	0.106	−0.171	0.106			32,162.224	0.120
Equation (7)	0.401	0.091 *	195.080	0.091 *			9.005	0.000 ***
Equation (8)	0.500	0.021 **	0.000	0.021 **			9.347	0.003 ***
Equation (9)	0.500	0.021 **	0.000	0.021 **			11,462.589	0.093 *
Equation (10)	0.500	0.021 **	1.000	0.005 ***			8724 × 10−5	0.000 ***
Romania
Equation (1)	0.551	0.009 ***	−15.796	0.009 ***			487.051	0.001 ***
Equation (2)	0.548	0.010 ***	−395.041	0.010 ***			1362.096	0.005 ***
Equation (3)	0.543	0.010 ***	9768.586	0.010 ***			−301.700	0.053 *
Equation (4)	0.552	0.035 **	11.836	0.921	−0.545	0.816	140.133	0.925
Equation (5)	0.654	0.001 ***	0.813	0.000 ***			12,433.867	0.472
Equation (6)	0.648	0.002 ***	−5.159	0.002 ***			1,133,145,329	0.829
Equation (7)	0.641	0.002 ***	127.392	0.002 ***			−0.873	0.572
Equation (8)	0.654	0.001 ***	−0.207	0.001 ***			9.428	0.000 ***
Equation (9)	0.654	0.001 ***	−0.207	0.001 ***			12,433.867	0.472
Equation (10)	0.654	0.001 ***	1.230	0.000 ***			8.043 × 10−5	0.472

Notes: * denotes significance at 10% level, ** denotes significance at 5% level, and *** denotes significance at 1% level.

. Following the analysis of the value of the parameters of each equation, it is noticed that both for the EU and RO, the nonlinear models are the most suitable: logistic (Equation (10)) for the EU and growth (Equation (8)) for Romania. The graphs of the regression curves are shown in Figure 3 (a—EU and b—RO). According to the data, it is noticeable that with an increase in the FEC, the GDP decreases both for the EU and for the RO (but the decrease is much smaller at the EU level). Therefore, there is a one-way relationship between FEC and GDP, so hypothesis H1 for the 1995–2020 period is verified.

For the 1995–2008 period, the estimation parameters of the linear and nonlinear regression equations between GDP and FEC at the EU and RO levels are in Appendix A 

Table A2. Estimation of parameters of linear and nonlinear equations for GDP and FEC (1995–2008).

Equations	R2	Regression p-Value	Coefficients
			Var 1	p-Value	Var 2	p-Value	Const.	p-Value
European Union
Equation (1)	0.814	0.000 ***	41.835	0.000 ***			−33,478.803	0.000 ***
Equation (2)	0.812	0.000 ***	41,721.58	0.000 ***			−279,825.078	0.000 ***
Equation (3)	0.809	0.000 ***	−4,156,172	0.000 ***			49,960.554	0.000 ***
Equation (4)	0.818	0.000 ***	−177.753	0.676	0.110	0.607	76,122.807	0.720
Equation (5)	0.841	0.000 ***	1.005	0.000 ***			54.667	0.139
Equation (6)	0.840	0.000 ***	5.004	0.000 ***			8.021 × 10−12	0.000 ***
Equation (7)	0.838	0.000 ***	−4988.37	0.000 ***			14.009	0.000 ***
Equation (8)	0.841	0.000 ***	0.005	0.000 ***			4.001	0.000 ***
Equation (9)	0.841	0.000 ***	0.005	0.000 ***			54.667	0.139
Equation (10)	0.841	0.000 ***	0.995	0.000 ***			0.018	0.139
Romania
Equation (1)	0.467	0.071 *	−4.531	0.371			174.551	0.179
Equation (2)	0.457	0.010 ***	−108.053	0.410			408.712	0.036 **
Equation (3)	0.447	0.455	2524.788	0.455			−40.394	0.065 *
Equation (4)	0.676	0.007 ***	190.096	0.010 ***	−3.743	0.003 ***	−2335.825	0.027 **
Equation (5)	0.532	0.101	0.913	0.000 ***			514.357	0.565
Equation (6)	0.517	0.032 **	−2.212	0.232			64,828.290	0.062 *
Equation (7)	0.501	0.067 *	52.890	0.267			1.838	0.036 **
Equation (8)	0.532	0.100 *	−0.091	0.001 ***			6.243	0.003 ***
Equation (9)	0.532	0.100 *	−0.091	0.001 ***			514.357	0.565
Equation (10)	0.532	0.100 *	1.095	0.000 ***			0.002	0.565

Notes: * denotes significance at 10% level, ** denotes significance at 5% level, and *** denotes significance at 1% level.

