1 Introduction

This article proposes an estimation of the level of RQ i.e., the perception of the ability of governments to promote the development of the private sector. RQ is defined by World Bank as a variable that captures perceptions of the ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development. The level of RQ as an index varies in a range between − 2.5 and 2.5. The analysis proposes an investigation of the relationship between RQ and a set of indicators connected to the World Bank's ESG database. In particular, RQ is an indicator which is part of the governance section and which has been analysed in its relationships with other variables relating to the environment and the social dimensions. The Environmental, Social and Governance-ESG model has been proposed as a tool for achievinlity. In fact, although the orientation towards the market society and the development of the private sector may seem banal, on a global level it is possible to witness a retreat of the private sector following a series of crises that have occurred recently. Covid-19, the Russo-Ukrainian war, inflation, the energy crisis, have once again placed the role of the state and the public economy at the centre, even in Western societies inspired by Anglo-Saxon capitalism. This succession of adverse macro-phenomena has in fact considerably weakened businesses, especially small and medium-sized enterprises, compressed the income of workers and families, and reduced life expectancy together with the size of the share capital of the population.

However, the Western capitalist system, i.e. Europe, Japan and Anglosaxon countries, needs to invest in the private sector, as the private sector provides important products, services and jobs that are essential for the development of economic, political, and social systems, also in the sense of sustainability. In fact, if it is true that access to the energy transition follows the trend of the Environmental Kuznets Curve, then it is necessary to further strengthen the private sector to ensure that the conditions are created for accessing the green economy.

Hence the need to focus on a set of elements that are not only aimed at a governance dimension, and which are instead also able to grasp aspects relating to the environment and the social dimension. No less important is also the question of social participation in political and democratic issues. In fact, countries that have high levels of RQ, i.e., Western countries, also experience a set of limitations in accessing democracy, as evidenced by growing inequality, abstentionism and violent phenomena such as the assault on the Capitol Hill in the US of the 6 January 2021.

It is therefore necessary to find a new sustainable balance between social, environmental and governance issues, and aim at strengthening private production that has been put to the test by the succession of adverse macro-economic phenomena.

Research question. The research question of the article is aimed at investigating the existing relationship between RQ and the set of variables that refer to the ESG model. That is, the idea of the article consists in verifying how RQ changes with respect to the Environment, Social and Governance components within the ESG context. This issue is increasingly relevant, especially in the application of the economic policy guidelines that are suggested by the UN in implementation of the Sustainable Development Goals-SDGs. It is therefore necessary to verify whether there are environmental, social or governance variables that have the ability to have an impact in terms of Regulatory Quality.

Research hypothesis. Our research hypothesis consists in the fact that there is a positive dependence between each of the three constituent elements of the ESG model. The hypothesis is introduced that the RQ value tends to grow with the presence of good results at the environmental level, at the social level and in terms of governance detected at the country level. In fact, countries that have low RQ levels can be characterized by high levels of pollution, the presence of poverty and social inequality, and high corruption. Reduced ESG performance may be able to identify low RQ values.

Gaps filled by the article. Although there are many articles in the literature that analyze the macro-economic significance of RQ, in reality there are few studies that consider the role of RQ in the context of ESG models. Since ESG models are strongly promoted by the UN as tools for implementing the Sustainable Development Goals-SDGs, it follows that our article fills the gap by proposing a systemic analysis capable of connecting the value of RQ to environmental, social and governance issues.

The article continues as follows: the second paragraph contains an analysis of the literature, the third presents the econometric model, the fourth shows the cluster analysis, the fifth analyses the prediction with machine learning algorithms, the sixth implements the network analysis, the seventh concludes. The appendix presents supplementary statistics, metrics and methodologies.

2 Literature review

In the following part, a brief review of the literature is presented to introduce the topic. In general, from the analysis it is possible to verify that RQ has positive effects on economic growth, economic development, financial development, energy transition and environmental sustainability. Regulatory Quality has no meaning in promoting economic growth in Middle East and Northern African-MENA countries [1]. The quality of regulation has a relevant role in promoting financial institutions in African countries [2,3,4]. There is a positive relationship between the quality of regulation and environmental degradation in Sub-Saharan African countries [5]. RQ has a positive impact in reducing \({C{O}_{2}}\) emissions in Brazil, Russia, India, China, and South Africa, i.e. BRICS countries, in the long run [6].

