*Article* **The Relationship between ROP Funds and Sustainable Development—A Case Study for Poland**

**Łukasz Mach 1,\* , Karina Bedrunka <sup>2</sup> , Ireneusz D ˛abrowski <sup>3</sup> and Paweł Fr ˛acz <sup>4</sup>**


**Abstract:** The aim of this research is to analyse the correlation between public intervention in Poland within the Regional Operational Programmes and the key macroeconomic variables for the sustainable development of regions, i.e., the labour market, with particular emphasis on the unemployment rate and the level of employment; the average monthly remuneration; the residential construction market, with particular emphasis on the number of permits issued for the construction of apartments and the number of apartments under construction. The research and the analyses carried out on the basis of the above-mentioned aspects made it possible to indicate the relations between the studied macroeconomic indicators and the EU funds spending in Polish provinces, which will enable the implementation of the sustainable development policy. The capitals used in the research process are very important components of the region's and country's sustainable development. In the research, a calculation methodology was applied based on the analysis of time variability of the examined determinants, their correlation and regression relationships. The tools and methods of data analysis used allowed the quantification of the relationship between the macroeconomic determinants studied and the pace and value of payments made. The conducted analyses have shown a positive influence of the payments made in Poland within the framework of Regional Operational Programmes on selected macroeconomic indicators, i.e., regional economic and social-institutional capitals. The research results obtained may have a practical decision-making aspect for regional and national authorities responsible for the disbursement of EU funds.

**Keywords:** sustainable development; determinants of sustainable development; regional operational programmes; European Union funds

#### **1. Introduction**

The weakening position of the European Union as the dominant global economy, including the deteriorating social, economic [1], and demographic situation [2] in Europe, forces the application of a new approach to programming activities whose basic goal is to strengthen the EU competitiveness. It is necessary that the concentration of intervention covered correctly diagnosed areas of development, which will result in the macroeconomic development of the European Union as a whole, as well as its individual member states and regions [3]. Economic growth is highly influenced by certain macroeconomic indicators [4]. Thus, the sustainable development of the EU, a country, or a region is a complex process influenced by numerous internal and external factors [5]. The shaping of development policy requires a thorough analysis of the factors as well as great courage, willingness, and readiness to actively and effectively minimise the negative impact of unfavourable trends [6].

**Citation:** Mach, Ł.; Bedrunka, K.; D ˛abrowski, I.; Fr ˛acz, P. The Relationship between ROP Funds and Sustainable Development—A Case Study for Poland. *Energies* **2021**, *14*, 2677. https://doi.org/10.3390/ en14092677

Academic Editor: Sergey Zhironkin

Received: 23 March 2021 Accepted: 26 April 2021 Published: 6 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In the national dimension, the Polish economy is an integral part of the global economic system; thus, it should be remembered that one of the key factors affecting Poland's economic development is the global economic situation [7,8]. The dynamics of the Polish economy and its dependence on cycles and development trends of the global system are influenced both by direct economic relations and global markets conditions, including the consequences of participation in the common market of the European Union and in multilateral free trade agreements [6]. It should also be borne in mind that the development of the country as a whole is a component of the development of its individual regions, whose growth potential has been and continues to be stimulated thanks to the support of the European Union structural funds. In Poland, this support has been in place since 1999 and significantly increased after accession in 2004. At the moment, the third perspective of the EU funds spending is coming to an end; these are the years 2004–2006, 2007–2013, and 2014–2020. Poland is the largest recipient of the EU assistance among all EU member states. In 2004, the Polish GDP per capita equalled 51% of the EU's average, and over a period of 15 years, it has grown by 15%, i.e., to 73% in 2019 [9]. Between 2014 and 2020, the amount reached over 87 billion euros. Over 35.9% of this allocation, i.e., 31.3 million euros, is assigned for 16 Polish regions under regional operational programmes. These funds are managed by regional authorities and are earmarked for increasing socio-economic competitiveness, including sustainable development [9].

Taking the above into account, the aim of the subject research is to analyse the relationship between the public intervention under Regional Operational Programmes (ROP) and macroeconomic variables, crucial for the development of the regions, i.e.,


The research, and the analyses carried out on its basis, will indicate the relations between the studied development determinants and the EU funds spending in the 16 Polish provinces. In the research, the following hypotheses were made:

**Hypothesis 1.** *There is observed a seasonality in the payments made in relation to the analysed variables.*

**Hypothesis 2.** *The correlation between the payment and macroeconomic variables depends on the amount of financial support.*

**Hypothesis 3.** *There is a time correlation between the payments and the analysed macroeconomic areas.*

**Hypothesis 4.** *The analysed macroeconomic variables are characterized by a different flexibility with relation to the payments made.*

The implementation of the research process was performed in several key stages. The first provides an in-depth analysis of strategic development planning from a transnational, national, and regional perspective. The second one is the literature analysis of the studied issue, and the third one contains calculations showing the influence, expressed quantitatively, between the EU funds spending and selected determinants of regional development. The conducted research will show the relationship caused by spending EU funds on selected regional macroeconomic variables. As a result of the literature analysis, the selection of variables for the analysis was narrowed down to the identification of the correlation between the EU spending and regional economic, social and institutional capitals of sustainable development. The selected capitals are very important economic and social components of sustainable development. It should also be strongly emphasised

that the conducted research is based on created simulation models, the aim of which is to show—in a simplified and generalised way—the researched interdependencies.

Undoubtedly, EU project-related payments are significant for the variables under study. This article focuses only on the regional dimension of EU funds. At the same time, it should be noted that in Poland, EU funds are also allocated within the framework of national programmes. Thus, the macroeconomic variables under study are influenced by other public funds and private capital on the market. It should also be noted that the effectiveness and structure of the obtained funds within the ROP programme in relation to the total value of implemented projects is usually only 30–40%. This creates problems in obtaining the remaining funds for the implementation of projects [10]. ROP programmes are sometimes criticized for supporting urban regions or rich regions that have their own sources of funding to implement projects. This, instead of balanced development of the regions, may cause even greater polarisation and increased economic disparities between regions [11]. An important issue is also the analysis of differences in the amount of funds absorbed by individual countries and regions [12].

#### **2. Cascading Strategy of Development Planning—Established Assumptions**

While presenting a cascading strategy description for economic and social development planning, first, the adopted assumptions for development at the transnational level were described, i.e., first, the European Union; then, the national level, i.e., Poland; and finally, the regional level, i.e., Polish provinces. Planning documents are shaped at the EU, national, and regional levels and are the basis for negotiations on structural funds for specific years.

The crisis has wiped out the results of many years of economic and social progress and exposed structural weaknesses in the European economy. At the same time, the world has been changing rapidly, and long-term issues, such as globalisation, increasing demands on limited resources, and ageing populations, are becoming more and more pressing. Europe must take care of its future. Europe can succeed if it acts together as a Union. Appropriate strategic planning is needed, including planning documents. The main one is the Strategy for smart, sustainable, and inclusive growth—Europe 2020 (hereinafter Europe 2020), which will make the EU economy smart, sustainable, and inclusive, with high rates of employment, productivity, and social cohesion. Europe 2020 is a vision of a social market economy for Europe in the 21st century. It comprises three interrelated priorities:


The European Union had to define where it wanted to be at the end of the described planning periods. To this end, several overarching and measurable targets have been proposed, relating to the following: the employment rates for people aged of 20–64 years (should be 75%); 3% of the Union's GDP should be invested in research and development; the "20/20/20" climate and energy targets should be met (including a reduction in carbon emissions of up to 30%, if conditions allow); the number of early school leavers should be reduced to 10%, and at least 40% of the younger generation should pursue higher education; the number of people at risk of poverty should be reduced by 20 million [13].

While presenting the adopted strategic planning process in the national perspective, it should be noted that for the financial perspective 2014–2020, European funds for Poland have been recognised as the main, although not the only, source of funding for investments ensuring dynamic, sustainable, and balanced development. Thus, the programming logic was based on the correlation of European expectations as regards the concentration on the objectives of Europe 2020 with the national objectives indicated in the medium-term national development strategy, i.e., the National Development Strategy 2020—Active society, competitive economy, efficient state, and operationalised in the integrated strategies. This

makes it necessary to look at Poland's development more broadly than just in the context of using the EU funds [14]. It contains recommendations for public policies, providing a basis for changes in the development management system, including the existing strategic documents with a long- and medium-term perspective (strategies, policies, and programmes); however, it also requires verification of other implementation instruments [14]. This means that the assumptions at the level of regions with regard to the implementation of the EU funds had their basis in it. While presenting specific measures, it should be reminded that in 2017 the Polish Government adopted the Responsible Development Strategy by 2020 (with the perspective by 2030). The main objective of the development measures designed in the Strategy is the creation of conditions for growth of income of the inhabitants of Poland with a simultaneous increase of cohesion in the social, economic, environmental, and territorial dimension. The strategy is geared towards inclusive socio-economic development. The document assumes that social cohesion is the main driver of development and a public priority. The strategy subordinates the activities in the economic sphere to achieving objectives related to the standard and the quality of life of the Polish citizens and puts emphasis on making the citizens, and the areas so far neglected in the development policy, benefit from the economic development to the extent greater than so far. The strategy presents a new development model—responsible development, i.e., the development that, while building competitive strength using new development factors, ensures participation and benefits to all social groups living in different parts of our country. This will be done by focusing legal, institutional, and investment actions on three objectives, i.e., sustainable economic growth based increasingly on knowledge; data and organisational excellence; socially responsive and territorially balanced development; effective state and institutions for growth and social and economic inclusion [15].

#### **3. Research Evolution and Development: Region, Development, Sustainable and Smart Growth, and Smart Specialisations**

Poland's accession to the European Union structures gave rise to intensified academic discussion on development, regions and regional development, sustainable and intelligent development, and the methods for their evaluation. There are many publications in Poland and Europe which describe these issues directly or indirectly. The following theoretical analysis of the issue has been carried out according to the procedure shown in Figure 1. *Energies* **2021**, *14*, x FOR PEER REVIEW 5 of 19

**Figure 1.** Diagram of relationship between EU Structural Funds and competitiveness of economy. **Figure 1.** Diagram of relationship between EU Structural Funds and competitiveness of economy.

The notion of development should be understood as any change in the economic, social, and environmental system; however, the attribute of such a change is its irreversi-The notion of development should be understood as any change in the economic, social, and environmental system; however, the attribute of such a change is its irre-

irreversibility is not a single attribute of development. It is worth adding another property to it, i.e., a positive evaluation of the changes taking place from the point of view of a

structure are located, have a chance to strengthen their competitiveness [5].

In the context of social and economic development, a region should be considered in terms of the relationship between the changes occurring at the local and global level [18] (p. 4). In the global economy, which is dominated by the process of globalisation, the area can become competitive only when it takes advantage of its individual characteristics while adapting to the conditions and requirements of the global environment [19]. Currently, the region is classified mainly in terms of economy, where it is possible to identify areas coherent by the role of a particular branch of services or industry [20]. Thus, the events and processes occurring in the region most often determine whether the region is developing or not. The region is identified as an element of developmental policy in terms of economic, institutional, demographic, natural, infrastructural, spatial, potential, and living conditions of inhabitants [21]. In the economic aspect, the region can be considered in relation to the functioning and mutual interaction of the private and the public sectors. In turn, taking into account the logic of market economy, regions treated as public sector entities function in a multi-level system. In this aspect, the national and transnational levels are most significant since the regions which receive financial support from central authorities and transnational institutions, and in which high-level institutions and infra-

In this context, the concept of regional development should be investigated. It is more and more frequently defined as a holistic, structural, and strategic process by which a region's resources and conditions, its technological and cultural potential, and the opportunities identified in regional, national, and global markets are exploited by companies [5]. J. Regional development is influenced by both internal (endogenous) and external (exogenous) factors. At the same time, regional development models, which define a comprehensive and coherent way of explaining the mechanisms of regional development, are concerned with identifying only the key (priority) potentials that are important for development; they mainly revolve around economic growth [5,22]. Regional development can be considered to be a systematic improvement of competitiveness of entities and living

particular system.

versibility [16]. Development refers to the desired positive transformations of quantitative, qualitative, and structural properties of a given system [17]. Thus, spatial and temporal irreversibility is not a single attribute of development. It is worth adding another property to it, i.e., a positive evaluation of the changes taking place from the point of view of a particular system.

In the context of social and economic development, a region should be considered in terms of the relationship between the changes occurring at the local and global level [18] (p. 4). In the global economy, which is dominated by the process of globalisation, the area can become competitive only when it takes advantage of its individual characteristics while adapting to the conditions and requirements of the global environment [19]. Currently, the region is classified mainly in terms of economy, where it is possible to identify areas coherent by the role of a particular branch of services or industry [20]. Thus, the events and processes occurring in the region most often determine whether the region is developing or not. The region is identified as an element of developmental policy in terms of economic, institutional, demographic, natural, infrastructural, spatial, potential, and living conditions of inhabitants [21]. In the economic aspect, the region can be considered in relation to the functioning and mutual interaction of the private and the public sectors. In turn, taking into account the logic of market economy, regions treated as public sector entities function in a multi-level system. In this aspect, the national and transnational levels are most significant since the regions which receive financial support from central authorities and transnational institutions, and in which high-level institutions and infrastructure are located, have a chance to strengthen their competitiveness [5].

In this context, the concept of regional development should be investigated. It is more and more frequently defined as a holistic, structural, and strategic process by which a region's resources and conditions, its technological and cultural potential, and the opportunities identified in regional, national, and global markets are exploited by companies [5]. J. Regional development is influenced by both internal (endogenous) and external (exogenous) factors. At the same time, regional development models, which define a comprehensive and coherent way of explaining the mechanisms of regional development, are concerned with identifying only the key (priority) potentials that are important for development; they mainly revolve around economic growth [5,22]. Regional development can be considered to be a systematic improvement of competitiveness of entities and living standards of inhabitants as well as an increase in the economic potential of regions, contributing to the social and economic development of the country [23].

Among researchers, there is no coherent approach to the concept of regional development because, due to the changing environment, it is subject to constant modification. Sustainable development is one of the concepts of regional development. It is defined as a process of changes in the states of dynamic balance among local economic, social, as well as ecological and spatial development. On the basis of respect for natural resources, the ultimate goal of this process is to improve the quality of life in a broad sense [24]. The development policy objectives formulated by public authorities are characterised by certain principles which make it possible to operationalise them [25]. Sustainable development paradigm in regional development policy contains some conceptual features and operating principles; these are the development maintenance and sustainability [26]. Sustainable development as a concept of development policy defines the process of changing the states of dynamic balance between regional social, economic, as well as environmental and spatial development. There are two integrated pillars of this concept, i.e., balancing social (including political), economic, and environmental governance as well as the sustainability of development capitals achieved through the creation and diffusion of innovations [27]. Capitals are identified by, inter alia, human capital [28], social and institutional capital [29], and by physical and natural (ecological) capital [30].