. An analysis of the value of the parameters of each equation for the period before the financial crisis found that for the EU, the most suitable model is growth (Equation (8)), obtaining the most suitable regression curve (Figure 4a). For Romania, it is quadratic (Equation (4)) (Figure 4b). At the EU level, it is noticed that with the increase in FEC, GDP also increases, and for RO, increasing FEC up to the critical value of 25.4 MTOE leads to an increase in GDP, after which increasing FEC leads to a decrease in GDP. So there is a relationship between FEC and GDP, so hypothesis H1 for the 1995–2008 period is verified.

For 2009–2020, the estimation parameters of the linear and nonlinear regression equations between GDP and FEC at the EU and RO levels are in Appendix A 

Table A3. Estimation of parameters of linear and nonlinear equations for GDP and FEC (2009–2020).

Equations	R2	Regression p-Value	Coefficients
			Var 1	p-Value	Var 2	p-Value	Const.	p-Value
European Union
Equation (1)	0.478	0.379	−10.625	0.379			22,563.665	0.073 *
Equation (2)	0.478	0.078 *	−10,238.9	0.378			82,668.229	0.005 ***
Equation (3)	0.479	0.377	9,855,109	0.377			2087.734	0.853
Equation (4)	0.479	0.092 *	−57.482	0.922	0.024	0.937	45,089.460	0.874
Equation (5)	0.484	0.362	0.999	0.000 ***			29,164.054	0.301
Equation (6)	0.484	0.361	−0.864	0.361			4,650,654.264	0.875
Equation (7)	0.484	0.060 *	831.057	0.060 *			8.553	0.000 ***
Equation (8)	0.484	0.362	−0.001	0.362			10.281	0.000 ***
Equation (9)	0.484	0.062 *	1.001	0.000 ***			29,164.054	0.301
Equation (10)	0.484	0.012 **	0.821	0.000 ***			3.429 × 10−5	0.000 ***
Romania
Equation (1)	0.535	0.007 ***	34.991	0.007 ***			−629.170	0.023 **
Equation (2)	0.525	0.008 ***	788.263	0.008 ***			−2295.729	0.011 **
Equation (3)	0.515	0.009 ***	−17,739.8	0.009 ***			947.391	0.003 ***
Equation (4)	0.815	0.001 ***	−1935.87	0.006 ***	43.304	0.005 ***	21,772.863	0.006 ***
Equation (5)	0.481	0.012 **	1.217	0.000 ***			1.857	0.511
Equation (6)	0.471	0.014 **	4.429	0.014 **			0.000	0.833
Equation (7)	0.462	0.015 **	−99,596	0.015 **			9.477	0.000 ***
Equation (8)	0.481	0.012 **	0.197	0.012 **			0.619	0.682
Equation (9)	0.481	0.012 **	0.197	0.012 **			1.857	0.511
Equation (10)	0.481	0.012 **	0.821	0.000 ***			0.539	0.511

Notes: * denotes significance at 10% level, ** denotes significance at 5% level, and *** denotes significance at 1% level.

. An analysis of the value of the parameters of each equation for the period before the financial crisis found that for the EU, the most suitable model is logistic (Equation (10)), obtaining the most suitable regression curve (Figure 5a). For Romania, it is quadratic (Equation (4)) (Figure 5b). There is an inverse relationship between FEC and GDP for the EU: increasing FEC leads to a decrease in GDP. For RO, increasing FEC up to the critical value of 22.4 MTOE leads to a decrease in GDP, after which increasing FEC leads to an increase in GDP. It is noticed that also for the 2009–2020 period, FEC variation determines the variation of GDP, so hypothesis H1 is verified.

A synthesis of all the information for the three periods shows that hypothesis H1 is verified: final energy consumption influences GDP.

After identifying the best models through the regression equations, we moved on to their validation through the neural network construction. First, to determine the effects of increasing final energy consumption on economic growth, we built the neural network model using FEC as an exogenous variable and GDP as an endogenous variable. The MLP model used has only one hidden layer, and this was the increase in energy efficiency. The analysis of the neural network was carried out on the basis of the estimation of the MLP network parameters synthesized in Appendix A 

Table A4. Estimation of MLP network parameters on FEC and GDP.