RQ has a relevant role in Brazil even if not all the laws are effectively implemented in the legal system [7] Regulation Quality has a negative impact on economic development in the short run and a positive one in the long run in the Economic Community of Western African States-ECOWAS [8, 9]. The quality of regulation has a negative impact on the inverse relationship between non-renewable energy and life expectancy in African countries [10]. RQ is positively associated to the adoption of renewable energies in a panel of 85 countries [11] Regulation Quality has a positive effect in boosting the contribution of Foreign Direct Investments-FDI on the exports of high tech products in developing countries [12] Historical, institutional and democratic factors can explain the heterogeneity in terms of RQ among European countries [13]. The quality of regulation RQ positively affect tourism in India [14]. RQ has a positive impact in promoting the economic performance either in oil either in non-oil developing countries [15]. Regulation Quality positively affect the stock market performance in a composite set of 23 countries [16]. Countries with higher levels of RQ recovery faster in case of financial distress [17]. There is a positive relationship between RQ and the ability of multi-Latinas to produce quality accounting reports in the period 2014–2020 for a sample of 77 corporations [18]. The quality of regulation RQ promotes financial inclusion and inclusive growth in Nigeria [19]. RQ is associated to a reduction in infant and maternal mortality in Sub Saharan Africa [20]. Regulation Quality is an essential tool to promote an increase in per capita income in 35 European countries [21]. RQ has a positive effect in boosting the finance-growth nexus [22]. The low level of the quality of regulation RQ in Pakistan is negatively associated to banking financial stability [23]. Regulation Quality improves environmental sustainability in a set of 177 countries [24]. RQ has a negative effect in attracting Chinese FDI in Africa [25]. The quality of regulation has a positive impact on the reduction of electricity prices in Europe [26]. There is a positive relationship between RQ and Initial Public Offerings-IPOs in Pakistan [27]. In summary, it is possible to note that there are positive effects that Quality Regulation produces on economic performance and environmental sustainability.

Either developed countries either developing countries should create the conditions to improve the level of RQ. The orientation toward private property, economic freedom and the liberalization of private sector have positive on the economic and social development of developed and developing countries.

2.1 Data and methods

The data used refers to the World Bank dataset dedicated to the Environmental, Social and Governance-ESG variables. These data refer to a set of variables that capture environmental, social and governance elements. This is a very large database that includes 193 countries, over 60 variables, and a historical series which in our case includes the period 2011 and 2021.

From a methodological point of view, a set of tools were used for data analysis, namely:

  • Econometric models: three econometric models were used namely Pooled OLS, Panel Data with Random Effects, Panel Data with Fixed Effects. The use of econometric models is necessary to verify the relationships existing between the variables of the analyzed dataset. Econometric models identify which variables have a positive or negative relationship with RQ. This analysis allows us to understand the dependencies between the socio-economic and environmental variables and the variable of interest or RQ;

  • Clusterization with k-Means algorithm optimized with the Elbow Method: clustering is introduced to verify whether there are any groupings between the analyzed countries. Since 193 countries are presented, through the use of clustering it is also possible to verify whether the countries belonging to the same clusters have common characteristics from a socio-economic and environmental point of view. Particularly relevant in clustering is the geographical question, i.e. verifying whether countries that are geographically bordering have the same characteristics in terms of RQ or not. Further interesting considerations in the case of clustering refer to per capita income levels. That is, it is possible to verify whether the countries that are part of the same cluster have convergent or divergent levels of per capita income. Since the k-Means algorithm is an unsupervised machine learning algorithm, it is necessary to identify an optimization tool that allows you to identify the number of k or clusters. In this regard, the Elbow method was chosen, a graphical method that allows the optimal number of clusters to be evaluated.

  • Prediction with machine learning algorithms: to predict the future value of the RQ variable, a comparison was carried out between eight different machine learning algorithms. Machine learning algorithms are classified based on statistical criteria, i.e. the ability to minimize statistical errors and maximize the R-squared value. The algorithms are then compared with each other and a score is assigned to each algorithm based on the statistical efficiency of the prediction. The algorithms are trained with 70% of the data while the remaining 30% is used for the actual prediction. The predicted data is presented in comparison with the historical series to verify which countries for which the algorithm predicts a growth or reduction in the RQ value.