Sustainable development should be viewed very broadly, including the way companies operate in the global economy. Currently, research is carried out in sustainable production [31]. Research is carried out to evaluate the progress in the implementation

of the concept of sustainable development in the social aspect of the European Union between 2014 and 2018, with particular emphasis on Poland [32]. It is posited that increased emphasis on knowledge and economy factors increases country's competitiveness, which contributes to its sustainable development [33]. Sustainable development is also influenced by fiscal issues [34], climate protection [35], sustainable product life-cycle management, big databases and the use of artificial intelligence in businesses [36,37], networked and integrated urban technologies and sustainable smart energy systems, as well as sensor-based big data applications and computational urban network in a smart energy management system [38,39].

Sustainable development in all EU Member States is regarded as an integral factor in the economic and social policy of the state [40]. At the same time, this approach promotes the growth model proposed in Europe 2020, which is based on three priorities: smart growth, sustainable growth, and inclusive growth [14]. Smart growth means increasing the role of knowledge and innovation as drivers of our future development. This involves raising the quality of education, improving research performance, promoting innovation and knowledge transfer throughout the Union, making full use of information and communication technologies, and ensuring that innovative ideas can be turned into new products and services that create growth, jobs, and solutions for societal problems in Europe and globally. Entrepreneurship, financial resources, consideration of users' needs, and market opportunities are also necessary [14]. Inclusive growth is understood as a set of actions meant to promote a high-employment economy that ensures social and territorial cohesion. It is implemented through the Agenda for new skills and jobs and the European Platform against Poverty [41]. Research shows the effects of the implementation of the Europe 2020 from the point of view of the objectives on poverty and social exclusion [42].

A number of evaluation methods and tools are available in the literature that can be used to evaluate elements of regional development policy, including sustainable development. In the conducted research, attention is primarily paid to its usefulness within the framework of multidimensional processes of regional development, in which it is necessary to take into account the social, economic, and environmental dimensions of sustainable development [25]. The method of ratio analysis can be used to evaluate the effectiveness of sustainable development [43]. The same method should also be used to study the effectiveness of strategies and programmes based on the capitals as well as on the orders of sustainability and regional development (the so-called integrated strategic effectiveness) from the point of view of effectiveness, efficiency, and feasibility [44].

In the ratio analysis of integrated performance evaluation and in the analysis of effectiveness and efficiency of sustainable development for orders and capitals, static, dynamic, and criterion analyses are taken into account, including the integrating orders criteria, and in the capital—the spatial and temporal criteria [45]. The complexity of the category of sustainable development—in the concept of a set of features, objectives, principles, and integration of orders—entails attempts to operationalise this concept and the size of the cross-section of the ratio analyses. Criteria for the classification of indicators include, among others, the extent to which the characteristics, objectives and principles as well as governance of sustainable and balanced development have been achieved [43].

The new EU financial perspective for 2014–2020 and the closely related strategic vision of Europe 2020 clearly define the approach to the environment and its natural resources; it is clearly based on a strong principle of sustainable development [46]. The concept of smart specialisation is conducive to directing regions towards the creation of eco-innovations, which are understood as intentional activity, characterised by entrepreneurship and which encompasses a product design phase and its integrated management throughout its life cycle, that contributes to the pro-ecological modernisation of societies by taking into account environmental concerns in the development of products and related processes [47,48]. Ecoinnovation reflects the concept of a clear focus on reducing environmental impacts, where such effects may or may not occur without limitations to product, process, marketing, or organisational innovation but also including innovation in social structures [49].

Intelligent and sustainable development is closely related. The process of arriving at smart specialisations in Regional Innovation Strategy of Podkarpackie Province was fully of an entrepreneurial discovery process. It basically covered two years, i.e., 2012 and 2013, although it used a number of documents and research findings. The methodology of creating of the Regional Innovation Strategy, including the methodology used for the evaluation of all stakeholders, as well as the criteria for the selection of smart specialisations, was of a uniform nature, showing the continuity and cohesion of individual stages. While preparing the document, a triangulation of methods was made, so that the final result was not derived from only one method used but was adopted when all methods used gave the same or similar result. The basic methods used in the process of creating the Strategy were the following: the analysis of strategic documents and other available sources of knowledge; the analysis of foresight projects carried out for the region; SWOT analysis in terms of social and economic potential of Podkarpackie; the analysis of stakeholders—also performed to identify the most important stakeholders; various forms of meetings and discussions, practiced on a continuous basis; the analysis of the potential and opportunities for development of clusters; and performing primary research with a very wide economic spectrum [50].

In Poland, in the Opolskie province, there has been developed an original model for the selection of regional smart specialisations and the creation of the Regional Innovation Strategy by 2020. It was based on the following methods and tools: content analysis; industry analysis; desk research; time series/trend forecasting; stakeholder consultation; Delphi method; creative imaging; impact assessment; PEST (Political, Economic, Sociocultural, Technological); logic diagram; environmental scan; visioning; and workshops on future occurrences [51,52]). At the same time, it broadly describes the monitoring process of the Strategy on the basis of the Action Plan and selected indicators, which—to a lesser extent—is visible in the works carried out for Podkarpackie Province.

Another interesting example of research in this area is the analysis of higher education institutions from the point of view of their role as innovation brokers in the context of smart specialisations [53], or analyses of the whole regional innovation system in the context of the backwardness of European regions [54].

#### **4. Analysis of the Correlation between the Regional Operational Programme and Selected Macroeconomic Determinants of Development—Research Perspective for Poland**

When analysing the correlation between payments made under the ROP for Poland and the selected macroeconomic determinants, three selected areas of the economy were described. In terms of macroeconomic theory, these areas are crucial for the country's and regions' sustainable development. The first is the area of the labour market (employment); the second is the average monthly remuneration, while the third area of analysis is the housing market, which was described by two dimensions, i.e., the number of building permits issued and the number of current construction projects in the housing market. The choice of the indicated areas of analysis results from the analysis of issues concerning capitals and governance described by the authors of that publication in Chapter 2. It should be reminded that the selected areas of analysis belong to economic, social, and institutional capitals and their analysis is aimed at showing the relationship between public intervention under regional operational programmes and the creation and consolidation of these capitals.

Each of the described areas was scrutinised according to the methodological scheme taking into account the following:


variables analysed with discrete distributions. *x<sup>i</sup>* and *y<sup>i</sup>* denote random sample values of these variables (*i* = 1, 2, . . . , *n*), while *x* and *y* are the mean values of these samples. Then, the estimator of the linear correlation coefficient was determined according to Equation (1).

$$\sigma\_{xy} = \frac{\sum\_{i=1}^{n} (\mathbf{x}\_i - \overline{\mathbf{x}})(y\_i - \overline{\mathbf{y}})}{\sqrt{\sum\_{i=1}^{n} (\mathbf{x}\_i - \overline{\mathbf{x}})^2} \sqrt{\sum\_{i=1}^{n} (y\_i - \overline{y})^2}} \tag{1}$$

• The functional multiple regression analysis based on the estimation of structural parameters of the analysed models. The estimation was made according to Equation (2).

$$
\begin{bmatrix} y\_1 \\ y\_2 \\ \dots \\ \mathbf{y}\_n \end{bmatrix} = \begin{bmatrix} 1 & \mathbf{x}\_{11} & \mathbf{x}\_{12} & \dots & \mathbf{x}\_{1k} \\ 1 & \mathbf{x}\_{21} & \mathbf{x}\_{22} & \dots & \mathbf{x}\_{2k} \\ \dots & \dots & \dots & \dots & \dots \\ 1 & \mathbf{x}\_{n1} & \mathbf{x}\_{n2} & \dots & \mathbf{x}\_{nk} \end{bmatrix} \begin{bmatrix} a\_0 \\ a\_1 \\ \dots \\ \dots \\ a\_k \end{bmatrix} + \begin{bmatrix} \varepsilon\_1 \\ \varepsilon\_2 \\ \vdots \\ \varepsilon\_n \end{bmatrix} \tag{2}
$$
 
$$
\text{where vectors } y = \begin{bmatrix} \mathbf{y}\_1 \\ \mathbf{y}\_2 \\ \dots \\ \mathbf{y}\_n \end{bmatrix} \begin{bmatrix} \mathbf{y}\_1 \\ \mathbf{y}\_2 \\ \dots \\ \mathbf{y}\_n \end{bmatrix}, \mathbf{a} = \begin{bmatrix} \mathbf{a}\_0 \\ \mathbf{a}\_1 \\ \dots \\ \mathbf{a}\_k \end{bmatrix}, \boldsymbol{\varepsilon} = \begin{bmatrix} \varepsilon\_1 \\ \varepsilon\_2 \\ \dots \\ \varepsilon\_n \end{bmatrix}, \boldsymbol{\varepsilon} = \begin{bmatrix} \varepsilon\_1 \\ \varepsilon\_2 \\ \dots \\ \varepsilon\_n \end{bmatrix}
$$
 
$$
\text{and matrix } \mathbf{X} = \begin{bmatrix} 1 & \mathbf{x}\_{11} & \mathbf{x}\_{12} & \dots & \mathbf{x}\_{1k} \\ 1 & \mathbf{x}\_{21} & \mathbf{x}\_{22} & \dots & \mathbf{x}\_{2k} \\ \dots & \dots & \dots & \dots & \dots \\ 1 & \mathbf{x}\_{n1} & \mathbf{x}\_{n2} & \dots & \mathbf{x}\_{nk} \end{bmatrix}
$$

contain the following values:

*y*—dependent variable, *a*—model parameters, ε—residual value, **X**—independent variable. For each correlation under analysis, there were estimated parameters of two functional correlations, i.e., linear (cf. 3) and logarithmic (cf. 4)

$$y = a\mathbf{x} + b \tag{3}$$

$$y = a \ast e^{\frac{-x}{\overline{\nu}}} + c \tag{4}$$

It should also be added that the extent to which the model fits the data, i.e., quality of the developed model was assessed based on the coefficient of determination *R* 2 (Formula (5)).

$$\mathcal{R}^2 = \frac{\sum\_{i=1}^n \left(\hat{y}\_i - \overline{y}\right)^2}{\sum\_{i=1}^n \left(y\_i - \overline{y}\right)^2} \tag{5}$$

where:


The data was obtained from the databases of the Central Statistical Office and from the databases of individual Marshal Offices. It was collected with a time interval of one month. The data used for analysis was collected from January 2015 to July 2020 (in aggregate, 66 values for each studied variable were collected). The collected data include:


*y*4—dependent variable—number of apartments under construction (data obtained from the Main Office of Statistics).

On the basis of the data presented above, a total of 4 groups of models have calculated (for each *y<sup>i</sup>* ) for which the cross-correlation, functional correlation relationship and parameters of the regression function have been described in detail. By computing 4 different models, knowledge was gained about the relationship between each dependent variable (*y<sup>i</sup>* ) analysed and payments made. It should also be noted that another approach in the conducted analyses may also be the simultaneous inclusion in the model of multiple dependent variables and conducting multiple regression analysis.

When analysing the first of the listed variables, i.e., payments made for Poland in total, it should be noted that the increased payments occurred annually at the end of each of the surveyed years. It should also be noted that there was an upward trend in the payments made during the period in question (see Figure 2). The seasonal character of the payments made under the ROP in the years covered by the study is caused, among other things, by the annual financial settlement of the programme-related activities. By subjecting to the analysis of the development of the employment rate in the studied period, we can also notice the tendency of its increase, especially visible in 2016–2018. Comparing the data in Figure 2 on the two horizontal diagrams on it, one can argue about the relationship between the payments made under ROP and the level of employment in Poland. It should also be noted that there are practically no time lags in the described variables in the relationships studied. This demonstrates the high elasticity of change between the studied variables. *Energies* **2021**, *14*, x FOR PEER REVIEW 10 of 19

**Figure 2.** Employment and payments made under ROP—Poland. **Figure 2.** Employment and payments made under ROP—Poland.

In order to confirm the occurrence of significant elasticity of changes between the examined variables, cross-correlation diagrams were prepared for the variable employment to the ROP payments made. From the presented Figure 3, from the obtained decreasing correlation values over time, it can be concluded that the highest correlation relationship is for periods 0, 1, and 2. The results obtained for the calculated cross-correlation confirm the almost immediate effect of payments on employment. Of course, one should be aware that the described correlations illustrate a simplified case based on the crosscorrelation model. It should be remembered that this correlation does not explain the cause-effect relationship, which should be the investigated into by experts dealing with sustainable development of regions. In order to confirm the occurrence of significant elasticity of changes between the examined variables, cross-correlation diagrams were prepared for the variable employment to the ROP payments made. From the presented Figure 3, from the obtained decreasing correlation values over time, it can be concluded that the highest correlation relationship is for periods 0, 1, and 2. The results obtained for the calculated cross-correlation confirm the almost immediate effect of payments on employment. Of course, one should be aware that the described correlations illustrate a simplified case based on the cross-correlation model. It should be remembered that this correlation does not explain the cause-effect relationship, which should be the investigated into by experts dealing with sustainable development of regions.

**Figure 3.** Cross correlation between employment and made payments.

**Figure 2.** Employment and payments made under ROP—Poland.

sustainable development of regions.

In order to confirm the occurrence of significant elasticity of changes between the examined variables, cross-correlation diagrams were prepared for the variable employment to the ROP payments made. From the presented Figure 3, from the obtained decreasing correlation values over time, it can be concluded that the highest correlation relationship is for periods 0, 1, and 2. The results obtained for the calculated cross-correlation confirm the almost immediate effect of payments on employment. Of course, one should be aware that the described correlations illustrate a simplified case based on the crosscorrelation model. It should be remembered that this correlation does not explain the cause-effect relationship, which should be the investigated into by experts dealing with

In the next step of the research, the relationship between the quantitative impact of the payments made on the labour market was analysed because the employment rate is one of key economic barometers. Figure 4 shows the graph of the estimated regression function along with the calculated value of determination coefficients. From the relationship obtained, it can be concluded that the nature of the relationships studied is in the form of a logarithmic function (higher value of the coefficient of determination). The obtained results of the research allow us to put forward a thesis that the effectiveness of the payments made and their impact on the labour market is high, up to payments of about 400 million euros. Above this value, employment growth is of a slowing nature. In the next step of the research, the relationship between the quantitative impact of the payments made on the labour market was analysed because the employment rate is one of key economic barometers. Figure 4 shows the graph of the estimated regression function along with the calculated value of determination coefficients. From the relationship obtained, it can be concluded that the nature of the relationships studied is in the form of a logarithmic function (higher value of the coefficient of determination). The obtained results of the research allow us to put forward a thesis that the effectiveness of the payments made and their impact on the labour market is high, up to payments of about 400 million euros. Above this value, employment growth is of a slowing nature.

**Figure 4.** Correlation function between ROP payments and employment—Poland. **Figure 4.** Correlation function between ROP payments and employment—Poland.