Period	Geo	Exogenous Variable		Endogenous Variable
				Hidden Layer 1	Output Layer
				H(1:1)	GDP
1995–2020	EU	Input Layer	(Bias)	0.603	-
			FEC	0.220	-
		Hidden Layer 1	(Bias)	-	0.034
			H(1:1)	-	−0.325
	RO	Input Layer	(Bias)	1.798	-
			FEC	−2.003	-
		Hidden Layer 1	(Bias)	-	−2.035
			H(1:1)	-	2.057
1995–2008	EU	Input Layer	(Bias)	−0.412	-
			FEC	−0.643	-
		Hidden Layer 1	(Bias)	-	−0.655
			H(1:1)	-	−3.290
	RO	Input Layer	(Bias)	−2.688	-
			FEC	4.507	-
		Hidden Layer 1	(Bias)	-	−2.427
			H(1:1)	-	−1.880
2009–2020	EU	Input Layer	(Bias)	0.126	-
			FEC	0.275	-
		Hidden Layer 1	(Bias)	-	−0.001
			H(1:1)	-	−0.990
	RO	Input Layer	(Bias)	3.539	-
			FEC	−4.552	-
		Hidden Layer 1	(Bias)	-	0.430
			H(1:1)	-	−1.887

.

The relationship between the FEC and GDP variables resulting from the construction of the neural network and presented by the multilayer perceptron models are shown in Figure 6, Figure 7 and Figure 8 (a—EU and b—RO) for the three analyzed periods.

Following the analysis of artificial neural networks built for 1995–2020 (Figure 6), with an input layer defined by FEC and an output level defined by GDP, it found that at the EU level, increasing FEC leads to a decrease in GDP, and at the RO level, decreasing FEC leads to an increase in GDP. So for this period, there is a validated correlation between FEC and economic growth, which means that hypothesis H1 is valid and the chosen regression models are validated.

For 1995–2008, the analysis of the neural networks built (Figure 7) shows that there is a direct relationship between the indicators at the EU level (increasing FEC leads to an increase in GDP) and inverse at the RO level (increasing FEC leads to a slight decrease in GDP). There is a validated one-way causality correlation between FEC and economic growth, which means that the chosen regression models are validated and that hypothesis H1 is valid.

The analysis of the artificial neural networks built for 2009–2022 (Figure 8) shows that at the EU level, the increase in FEC leads to a decrease in GDP, and at the RO level, the decrease in FEC leads to a decrease in GDP. Thus, there is validated causality between FEC and economic growth, which means that the chosen regression models are validated and that Hypothesis H1 is valid.

Using the hyperbolic tangent function shows that the hidden layer (H(1:1)) (which can be represented by increases in energy efficiency) has a significant impact on neural network performance.

Synaptic weight identifies an indirect relationship between FEC and GDP at the EU level for 1995–2020 and 2009–2020 and is more significant for the 2009–2020 period. These results demonstrate the validity of the logistic model for 1995–2020 and the growth model for 2009–2020. For Romania, synaptic weight identifies an indirect relationship between FEC and GDP at the EU level for the 1995–2008 period, which proves that the quadratic model is valid.

Because MLP uses bias as an additional parameter, this proves that the constructed neural network is the most suitable for the analyzed data.

4.2.2. Analysis of the Relationships between Final Energy Consumption by Sector and GDP—Testing Hypotheses H2–H5

To test the validity of hypotheses H2–H5, we moved on to estimate the regression equations for the period 2009–2020, considering GDP as the dependent variable (y) and FEC_I, FEC_T, FEC_C, and FEC_H as independent variables (x). Following the analysis of the estimation parameters of each equation, the best regression models (for the EU and RO) were identified (

Table 4. Estimation of parameters of the most suitable equations for estimating the relationship between GDP and FEC by sector.

Hypothesis	Regression Equations	R Square	Regression p-Value	Coefficients
				Var 1	p-Value	Var 2	p-Value	Constant	p-Value
European Union
FEC_I	S	0.506	0.014 **	−78.289	0.014 **			9.732	0.000 ***
FEC_T	Quadratic	0.619	0.013 **	−3705.857	0.005 ***	6.853	0.004 ***	512,311.907	0.004 ***
FEC_C	Logistic	0.581	0.068 *	1.008	0.000 ***			2.961 × 10−5	0.076 *
FEC_H	Growth	0.598	0.066 *	−0.004	0.066 *			10.495	0.000 ***
Romania
FEC_I	Quadratic	0.490	0.015 **	3331.929	0.088 *	−252,400	0.088 *	−10,814.824	0.092 *
FEC_T	Linear	0.940	0.000 ***	61.656	0.000 ***			−183.741	0.000 ***
FEC_C	Inverse	0.475	0.013 **	−1098.605	0.013 **			766.914	0.003 ***
FEC_H	Quadratic	0.433	0.003 ***	4600.369	0.059 *	−299.202	0.057 *	−17,498.341	0.065 *

Notes: * denotes significance at 10% level, ** denotes significance at 5% level, and *** denotes significance at 1% level.

