“The impact of state regulation in a sphere of education on sustainable development of national economy”

Education is a core element of the Sustainable Development Concept. It is not only because of the declaration of SDG 4 within the 2030 Agenda but also its embeddedness in other goals, targets, and indicators. Thus, the study aims to generalize approaches to define the relationship between the efficiency of the strategy of sustainable development of the national economy and state regulation of education. The research is accomplished for 14 Central and Eastern European countries (2006–2016) using the combination of principal components method and parametric method of stochastic frontier analysis in the software package STATA 11 and FRONTIER 4.1. As a result, the empirical proofs of the strong and adequate link between the efficiency of the sus- tainable development strategy of the national economy and state regulation of education are identified. The technical efficiency indexes were also calculated that allowed forming three clusters for Central and Eastern European countries distributed by the level of state regulation of education and efficiency of sustainable development strategy implementation. It helps to distinguish the main measures to reform the state regulation of education in Ukraine considering the experience of Slovenia, Poland, the Czech Republic, countries that proved to be the leaders in a sphere of sustainable development strategy implementation. The recommendations for further improvements in educational policies were defined. For instance, effective and sustainable state regulation of education should focus on decentralizing education, developing private-public partnerships, stimulating adult education development, etc. implementing the SDGs, the seminal work of Stafford-Smith et al. (2017) should be mentioned. This study is devoted to the conceptualization of the cooperation model between actors under the 2030 Agenda. The scholars and researchers have declared the SDGs system as a new opportunity to create a viable network of countries to integrate the efforts for a common future at a new level (Le Blanc, 2015). Interdisciplinary of the sustainable development concept and its relatedness to the education process was developed in papers of Steiner and Posch (2006) and Arbuthnott (2009). If the first work is about cross-country analysis, the other is accomplished for attitude‐ behavior relationships at an individual level. However, the issue of ef-©


INTRODUCTION
The sustainable development concept is widely known and attracts the interests of scholars, researchers, policy-makers, and social activists. The analysis of academic citations through the Publish or Perish software had revealed top-cited works. Among the most cited papers in the field of implementing the SDGs, the seminal work of Stafford-Smith et al. (2017) should be mentioned. This study is devoted to the conceptualization of the cooperation model between actors under the 2030 Agenda. The scholars and researchers have declared the SDGs system as a new opportunity to create a viable network of countries to integrate the efforts for a common future at a new level (Le Blanc, 2015). Interdisciplinary of the sustainable development concept and its relatedness to the education process was developed in papers of Steiner and Posch (2006) and Arbuthnott (2009). If the first work is about cross-country analysis, the other is accomplished for attitudebehavior relationships at an individual level. However, the issue of ef-ficiency of specific systems and branches of the national economy as the subject of study in relatedness to sustainability are less frequent. The 4th SDG expresses the following vision of the desired state in a field of education 'Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all', according to the 2030 Agenda (UN, 2015). The SDGs achievements are at the center of scholars' and practitioners' attention, and there are many papers where debating and conceptualizing sustainable development took place. However, few studies on cross-country analysis combined the evaluation of national economic efficiency, sustainable development progress, and social institutions regulations. In this regard, the study by Lo Storto and Goncharuk (2017) on benchmarking analysis for some European countries' national healthcare systems should be analyzed. The scholars use the non-parametric frontier method based on Data Envelopment Analysis (DEA). In their work, Jikia et al. (2017) presented an approach to assessing the lifelong learning system's financial support in Ukrainian regions through stochastic frontier analysis. Similar studies on the evaluation of efficiency in specific sectors of the national economy are performed by Obeid