The second variable analysed is remuneration. For this variable, in the first step, the course of its variability was checked, and its course was compared with the variability of

iables was also examined (Figure 6) and, after functional estimation for the described re-

lationships, their regression dependence was assessed (Figure 7).

**Figure 5.** Salaries and payments made under ROP—Poland.

The second variable analysed is remuneration. For this variable, in the first step, the course of its variability was checked, and its course was compared with the variability of made payments within ROP (Figure 5). The significance of lags between comparable variables was also examined (Figure 6) and, after functional estimation for the described relationships, their regression dependence was assessed (Figure 7). The second variable analysed is remuneration. For this variable, in the first step, the course of its variability was checked, and its course was compared with the variability of made payments within ROP (Figure 5). The significance of lags between comparable variables was also examined (Figure 6) and, after functional estimation for the described relationships, their regression dependence was assessed (Figure 7).

**Figure 4.** Correlation function between ROP payments and employment—Poland.

*Energies* **2021**, *14*, x FOR PEER REVIEW 11 of 19

In the next step of the research, the relationship between the quantitative impact of the payments made on the labour market was analysed because the employment rate is one of key economic barometers. Figure 4 shows the graph of the estimated regression function along with the calculated value of determination coefficients. From the relationship obtained, it can be concluded that the nature of the relationships studied is in the form of a logarithmic function (higher value of the coefficient of determination). The obtained results of the research allow us to put forward a thesis that the effectiveness of the payments made and their impact on the labour market is high, up to payments of about

400 million euros. Above this value, employment growth is of a slowing nature.

**Figure 6.** Cross correlation between employment and made payments. **Figure 6.** Cross correlation between employment and made payments.

**Figure 7.** Correlation function between ROP payments and remuneration—Poland.

bles under study is characterised by a six-month period.

Comparing the time courses for the remuneration variable and made ROP payments, we can see an increasing trend for both variables studied. It should be noted that the remuneration variable is characterised by seasonality in the beginning/end of the year. This periodicity is due to the nature of the remuneration paid in Poland, where it is customary to pay additional remuneration at the end of the year, such as awards or annual bonuses. On the other hand, at the beginning of the year, in many companies, the so-called thirteenth salary is paid (see Figure 5). In the attempt to check the relationship between the remuneration variable and made payments, we can see (cf. Figure 6) that a six-month delay is the one with the highest value. This indicates that the time shift between the varia-

**Figure 6.** Cross correlation between employment and made payments.

**Figure 7.** Correlation function between ROP payments and remuneration—Poland. **Figure 7.** Correlation function between ROP payments and remuneration—Poland.

Comparing the time courses for the remuneration variable and made ROP payments, we can see an increasing trend for both variables studied. It should be noted that the remuneration variable is characterised by seasonality in the beginning/end of the year. This periodicity is due to the nature of the remuneration paid in Poland, where it is customary to pay additional remuneration at the end of the year, such as awards or annual bonuses. On the other hand, at the beginning of the year, in many companies, the so-called thirteenth salary is paid (see Figure 5). In the attempt to check the relationship between the remuneration variable and made payments, we can see (cf. Figure 6) that a six-month delay is the one with the highest value. This indicates that the time shift between the variables under study is characterised by a six-month period. Comparing the time courses for the remuneration variable and made ROP payments, we can see an increasing trend for both variables studied. It should be noted that the remuneration variable is characterised by seasonality in the beginning/end of the year. This periodicity is due to the nature of the remuneration paid in Poland, where it is customary to pay additional remuneration at the end of the year, such as awards or annual bonuses. On the other hand, at the beginning of the year, in many companies, the so-called thirteenth salary is paid (see Figure 5). In the attempt to check the relationship between the remuneration variable and made payments, we can see (cf. Figure 6) that a six-month delay is the one with the highest value. This indicates that the time shift between the variables under study is characterised by a six-month period.

While interpreting the results obtained for the calculated autocorrelation functions (cf. Figure 7), we can see that the values of determination coefficients for the linear function and the logarithmic one are close to each other. Based on the results of the linear trend function, it can be noticed that the salaries grow along with the increased level of payments under the ROP in Poland. The average statistic increase in the average salary in relation to the increase amount of payments is expressed by formula *y<sup>t</sup>* = 1.579*t* + 3651.

The last area examined is the residential construction market. The research examined the relationship between made payments and the first two stages of the housing construction process, which included the number of permits issued for the construction of new housing units and the number of units under construction. In Figures 8 and 9, we can see that for both examined variables there is a dynamic increase of values at the beginning of each examined year. It may also be noted that the execution of a construction project, as described by commenced construction, has a visible periodic component, which results from a strong dependence of the execution of construction projects on seasonal variability in the housing market. These phenomena result, among other things, from the differences between the climatic seasons in Poland.

between the climatic seasons in Poland.

between the climatic seasons in Poland.

**Figure 8.** Permits issued for the construction of new apartments and payments made under ROP. **Figure 8.** Permits issued for the construction of new apartments and payments made under ROP. **Figure 8.** Permits issued for the construction of new apartments and payments made under ROP.

While interpreting the results obtained for the calculated autocorrelation functions (cf. Figure 7), we can see that the values of determination coefficients for the linear function and the logarithmic one are close to each other. Based on the results of the linear trend function, it can be noticed that the salaries grow along with the increased level of payments under the ROP in Poland. The average statistic increase in the average salary in relation to the increase amount of payments is expressed by formula = 1,579 + 3651. The last area examined is the residential construction market. The research examined the relationship between made payments and the first two stages of the housing construction process, which included the number of permits issued for the construction of new housing units and the number of units under construction. In Figures 8 and 9, we can see that for both examined variables there is a dynamic increase of values at the beginning of each examined year. It may also be noted that the execution of a construction project, as described by commenced construction, has a visible periodic component, which results from a strong dependence of the execution of construction projects on seasonal variability in the housing market. These phenomena result, among other things, from the differences

While interpreting the results obtained for the calculated autocorrelation functions (cf. Figure 7), we can see that the values of determination coefficients for the linear function and the logarithmic one are close to each other. Based on the results of the linear trend function, it can be noticed that the salaries grow along with the increased level of payments under the ROP in Poland. The average statistic increase in the average salary in relation to the increase amount of payments is expressed by formula = 1,579 + 3651. The last area examined is the residential construction market. The research examined the relationship between made payments and the first two stages of the housing construction process, which included the number of permits issued for the construction of new housing units and the number of units under construction. In Figures 8 and 9, we can see that for both examined variables there is a dynamic increase of values at the beginning of each examined year. It may also be noted that the execution of a construction project, as described by commenced construction, has a visible periodic component, which results from a strong dependence of the execution of construction projects on seasonal variability in the housing market. These phenomena result, among other things, from the differences

*Energies* **2021**, *14*, x FOR PEER REVIEW 13 of 19

**Figure 9.** Apartments under construction and ROP payments made. **Figure 9. Figure 9.** Apartments under construction and ROP Apartments under construction and ROP payments made. payments made.

Making an attempt at a quantitative analysis of the examined dependencies, taking into account the linear regression models constructed, it may be noticed that if we increase the payments within the framework of ROP in Poland by 1 million euros, we will obtain an average increase of 110,500 building permits issued, while in the case of apartments under construction, an increase in payments by 1 million euros will result in an average increase of 114,300 units under construction. Comparable values of estimated parameters of regression functions for the analysed variables prove similar sensitivity of changes (cf. Figures 10 and 11).

Figures 10 and 11).

Figures 10 and 11).

**Figure 10.** Correlation function between ROP Opolskie Province payments and permits issued for the construction of new apartments. **Figure 10.** Correlation function between ROP Opolskie Province payments and permits issued for the construction of new apartments. **Figure 10.** Correlation function between ROP Opolskie Province payments and permits issued for the construction of new apartments.

Making an attempt at a quantitative analysis of the examined dependencies, taking into account the linear regression models constructed, it may be noticed that if we increase the payments within the framework of ROP in Poland by 1 million euros, we will obtain an average increase of 110,500 building permits issued, while in the case of apartments under construction, an increase in payments by 1 million euros will result in an average increase of 114,300 units under construction. Comparable values of estimated parameters of regression functions for the analysed variables prove similar sensitivity of changes (cf.

Making an attempt at a quantitative analysis of the examined dependencies, taking into account the linear regression models constructed, it may be noticed that if we increase the payments within the framework of ROP in Poland by 1 million euros, we will obtain an average increase of 110,500 building permits issued, while in the case of apartments under construction, an increase in payments by 1 million euros will result in an average increase of 114,300 units under construction. Comparable values of estimated parameters of regression functions for the analysed variables prove similar sensitivity of changes (cf.

*Energies* **2021**, *14*, x FOR PEER REVIEW 14 of 19

**Figure 11.** Correlation function between ROP Opolskie Province payments and housing units whose construction has begun. **Figure 11.** Correlation function between ROP Opolskie Province payments and housing units whose construction has begun. **Figure 11.** Correlation function between ROP Opolskie Province payments and housing units whose construction has begun.

Trying to assess significant time lags between the examined variables, it should be noted (cf. Figures 12 and 13) that no single significant time lag can be unambiguously identified for the examined relationships. This may testify to the fact of cyclical changes on the residential property market, and this study covered the analysis of seasonal fluctuations over a period of 10 months.

ations over a period of 10 months.

ations over a period of 10 months.

*Energies* **2021**, *14*, x FOR PEER REVIEW 15 of 19

**Figure 12.** Cross correlation between completed payments and permits issued for new residential construction. **Figure 12.** Cross correlation between completed payments and permits issued for new residential construction. **Figure 12.** Cross correlation between completed payments and permits issued for new residential construction.

Trying to assess significant time lags between the examined variables, it should be noted (cf. Figures 12 and 13) that no single significant time lag can be unambiguously identified for the examined relationships. This may testify to the fact of cyclical changes on the residential property market, and this study covered the analysis of seasonal fluctu-

Trying to assess significant time lags between the examined variables, it should be noted (cf. Figures 12 and 13) that no single significant time lag can be unambiguously identified for the examined relationships. This may testify to the fact of cyclical changes on the residential property market, and this study covered the analysis of seasonal fluctu-

**Figure 13.** Cross correlation between payments made and dwellings started. **Figure 13.** Cross correlation between payments made and dwellings started. **Figure 13.** Cross correlation between payments made and dwellings started.

#### **5. Results**

**5. Results** The research carried out facilitated the identification and analysis of the relationship between the payments made throughout Poland under the regional operational programmes and selected macroeconomic variables. The analysis covered key macroeconomic aspects directly affecting, inter alia, the creation of the sustainable development **5. Results** The research carried out facilitated the identification and analysis of the relationship between the payments made throughout Poland under the regional operational programmes and selected macroeconomic variables. The analysis covered key macroeconomic aspects directly affecting, inter alia, the creation of the sustainable development The research carried out facilitated the identification and analysis of the relationship between the payments made throughout Poland under the regional operational programmes and selected macroeconomic variables. The analysis covered key macroeconomic aspects directly affecting, inter alia, the creation of the sustainable development potential of 16 Polish provinces and, consequently, the creation of Poland's competitive position in Europe and worldwide.

In order to perform a possibly systematic research inference, the literature analysis of the issue was conducted in the first stage. This analysis presents the validity of the cascading strategy planning process from the perspective of spending the European Union funds. It comprehensively describes the evolution of the perception of development of individual countries and regions, i.e., sustainable development, smart development, and

inclusive growth, including the importance of smart specialisations. It is important from the point of view of shaping the directions of spending structural funds in particular periods of European Union programming.

Discussing the utilitarian research dimension of the conducted analyses, it is stated as follows:


It is worth underlining that it is not easy to assess the impact of structural funds on the economy. The authors are aware that in practice, it is often difficult to indicate how much public intervention is a direct cause of a region's social and economic development, including its sustainable development. When interpreting the results described in this study, one should be aware of their model approach, i.e., an approach showing a simplified picture of the reality which, by rule, focuses only on correlative and regressive relationships, without allowing for the cause-and-effect relationships present in economy.

The analyses carried out showed a positive relationship between the payments made under ROP and the selected macroeconomic indicators. The results obtained from the research may have a practical aspect for decision-making for both regional and national authorities responsible for disbursement of the EU funds. Referring to the practical goal of the research, recommendations for authorities at all levels of the EU spending are as follows:


of macroeconomic indicators, important for the development of economy, including job creation, the level of wages, or the pace of housing construction.

In conclusion, the economic and social position of the European Union on the global stage is a determinant for coordinated actions by regional and national authorities in the twenty-eight individual Member States. For Poland, it is of particular importance because it was the largest recipient of the EU funds between 2014 and 2020 as well as in the new EU perspective for 2021–2027. Structural Funds are the main vehicle for project initiatives and have a positive impact on the country's macroeconomic indicators. This situation leads to the emergence of new barriers that need to be eliminated in the short term to achieve the best possible results in the disbursement of the EU funds.

The authors have analysed ROP payments and their correlation with the selected macroeconomic indicators. It should be emphasized that it is worthwhile to continue the research that would focus on the influence of other public funds on selected indicators.

**Author Contributions:** Conceptualization, K.B. and Ł.M.; methodology, K.B. and Ł.M.; software, Ł.M.; validation, P.F. and I.D.; formal analysis, Ł.M. and I.D.; investigation, K.B. and P.F.; resources, Ł.M.; data curation, K.B.; writing—original draft preparation, K.B.; writing—review and editing, Ł.M.; visualization, K.B. and Ł.M.; supervision, I.D.; project administration, P.F.; funding acquisition, P.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** The APC was funded by Opole University of Technology.

**Acknowledgments:** The paper presents the personal opinions of the authors and does not necessarily reflect the official position of Marshal Office of Opolskie Voivodship.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Mariusz Malinowski**

Department of Economics, Faculty of Economics, Poznan University of Life Sciences, 60-639 Poznan, Poland; mariusz.malinowski@up.poznan.pl

**Abstract:** The author intended to present the relationship between the standard of living of EU citizens and the level of the development of renewable energy. It is particularly important in the context of the implementation of the sustainable development idea, by ensuring a high standard of living for both current and future generations, with rational use of available natural resources. The first, theoretical part of the article presents the problem related to the impact of renewable energy on the standard of living in a synthetic way. The second part involves empirical research conducted in all countries of the EU. To evaluate the level of renewable energy development and the standard of living, the author constructed original measures based on the TOPSIS method. Variables were selected on the basis of substantive, statistical and formal criteria (primarily the completeness and availability of data in 2019). Within the framework of the conducted study, the author obtained, among other things, a relatively high value of Spearman's rank correlation coefficient between the constructed synthetic measures (0.47). Canonical analysis was used to identify the relationship between them. Numerous indicators, including canonical correlations, complete redundancy and extracted variances, were determined with the use of canonical analysis. Seven statistically significant canonical variables were identified. The value of the greatest and most statistically significant canonical correlation exceeded 0.94, and for the last statistically significant canonical variable, the value reached over 0.31. Statistical data were primarily obtained from the publicly available EUROSTAT database.