  • Network Analysis: finally, a network analysis is presented to verify the existence of network structures between the countries being analyzed and what the relationships are between the countries also weighted from a numerical point of view. In this way it is possible to have a map of the countries that are connected within network structures in the sense of RQ. These are countries for which the growth or reduction in the RQ value can lead to a growth or reduction in the corresponding value at the country level.

The set of these methodological tools used allows us to understand the relationships between RQ and ESG variables, the presence of groupings based on clustering, the prediction of the future value of RQ, and the characteristics of network structures at country level.

3 The econometric model for the estimation of the value of regulatory quality

In the following part, an econometric estimate of the level of regulatory quality in 193 countries over the period 2010–2021 is presented using a set of econometric techniques, i.e. panel data with fixed effects, panel data with random effects, Pooled OLS. The variables used in the economic estimation model are indicated in Table 1.

Table 1 List of Variables Used in the Econometric Model
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Specifically, the following equation was estimated: \(Regulatory\,Qualit{y}_{it}=\alpha +{\beta }_{1}{\left(Adjusted\,Savings\,Natural\,Resources\,Depletion\right)}_{t}+{\beta }_{2}{\left(Annualized\,Average\,Growth\,Rate\,in\,Per\,Capita\,Real\,Survey\,Mean\,Consumption\,Or\,Income\right)}_{it}+{\beta }_{3}{\left(Energy\,Intensity\,Level\,of\,Primary\,Energy\right)}_{it}+{\beta }_{4}{\left(Energy\,Use\right)}_{it}+{\beta }_{5}{\left(Fertility\,Rate\,Total\right)}_{it}+{\beta }_{6}{\left(Forest\,Area\right)}_{it}+{\beta }_{7}{\left(GHG\,Net\,Emissions\right)}_{it}+{\beta }_{8}{\left(Heat\,Index35\right)}_{it}+{\beta }_{9}{\left(Mean\,Drought\,Index\right)}_{it}+{\beta }_{10}{\left(Mortality\,Rate\right)}_{it}+{\beta }_{11}{\left(Nitrous\,Oxide,Emissions\right)}_{it}+{\beta }_{12}{\left(People\,Using\,Safely\,Managed\,Drinking\,Water\,Services\right)}_{it}+{\beta }_{13}{\left(Renewable\,Electricity\,Output\right)}_{it}+{\beta }_{14}{\left(Renewable\,Energy\,Consumption\right)}_{it}+{\beta }_{15}{\left(Research\,and\,Development\,Expenditure\right)}_{it}+{\beta }_{16}{\left(Rule\,of\,Law\,Estimate\right)}_{it}+{\beta }_{17}{\left(School\,Enrollment\,Primary\,and\,Secondary\right)}_{it}+{\beta }_{18}{\left(Strength\,of\,Legal\,Rights\,Index\right)}_{it}+{\beta }_{19}{\left(Voice\,and\,Accountability\,Estimate\right)}_{it}\)

$$t=\left[2011;2020\right];\,i=193$$

The main results of the econometric analysis are summarized in the Table 2.

Table 2 Main results of the econometric analysis
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Results show that Regulatory Quality is positively associated to the following variables i.e.:

  • Greenhouse Gas-GHG net emissions/removas by Land Use Change and Forestry LUCF: It is a variable that takes the net emissions of GHG as a reference point considered as net changes of the levels of greenhouse gases in the atmosphere. Countries that have the most the levels of RQ are also the countries that have the greatest levels of GHG. In fact, since these are industrialized western countries, they have high levels of GHG emissions. Since RQ allows to enhance the private sector, it follows that these countries have a more solid industrial system with the development of and industrial system that have a negative impact for the environment. In addition, the countries that have larger levels of RQ have also greater GHG emissions following the greater distribution of polluting cars and means of transport. It follows that the set of industrial production activity and population consumption models in western countries tends to generate growth in terms of GHG. The green oriented policies that most countries have embraced should reduce the level of GHG.

  • Mean Drought Index: it is a measure of drought. Countries that have larger levels of RQ also tend to have greater drought levels. However, the growth of drought is a generalized phenomenon connected to the climate change. It is very difficult to evaluate whether the green oriented economic policies that have been designed by Western countries are able to introduce changes in terms of reversal of the phenomenon of drought. However, the reduction of rains, the retreat of glaciers in Europe poses problems both to agriculture, and industry and the population in general. It is very probable that in the future the phenomenon of drought will be even more relevant worldwide by decreeing a condition of difficulty of the countries that could generate food famine and economic and financial crises.