LITERATURE REVIEW
There are at least two dimensions for the literature review in the current study. The first dimension is about how to combine the previous findings on sustainability, regulations in the educational sphere, and methodology evolution in the research field. Another dimension is devoted to analyzing the previous findings in efficiency evaluation.
To start with the complex analysis of multidisciplinary research, the verified techniques and bibliometric measurement were performed. Among existing bibliometric tools, Publish or Perish software is one of the most helpful in identifying seminal, top-cited papers in the domain. Thus, the search using the combination of keywords 'state regulation', 'education', 'efficiency,' and 'sustainable development goals' was accomplished for 2019-2019. The content analysis enabled to select TOP-15 works in research out of the first 200 items ranked by Google Scholar Ranking, as shown in Table 1. Among items, there were books, conference notes, editorials, and papers. For further content analysis, the papers were selected only with a high Google Scholar Ranking (GSR). Notably, the GSR returns outcomes (as 1, 2, 3) in the order of relevance of query results. The cites ranking may result in irrelevant papers, so in this case, three tools were combined as presented further (see Table 1). By doing so, the simplified outcomes of content analysis of selected papers are presented too (see Table 1).
Among the most cited works, the work of Martinez-Alier et al. (2010) is worth attention, where the sustainable development paradigm faces the degrowth concept. The comparison between these two flows of thinking made the disadvantages of the latter visible. The challenges in sustainable development should still be discussed in further research, especially in terms of scale and scope, ethical boundaries, technical, economic, and institutional tools.
The study that proves the urgency of radical reorientation in educational policies towards innovative strategies and sustainable development that meets the social needs (Breidlid, 2009) resonates with the study of Khalili et al. (2015) devoted to the role of academia in the promotion and acceleration of sustainable development movement. The researchers accomplished the cross-country survey to understand how cleaner production concepts may infuse academic programs and how to support sustainable development and encourage sustainable education. Another qualitative study was done later (Yuan & Zuo, 2013), but for China only. The respondents (1,134 people) were students of educational institutions, and the results showed the level of awareness of sustainability issues in the community. Most Chinese institutions use a top-down approach to incorporate sustainable development. Therefore, the education may offer the optional way of implementing a bottom-up approach and the existing one.
One more qualitative study but narrowed to the case analysis and reasoning was done by French researchers L. Simonneaux and J. Simonneaux (2009). This study has a specificity (ecological niche) and yet brought the findings in the field to the academic community for further discussion.
In the content analysis process, it was revealed that most of the cited papers are devoted to the conceptualization of sustainable development (Maroy, 2009 There are studies worth mentioning for the literature on interlinks between SDG progress, regulation policies, and education. Governments' intentions to achieve the accepted SDGs are the subject of several scientific discussions (G. Karnitis  Accordingly, the second dimension of the literature review is the comprehensive framework of efficiency evaluation, which is the bottom line of the current research. According to the Longman Business Dictionary (2000), efficiency is considered a quality that shows "how well an industrial process, factory, or business works so that it produces as much as possible from the time, money, and resources that are put into it". Other than that, there is a well-known approach, according to which the efficiency is a "ratio between outcome and costs (resources) to achieve it" (Andriychuk, 2005). Many studies deal with efficiency rather than effectiveness; even if both measure the performance, these terms should be distinguished properly. Detailed research of Mouzas (2006) gave a systematic understanding of similarities and differences of the mentioned terms, and in the current study, the term "efficiency" is used following the logic of DEA (Karlaftis, 2004) as a non-parametric approach to efficiency measurement. On the other hand, the effectiveness is performed at the standard ISO 9000:2015 as "the extent to which planned activities are realized, and planned results are achieved" (ISO 9000:2015, n.d.).
In the opinion of another scholar, Pylypenko (2016), the efficiency may be considered in three dimensions: (a) economic dimension -when the usage of existing resources (natural, financial, human, etc.) are compared to the achieved results; (b) organizational dimension -when the efficiency of management and decision-making system is taken into account; and (c) social -when the costs and resources (input) are compared to the social outcomes or result (i.e., social security, equity, and equality, etc.). These three types of efficiency are related to each other and allow measuring certain object at the microlevel (entity or organization) and the level of country or governance.
In this matter, the study of Nazarko and Šaparauskas (2014) should be mentioned, where the DEA method was implemented for the efficiency evaluation of public higher education institutions. This study encourages searching for a comprehensive toolbox to understand if there is a relationship between educational policies and progress in sustainable development. The mentioned study is less relevant to SDG, but more to the economic and technological efficiency of HEIs performance; still, it showed that the comparison between educational systems of different countries might be representative; therefore, the quantitative study was chosen for current research.
Talking about the efficiency evaluation methods, at least several groups of methods may be distinguished: index methods, which mean that certain aspects or activities may be measured in absolute or relative terms, and they can be performed on average or as an integral index; the expert methods that implies surveys, focus-group, qualitative data collection and data processing, balanced assessment. The next one is econometric methods; they involve more complex econometric analysis models and various analytical tools. Moreover, there are blended methods, which combine the abovementioned. In a broad sense, all the methods of evaluating efficiency can be divided into parametric and non-parametric. For the current study, the parametric method of econometric analysis was chosen to establish the objective function and determine the influence of individual factors on the dependent variable.
Among the great variety of econometric analysis methods, stochastic frontier analysis (SFA) was chosen for several reasons. It allows determining the possible deviations of the actual and potential level of efficiency and receiving optimum value concerning the object of research. This method was first introduced by a group of scientists led by Aigner (Aigner et al., 1977) and was used mainly in production analysis. Later, it began was widely distributed in other fields, as evidenced by the works of Battese and Coelli (1992), Coelli (1996), Farrell (1957), Meeusen et al. (1977), etc.
This method's main essence is to consider a particular situation or entity (in the current case -the country) as a complex system with a set of input parameters and output parameters. In mathematical form, this method of analysis is most often expressed using the production function (Aigner et al., 1977): where i Y is level of benefits of entity (or a produc- X is variable vector of factors for an entity (or a producer) i; β is vector of unknown parameters; i V is standard error; i U is inefficiency index for an entity (or a producer) i.
The stochastic frontier analysis needs a so-called efficiency limit to be established for a given situation or entity, mainly in the form of a specific regression dependence. Note that the following formula determines the evaluation of efficiency: EF is the index of technical efficiency of activity of entity i, E is expectation.
It is important to understand that the method outlined above is based on technical efficiency and to distinguish this type of efficiency from others is crucial. For understanding the technical efficiency, the definition of Farrell (1957) who defined it as a firm's success "…in producing maximum output from a given set of inputs" (Farrell, 1957, p. 259) was accepted as initial. The same scholar noted that technical efficiency always, to some extent, reflects the quality of its inputs. Therefore, the following fact should be considered: technical efficiency is measured concerning a given set of parameters (firms), and any dynamic of inputs will affect the outcomes. However, these limitations, according to Farrel (1957), are natural. However, despite the numerous studies listed above in this area, they remain fragmented; namely, they are either related separately to the educational sphere and the results of its activities or issues of sustainable development and related transformations in the national economy, or efficiency evaluation. Based on this, the current study aims to generalize approaches to define the relationship between the efficiency of the strategy of sustainable development of the national economy and state regulation of education.