**Keywords:** standard of living; renewable energy; linear ordering; canonical analysis; sustainable development

#### **1. Introduction**

It is hard to disagree that energy, regardless of its form, constitutes the basis of any economic activity. Availability of energy is currently the basis of human existence and society will become more and more dependent on energy sources, mostly since all kinds of everyday devices are powered with electricity. The development of electricity (the increase in uninterrupted energy supply) has played a special role in health care, decreasing infant mortality, development of agricultural production and industry, thus affecting the standard of living of the population. Electric energy will remain an important determinant of an adequate standard of living and the importance of energy security in each country (broadly understood as the ability to satisfy the demand for energy in terms of quantity and quality, at the lowest price possible and maintaining environmental protection) will grow. Due to these demands, new sources of energy are needed. The demand for energy increasing along with civilizational progress [1], as well as the simultaneous depletion of discovered and accessible conventional energy sources (mainly fossil fuels) and progressive degradation of the environment, makes renewable energy sources (the so-called "green energy") the desired direction for energy generation. As a result, renewable energy sources (the so-called "green energy") has become desired methods of energy production. Various solutions, adapted to regional and local conditions, are adopted for this purpose. Energy is obtained with the use of the wind, the sun, tides and ocean currents, river drops, or energy obtained from biomass (most often hay from crop cultivation and firewood). Landfill biogas and biogas obtained from sewage disposal processes or decomposition of components of plant

**Citation:** Malinowski, M. "Green Energy" and the Standard of Living of the EU Residents. *Energies* **2021**, *14*, 2186. https://doi.org/10.3390/ en14082186

Academic Editor: Sergey Zhironkin

Received: 26 March 2021 Accepted: 12 April 2021 Published: 14 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

or animal remains are also listed among such sources. The increase in the importance of such energy sources stems from, among other things, their positive impact on the environment or increasing of energy security (apart from the effective way of storing the produced energy). It is particularly important in the context of the implementation of the sustainable development idea, by ensuring a high standard of living for both current and future generations, with rational use of available natural resources. For this reason, increasing the share of energy obtained from renewable sources in energy balances of different countries constitutes an important aspect of the adopted sustainable development strategy. At this point, it must also be noted that a sort of coexistence of renewable energy sources and modern ways of utilising conventional energy sources (e.g., lignite) sometimes occurs as well. An example is Germany, one of the leaders in the European Union [1] (and in the world in general) in terms of lignite mining; at the same time, in the first quarter of 2019, the share of renewable energy in the amount of electricity supplied in Germany surpassed the share of electricity generated there using fossil fuels. [2].

Although the Europe 2020 Strategy is about to expire, this approach is in line with the "TOWARDS A SUSTAINABLE EUROPE BY 2030" document, which envisions a European Union-level transition to a low-carbon, climate-neutral, resource-efficient and biodiverse economy [3]. In turn, according to the European Green Deal strategic programme established by the European Commission, the goal is to make Europe a climate-neutral continent by 2050. The most important initiatives included in the programme are achieving global CO<sup>2</sup> emissions neutrality, incorporating a wide range of renewable energy sources into the energy system, establishing a circular economy and achieving zero emissions of pollutants [4].

In the subject literature, the impact of renewable energy on the standard of living was analysed in the context of energy poverty (by such scholars as C.W. Njiru and S.C. Letem [5], E.M. Getie [6], or M.A. Hussein and W.L. Filho [7].

In the literature, the problem of the impact of renewable energy on the standard of living has been analysed in the context of energy poverty. Less frequently renewable energy is strictly treated as a livelihood enabler.

This article aims to determine the correlation between the level of renewable energy development and the standard of living of EU citizens. An additional goal assumed by the author was to popularize the relatively rarely used canonical analysis. The aim, however, was not to scrupulously explain this calculation method in detail, but rather demonstrate its usefulness. To create a measurement tool for the analysed phenomena, the author used a multi-dimensional comparative analysis, which was a set of methods of the construction of synthetic measurements and linear ordering of objects described by a large number of variables (including the TOPSIS method). A correlation analysis was conducted to determine the direction and the strength of the correlation between the constructed, original synthetic measures of the standard of living and the level of "green energy" development. On the other hand, the author used canonical analysis, one of the advanced methods of multidimensional statistical analysis, to identify multidimensional correlations between the standard of living and the level of renewable energy development. The study involved 27 member states of the EU. Statistical data obtained from international statistical institutions, mainly EUROSTAT [8], were used in the paper. The data concerned the year 2019.

#### **2. The Standard of Living and Renewable Energy—The Theoretical Aspect**

The notion of the standard of living is commonly applied in everyday life while its meaning varies, which results primarily from the fact that it constitutes the subject of research in many scientific fields (including sociology, philosophy, economics, physiology, or psychology). On the one hand, there is a broad interdisciplinary research perspective both problem-related and methodological—while on the other hand, there is a problem of operationalisation of this research category. What is missing in the numerous and constantly evolving literature on the subject is one commonly accepted definition.

In 1954, the UN expert committee defined the standard of living of the inhabitants as the entirety of their actual living conditions, as well as the level of material and cultural satisfaction of needs through numerous goods and paid services, as well as those derived from the social funds (quoted after [9]). This interpretation has become the basis for many other definitions, formulated in the future. A. Luszniewicz (1982) defined the standard of living as the degree to which material and cultural needs of households are met (i.e., its security) through the streams of paid goods and services and funds for collective consumption [10]. U. Grzega considered the standard of living to be "the degree of satisfaction of human needs, resulting from the consumption of material goods and services, as well as the use of the values of the natural and social environment" [11]. According to One Global Economy, the standard of living is, first and foremost, defined by three categories [12]: income (changes in annual income, savings, employment and career, entrepreneurship); education (finishing high school, university admission); health (availability of the health care system, disease management programmes, preventive medicine (including prenatal care, sanitation services, vaccinations).

The category if the standard of living is largely based on the theory of needs (see: Table 1). If human needs are satisfied to a large extent, it means that the standard of living is high. A need is defined as a perceived state of absence of something, while social needs are needs whose fulfilment requires the existence and action of various social institutions for the intended purposes. A characteristic feature of needs is their variability over time, which is less related to basic needs (e.g., food, shelter) and more to the higher (luxurious) ones [13]. According to A. Chabior et al., a need is a state of a deficiency, absence, imbalance in the qualities of the organism or environment that are important to a person. Therefore, a need means a lack of something that motives one to initiate action aimed at compensating for such lack and restoring the disturbed optimum in life [14]. According to K.W. Frieske and P. Poławski needs are conditions that must be met to make people able to cooperate, take autonomous decisions and in general participate in collective life [15]. In T. Tomaszewski's approach, the most detailed needs mentioned in the literature can be classified into three categories: biological (or elementary) needs, social needs and cultural needs. Social or elementary needs are understood as needs related to the structure of the human organism, the satisfying of which is necessary to keep a given organism or species alive (the need for food, water, oxygen). In turn, based on the fact that humans are in a certain sense dependent on others, we can distinguish social needs (such as the need to be accepted by others, the need to be loved or recognized). The third group of needs constitutes an expression of human dependency on the creations of human culture and the operation of social institutions. Such needs can be called cultural needs, which include products of material culture (accommodation, radio, fridge, car) and creations of spiritual culture (books, the cinema and the theatre, social conversation) [16].

T. Słaby observes that in terms of economy the need to have or feel for any purpose constitutes the basis for the production and exchange of goods. The need for goods and services constitutes the basic component of rational environmental management towards sustainable development [20].

As a multidimensional phenomenon, the diversity of the standard of living is conditioned by several factors, which generally may be divided into external and internal. External factors influence the variability of the said standards in time, while internal factorsin space. Internal factors are directly or indirectly influenced by the inhabitants of a given region. This group of factors includes, among others, the manner of managing the local self-government unit, which is reflected in the organisation of life (spatial plans and their implementation, the location of jobs, housing construction, provision of social, educational, health and other services) and the level of economic development. External factors include the dynamics of population development and its structure, as well as equipment with the technical infrastructure [21]. According to J. Piasny, in socio-economic terms, the standard of living includes all circumstances characterizing material and cultural as well as social conditions of the life of society. According to the author, the determinants include work

conditions (e.g., whether it was easy to obtain it, its difficulty, the length of the working week), wage or income level, consumption, housing situation, the possessed durable consumer goods, the level of health and social care, the condition of education and culture, the provision of water to households, gas, electricity, sewage systems etc. [22].

**Table 1.** Categories of human needs.


Source: own elaboration based on [13,17–19].

Disparities in the level of life and social inequalities (like the use of renewable energy sources) have recently become a persistent focus of economic analyses. A. Zelia´s [23] explains the growing interest of researchers in the economic category that is the standard of living with the transition from the stage of fascination with the pace of technical and economic progress into the stage of reflection on the benefits and dangers of the civilizational progress. The adverse phenomena that economic brings include [24,25]: accelerated degradation of the natural environment, threatening the lives of humans and animals; a significant increase in morbidity and premature deaths due to certain diseases, mainly the so-called "civilization diseases" (such as cardiovascular diseases, cancer); an increase in various social pathologies (such as frustration, crime, alcoholism); a rapid increase in the number of traffic accidents and accidents at work; disorientation in the value system, destruction of old systems without the creation of new ones instead; an increase in social disparities in various social cross-sections and so on; excessive consumption of products and goods, resulting in environmental pollution; inability to produce substitutes for nonrenewable resources without increasing ecological risk for the environment and humans.

In recent decades, amidst the transformation of many EU economies, the standard of living was determined by many factors as well as socio-economic and political processes. Nowadays, environmental issues, including the use of renewable energy sources, are becoming particularly important.

The contemporary economic system is characterized by cost externalization and "nonpayment of bills" as well as the "grow first and clean up later" strategy. As a result of this phenomenon, there is an imbalance in the economic system, which is reflected in environmental pollution of water, air and land. Increasing environmental pollution has an impact on the standard of living and production capacity—production costs are growing because technological processes require the use of clean water and clean air. In the long term, it may lead to irreversible changes in the natural environment [26]. As it has already been mentioned, ensuring a high standard of living to both current and future generations with rational use of the available natural resources constitutes a basic prerequisite for sustainable development. Such an approach dominates international economic relations, and in recent decades we have been observing a concentration of actions oriented towards the transformation of socio-economic systems into the so-called green economy.

The concept of a "green economy" is relatively new. The term itself first appeared in 1989 in the report entitled Blueprint for a Green Economy, prepared for the government of Great Britain (to support the introduction of the sustainable development idea) by D. Pearce, A. Markandya and E.B. Barbier [27]. From the perspective of these considerations, it is worth quoting the definition of "green economy" adopted by UNEP, which provides that it is an economy that improves welfare and social equality (justice) while reducing environmental risk and the use of natural resources [28]. It can be assumed that an important role in the initiation thereof was played by the United Nations Environmental Protection Programme of 2008, which called for the conclusion of an agreement, the socalled Global Green New Deal, within the framework of which opportunities and chances to recover from the global economic crisis through the development of "green" economy sectors were indicated. The Global Green New Deal. Policy Brief report, published in 2009, recommended investing in environmentally important areas with the greatest potential for transformation, headed towards "green economy", such as, among other things: renewable energy, clean technologies, energy-efficient construction, recycling and waste management, sustainable use of land, green coal mining techniques (including the underground coal gasification process) [29]. Energetic self-sufficiency, defined by the ratio of the amount of energy obtained to the amount of energy used in a given country/region, became one of the most important indicators characterizing sustainable development [30]. The green economy thus becomes a path to achieve sustainable development.

The concept of sustainable development is supposed to contribute to solving the main challenges of contemporary economies, which comprise fears related to climate changes and excessive air pollution, but also depletion of natural resources and energy security. In the face of these challenges, the development of renewable energy seems to be an important element in the implementation of the new energy policy. Two main areas can by confirmed by the effects of implementing sustainable development:


The processes of transitioning to a low-carbon fossil-fuel-free economy to a certain extent stem from the obligations imposed on governments and national economies by international organizations, mainly within the framework of the United Nations Framework Convention on Climate Change (UNFCCC or FCCC) and the Kyoto Protocol, and partially result from the emergence of new technologies and innovations that are climate-friendly and provide a competitive advantage [32]. Although the guidelines stemming from the concept of the green economy should not be ignored by any country, the condition and implementation thereof in most of them is still not satisfactory. The basic problem in many countries is not the amount of energy produced and used, but the fact that the source thereof are fossil fuels. It is estimated that the total technical potential of renewable energy can be 100 times higher than the current global demand for energy [33].

Nowadays, the energy needs of consumers are impacted by a wide variety of factors, including the level of development of a society to which a consumer belongs, economic and cultural traditions; geographical location; mobility and development aspirations and so on [34].

Until 2050, the technological revolution will take place not only with a share of an increase in energy efficiency and renewable energy sources but also with a growing

role of energy prosumers in the economy [35]. Therefore, the involvement of the main stakeholders-citizens of individual countries and regions, who must participate in the creation of their (as well as local/regional) energy security—is necessary to make the energy revolution possible. Already in 1947, M. McLuhan and B. Nevitt [36] formulated a thesis that with the development of new electrical technologies, the consumer will be increasingly often becoming the producer. Businesses (including households) using new technological solutions for the production of electricity (and/or heat energy) that satisfies their needs are referred to as prosumers in the energy market. A prosumer is a participant in the prosumption process, in other words—both a user and a consumer, producing a product to consume it on its own. A prosumer is an active consumer-customer, who not only buys electricity (and/or heat energy) from traditional suppliers but also engages in active purchase and sale relations with them. It produces energy with the use of distributed power generation equipment (DPGE) and sales the surplus. It also sells system services, such as demand reduction. It is equipped with storage DPGE technologies which provide it with back up power, especially electricity, in the case of grid failures [37]. Pro-consumer energy represents the lowest level of distributed energy. It includes such microgeneration installations as solar collectors, photovoltaic microsystems, biomass boilers, micro wind turbines, biogas-powered cogeneration microsystems, heat pumps. The most important prosumer groups include households, small and medium-sized farms as well as small and medium-sized enterprises (located mainly in rural and suburban areas).

The development of prosumer energy has many benefits for prosumers (it impacts the standard of living in the case of households), national economies and the environment. The benefits are as follows [38]: a prosumer lives in a household that generates profit by selling the surplus of produced energy; with the use of energy storage devices together with the use of microgeneration devices, a prosumer has constant access to the electricity grid, even during grid failure; by using smart power intake management capabilities, the prosumer can create their own energy tariffs, which leads to a decrease in the cost of electricity use; a prosumer becomes independent of increases in the prices of conventional energy carriers.