  • Heat Index 35: is an indicator that considers the average number of days per with a temperature above 35 Celsius degrees. There is a positive relationship between the RQ and the Heat Index 35. It follows that the western countries with high per capita income, which are the same that have high levels of RQ, experience a growing temperature. The number of days in which the temperature grows above 35 degrees tends to increase in countries with high RQ levels. This condition is serious as it involves growth in energy expenditure for air conditioners, with a further aggravation of polluting emissions, a growth in energy consumption and the worsening of global climatic condition. The positive relationship between RQ and Heat Index 35 suggests the urgency of a legislation sensitive to the environmental question in high-income-income countries to counter the adverse effect of the climate change.

  • School Enrolment primary and secondary, gender parity index: is an indicator that takes into consideration the ratio between girls and boys enrolled in both public and private primary and secondary schools. There is a positive relationship between the RQ and the value of gender equality in primary and secondary schools. Hence the consideration that the countries that have a higher RQ also have the possibility of experiencing greater gender parity. The presence of legislation in favour of the private sector is not only an economic fact, but also have social effects promoting the civil emancipation of female students and workers. In fact, the promotion of the private economy leads to a greater presence of women in the labour market, and therefore society accepts more easily that women can study and train to actively participate in the production of added value at a national level. It follows that even the primary and secondary education sectors are involved in the process of women's emancipation by offering training not only oriented towards work but also towards citizenship, social activism and civil protagonism.

  • Research and Development Expenditure % of Gross Domestic Product GDP: is a variable that considers spending on research and development as a percentage of GDP. This indicator takes into account either the capital expenditures either the current expenditures in four sectors i.e.: private for-profit sector, government, public education, and private non-profit. Expenditure on Research and Development covers basic research, applied research and experimental development. There is a positive relationship between the value of R&D expenditures and RQ. Indeed, countries that have high RQ levels also tend to have a more entrepreneurially active private sector. To be able to compete, companies need to invest in research and development to produce new goods and services. Furthermore, since many of the countries that have high levels of RQ are also democratic countries, it follows that also the public sector and the non-profit sector, as well as the education sector, are engaged in research and development, to offer new services and products to citizens. This demand for research and development by the private, public and non-profit sectors generates a growth in R&D expenditure as a percentage of GDP, which leads countries leading in RQ to also be world leaders in science and technology.

  • Annualized Average Growth in per capita real survey mean consumption or income, total population: is a variable that considers the average growth rate of consumption of the population. The rate is considered per capita in relation to the real income of the population. The data is acquired through sample surveys on households relating to income distribution over five-year periods. Average consumption or per capita income is measured on the basis of 2017 PPP purchasing power parity. There is a positive relationship between countries that have high levels of RQ and countries that have high levels of consumption based on per capita income growth rates. This condition derives from the fact that the countries that have high levels of RQ are also countries that have high levels of per capita income, where the labour force is larger, and household consumption tends to grow either in connection with GDP growth either in application of redistributive policies. Therefore, the promotion of a legislation favourable to the private sector increases the possibility of households to consume and raises the standard of living of the population.

  • Forest Area as percentage of land area: is a variable that considers the forest area without considering the trees that are planted for agricultural production, the trees in parks and urban gardens. There is a positive relationship between the RQ value and the value of forest areas not dedicated to agriculture. This structure is mainly due to the presence among the top countries in terms of RQ of some countries such as Finland, which has an amount of forest areas equal to 73.72%, Sweden with a corresponding value of 68.69%. But, we also have to consider that the average coefficient of the regression is equal to 0,079903 i.e. a value close to zero. This means that even if there is positive relationship between RQ and the degree of forest area as percentage of land, it is a value that is closed to zero.

  • Energy intensity level of primary energy: is a variable that considers the relationship between energy supply and gross domestic product at purchasing power parity. It is a measure that calculates the relationship between the energy consumed and the gross domestic product. If the ratio grows, it means that an increasing value of energy is required to produce a certain amount of output. Conversely, if the value decreases, it means that fewer energy resources can be used to produce a certain amount of energy. Countries that have an increasing level of RQ also have an increasing level of energy use per amount of value added produced. This positive relationship is because countries that have high levels of RQ are also countries that have highly evolved industrial systems that require the use of large energy sources. Furthermore, they are also countries in which the service sector plays a significant role that is generally located in densely populated areas with a great consumption of energy.