).

The graphs of the regression curves of the best-fitting models for the analysis of the relationship between GDP and final consumption in the industry sector are shown in Figure 9 (a—EU and b—RO).

At the EU level, the regression curve analysis shows that an increase in FEC_I causes an increase in GDP. At the RO, up to a FEC_I certain value (6.6 MTOE), the increase positively influences GDP growth, after which it is negatively influenced. Thus, hypothesis H2 is partially verified.

The regression curves for the most suitable models for the analysis of the relationship between GDP and FEC_T are shown in Figure 10. At the EU level, an increase in FEC_T consumption up to the critical point of 270.4 MTOE leads to a decrease in GDP, after which increasing FEC_T has a positive effect on GDP. In conclusion, hypothesis H3 is validated.

The regression curve analysis for the most suitable models for the relationship analysis between GDP and FEC_C (Figure 11) shows opposite trends for RO compared with the EU, so hypothesis H4 is partially verified. The increase in FEC_C at the EU level leads to a decrease in GDP, while at the RO level, it leads to an increase.

The analysis of the regression curves for the most suitable models for the GDP—FEC_H relationship (Figure 12) shows that at the EU level, the FEC_H increase causes a decrease in GDP. At the RO level, the FEC_H increase up to the value of 7.7 MTOE causes an increase in GDP, after which leads to a decrease in GDP. According to these results, hypothesis H5 is partially verified.

After identifying the most suitable regression models for estimating the energy consumption of each sector and GDP, we moved on to building neural networks to validate them. Neural network models determine the effects of the increase in the final energy consumption of each sector on economic growth, using FEC for each sector as an exogenous variable and GDP as an endogenous variable. The estimation of MLP network parameters is shown in Appendix A 

Table A5. Estimation of MLP network parameters regarding final energy consumption by sector and economic growth.

Relation	Geo	Exogenous Variable		Endogenous Variable
				Hidden Layer 1	Output Layer
				H(1:1)	GDP
FEC_I—GDP	EU	Input Layer	(Bias)	0.196	-
			FEC_I	0.337	-
		Hidden Layer 1	(Bias)	-	−0.211
			H(1:1)	-	0.335
	RO	Input Layer	(Bias)	−0.007	-
			FEC_I	−0.107	-
		Hidden Layer 1	(Bias)	-	−0.440
			H(1:1)	-	0.279
FEC_T—GDP	EU	Input Layer	(Bias)	−4.393	-
			FEC_T	4.354	-
		Hidden Layer 1	(Bias)	-	1.856
			H(1:1)	-	2.501
	RO	Input Layer	(Bias)	0.084	-
			FEC_T	−0.402	-
		Hidden Layer 1	(Bias)	-	−0.057
			H(1:1)	-	−5.059
FEC_C—GDP	EU	Input Layer	(Bias)	0.233	-
			FEC_C	−0.600	-
		Hidden Layer 1	(Bias)	-	0.083
			H(1:1)	-	0.764
	RO	Input Layer	(Bias)	0.227	-
			FEC_C	2.381	-
		Hidden Layer 1	(Bias)	-	−0.545
			H(1:1)	-	1.323
FEC_H—GDP	EU	Input Layer	(Bias)	0.693	-
			FEC_H	−1.038	-
		Hidden Layer 1	(Bias)	-	−0.044
			H(1:1)	-	1.006
	RO	Input Layer	(Bias)	0.912	-
			FEC_H	−1.092	-
		Hidden Layer 1	(Bias)	-	−1.093
			H(1:1)	-	0.856

.

The relationships between final consumption for the industry sector (FEC_I) and GDP resulting from the construction of MLP neural networks with a single hidden layer (represented by the increase in energy efficiency) are shown in Figure 13 (EU (a) and RO (b)).

The analysis of artificial neural networks built with an input layer defined by FEC_I and an output level defined by GDP finds that there is a direct effect at the EU level (increasing FEC_I leads to an increase in GDP) and an inverse connection for RO (decreasing FEC_I leads to an increase in GDP). These results concluded that hypothesis H2 is partially valid and that the chosen regression models are validated. The effect exerted by the final energy consumption in the industrial sector on economic growth is amplified by the increase in energy efficiency.

The analysis of the neural networks built with FEC_T as an input layer and GDP as an output layer (Figure 14) shows that there is a direct effect both at the EU level (an increase in FEC_T leads to an increase in GDP) and at the RO level (a decrease in FEC_T leads to a decrease in GDP). There is a validated correlation between FEC_T and economic growth, which means that hypothesis H3 is valid.