RESEARCH METHODS
At the first stage, the data set is formed. In the current study, identifying independent, additional, and dependent variables and data collection took place. As dependent variables, the unified integral index of SDGs achievements (I SDG ) was calculated and, therefore, the progress in implementing the respective strategies in different countries. The integral index calculation method is based on indicative SDGs formed using principal component analysis. Firstly, it provides normalization by comparing initial data with maximum and minimum values (for stimulants and destimulators). Secondly, the components' weight determination takes place according to their correlation proportion and dispersion. Thirdly, the integral index is calculated by the weighing of normalized data. It should be noted that the same algorithm is accomplished for each SDG, and then the integral index for all SDGs achievements is performed.
The second stage is about forming the factors that influence the process of achieving SDGs. In the current study, two groups are considered -1 st group, "Harmonization of the Educational Environment under the State Regulation of Education (HE)," and 2 nd group of additional corrective variables that reflect the set of parameters that indicate specialization of a national economy (NEI).
The third stage is about to design an appropriate model based on the parametric method of stochastic frontier analysis and verification of its adequacy. As mentioned earlier, within the SFA framework, the function has a production form and may take many forms depending on specification. The most common is the Kobb-Douglas function or its complicated version -the translogarithmic function. The reliability and adequacy of the obtained results of performance evaluation depend on the choice of specification. The maximum likelihood ratio test was used to compare the criteria set of the Kobb-Douglas function and the translogarithmic function to select the analysis method.
The calculations were performed via software FRONTIER 4.1. and STATA 11.
The last stage of the study is cluster analysis using the results of parameter values and the interlinks between them.