The main reasons for an energy policy including renewable sources are benefits (Table 2), which can be synthetically divided into three groups [39–41]:


M. Wozniak and B. Saj point out that energy generated from renewable sources makes it possible to [39]: diversify the available energy sources, create active prosumer attitudes concerning the use of renewable energy in the general energy system of a given country, manage fossil fuels in a reasonable way, obtain relatively cheap, renewable electricity; significantly reduce the negative impact on the environment; reduce the costs related to energy transfer; increase social awareness in terms of ecology; improve the stability of energy supplies (especially in rural areas); expand the entrepreneurial attitudes of residents.


**Table 2.** Advantages and disadvantages of the impact of renewable energy sources.


**Table 2.** *Cont.*

Source: Own study based on [39–41].

In the context of identifying economic benefits, it is important to assess the profitability of investments in renewable energy sources, for which mainly methods based on cash flow (static and dynamic) are used. Statistical methods used in this regard are pay-back period and rate of return. The pay-back period of the investment in RES is the time after which the revenues cover the expenses. For any investor, a higher level of investment evaluation is when the time is as short as possible. On the other hand, the rate of return of investment outlays in RES is determined based on the relation of revenues obtained as a result of the investment and the amount of the capital employed. The most often used dynamic methods to assess the cost-efficiency of the investment include the net present value (NVP), the internal return rate (IRR) and the modified internal return rate (MIRR). It is often difficult to assess the profitability of investments in the market of energy obtained from renewable sources, due to limitations associated with the lack of complete information on the current and, especially, the future operation of this market, and, in particular, the lack of sufficient information on financial forecasts, future CO2 emission costs and, most importantly, the direction of changes or stability of the existing legislation [42].

Without much reservation, it can be assumed that the main argument for the use of green energy is the prevention of environmental changes and that it is of particular importance in the context of air pollution reduction and prevention of global warming. Global warming changes the environment, increasing the frequency and intensity of extreme weather events.

In 2017, weather-related disasters caused record economic losses, amounting to EUR 283 billion. The European Commission predicts that by the year 2100, such a disaster could affect approximately two-thirds of the population of Europe, while only 5% of the population is affected by them these days. For example, annual damage from river flooding in Europe could rise to EUR 112 billion from the current EUR 5 billion. It is estimated that reduction in predicted food availability with global warming by 2 ◦C is more significant than with global warming of 1.5 ◦C (as per the "aim of the Paris Agreement"), including the regions of key importance for the safety of the EU, such as Northern Africa and the rest of the Mediterranean. It could undermine security and prosperity in the broadest sense, harming the economic, food, aquatic and energy system, which would, in turn, cause conflicts and migration pressures [43].

From the perspective of these considerations, it is worth mentioning at this point that the most important negative health effects resulting from air pollution (reflected in the standard of living) include [44]: problems with memory and concentration, depression, anatomical changes in the brain, accelerated ageing of the nervous system, stroke; breathing problems, cough, runny nose, sinusitis; myocardial infarction, hypertension, ischaemic heart disease, cardiac arrhythmias, heart failure; exacerbation of asthma, lung cancer, exacerbation of chronic obstructive pulmonary heart disease, more frequent respiratory infections; low birth weight, missed abortion, premature birth.

At this point, it is also worth mentioning the results of studies conducted by M. Szyszkowicz et al. [45] which show that there is a statistically significant correlation between air pollution with carbon monoxide, sulphur dioxide, nitrogen dioxide and the number of suicide attempts in Vancouver. It has been empirically proven that air pollution is associated not only with respiratory problems but also with depression, anatomical changes in the brain, accelerated ageing of the nervous system, the likelihood of stroke, missed abortion. According to the report by the Jagiellonian University, approx. 44,000 in Poland, one of the infamous European leaders in the level of air pollution, die due to air pollution every year [46]. In its 2015 report Economic Cost of the Health Impact of Air Pollution in Europe, the World Health Organisation states that the estimated economic cost of deaths occurring in Europe as a result of environmental pollution is approximately USD 1.6 trillion per year [47].

According to the BP Energy Outlook 2020 report, there is a clear upward trend in energy consumption all over the world, which leads to many environmental threats. The report shows that oil and coal continue to be the basic source of energy (the trend, however, is downward), and the share of renewable energy sources has been increasing for another year in a row [1].

As M. Tomala [48] correctly observes, renewable energy frequently still turns out to be more expensive than the traditional one, but the use of ecological energy must be based on a high level of social awareness consisting in the understanding of the fact that the wealth of a country does not depend solely on the accumulated capital, but also on the standard of living (as it is in the Nordic countries).

It seems that the cost of investment and operating costs of an energy or heat/cold source remains the most important criterion for the selection of energy production technology. Technologies using renewable energy sources require a relatively large initial investment, but the cost of their ongoing operation is low (solar, wind, water energy). From the perspective of these considerations, an important thing is that lower prices of renewable energy will increase the fund of free decisions of consumers, who will be able to spend the money saved on energy bills on products and services. For this reason, apart from the direct costs of financial investments in RES, we should also take into account the benefits stemming from the use of renewable resources, which to a greater or lesser extent also affect the standard of living of residents (Figure 1). *Energies* **2021**, *14*, x FOR PEER REVIEW 10 of 35 LCOE coefficient for wind and solar energy will have decreased by 35% (by 2030) and 50% (by 2050), respectively [33].

**Figure 1.** The impact of RES on the standard of living. **Figure 1.** The impact of RES on the standard of living.

M. Iganrska observes that the development of the RES sector has a positive impact on the labour market, thus determining the standard of living of residents. This is The amount of the initial capital investment has a large impact on the economic competitiveness of a given technology, especially when estimating the LCOE coefficient (levelized cost of energy). Due to the need for large expenditures at the beginning of the

construction of power generating facilities and modernization of the existing ones. Employment can also be expected to increase in the banking sector, due to the expansion of programmes financing green energy investments. There will be a shift of human capital from traditional to highly innovative sectors, which will consequently contribute to the

Areas allocated for RES investments do not lose their tourist and utility value. Such investments can also result in other types of investments. The areas where RES investments are implemented are perceived as investor-friendly regions, fostering the development of new technologies and protecting the environment, which makes them

In the context of the use of renewable energy sources and their impact on the standard of living of residents, it is worth mentioning the change in the time needed for the operation of thermal energy source. In general, taking into account the operation time, we can distinguish two groups of thermal energy sources unmanned sources (such as oil and gas boilers, heat pumps, solar collectors and electric heating) and sources requiring constant maintenance (all kinds of solid fuel and biomass boilers). Their time-consuming nature is dependent and can vary. In the case of changing the power source from group one to group two, the time needed for service will increase, thus generating costs of lost free time. Switching from group one to group two, however, will bring benefits associated with saving free time. Changing an individual source of thermal energy production may be associated with changes in the time needed for the operation of the source. The time needed for the following should be particularly taken into account: operation of the source producing thermal energy (supplying the source with fuel as well as other operationrelated activities) during and outside the heating season; fuel management on the

property (for example reloading the imported fuel from the storage area) [51].

All 27 member states of the European Union were included in the empirical analysis. The aim of the analysis was not to compare national fuel resources in individual countries, the structure of energy production by the source, or the share of renewable energy in electricity production as it is the subject of many widely available scientific analyses and reports (more in REN21 [52], bp Statistical Review of World Energy [53], IRENA— RENEWABLE CAPACITY STATISTICS [54]). The author aimed to construct original,

development of the knowledge-based economy [49].

worth investing in. [50].

**3. Materials and Methods** 

operation, renewable energy sources, especially those using solar technologies, frequently have a higher LCOE coefficient than conventional technologies. This argument is frequently put forward to prove that the use of renewable energy sources is too expensive. Even though the comparison of costs of energy production from renewable and conventional sources depends on the location and conditions in a given country, the LCOE coefficient suggests that using renewable energy sources we can already offer energy services at a competitive price. Moreover, it is believed that technological advancement and greater efficiency will further increase the price competitiveness of all types of RES, compared to conventional technologies. For example, it is assumed that the LCOE coefficient for wind and solar energy will have decreased by 35% (by 2030) and 50% (by 2050), respectively [33].

M. Iganrska observes that the development of the RES sector has a positive impact on the labour market, thus determining the standard of living of residents. This is especially true for the industries manufacturing renewable energy and construction equipment, due to an increase in the demand for construction services related to the construction of power generating facilities and modernization of the existing ones. Employment can also be expected to increase in the banking sector, due to the expansion of programmes financing green energy investments. There will be a shift of human capital from traditional to highly innovative sectors, which will consequently contribute to the development of the knowledge-based economy [49].

Areas allocated for RES investments do not lose their tourist and utility value. Such investments can also result in other types of investments. The areas where RES investments are implemented are perceived as investor-friendly regions, fostering the development of new technologies and protecting the environment, which makes them worth investing in [50].

In the context of the use of renewable energy sources and their impact on the standard of living of residents, it is worth mentioning the change in the time needed for the operation of thermal energy source. In general, taking into account the operation time, we can distinguish two groups of thermal energy sources unmanned sources (such as oil and gas boilers, heat pumps, solar collectors and electric heating) and sources requiring constant maintenance (all kinds of solid fuel and biomass boilers). Their time-consuming nature is dependent and can vary. In the case of changing the power source from group one to group two, the time needed for service will increase, thus generating costs of lost free time. Switching from group one to group two, however, will bring benefits associated with saving free time. Changing an individual source of thermal energy production may be associated with changes in the time needed for the operation of the source. The time needed for the following should be particularly taken into account: operation of the source producing thermal energy (supplying the source with fuel as well as other operation-related activities) during and outside the heating season; fuel management on the property (for example reloading the imported fuel from the storage area) [51].

#### **3. Materials and Methods**

All 27 member states of the European Union were included in the empirical analysis. The aim of the analysis was not to compare national fuel resources in individual countries, the structure of energy production by the source, or the share of renewable energy in electricity production as it is the subject of many widely available scientific analyses and reports (more in REN21 [52], bp Statistical Review of World Energy [53], IRENA— RENEWABLE CAPACITY STATISTICS [54]). The author aimed to construct original, synthetic measures of the standard of living and the level of renewable energy development and, on the basis thereof, conduct an assessment of development diversification in the countries of the EU as well as use an advanced, multivariate exploratory technique, i.e., canonical analysis, to assess the correlations between them.

In the literature, the problem of the impact of renewable energy on the life situation of residents was most often analysed in the context of energy poverty—a situation when a household cannot afford energy or energy services to satisfy their basic, daily needs."

Less frequently renewable energy is strictly treated as a livelihood enabler. The use of renewable energy as a tool that eliminates energy poverty and, consequently, contributes to improving the standard of living was emphasized by, among others, C.W. Njiru and S.C. Letema [5] who demonstrated that energy poverty has an impact on the physical health, well-being and welfare of the people living in the Kirinyaga province, Kenya. Similar studies were conducted by E.M. Getie [6] conducted similar studies which revealed that energy poverty has a direct or indirect impact on the standard of living of people in Ethiopia (including human resource development, residents' health and agricultural automation which improve the standard of living). M.A. Hussein and W.L. Filho [7] analysed the quantitative relationship between energy availability and improved living conditions and elimination of poverty in sub-Saharan Africa. According to the authors, renewable energy technologies play a special role in the improvement of access to energy services for poor people and isolated rural communities. At this point, it is also worth mentioning a study that investigated the relationship between the level of economic development and renewable energy. M. Simionescu et al. [55] showed that there was a potential relationship between the share of renewable energy sources in total electricity and the real GDP per capita. Based on the constructed models for panel data, the authors indicated that GDP per capita had a positive, but very low impact on the share of RES in electricity in the years 2007–2017 in EU countries, except for Luxembourg. On the other hand, based on data from 1992–2018, J. Grabara et al. [56] analysed the relationships between economic growth and the use of renewable energy consumption and direct foreign investments in Kazakhstan and Uzbekistan. Based on the results of the Granger causality test it was, among other things, demonstrated that there is a relationship between direct foreign investments and the use of renewable energy in the countries under consideration. Based on a very extensive literature review of the problem, C. Llamosas and B.K. Sovacool [57] indicate numerous benefits resulting from the construction and operation of transboundary dams. According to them, the economic benefits include the possibility of exporting electricity, effectively generating income for hydropower exporters, while the catalytic benefits include knowledge transfer, as well as building confidence and industry experience.

An initial determination of variables describing the analysed objects (EU countries) constituted the first stage of constructing synthetic measures of EU residents' standard of living and the level of the development of renewable energy sources (a kind of "green energy index"), according to the multivariate analysis. Both in the case of the quantification of the standard of living and the level of renewable energy development, the variables should be selected in such a way so as to reflect various aspects of these multivariate categories. As M. Walesiak correctly observes, the selection of variables is among the most important and most difficult issues. This is because the quality of variables determines the reliability of the final classification results and the accuracy of the decisions made on their basis. Only the variables which can discriminate a set of objects should be included in the classification procedure [58].

On the one hand, issues related to the assessment of the standard of living (and the quantification of environmental aspects, including those related to renewable energy) enjoy a great interest of researchers, but on the other—they are controversial. This is largely due to the multifaceted and interdisciplinary nature of this research category, which fosters the emergence of various measures and indicators relating to this phenomenon. No single, universally accepted method of measuring the standard of living of residents has been developed to date. To illustrate, at least partially, the results of works on the construction of synthetic measures obtained so far, listed below are those which in the author's opinion are most popular in the literature in the context of the assessment of the living standard (and related categories, such as the quality of life or living conditions) and the degree of sustainability of socio-economic development ("greening of the economy" (including the use of renewable energy sources), the level of sustainable development):

• Index of the Economic Aspects of *Welfare* (EAW) is one of the first measures of economic welfare to more broadly incorporate the ecological aspect and a broad spectrum

of qualitative factors. It was applied for the first time by X. Zolotas in 1981. Its structure is focused on the current flow of goods and services. It takes into account expenditures on public buildings, the value of household works, expenditures on durable consumer goods, advertising, the value of free time, the value of public sector services, corrected by the expenditures related to health care and education, costs of environmental pollution and the depletion of natural resources [59,60].


pollution, satisfaction with water quality), personal security (homicide rates, the sense of safety while walking alone), satisfaction with life [66].


Among synthetic measures more focused on the environmental aspects, the following are worth mentioning:


According to J. Piasny [22], synthetic measures, rather than partial indicators, are a more appropriate measure of the inhabitants' standard of living. However, some limitations on the use of synthetic measures should be kept in mind [72]: subjective selection of diagnostic variables used for the construction of a synthetics measure; subjective selection of weights for individual variables in the aggregation formula.

Considering the limited availability of statistical data, it is difficult to conduct a complex measurement of the standard of living, because the level of this multifaceted phenomenon is determined by the level of satisfaction of the above-described needs, both material and non-material. In the context of multidimensional phenomena, K. Nermend [73] indicates what, in terms of content and form, the analysed variables should be characterised by, which includes capturing the most important properties of studied phenomena, being precisely defined, logically interrelated, measurable (directly or indirectly), expressed in natural units (in the form of intensity indicators), containing a significant information load, and being characterised by high spatial variability.