The neural networks built with FEC_C as the input layer and PIB as the output layer are shown in Figure 15. An analysis of them demonstrates that there is an inverse link between the indicators at the EU level (a decrease in FEC_C leads to an increase in GDP) and a direct link between them at the RO level (an increase in FEC_C leads to an increase in GDP). Thus, there is a partially validated correlation between FEC_C and economic growth, which means that hypothesis H4 is partially valid and that the chosen regression models are validated.

The analysis of the artificial neural networks built with a FEC_H input layer and a PIB output layer (Figure 16) shows that there is an inverse relationship between the indicators (a decrease in FEC_H leads to an increase in GDP) at both the EU and the RO levels. There is thus a validated correlation between FEC_H and economic growth, which means that hypothesis H5 is valid.

MLP’s use of the additional parameter of bias demonstrates that the constructed neural networks are the most suitable for the analyzed data. Thus, the chosen regression models are validated. The analysis of the obtained information leads to the conclusion that hypotheses H1–H5 are fully or partially verified for both the EU and Romania.

4.3. Ranking of Sectors by the Impact of Energy Consumption on Economic Growth

Starting from the hypotheses previously tested by regression equations and validated by neural networks, we built artificial neural networks to rank sectors whose energy consumption has a significant influence on economic growth (for the EU and RO). Neural networks are built based on the structural components of the FEC to determine the hierarchy of the impacts of the energy consumption of the four sectors on economic growth. Thus, GDP was considered the endogenous variable and energy consumption by sector (FEC_I, FEC_T, FEC_C, and FEC_H) the exogenous variables. The estimated parameters of the neural networks constructed for the EU and RO using the MLP network with a single hidden layer (increasing energy efficiency) are shown in

Table 5. Estimation of MLP network parameters on final energy consumption by sector and economic growth.

Geo	Exogenous Variable		Endogenous Variable
			Hidden Layer 1	Output Layer
			H(1:1)	GDP
European Union	Input Layer	(Bias)	0.004	-
		FEC_I	0.211	-
		FEC_T	0.138	-
		FEC_C	−0.372	-
		FEC_H	−0.869	-
	Hidden Layer 1	(Bias)	-	0.074
		H(1:1)	-	0.744
Romania	Input Layer	(Bias)	−0.186	-
		FEC_I	−0.305	-
		FEC_T	1.049	-
		FEC_C	0.850	-
		FEC_H	−0.003	-
	Hidden Layer 1	(Bias)	-	−0.140
		H(1:1)	-	2.454

.

The relationships between the final consumption of energy from renewable sources by sector and GDP, at the EU and RO levels, obtained by building the neural network are presented in Figure 17.

Using the hyperbolic tangent function shows that the hidden layer (H(1:1)) represented by increasing energy efficiency has a significant impact on the performance of the neural network. The bias parameter and the use of the sigmoid function for the output layer demonstrate that the constructed neural networks best fit the analyzed data. The synaptic weight identifies that at both the EU and the RO levels a decrease in FEC_H consumption leads to an increase in GDP (the influence is much more significant in the EU) and that an increase in FEC_T leads to an increase in GDP. At the same time, the decrease in energy consumption leads to an increase in GDP for the FEC_C sector for the EU and the industry sector in RO. The increase in consumption in the other sectors (FEC_I for EU and FEC_C for RO) leads to an increase in GDP.

The relative importance of each input predictor was calculated in terms of normalized relative importance ranking (expressed as %) by using a sensitivity analysis, as presented in

Table 6. Normalized and relative importance by variable.

Geo	Predictors (Independent Variables)	Average Relative Importance	Normalized Importance (%)	Ranking
EU	FEC_I	0.112	19.8	3
	FEC_T	0.078	13.8	4
	FEC_C	0.244	43.1	2
	FEC_H	0.566	100.0	1
RO	FEC_I	0.064	11.9	3
	FEC_T	0.541	100.0	1
	FEC_C	0.394	72.8	2
	FEC_H	0.001	0.1	4

and Figure 18.

The variable with the most impact on GDP at the EU level is the final energy consumption in the household sector, and at the RO level, it is the final energy consumption in the transport sector. Energy consumption in the commercial and public services sector and in industry in both geographical entities occupy the same places (2 and 3, respectively). At the EU level, the energy consumption of the household sector significantly influences the GDP and is attributable to the developed states of the EU. As for RO, which is an emerging state, this consumption is almost insignificant in terms of its influence on GDP.