  • Adjusted savings natural resources depletion: is a variable that calculates the value of the depletion of natural resources, i.e. forests, mineral resources and energy. There is a positive relationship between countries that have high levels of RQ and countries that have high levels of natural resource depletion. This relationship is because the countries that have high levels of RQ are also the countries that exploit their territory more intensely from the point of view of natural resources. This trend obviously highlights the inefficiency of the economic policies put in place to combat climate change, at present. However, it is highly probable that the positive effects of environmental economic policies will occur over a long period of time without considering highly improbable phenomena that could reduce the probability of a real energy transition such as, for example, in the case of conflict, famine or decreases in the international trading. However, this report highlights how difficult it is at present to refer to the energy transition that has taken place in upper-middle income countries.

  • People using safely managed drinking services as percentage of population: is a variable that considers the percentage of people who drink potable water from improved sources. Improved sources include piped water, boreholes, protected wells, protected springs, packaged water. There is a positive relationship between the percentage of the population drinking potable water from improved sources and RQ. This relationship may be because in countries with a high RQ, there are also more evolved markets, and companies, both public and private, operating in the extraction and distribution of water. This condition makes it possible to increase the percentage of the population that has access to water. However, from a strictly metric point of view, it is necessary to consider that the average of the value estimated with the econometric models for the variable analysed is equal to 0.015 units. This is a small value, close to zero. It therefore follows that the relationship is weakly positive on average and that it could easily change in the future in the presence of even marginal modifications in the markets for water extraction, processing and distribution.

  • Mortality rate under-5: is an indicator that considers the probability in 1,000 that a new-born will die before reaching the age of five. There is a positive relationship between this indicator and the RQ value. However, it is necessary to consider that the average value deriving from the application of the econometric models tested for the variable of interest is equal to 0.001477. This is evidently a positive value, however close to zero. Therefore, it might be correct to refer to a weak positive relationship between the two variables or to a potential neutrality. In fact, since the countries that have a high level of RQ are also the countries that have the highest levels of health services, it follows that the presence of a positive relationship between the RQ and infant mortality under five has low credibility. However, the metric analysis in this case suggests that the relationship between the two variable is close to zero.

  • Fertility Rate Total: is a rate that considers the number of children that would be born to a woman if she lived to the end of her childbearing years and gave birth according to average fertility rates calculated at country level. There is a positive relationship between the value of the total fertility rate and the RQ value at the country level. However, also in this case, as in the previous one, the average value deriving from the analysis of the various econometric models proposed is low and basically equal to zero, i.e.: 0.001201. In fact, the countries that have a high RQ, i.e. the Western countries, also have a low birth rate, with a demographic balance in the balance in many countries. Furthermore, very often in countries with a high RQ it is immigrants who keep the birth rate high. However, in the proposed variable it is not possible to distinguish between the birth rate of immigrants and the birth rate of natives. In this sense, therefore, it should be emphasized that this relationship is weakly positive and not perfectly verified for many countries with a high RQ in the western world.

  • Nitrous Oxide Emissions: Nitrous oxide emissions are emissions from the combustion of agricultural biomass, industrial activities and livestock management. There is a positive relationship between the nitrous oxide value and RQ. This relationship is because countries with a high RQ are also countries in which a series of activities are widely spread, such as, for example, breeding and the combustion of agricultural biomass, as well as industrial emissions. However, the mean value of the econometric relationship estimated through a set of models is very small and equal to an amount of 0.001201. That is, although this relationship is significant in terms of p-value, it turns out to be substantially very close to zero from a quantitative point of view.

The econometric results also show that the level of Regulatory Quality is negatively associate to the following variables:

  • Energy Use: is a variable that takes into consideration the value of energy consumption with respect to the development of production, household consumption and transport systems. However, energy consumption does not depend only on demand, as it is also sensitive to the price of energy and a series of climatic, geographical and economic factors. Energy consumption tends to be growing either in low middle income either high-income countries. The growth in energy consumption and the growth in energy prices has prompted many governments to consider energy economic policies as strategic with respect to industry and households welfare. Energy efficiency makes it possible to reduce emissions and improve energy security. There is a negative relationship between countries that have high RQ levels and countries that have a high level of energy use. This condition is because countries that have high levels of RQ also have more efficient energy markets in terms of both production and distribution and also have available technologies that can allow the application of energy savings. Furthermore, countries that have a high RQ, also thanks to the development of the private sector, offer their customers, be they households or businesses, a set of alternative options relating to the possibility of sourcing energy at affordable prices.