The procedure of diagnostic variable selection consisted of two stages (both in the case of variables related to the standard of living and renewable energy). In the first stage, a set of potential diagnostic variables was proposed based on the above-listed formal and substantive premises (the data was obtained from the EUROSTAT database— Tables A1–A3). The selection primary of sets of variables, apart from the substantive and formal criteria, was largely determined by the availability, completeness and the fact that

this data is up-to-date. It was assumed that the included partial variables will be indicative and will not be absolute values, which was aimed at eliminating the distortion related to the fact that some objects (EU countries) have some characteristic traits (eg. a significantly larger area than other objects).

As a result, 29 potential diagnostic variables related to the standard of living were proposed. The variables were then divided according to substantive criteria into seven thematic groups [9,13,74,75]:


The multitude of variables (being carriers of various information) describing the analysed objects in multidimensional comparative analyses makes it necessary to choose the most important ones from the research point of view. Therefore, at the second stage of variable selection, to limit the number of potential diagnostic variables, statistical procedures were used so that the selected variables characterized the studied objects as fully as possible and, simultaneously, created a set as small as possible. As M. Walesiak [58] correctly observes, the approach which is to take account of as many variables as possible is

unsubstantiated as adding one or several irrelevant variables to the set makes it impossible to detect the proper structure in the set of objects.

Studying variability and the degree of correlation of potential diagnostic data (information criterion) is of particular importance in the process of variable selection.

During variable selection, it is required that individual observations exhibit adequate variability (discriminatory ability) as poorly varied variables provide little analytical value. It was assumed that those traits will be eliminated from both primary sets for which the absolute value of classic variability coefficient will be below the arbitrarily determined, critical threshold value of this coefficient at the level of 10% (the traits were considered quasi-constant, not bringing significant information on the studied phenomenon). Subsequently, the degree of variable correlation (information capacity) was investigated, since it is assumed that two highly correlated variables are carriers of similar information, which makes one of them redundant. For this reason, in order to conduct information value assessment, one of the methods of feature discrimination depending on the value of correlation matrix—the so-called method of inverse correlation matrix—was used (more in: [76]). Based on the correlation matrix, the inverse correlation matrix was calculated for each thematic variable subgroup

$$\mathcal{R}^{-1} = [\widetilde{r}\_{\overline{j}|\prime}]j\_{\prime}j\prime = 1,2,\dots,m,\text{ where } \colon \tag{1}$$

<sup>e</sup>*rjj*<sup>0</sup> <sup>=</sup> (−1) *j*+*j*0 |*Rjj*0| |*R*| , where: *Rjj*0—the matrix reduced by deleting the *j*-th row and the *j*'-th column; *R*, *Rjj*<sup>0</sup> —determinants of the *R* and *Rjj*<sup>0</sup> matrices respectively.

In features that are overly correlated with other diagonal elements of the inverse correlation matrix are much greater than 1 (which means that the matrix is ill-conditioned). According to this method, the overly correlated feature (which corresponds to the diagonal element of the inverse correlation matrix characterized by the value exceeding the arbitrarily determined threshold value (most often r\* = 10) is eliminated from the primary set of features. Then the inverse correlation matrix is calculated again, and it is analysed whether the diagonal values do not exceed the determined threshold value. The procedure is continued until all diagonal values not exceeding the determined threshold are obtained (i.e., until the stability of the inverse correlation matrix is achieved).

As a consequence, taking into account the discriminatory criterion, 4 variables (S1, S6, S9, S14) should be eliminated from the set of variables relating to the standard of living. On the other hand, all variables in the set of variables relating to the level of renewable energy development were characterized by a variable coefficient greater than the adopted critical threshold of 10%. For this reason, all variables in this set were further analysed. After conducting the assessment of the information potential (based on the results obtained with the use of the inverse correlation method) variables R4, R7 and R11 were eliminated from the set describing the level of renewable energy development, while variables S12 and S29 were eliminated from the set relating to the standard of living.

In studies aimed at linear ordering of a set of objects, variable classification by preferences among variables is of particular significance. In this context, we distinguish stimuli (high values desired from the perspective of the essence of the phenomenon under consideration), dampers (desired low values) and neutral variables (where certain nominal values constitute the optimal value, and deviations from the value worsen the evaluation of the analysed phenomenon). In the set of data relating to the standard of living, the following variables were included in the damper set: S3 (population density); S4 (infant mortality rate); S8 (young people not in employment and not attending any school (age 15–24)); S13 long-term unemployment rate (12 months and above) and S15 (unemployment rate); S16 (percentage of people at risk of poverty and social exclusion); S19 (percentage of people with chronic diseases or health problems); S25 (degree of significant housing deprivation); S28 (production of dangerous waste). The other variables were treated as stimuli. This also applies to the variables describing the sphere of tourism, assuming that the higher values of considered variables, the greater the tourist attractiveness and the more

opportunities for leisure activities. In the set of variables relating to the level of renewable energy development, all variables under consideration were classified as stimuli.

In studies using linear ordering and classification methods, there is a need to de-value variables and standardise orders of magnitude to render them comparable. This operation is known as normalization transformation. The most common methods of data normalization include standardization, unitization and quotient transformation. Normalisation was performed by standardizing the value of a variable. The purpose of standardisation is to obtain variables with a distribution with an average of 0 and a standard deviation of 1. On the other hand, the most popular [58,77] standardization formula has the form:

$$z\_{ij} = \frac{\mathbf{x}\_{ij - \overline{\mathbf{x}}\_{j}}}{S\_{j}} \tag{2}$$

where: *xj*—arithmetic mean; *Sj*—standard deviation of variable *xij*; *i* = 1, 2, ..., *n*; *j* = 1, 2, ..., *m*.

The so selected and initially transformed set of values, became the basis for linear ordering of the considered objects (as well as further analyses). The classic TOPSIS (the Technique for Order of Preference by Similarity to Ideal Solution) method, which is considered to be a model method, was used to facilitate linear ordering of the selected countries of the European Union in terms of the standard of living of the residents and the level of renewable energy development. This method makes it possible to determine the hierarchy of objects in accordance with the adopted criteria. It is a certain modification of Hellwig's method, which is popular among scientists. In this method, the synthetic measure is constructed taking into account the Euclidean distance of observation not only to the pattern (the most desired variant) but also from the anti-pattern, known as the anti-deal reference solution (in contrast to Hellwig's method, in the case of which only the distance from the patter is considered). The following stages in the construction of a synthetic measure can be distinguished in this method [78]:

• Creating a standardized decision matrix based on the quotient transformation.

$$z\_{i\circ} = \frac{\mathfrak{x}\_{i\circ}}{\sqrt{\sum\_{i=1}^{m} \mathfrak{x}\_{ij}^{2}}} \text{ for } i = 1, 2, \dots \text{ } m \text{ and } j = 1, 2, \dots, m \tag{3}$$

where: *xij* —the observation of the *j*-th variable in the *i*-th object.

• Constructing a matrix of weights using weighing of variables and subsequently creating a weighted standardized decision matrix (as a result of multiplying the standardized values by the weights):

$$w\_{\rm ij} = w\_{\rm j} \cdot z\_{\rm ij} \tag{4}$$

• Based on the standardized decision matrix, the value vector for the pattern (A<sup>+</sup> ) and the anti-pattern (*A* −) is determined:

$$A^{+} = \begin{array}{c} \left( \max(v\_{i1}), \quad \max(v\_{i2}) \right) \quad \text{max}(v\_{iN}) \ ( \\ \vdots \end{array} \\ \left( \begin{array}{c} \max(v\_{iN}) \end{array} \right) \ = \left( v\_1^{+}, v\_2^{+}, \dots, v\_n^{+} \right) \text{.} \tag{5}$$

$$A^{-} = \begin{pmatrix} \min(v\_{l1}), & \min(v\_{l2}) & \min(v\_{lN}) \\ i & i & \end{pmatrix} \\ \quad = \begin{pmatrix} v\_1^- \ v\_2^- \dots \ v\_n^- \end{pmatrix} \\ \tag{6}$$

• Indicating the distance from the pattern and the anti-pattern for each analysed object based on the Euclidean metric:

$$s\_i^+ = \sqrt{\sum\_{j=1}^N \left(v\_{ij} - v\_j^+\right)^2}; \ s\_i^- = \sqrt{\sum\_{j=1}^N \left(v\_{ij} - v\_j^-\right)^2}, i = 1, 2, \dots, M, \ j = 1, 2, \dots, N \tag{7}$$

• Determining the value of the synthetic variable which defines the similarity of objects to the "model" solution, in accordance with the following formula:

$$\mathcal{C}\_{i} = \frac{s\_{i}^{-}}{s\_{i}^{+} - s\_{i}^{-}}, \text{ where } 0 \le \mathcal{C}\_{i} \le 1 \tag{8}$$

The smaller the distance of a given object from the model unit and, therefore, the greater the development anti-pattern, the closer the value of the synthetic feature to 1.

A classification of the EU countries by the standard of living of their residents and the level of renewable energy development was conducted with the use of the PAM (Partitioning Around Medoids) method to determine groups of objects similar to each other in terms of variables describing them. As correctly observed by J. Korol and P. Szczuci´nski [79], classification methods make it possible to divide the analysed object sets into adequate subsets (classes) in such a way that the objects belonging to the same subset are most similar to each other, while those belonging to different subsets are least similar to each other. The idea behind clustering methods is to delimit a set of objects into homogenous subgroups, enabling better description thereof from the perspective of the purpose of structural comparisons.

The PAM method is among relatively new classification methods (the mechanism of clustering around medoids was proposed by Kaufman and Rousseeuw in 1987) (more in: [80,81]). The idea behind this method is to search for *k* objects, so-called representatives, which are centrally located in clusters (so-called medoids). An object in which the mean dissimilarity (distance to the representative) of all objects in the cluster is the smallest is considered to be the representative of the cluster. In reality, the algorithm minimizes the sum of dissimilarities instead of the mean dissimilarity. The selection of *k* medoids is a process consisting of two steps. First, an initial clustering is obtained by successive selection of "representative" objects until *k* objects are checked. The first object is the one for which the sum of dissimilarities for all other object is as small as possible (it is a certain kind of a "multidimensional median" of *N* objects, hence the term "medoid). In each subsequent step, the object which to the greatest extent contributes to the decreasing of the objective function (the sum of dissimilarity) is selected. The next stage is a sort of attempt to correct the set of representatives. It is done by including all pairs of objects (*i*, *h*) for which *i* object was selected for the set of representatives, and an *h* object does not belong to the set of representatives, checking whether after changing the *i* into the *h*, the objective function decreases. The final mean distance (dissimilarity), which is interpreted as the measure of the "goodness" of the final clustering of the considered objects, is expressed by the following formula:

$$F = \frac{\sum\_{i=1}^{N} d\_{i,m(i)}}{N} \tag{9}$$

where: *m*(*i*) is the representative (medoid) of the closest *i* object.

Two types of isolated clusters can be distinguished in the algorithm of this method: the *L-cluster* and the *L*\*-*cluster*. The *C* cluster is an *L-cluster* if the following condition is met for each *i* object belonging to *C*:

$$\min\_{\substack{j \in \mathcal{C} \\ j \in \mathcal{C}}} d\_{\text{ij}} < \min\_{h \notin \mathcal{C}} d\_{\text{ih}}.\tag{10}$$

In turn, the *C* cluster is an *L\*-cluster* if:

$$\max\_{i,j \in \mathcal{C}} d\_{ij} < \min\_{l \in \mathcal{C}, \ h \notin \mathcal{C}} d\_{lh}. \tag{11}$$

The diameter of the *C* cluster, defined as the greatest dissimilarity (distance) between the objects belonging to *C*, is determined in this method:

$$D\_{\mathbb{C}} = \max\_{i,j \in \mathbb{C}} d\_{ij} \tag{12}$$

When *j* is the medoid of the *C* cluster, the mean distance from the considered *C* objects to *j* is calculated as follows:

$$\overline{d}\_{\dot{l}} = \frac{\sum\_{i \in \mathbb{C}} d\_{\dot{i}\dot{j}}}{N\_{\dot{l}}} \tag{13}$$

In addition, the maximum distance of all *C* objects to *j* is calculated as follows:

$$DIST\_{\max} = \max\_{i \in \mathcal{C}} d\_{ij} \tag{14}$$

It was arbitrarily assumed that there would be 4 clusters.

Subsequently, a canonical analysis was conducted to present multidimensional correlations between the sets of variables relating to the standard of living of EU residents and the level of renewable energy development. Canonical analysis can be viewed as a generalization of the linear multiple regression (in which the variability of one endogenous variable may be explained by the variability of a set of exogenous variables) into two sets of variables (endogenous and exogenous). If the set of response features consists of only one feature, the method is equivalent to multiple regression. Therefore, canonical analysis searches for an answer to the question of what is the extent of the simultaneous influence of the whole set of endogenous variables on the whole set of exogenous variables. Analysis of correlations between two sets of variables comes down to analysing the relationships between two new types of variables (so-called canonical variables, also known as canonical roots). Canonical roots constitute the weighted sums of the first and second primary data sets. The weights are generated in a manner that maximizes the mutual correlation of the weighted sums. If this condition is met, it means that pairs of canonical variables are considered to be good representations of the initial data within the framework of the adopted model. Maximum correlation is sought with the use of the Lagrange multiplier method (see: [82–87]). Considering the arrangement of two random variables [*x*, *y*], where: *x* = - *x*1, *x*2, . . . , *x<sup>p</sup> T* is a vector of exogenous variables, *y* = - *y*1, *y*2, . . . , *y<sup>q</sup> T* is a vector of endogenous variables, the aim is to maximize the value of the expression:

$$r\_l = \frac{\left(w\_{\mathbf{x}}^T \mathbf{R}\_{\mathbf{x}\mathbf{y}} w\_{\mathbf{y}}\right)}{\sqrt{\left(w\_{\mathbf{x}}^T \mathbf{R}\_{\mathbf{x}\mathbf{x}} w\_{\mathbf{x}} w\_{\mathbf{y}}^T \mathbf{R}\_{\mathbf{y}\mathbf{y}} w\_{\mathbf{y}}\right)}},\tag{15}$$

where: *Rxx*—the correlation matrix of exogenous variables, *Ryy*—the correlation matrix of endogenous variables, *Rxy*—the correlation matrix of both types of variables, *wx*, *wy* weights for the first and second type of canonical variables; *rl*—the canonical correlation coefficient.