The influence analysis of energy consumption in each sector on GDP is shown in

Table 7. Impact of sector-specific final energy consumption on economic growth.

Level	Significance Impact FEC by Sector
	Direct		Indirect
	1	2	1	2
RO	FEC_T	FEC_C	FEC_I FEC_H
EU	FEC_I	FEC_T	FEC_H FEC_C

Notes: 1—very strong impact; 2—medium impact.

.

A direct relationship between the exogenous variable FEC_T and the endogenous variable PIB and an indirect relationship between FEC_H and GDP are identified at both the EU and the RO levels. The type of relationship between the other exogenous variables and the endogenous variable (GDP) at the EU level is the opposite of those at the RO level. There is a direct relationship between FEC_I and GDP for the EU and an indirect one for RO; an indirect relationship between FEC_C and GDP for the EU; and a direct relationship for the RO.

5. Discussions

In general, the economic growth (expressed by GDP) tended to be coupled with an increase in energy consumption, in proportion to increases in the number of people who generate more goods and services. The COVID-19 pandemic and the Russo-Ukrainian War have alerted EU states to the importance of ensuring their energy security for achieving economic growth. At the same time, they have considered decoupling energy consumption from economic growth so that economic growth may be dependent only on energy consumption, by creating service economies (less energy-consuming), increasing energy efficiency, and increasingly the use of advanced technologies that can lead to a substantial reduction in energy consumption. Following the analysis, a decoupling of economic growth rates (constantly increasing) from the variation of energy consumption (increasing, but less abrupt) was found—similar results were also found by other studies [24,64].

The results of the study show that there is a link (positive or negative) between final energy consumption and economic growth, but this link is differentiated by periods and geographical regions. For specific, short periods, energy consumption registers a negative influence on economic growth, results that have been confirmed by other scientific studies [9,11,101]. For different periods, the increase in energy consumption can stimulate economic growth, results that have confirmed by other studies [10,77,78,98,99,100,102,103].

At the EU level (where the developed countries and large energy consumers have a powerful impact), the results are the opposite of the ones from Romania, which is an emerging country, and these results have also been confirmed by other studies [8]. During the periods 1995–2008 and 2009–2020 in Romania, the relationship between energy consumption and economic growth has intervals of positive and negative influence, but opposite findings have been validated by other research studies [77,78].

Energy consumption by sector plays an important role in a country’s total energy consumption. Until 2019, Romania recorded its highest energy consumption in the residential sector, followed by the industrial and transport sectors, so the pandemic affected energy consumption quite a bit. In the EU, especially in developed states, the contribution of the transport and commercial and public services sectors to total energy consumption has a significant impact on energy consumption and implicitly on economic growth; thus, the COVID-19 pandemic had a strong effect on them, which has been demonstrated in other studies [56,71].

In the period preceding the 2008–2009 financial crisis (1995–2008) at the EU level, the final energy consumption had an upward trend, while at the RO level, it had a downward trend because it closed large energy-consuming industries. After the financial crisis, the final energy consumption in Romania generally registered an upward trend (less than the 2013–2014 level), which was interrupted by the beginning of the COVID-19 pandemic, just like in other countries of the world [47,65]. At the EU level, the final energy consumption generally had a downward trend because the states, through their national energy policies, had to meet the objectives set by the European Commission [37,38,39,40]. A comparative analysis of the final energy consumption evolution of the two crisis periods (financial and COVID-19) leads to the conclusion that the final energy consumption is characterized by a sudden decrease during the onset of the crises. The EU was more affected by the COVID-19 crisis, while RO was affected by the 2008–2009 financial crisis (like all emerging states) [50,51].

Following the analysis of artificial neural networks built with an input layer defined by FEC and an output layer defined by GDP, it is found that there is a proportional inverse effect at the level of the EU (for the period 1995–2020 and 2009–2020) and RO (for the period 1995–2008). Final energy consumption exerts an effect on economic growth, amplified by increased energy efficiency. From the study results, it can be concluded that the chosen regression models are validated. On some time intervals, there is a correlation of inverse proportionality between FEC and economic growth (final energy consumption has a negative influence on economic growth), the results of which have been confirmed by other specialist studies [9,11,101]. At the same time, for short periods, an increase in energy consumption stimulates economic growth, results that have also been confirmed by some studies [10,98,99,100,102].

At the European Union level (where the developed countries and large energy consumers have a powerful impact), the results are opposite to those of Romania (an emerging country), which also matches results from other studies [8]. During certain periods in Romania, it is found that energy consumption differently influences economic growth. In the 1995–2008 period, energy consumption positively influences economic growth up to a critical value, and above this level, the final energy consumption leads to a decrease in economic development. For the 2009–2020 period, the effect is the opposite: the increase in energy consumption up to a certain level leads to a decrease in economic growth, and an increase above the critical value of energy consumption has a positive effect on economic growth—findings that have also been validated by another studies [77,78].