EMPIRICAL RESULTS
The following values of integral indexes were obtained at the first stage and compared for 2006 and 2016 (see Figure 1).
At the second stage, the following components for the groups of variables were offered: • 1 st group "Harmonization of the Educational Environment under the State Regulation of Education (HE)" is represented by the variables as follows: state funding of education (amount of allocated funds), total education coverage ratio, teacher-student ratio in preschool, primary, secondary and higher education, duration of compulsory schooling; • 2 nd group of additional corrective variables that reflect the set of parameters that indicate specialization of a national economy (NEI): indicators of change in GDP, GNI, the share of agriculture, industry, and services in the economy, the share of exports and imports of goods and services, and exports of high-tech ICT technologies and services, etc.
The results of the maximum likelihood ratio test are performed further. This method compares the criteria set of the Kobb-Douglas function and the translogarithmic function (see Table 2).
The calculation results proved the necessity of using a translog function (3), which is more flexible and involves various types of dependencies of outcomes on inputs.  β is vector of unknown parameters; i U is nonnegative random variables, assumed to account for technical inefficiency; i V is random variables.
The results of the evaluation of the parameters based on the translogarithmic function are presented in Table 3. These calculations describe the relationship between harmonizing the educational environment (HE) and the efficiency of sustainable development strategies implementation in selected countries (NEI). The evaluation presented above revealed the following dependencies that are adequate and statistically significant: To study the changes of this indicator within the group of analyzed countries, they were divided into three clusters, defining a uniform range of the interval ( Table 4).
As a result, the leaders with a high level of influence of state regulation of education on the efficiency of the strategy of sustainable development of the national economy were identified (primarily Slovenia, the Czech Republic, and in 2016 -Poland). On the other hand, Ukraine has consistently remained in the first cluster, which shows signs of a low level of efficiency in the implementation of the sustainable development strategy.
In this regard, the main measures to reform the state regulation of education were revealed, which should be taken into account for Ukraine to increase the efficiency of the strategy of sustainable  Table 5). Besides the mentioned in Table 5, there are several more promising directions of the reforming. Firstly, one of them is the lifelong learning concept and adult learning development. Another is a privatepublic partnership; for instance, the relationships "Employers -HEIs and stakeholders -Government" can be established in a sustained system. That triad system will generate opportunities in labor markets via contractual and mutually beneficial relationships between employers and educators. It will lead to the creation of new hubs and networks through the innovations boost, direct educational services supply chain, etc. Otherwise, the labor migration will go on and will increase the depopulation crisis in Ukraine. The cooperation between the institutions may be implemented through many forms and models, for instance, known as the coopetition model of institutional partnership, and that can be a direction for further research.

DISCUSSION
Nevertheless, the study reveals the relationship between the state regulation of education and the sustainable development of the national economy; there are limitations and knowledge gaps to be further investigated. For instance, Switzerland is a leader in green economy development; therefore, sustainable development strategy efficiency is high there, while Scandinavian countries are the leaders in terms of quality of education. The current study focuses on Central and European countries owing to the shared history and similarities of institutions, and for the same reason, the sample is accepted as representative. For the more verified results, the sample of data should be expanded and include the pure leaders in education (Finland) and pure leaders in green innovations (Switzerland) to reveal the patterns. Besides, the stakeholder factors are left beyond the study and components that show transparency and quality of educational services. The challenges in scaling up the transformations in the sphere of sustainable education were addressed but partly, only in a sphere of state regulations. One more aspect should be investigated -the informal education and its influence on the market players' behavior via consulting (Goncharova, 2015) and their sustainability-related practices.
Despite these limitations, the research proved the interlinks between educational policies, educational technologies, ploys and patterns, and sustainable development movement outcomes.

CONCLUSION
The study confirms the dependence of the efficiency of the strategy of sustainable development of the national economy on the state regulations of education for selected countries of Central and Eastern Europe. As the modeling showed, the harmonization of the educational environment has almost 4.8 times more impact on the efficiency of the strategy of sustainable development of the national economy than the national economy's sectoral and technological specialization.
The main contribution of the research is formed methodology for cross-country comparison of achievements in the fields of education and sustainable development. Moreover, this study combines the evaluation of national economic efficiency, sustainable development progress, and social institutions regulations indicators.
The empirical results allowed clustering the sample countries and determining the list of measures to reform the system of state regulation of education in Ukraine, depending on the leading countries' experience, taken as a guide. Ukraine, being in the cluster with the lowest level of influence of state regulation of education on the efficiency of the strategy of sustainable development of the national economy, should focus on the insights from the leaders (Poland, Czech Republic, Slovenia), defining features of decentralization of education, developing private-public partnership, stimulating the development of adult education, etc.
The best practices performed in countries-leaders may become a basis for the roadmap of future reform development, which may become a beacon for further research.
By proving the dependence of the national sustainable development strategy's integrated efficiency on the interventions and regulations of government in the sphere of education, the key guidelines for further transformations in Ukraine are justified. One of the most promising directions is a private-public partnership in the field, educational services providers' autonomy, and support of lifelong learning concept and education for adults.