The literature review concerning the application of canonical analysis indicates that this technique remains one of the least commonly used statistical methods in social sciences. Thus, it is also a rarely used tool in the context of the issues of living standards and factors determining the level of this phenomenon. Here, we can mention the studies of O.R. Ebenezer who conducted a canonical analysis which showed that there is a positive correlation between the levels of poverty and literacy concerning data from the state of Ekiti in central Nigeria [88]. In contrast, K. Chin-Tsai [89] conducted a canonical analysis to evaluate correlations between quality of life and professional satisfaction among cyclists. In the context of energy sources, a canonical analysis has been used, for instance, by T. Saeed and G.A. Tularam [90] to identify relationships between fossil fuel prices (oil, natural gas and coal) and climate change (expressed by variables related to green energy, carbon

emissions, temperature and precipitation indexes). F.J. Santos-Allamilos et al. [91] used a canonical analysis to assess the spatio-temporal balance between regional resources of solar and wind energy. The conducted analysis indicated the optimal distribution of wind farms and solar power plants throughout the analysed territory (south of the Iberian Peninsula) to minimise the variability of total energy contribution in the power system.

It appears that the relatively low popularity of this tool among researchers and in economic analyses (compared to, for example, classical correlation analysis or regression analysis) may result from at least two reasons. Firstly, the method itself is quite complicated (it requires knowledge of, e.g., multiple regression). Secondly, there are some difficulties in interpreting the obtained results (e.g., a high number of determined indicators). Considering the multifaceted nature of both the standard of living and the level of renewable energy development, the use of this multidimensional exploratory technique to assess interactions occurring between the two appears substantiated. In the context of the multifaceted phenomena analysis, the use of, e.g., multiple regression models and separate analysis of each endogenous variable (in this case, concerning the standard of living), could entail certain "information noise" and thus the risk of narrowing down and distorting the results of conducted analyses. This may result in the loss of crucial information concerning the correlation occurring in the set of endogenous variables. Furthermore, it appears insufficient to conduct only a classical correlation analysis (e.g., Pearson's) for pairs of studied variables, as it does not take into account the correlations occurring within the analysed sets of variables.

At this point, it should be noted that to obtain reliable results of the analysis, it is necessary to operate on a sufficiently large sample. T. Panek and J. Zwierzchowski [92] believe that a sample size of 50 observations may be considered sufficient. Therefore, to increase the reliability of results obtained based on the canonical analysis, the following assumptions were made:


The results of the canonical analysis are sensitive to outliers. For this reason, it was preceded by the analysis of the internal structure of studied variables to identify outlier observations that may arise, for example, from transcription errors. For this purpose, the "three-sigma" rule was applied (see [93,94]), according to which, observations outside the range [mean3\*standard deviation; mean+3\*standard deviation] are eliminated. If outliers were identified, they were replaced with average values calculated for all regions of a given country, in which there where units characterised by partial variables exceeding the limit values. Such a necessity occurred 17 times for the set of variables concerning the standard of living (14 times as a result of exceeding the upper limit of the aforementioned range and 3 times the lower limit) and 7 times for the level of renewable energy development (as a result of exceeding the upper limit of the range).

In the canonical analysis, the key issue is to determine (by testing the statistical significance) how many pairs of canonical variables should undergo an in-depth evaluation. In significance tests in the canonical correlation analysis, the null hypothesis assumes that

there are no correlations between two sets of input variables. The null hypothesis was verified using the Λ-Wilks canonical correlation significance test (Wilks' lambda). The test statistic for the *s-k* set of variables adopts the following form [95,96]:

$$
\Lambda\_k = \prod\_{l=k}^s \left( 1 - r\_l^2 \right) \tag{16}
$$

where: *s*—number of canonical elements, *k*—number of removed canonical elements, *r* 2 *l* a squared canonical correlation coefficient for the *l*-th canonical variable.

This statistic is characterised by the Λ-Wilks' probability distribution, assuming the truth of the null hypothesis with parameters *n*—1, *p*, *q.*

To facilitate the interpretation of canonical weights, the literature on the subjects includes recommendations for using a standardised data matrix [92]. For this reason (as mentioned earlier), both analysed sets of variables were subjected to a standardisation process.

As part of the conducted analyses, values of extracted variance were determined for each generated canonical variable. Such an indicator provides information about the percentage of the input variable variance explained by the said canonical variables. It is determined by adding the squares of canonical factor loadings located by a given variable in the set for a particular canonical root and subsequently dividing the result by the number of variables. The analytical form of the indicator may be presented as follows:

$$\overline{R\_{\boldsymbol{\mu}\_{l}}^{2}} = \frac{1}{q} \sum\_{j=1}^{q} c\_{jl}^{2} \text{ or} \\ \overline{R\_{\boldsymbol{\nu}\_{l}}^{2}} = \frac{1}{m-q} \sum\_{j=q+1}^{m} d\_{jl\boldsymbol{\nu}}^{2} \text{ } l = 1 \text{ } 2, \dots, \text{ s.} \tag{17}$$

where: *q*—the number of input variables; *cjl*—is the canonical factor loading of the *j-th* basic variable and the *l-th* canonical variable of the first type; *djl*—is the canonical factor loading of the *j-th* basic variable and the *l-th* canonical variable of the second type.

The product of the said mean and the square of the canonical correlations, referred to as the redundancy index, was subsequently determined (more information in [97]). Its value indicates how much of the average variance in one set is explained by a particular canonical variable, with another given set of variables. The analytical form of this index may be presented as follows:

$$\mathbb{R}^{2}\_{\mathbb{U}\_{l},\mathbf{x}^{2}} = \overline{\mathbb{R}^{2}\_{\mathbb{U}\_{l}}} \cdot \lambda\_{l} \text{ or } \mathbb{R}^{2}\_{\mathbb{U}\_{l},\mathbf{x}^{1}} = \overline{\mathbb{R}^{2}\_{\mathbb{U}\_{l}}} \cdot \lambda\_{l\prime} \text{ } l = 1, 2, \dots, \text{ s},\tag{18}$$

where: *λl*—the characteristic element of the square matrix of canonical correlation.

The said index is also referred to as the composite coefficient of determination or composite determination.

A single significance level of *α* = 0.05 was assumed throughout the analysis, which covered only those "categories", for which the *p*-value was less than the assumed significance level.

#### **4. Study Results: A Multivariate Analysis of Correlations Between the Standard of Living of the EU Residents and the Level of Renewable Energy Development**

Countries of the European Union are significantly differentiated and disproportionate in terms of infrastructure and equipment supporting the development of RES, the system of obtaining energy from renewable sources and the share of RES in energy consumption. As a result, the constructed synthetic measures of the renewable energy development level exhibited relatively high variation. Significant discrepancies between energy systems (and energy intensity of economies) of the EU countries are influenced by numerous factors, among which the most important are [30]: geographic location and endowment with natural resources; energy, transport and housing infrastructure facilities; human capital; equipment with capital and access to assistance programmes and support funds; interest in and acceptance of solutions applying RES; innovativeness of the economy (enterprises)

and equipment in R&D facilities; historical and political conditions of local, regional and national scale.

The highest value of the TOPSIS-based measure of renewable energy development level (over 0.56) was recorded in Sweden (see Table 3). In recent years, residents of Sweden have dramatically reduced the use of fossil fuels (Sweden pays the highest carbon tax in the world) and became significantly involved in the development of renewable energy. They adopted a policy of developing energy clusters based on modern technology and RES, and aim to generate energy exclusively from renewable energy sources by 2040. Austria (where the synthetic measure of the renewable energy development level was over 0.43) and Denmark (0.42) were placed at further positions in the created ranking. Austrian energy is based primarily on hydropower, and it is assumed that it will be completely derived from renewable energy sources by 2030. In turn, Denmark is the global energy leader in the wind sector, assumed to completely transition to renewable energy by 2050.

**Table 3.** Values of the synthetic measures of the standard of living and renewable energy development level.


I—Synthetic measure of the standard of living, II—Synthetic measure of the renewable energy development level, AA—arithmetic average, Vs—coefficient of variation, SD—standard deviation, MED—median, Q1—first quartile, Q3—third quartile. Source: Own study based on [8].

Sweden, Austria and Denmark assumed leading positions in the world's 2020 energy transition ranking compiled by the World Economic Forum (Energy Transition Index— ETI). The ranking classifies countries according to the performance of their current energy systems and readiness for the energy transition. Sweden assumed the top global position in this respect; Denmark placed fourth while Austria ranked sixth (more information: [98]).

High values of the constructed synthetic measures of the renewable energy development level in these countries are derived from high or very high values of partial variables concerning primarily the share of renewable energy in final electricity consumption, the production of electricity and derived heat based on renewable municipal waste, as well as the production of electricity and derived heat based on wind energy.

What draws attention is that ten countries rated lowest in terms of the renewable energy development level are relatively new members of the European Union (all of these countries joined the Community in 2004 or later). These countries recorded low or very low values of the analysed partial variables used to construct the synthetic measure. In particular, they included variables concerning the production of electricity and derived heat based on renewable municipal waste and wind energy, as well as the solar collector surface.

Poland was the lowest-rated country in this respect. According to the data from Statistics Poland, the share of energy from renewable sources in the acquisition of total primary energy increased from 13.25% in 2015 to 15.96% in 2019. In 2019, the share of renewable energy in gross final energy consumption in power engineering increased by 1.31 percentage points compared to the previous year. Factors contributing to the increase in this measure consisted of a rise in gross final renewable electricity consumption (by 9.52%) and a decrease in gross final renewable electricity consumption (by 0.81%). Energy derived from renewable sources in Poland in 2019 comes primarily from solid biofuels (65.56%), wind energy (13.72%) and liquid biofuels (10.36%) [99].

For the partial variables included in the study, the coefficient of variation for the constructed measure of the level of renewable energy development was over 47%, while the standard deviation was nearly 0.12 (with a mean value of nearly 0.25). This confirms the significant variation in the level of renewable energy development in the European Union. The said measure was characterised by right-side asymmetry (the classical asymmetry coefficient was 0.66), which indicates the prevalence of values not exceeding the arithmetic mean.

In turn, the assessment of the standard of living of the European Union population based on the synthetic measures constructed shows that the highest level of this phenomenon (for the partial variables considered) occurred in the case of Sweden (where the synthetic measure of the standard of living was over 0.54), France (0.52) and Finland (0.51). High values for variables related to such things as the number of students enrolled in early childhood education, average wages, nights spent in tourist accommodation, and the average number of rooms per person were reported in the case of these countries.

In turn, for the included partial variables, the lowest values of the synthetic measure of the standard of living were characteristic of Hungary (0.37), Italy and Latvia (slightly over 0.38 each). These countries recorded relatively low values of partial variables concerning, for example, the number of doctors per 1000 inhabitants, the average number of rooms per person and the percentage of people with higher education.

The synthetic measure of the standard of living of the European Union inhabitants was characterised by left-side asymmetry, which indicates that most countries recorded values above the level of the arithmetic mean. The classical asymmetry coefficient was −0.06, which allowed assessing the degree of the asymmetry as weak. The classical variation coefficient was less than 10.5%, which indicates a relatively weak differentiation of the analysed phenomenon (for the analysed set of partial variables). In the case of threequarters of the EU countries, the value of the synthetic measure did not exceed 0.49 (with a minimum value of 0.37 and a maximum value of 0.54).

To conduct more in-depth analyses, the EU countries were classified using the previously discussed PAM method (Table 4). The identified groups incorporate countries with

similar standards of living and levels of renewable energy development, yet the composition of a given group does not provide information about the degree of development of the analysed phenomenon. The PAM method (or non-linear ordering methods in general) does not allow determining the hierarchy of the analysed multifaceted objects. The obtained grouping results may be compared with results of the linear ordering (in this case, the results obtained using the TOPSIS method), although they may not completely coincide. To facilitate interpretation, the results of the classification procedure were presented in a tabular form and numbered in descending order according to the arithmetic means of synthetic measures (obtained using the TOPSIS method) within a given group.

**Table 4.** Results of grouping the EU countries according to the standard of living and the level of renewable energy development.


Source: Own study based on [8].

With regard to the results of grouping EU countries according to the standard of living of their inhabitants using the PAM method, the last group was the most numerous (11 countries). Group IV included the highest number of countries (15) also in terms of the level of renewable energy development. In the case of both the standard of living of the inhabitants and the level of renewable energy development, group I, characterised by the highest level of analysed phenomena, was relatively small (3 countries and 1 country, respectively). The application of the PAM method allowed identifying certain regularities, including:


In the next step, a correlation analysis was conducted to examine the relationship between the standard of living of the EU residents and the level of renewable energy development (measured using the author's synthetic measures). For this purpose, the non-parametric Spearman's rank correlation coefficient was applied.

Spearman's rank correlation coefficient is not only more resistant to outliers than the commonly used Pearson's correlation coefficient, but it is also recommended if the sample distribution does not meet the assumption of a normal distribution [100]. The value of Spearman's rank correlation coefficient between the synthetic measure of the standard of living of the EU residents and the level of renewable energy development was 0.4652, which allows assessing the strength of this correlation as average. The determined correlation coefficient was statistically significant at the significance level *p* < 0.05. For the purpose of the in-depth study, a canonical analysis was conducted, which determines the interdependencies between two sets of variables (rather than individual variables).

In the conducted canonical analysis, the number of generated canonical roots is equal to the minimum number of variables included in one of the analysed sets. In this case, it is eight canonical variables (roots), since this is the size of the reduced set of variables describing the level of renewable energy development. The first generated pair of canonical variables, which synthetically illustrates correlations between the analysed sets of variables, explains the majority of relationships between these sets. In practice, most attention is paid to the correlation for the first canonical variable. However, it is necessary to bear in mind that the first pair of canonical variables does not completely explain the relationships between the variables under study. Therefore, it becomes necessary to determine successive pairs of canonical roots that explain relationships in other (less significant) dimensions. Calculations are conducted until all canonical variables are determined—their number is equal to the minimum number of variables in any of the sets. Only statistically significant canonical variables should be subject to in-depth analysis. To identify such variables, the previously described Wilks' lambda test was conducted (Table 5).


**Table 5.** Wilks' lambda test results.

Source: Own study based on [8].

In the last isolated pair, canonical variables do not correlate with each other in a statistically significant manner, therefore they were omitted in further description and interpretation.

In the first stage of the study, canonical weights were determined (as part of the canonical analysis) for the first pair of canonical variables that has the greatest contribution in explaining correlations between the analysed phenomena. Then, the magnitudes of weights for subsequent statistically significant canonical variables were determined. The weights created for standardised sets of variables are equivalent to *beta* coefficients in multiple regression. They inform about the contribution of each variable to the generated weighted sum. As their absolute value increases, so does the contribution (positive or negative) in the generation of the canonical variable.