The analysis of artificial neural networks built for sectoral consumption highlights the effect exerted by consumption, by sector (FEC_I, FEC_T, FEC_C, and FEC_H), on economic growth, directly or indirectly and with different intensities—results that have also been found in other studies [1,75,83].

After testing the models, it is found that at the EU level, the increase in FEC_I causes an increase in GDP. This is because developed countries are high-energy consumers, and their industrial sector is continuously growing. These results are verified by other studies [15]. According to the long-term climate strategy established by the European Commission, developed states must consider how to implement the transition plan for the energy efficiency of energy-intensive industries and the transition of industrial sectors to a low-carbon economy [44].

Regarding the situation at the level of Romania, it is observed that although for the analyzed period, the energy consumption in the industrial sector initially tended to have a positive effect on GDP, for the total period, it had a negative influence on GDP. This is due to the change in the industry structure required for the EU directives [38] and the adoption of a series of energy efficiency measures, to reduce consumption and optimize production costs. At the same time, the increase in industrial production is ensured by branches with low energy consumption, and energy-intensive industries have decreased their production.

Transport energy consumption, at both the European Union and the Romania levels, has a significant positive influence on economic growth—results that have also been found in other studies [41,75]. This is due to the increase in transport activity (passenger and goods traffic) under the conditions that have improved the efficiency of cars, trucks, airplanes, etc. The European Union, to meet the objectives of reducing greenhouse gas emissions in total energy consumption, pays increasing attention to replacing conventional cars that have internal combustion engines with electric ones [55,56]. The powerful impact on the environment from the increase in energy consumption in the transport sector has led to the adoption of regulations at the European Union level and at the level of each state to move toward more-ecological transport.

The decrease in energy consumption in commercial and public services leads to an increase in GDP in the EU, which reflects changes in the composition of the economy of the EU states—results that have also been found in other studies [71]. Advanced economies tend to become service economies, the energy intensity of service sectors is substantially lower than that of industrial sectors, and energy is used with increased efficiency. At the level of Romania, which is a country with an emerging economy, the increase in the consumption of the commercial and public services sector has a positive effect on GDP thanks to the spectacular increase in the demand for products (refrigerators, washing machines, and air conditioners), and the use of, to a small extent, smart appliances and innovative applications to reduce energy intensity.

The decrease in household energy consumption leads to an increase in GDP at both the European Union and the Romania levels, results confirmed by other studies [45,104,115]. The relationship between FEC_H and GDP is due to the decrease in energy intensity and the increase in energy efficiency in this sector, energy performance for electrical equipment and appliances used, building envelope, etc. Energy intensity will decrease as new, energy-efficient technologies are adopted.

We find that sectoral energy consumption has heterogeneous behaviors on GDP—results that have also been found in other studies [73,85]. The final energy consumption influences GDP in different ways at the European Union and Romania levels. At the level of the European Union, energy consumption from the industrial and transport sectors has a positive influence on GDP, and energy consumption from the other sectors reduces GDP. For Romania, energy consumption from the transport and commercial and public services sectors has a positive influence on GDP. Energy consumption from the industry and household sectors reduces GDP.

It is observed that the general trend of FEC at the level of the European Union is given by the consumption of the FEC_C and FEC_H sectors, and at the level of Romania by the FEC_C and FEC_T sectors. Under these conditions, to test this conclusion, we extended the investigation and carried out a structural analysis to determine the impact of each sector on GDP.

6. Conclusions

The COVID-19 pandemic, through the restrictions imposed at the level of European states, strongly disturbed the economic activity and energy consumption of the European Union. Then, in 2021, with the lifting of the restrictions imposed by the pandemic and the resumption of economic activities, energy consumption began to increase, and the prospects for the European Union economy showed a period of long-term, strong economic growth. However, barely out of the pandemic, the countries of the European Union are sinking again into a period of economic turbulence caused by the energy crisis from the Russo-Ukrainian War. The war brought economic uncertainty back to Europe, forcing a reassessment of the economic outlook as energy policy starts to raise problems for European Union states and tremendously impact Europe’s energy mix.

Thus, the European Union’s plan for ensuring energy security could be realized much faster than what was forecast. The challenges of energy insecurity require a reshaping of economic and political relations, creating new alliances. Governments must step up their efforts to ensure the flexible energy infrastructure needed for diverse power generation, with substantial shares of renewable energy. At the same time, they must bear in mind that energy efficiency is one of the main factors in achieving the European Union’s long-term energy and climate objectives, as the most cost-effective way to reduce emissions, improve energy security, increase competitiveness, and make energy consumption more affordable for all consumers. Energy efficiency is becoming a strategic priority for the European Union, as it can contribute to lower energy consumption with the adoption of new technologies with high energy efficiency.

Much of the literature has focused over time on determining the role of energy consumption on economic growth, but no clear relationship between them has been found. In the conditions of the uncertainty caused by the pandemic and the Russo-Ukrainian War, we considered it appropriate to carry out this study, which we structured in three main directions. The first direction consisted of a comparative analysis (Romania with the European Union) on the evolution of economic growth and final energy consumption, globally (1995–2020) and by sector (2009–2020). The second direction consisted of analyzing the relationship between final energy consumption and economic growth (for the European Union and Romania) by testing 10 regression models, identifying the best models, and validating them through neural networks. The third direction aimed to identify the sectors whose consumption has the highest contribution to economic growth for the European Union and Romania.

In this way, we consider that the study has several theoretical and practical implications that may be relevant given that energy consumption is of upmost importance both for the European Union in general and for each member state to ensure energy security and achieve sustainable development that ensures a better future for community members. This study adds value to existing research by addressing neural networks that correctly identify the meaning of the relationship between energy consumption and economic growth. At the same time, the neural network approach for ranking the impact of energy consumption by sector on economic growth is a novelty in the literature.

The study has a series of theoretical implications arising from the identification of the impact of final energy consumption and energy consumption by sector on economic growth, at both the European Union and the Romania levels. Thus, the results of this study can play an important role in establishing energy policy strategies at the national level (for emerging states) to stimulate the increase in energy efficiency in all sectors and to implement programs to stimulate deficit sectors so much that member states of the European Union could achieve the proposed target objectives for 2030. At the same time, it can be the basis for carrying out other research both on European Union states and on other states.

This research contributes to the enrichment of specialized literature through the originality of the structural model that allowed the examination of the energy consumption impact of each sector on economic growth. In the context of the consequences of the COVID-19 pandemic and the uncertainty caused by the Russo-Ukrainian War, we believe that the research findings are robust and support the stability of the conceptual model.

The downward trend of the GDP caused by the pandemic at the level of Romania makes us consider that the average GDP growth rate will not be sufficient to recover from the gaps compared with the EU development average. Because the overall impact of the COVID-19 crisis and the Russo-Ukrainian War cannot yet be known, the outlook for economic growth and energy consumption is uncertain.

The practical implications of our empirical research for Romania and the European Union allow us to state that the increase in energy consumption has a significant positive influence on economic growth (expressed in macroeconomic terms through GDP). At the same time, we found that an attempt is being made to decouple energy consumption from economic growth through states’ transitioning to less-energy-consuming economies, through an increase in energy efficiency and through the use of advanced technologies.

The decrease in energy intensity, the increase in energy efficiency, and the changes in energy mix (increase in consumption from renewable energy sources) can lead to stagnation or even a reduction in energy consumption without affecting economic growth. At the same time, improving energy efficiency can be a powerful tool for achieving sustainable economic development and most important for reducing energy consumption and environmental pollution at both the Romanian and the European Union levels. In this sense, European policies are needed to stimulate sustainable economic growth in response to the energy crisis and to help the member states of the European Union to take appropriate measures to provide support to the sectors particularly affected and to the citizens.

A structural analysis of the impact of final energy consumption by sector on economic growth can be the basis for adopting governmental and European policies to stimulate sustainable development and economic growth and take appropriate measures to provide support to disadvantaged sectors.

The crisis caused by COVID-19 and the energy crisis caused by the war between Russia and Ukraine demonstrated the need for the countries of the European Union not to depend only on traditional sources of energy from other countries outside the European Union and to become more involved in increasing production and energy consumption from renewable sources that will have substantial implications in all sectors of economic and social life, while also having a positive influence on general economic growth.

In addition to theoretical and practical contributions, this study also has limitations, which are worth studying and may suggest future research directions. One limitation is that the research was conducted at the level of the European Union and that of Romania, and the situation of European Union countries presents significant differences. Future research should therefore conduct comparative analyzes across country groups (emerging/developed, European countries vs. countries from other regions, etc.) to test which of the models fit best, thus verifying whether the findings of this study hold. Potential future research directions can extend the analysis by using a cluster analysis, by testing the impact of other factors on energy consumption and implicitly on economic growth.