Since the variables used for canonical analysis were subjected to the standardisation process, it is possible to directly compare the absolute values of the canonical weights determined (Table 6). Based on the conducted calculations, it is possible to conclude that for the first canonical variable, the S11 (0.7501) and R6 (0.4637) variables exhibit the greatest (absolute) weight values. Therefore, it can be assumed that the first canonical variable was the most significantly influenced by the correlation between the average wage and the share of renewable energy in final electricity consumption. For the assumed partial variables, the greatest contribution in the determination of the second canonical variable was made by variables S27 (−0.8422), describing the forestation rate, and R8 (0.7086), referring to the share of energy from renewable sources in energy used in transport. Variables S16

(the percentage of people at risk of poverty and social exclusion) and R3 (production of electricity and derived heat based on photovoltaic energy) had the greatest contribution in the generation of the third canonical variable, while the fourth canonical variable was influenced mostly by variables S10 (the percentage of people with higher education) and R5 (production of electricity and derived heat based on renewable municipal waste). Variables S18 and R1, S26 and R5, as well as S13 and R5 had the greatest contribution in the determination of the fifth, sixth and seventh canonical variables, respectively. Due to the large number of variables used and statistically significant, canonical variables generated, results of the canonical analysis were presented in a tabular form rather than using canonical models.


**Table 6.** Canonical weights and factor loadings.

\* The value 0.00 results from the adopted format of data presentation. In reality, a value greater than 0. Source: Own study based on [8].

In the subsequent step, canonical factor loadings and redundancy values were determined (see Table 7). Factor loadings are interpreted as values of correlation between canonical and interchangeable variables in each analysed set. The greater they are (in terms of an absolute value), the more emphasis should be placed on this variable during the interpreting. T. Panek and J. Zwierzchowski [92] recommend interpreting variables for which the square of this correlation coefficient is greater than 0.50. In turn, G. Wi˛ecek and

A. S˛ekowski [101] propose analysing only those variables for which the value of loads (not their squares) is greater than 0.30. For this analysis, it was assumed that the critical value of the correlation coefficient square is 0.20 (to facilitate the interpretation, those values were presented in Table 6 in bold and italics).


**Table 7.** Isolated variances and redundancies.

Source: Own study based on [8].

In the set of variables concerning the standard of living of the residents, for the first canonical root, the highest factor loading is presented by variable S27 (0.6762); for the second canonical variable, the highest factor load is shown by variable S10 (0.4852), for the third—variable S27 (0.3987), for the fourth—variable S11 (−0.3931), and the fifth—variable S17 (−0.3477). For the last two significantly static canonical roots, the greatest factor loadings were exhibited by variables S17 and S13 (-0.3031 and -0.3986, respectively). With regard to the set of variables concerning the renewable energy development level, for the first canonical variable, the highest factor loading is carried by variable R1 (0.7932), for the second—variable R5 (0.5088), for the third—variable R3 (−0.7187), for the fourth—variable R9 (0.3963), for the fifth—variable R1 (−0.5072), for the sixth and seventh—variable R9 (0.4900 and −0.5868, respectively).

In the literature on the topic, there are opinions, which claim that, in the interpretation of results obtained based on the canonical analysis, the interpretation of individual variables should be conducted using values of canonical factor loadings. This is substantiated by the fact that they are easy to understand intuitively. However, it is necessary to note that the values of such coefficients indicate correlations of individual input variables with canonical variables and, unlike the canonical weights, do not take into account the effects of covariance within a given set of input variables. As a result, the interpretation of canonical roots based on the values of correlation coefficients may lead to different conclusions than a more complete "multidimensional" interpretation based on canonical weights [93].

Based on the values of canonical weights and factor loadings, it can be concluded that the first statistically significant canonical root explained the following relationships:


Based on the values of canonical weights and factor loadings for the second canonical root, it can be concluded that there is a positive correlation between the production of electricity and derived heat based on renewable municipal waste and the percentage of people with higher education in the age group 25–64 (S10). In turn, based on the fourth

canonical root (or, more precisely, its weights and canonical loads), it can be concluded that the percentage of people at risk of poverty and social exclusion (S16) decreases as the production of electricity and derived heat based on hydroenergy (R1) increases. However, based on the values of canonical weights and factor loadings for the last necessary significant variable, it may be concluded that, as the installed heat pump capacity (R9) increases, the percentage of people with chronic diseases or health problems (S19) decreases.

When analysing factor loading values for the third, fourth and sixth canonical roots, it is possible to notice that in at least one analysed set, the square of the correlation coefficient between canonical variables and partial variables was less than 0.2 for all considered variables. For this reason, such canonical variables were not interpreted in terms of factor loadings and canonical weights.

In the subsequent step, the mean of the factor loading squares of every analysed set was determined for each statistically significant canonical variable, thus obtaining an indicator referred to as the extracted variance. In turn, by multiplying the said mean by the square of the canonical correlation, the redundancy value was obtained. The table below presents the values of the extracted (isolated) variance and redundancies (Table 7).

The most statistically significant canonical variable isolates more than 31% of the variance in the set of variables relating to the level of renewable energy development and nearly 7% in the second set (concerning the standard of living of EU residents). In turn, the second and third canonical variables isolate respectively 11.6% and 16% of the variance in the set describing RES, as well as 8% and 4% in the set of variables related to the standard of living. In the case of subsequent canonical variables, the degree of variance isolation in the set concerning the level of renewable energy development is significantly smaller; in the second set, the extracted (isolated) variance did not exceed 7%. The last statistically significant canonical variable isolates nearly 8% of the variance in the first set and 6% in the second set.

For the set of variables related to the standard of living of the EU residents, it is possible to explain 6.1%, 5.7%, 2.4%, 2.2%, 2.7%, 0.7%, and 1.4% of the variance of the set of variables describing the level of renewable energy development, respectively. In turn, with regard to the set of primary variables concerning the level of renewable energy development, it is possible to explain 27.5%, 8.1%, 8.9%, 2.5%, 3.2%, 2.3%, and 1.8% of the variance based on the first seven statistically significant canonical variables, respectively. Therefore, the fourth and subsequent statistically significant canonical variables already make a small specific contribution to explaining this variation. When comparing the amount of explained variance in both analysed sets of variables, it can be seen that in terms of each generated canonical root, the group of variables describing the level of RES development has a greater contribution to explaining the standard of living of the residents. This results in a research-relevant conclusion: variables describing the RES development level constitute a better predictor of variation in the standard of living that vice versa.

The next step involves the calculation of the total redundancy, interpreted as the average percentage of the variance explained in one set of variables for a second given set, based on all canonical variables. The conducted calculations show that the knowledge of values of variables describing the renewable energy development level allows explaining nearly 55.5% of the variance of variables from the set describing the standard of living of the EU residents. This value may be assessed as relatively high, and to obtain even better results, further research should be conducted in the future, using a different set of input variables and a changed number of such variables.

When studying multidimensional correlations between the standard of living and level of renewable energy development, it is worth noting the high and, more importantly, statistically significant (see Table 5) canonical correlation values. However, at this point, it should be emphasised that canonical correlation cannot be interpreted in the same manner as classical correlation (e.g., Pearson's). These values are interpreted as correlations between the weighted sum values in each set and the weights calculated for subsequent canonical variables. The value of the greatest and most statistically significant canonical

correlation was 0.94. For the last (seventh) statistically significant canonical variable, this value was nearly 0.49. The square of these canonical correlations constitutes a measure of the degree of explanation, through linear relationships, of the variability of one set of variables by the other input set, through successive pairs of canonical variables. For the first statistically significant canonical variable, the square of the canonical correlation is over 0.88, while for the second one, it is nearly 0.70. For the last statistically significant canonical variable (seventh), this coefficient is close to 0.24. It can be assumed that this generated model describes the analysed data sets relatively well. *Energies* **2021**, *14*, x FOR PEER REVIEW 29 of 35

> The figure below presents the scatter plots of the first and last statistically significant canonical variable (Figure 2). The OX axis refers to the set of variables concerning the level of renewable energy development while the OY axis refers to the standard of living of the EU inhabitants. significantly smaller amount of information about the covariance of two analysed variables than the first pair of canonical variables.

**Figure 2.** Scatter plot of the first and last statistically significant canonical variable. **Figure 2.** Scatter plot of the first and last statistically significant canonical variable.

**5. Conclusions**  Initially, renewable energy was marginalised due to very high investment costs. However, their progressive decline indicates that renewable energy is currently perceived not only as a source of energy but also as an instrument that facilitates resolving many other global problems. Among other things, it is crucial for ensuring energy security, reducing the effects of environmental contamination and mitigating the influence of excessive greenhouse gas emissions, which is particularly important in the context of implementing the concept of sustainable development. One of the basic tasks of the state consists in ensuring energy security (especially important nowadays, from the perspective of the standard of living) which should not, however, take place at the cost of environmental degradation. Renewable energy sources generate zero to small amounts of For the first canonical variable, the scatter plot does not present any strong scatter of points representing the analysed objects. These points are arranged along a straight line. This indicates that the generated pairs of canonical variables carry a significant amount of information about the covariance of the two analysed sets of input variables. The proximity of most points (which in the case of canonical analysis represent the European Union regions) may indicate a similar structure of input variables. In the scatter plot compiled for the last statistically significant canonical variable, points representing the analysed objects are also arranged along an upwardly inclined line, yet are more scattered relative to the said line. This indicates that such a pair of canonical variables carries a significantly smaller amount of information about the covariance of two analysed variables than the first pair of canonical variables.

#### pollution, which in the face of a deteriorating condition of the natural environment is an **5. Conclusions**

undeniable advantage. The conducted studies aimed to detect correlations between the sets of variables describing the standard of living of the EU inhabitants and the level of renewable energy development. The canonical analysis appears to be the most appropriate statistical tool, which may be used to study multidimensional interactions between two sets of variables. Due to the multifaceted character of the analysed categories, the sole use of classical correlation analysis or multiple regression analysis seems to be inadequate. According to the author, for the analysis of socio-economic phenomena, it is important to popularise the use of multidimensional exploratory methods (such as canonical analysis) to identify correlations between compiled, multidimensional categories. In the conducted studies, the canonical analysis was preceded by the creation of the Initially, renewable energy was marginalised due to very high investment costs. However, their progressive decline indicates that renewable energy is currently perceived not only as a source of energy but also as an instrument that facilitates resolving many other global problems. Among other things, it is crucial for ensuring energy security, reducing the effects of environmental contamination and mitigating the influence of excessive greenhouse gas emissions, which is particularly important in the context of implementing the concept of sustainable development. One of the basic tasks of the state consists in ensuring energy security (especially important nowadays, from the perspective of the standard of living) which should not, however, take place at the cost of environmental degradation. Renewable energy sources generate zero to small amounts of pollution, which in the face of a deteriorating condition of the natural environment is an undeniable advantage.

author's synthetic measures and the determination of the correlation coefficient between them. For the partial variables included in the study, the coefficient of variation for the

the standard deviation was nearly 0.12 (with a mean value of nearly 0.25). This confirms the significant variation in the level of renewable energy development in the European Union. In turn, for the constructed synthetic measure of the standard of living, the classical variation coefficient was less than 10.5%, which indicates a relatively weak differentiation of the analysed phenomenon (for the analysed set of partial variables). In the case of threequarters of the EU countries, the value of the synthetic measure did not exceed 0.49 (with a minimum value of 0.37 and a maximum value of 0.54). Based on the conducted correlation analysis, it can be concluded that there is a positive, moderate and statistically significant correlation between the standard of living of the EU residents and the level of

The conducted studies aimed to detect correlations between the sets of variables describing the standard of living of the EU inhabitants and the level of renewable energy development. The canonical analysis appears to be the most appropriate statistical tool, which may be used to study multidimensional interactions between two sets of variables. Due to the multifaceted character of the analysed categories, the sole use of classical correlation analysis or multiple regression analysis seems to be inadequate. According to the author, for the analysis of socio-economic phenomena, it is important to popularise the use of multidimensional exploratory methods (such as canonical analysis) to identify correlations between compiled, multidimensional categories.

In the conducted studies, the canonical analysis was preceded by the creation of the author's synthetic measures and the determination of the correlation coefficient between them. For the partial variables included in the study, the coefficient of variation for the constructed measure of the level of renewable energy development was over 47%, while the standard deviation was nearly 0.12 (with a mean value of nearly 0.25). This confirms the significant variation in the level of renewable energy development in the European Union. In turn, for the constructed synthetic measure of the standard of living, the classical variation coefficient was less than 10.5%, which indicates a relatively weak differentiation of the analysed phenomenon (for the analysed set of partial variables). In the case of three-quarters of the EU countries, the value of the synthetic measure did not exceed 0.49 (with a minimum value of 0.37 and a maximum value of 0.54). Based on the conducted correlation analysis, it can be concluded that there is a positive, moderate and statistically significant correlation between the standard of living of the EU residents and the level of renewable energy development (measured by synthetic measures constructed using the TOPSIS method) (Spearman's rank correlation coefficient was nearly 0.47). Seven statistically significant canonical variables were identified using canonical analysis. Based on the value of the redundancy coefficient determined as part of the canonical analysis, it can be concluded that, with the knowledge of the considered variables describing the level of renewable energy development in the EU, it is possible to explain nearly 55.5% of the variance of variables from the set concerning the standard of living of the residents. In other words, more than half of the variation associated with the standard of living of the EU residents is determined by partial variables relating to the level of renewable energy development that were taken into account. It should also be mentioned that high values of canonical correlation coefficients were identified for statistically significant canonical variables. For the most statistically significant canonical variable, this coefficient was 0.94, while for the least statistically significant, it was 0.31.

The results of conducted studies (i.a. the ranking of countries in terms of the standard of living of the residents), can be used indirectly by, for example, central and selfgovernment authorities responsible for local and regional development (including undertaking pro-social and pro-environmental actions) in the context of selecting the direction of socio-economic restructuring of individual countries and self-government units (taking into account the financial capacity of the society). Furthermore, the results of the studies may indirectly prompt self-government authorities to undertake actions directed towards more efficient use of the capacity for funding investment projects aimed to develop renewable energy technologies. Quantification of such important economic categories as the standard of living and the renewable energy sources development level in comparison with other areas may be conducive to initiating activities (e.g., of local authorities in shaping sustainable development strategies) directed towards stimulation of development aimed to achieve the highest standard of living while respecting natural resources. The conducted studies and obtained results may constitute the starting point for further analyses using different statistical methods (e.g., Granger causality analysis) and/or diagnostic variables, or to encourage similar studies at the level of other countries and self-government units. In further analyses, it would also be worth it to examine the spatial interactions between the phenomena analysed, including analysing autocorrelation and spatial heterogeneity, as well as constructing spatial regression models (including SEM and SLM models). It

is possible to consider weighting the applied diagnostic variables based on expert opinions and/or statistical methods, which, however, in the case of spatial unit analyses, is a controversial solution.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on the Eurostat website (https://ec.europa.eu/eurostat/ web/main/data/database, accessed on 12 April 2021).

**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A**


**Table A1.** Data on the standard of living—part 1.

Source: own study based on [8].


**Table A2.** Data on the standard of living—part 2.

Source: own study based on [8].

**Table A3.** Data on the level of development of renewable energy sources.



**Table A3.** *Cont.*

Source: own study based on [8].

#### **References**


*Article*