  • Strength of legal rights index: measures the degree to which collateral and bankruptcy laws protect the rights of borrowers and creditors and thereby facilitate lending. The index ranges from zero to 12, with higher scores indicating these laws are better designed to expand access to credit. There is a negative relationship between the RQ value and the value of the legal rights index. This indication indicates that in countries with a high level of RQ there are no excessively favourable laws towards creditors. This condition may seem paradoxical. However, it is the improvement in the condition of the debtors that has allowed the development of the credit system. A legislation more favourable to debtors can promote deeper culture of risk in business and economic organizations. Countries that have too strict legislation on debtors can inhibit the ability of economic operators to invest in business activity. In this case, the insolvent debtors could look with concern at the consequences of a failure to repay the loan with a reduction in the investment in risk capital and in the business activity. The market society is based not only on easier access to credit but also on the tolerance of the failures of entrepreneurs and companies.

  • Renewable Electricity Output: is the share of electricity generated by renewable energy plants in the total electricity generated by all types of plants. There is a negative relationship between the RQ value and the value of renewable electricity output. This relationship indicates that countries that have high RQ levels have low levels of renewable energy output. In fact, the percentage of renewable energy output tends to be high for countries with low per capita income, especially African countries, which also have a low level of institutional quality. There are however exceptions. In fact, Norway, Switzerland, Austria and Iceland have high levels of both RQ and of renewable electricity outputs thanks to the use of hydroelectric and geothermal energy. The other high-middle-income countries that also have high levels of RQ instead tend to have a low value of renewable electricity output and consume an energy mix characterized by high levels of non-renewable energy such as coal and oil. However, it is probable that with the change in environmental policies at a global level and the introduction of new technologies for the production of renewables, there will be a shift in the relationship between RQ and renewables.

  • Renewable energy consumption: is the share of renewable energy in the total final energy consumption. It should be considered that there is a negative relationship between the consumption of renewable energy and the global RQ value. This condition is due, as in the case of the previous point, to the fact that countries with high per capita incomes, which are also countries with high RQ levels, tend to consume low values of renewable energy compared to countries low per capita income. Economic growth is an energy-intensive process, which requires the use and consumption of large quantities of energy. Since energy efficiency and the continuity of renewables tends to be variable, then countries with high per capita incomes use energy mixes in which the non-renewable energy component is significant. It is probable that the change of technologies that are available for the production of renewable energy together with the investment in research and development for sustainable energies could lead in the future to a change in the relationship between RQ and consumption of renewable energy worldwide.

  • Voice and Accountability: captures perceptions of the extent to which a country's citizens are able to participate in the selection of their government, as well as freedom of expression, freedom of association and freedom of the media. There is an inverse relationship between the Voice and Accountability value and the RQ value. This relationship may appear counterfactual considering that almost all countries that have high levels of RQ are also democratic countries and therefore should allow a high level of Voice and Accountability. There are many countries which, although having high levels of RQ, have low levels in terms of Voice and Accountability with for example Singapore with respective values of 2.23 and − 0.13, United States with 0.145 and 0.90, Israel with 0.68 and 1.20, United Arab Emirates with − 1.19 and 1.0, and Qatar with − 1.17 and 0.86. It therefore follows that the relationship between RQ and democratic participation can be paradoxical, and even have negative values, such as those indicated in the econometric analysis considered.

  • Rule of Law: captures perceptions of the extent to which officers trust and respect society's rules, and in particular the quality of contract enforcement, property rights, police and courts, as well as the likelihood of crime and violence. There is a negative relationship between the rule of law value and the RQ value. This is certainly a counterfactual result since generally the two elements should be closely connected. However, the value of the relationship turns out to be negative both by controlling for the Random Effects, for the Fixed Effects and for the Pooled OLS.

4 Rankings and clusterization with the k-means algorithm optimized with the elbow method

There is a great heterogeneity among countries for the level of RQ. The top ten countries in 2021 are: Singapore with a level of RQ equal to 2,2310 followed by Luxembourg with 1.9152, Finland with 1.89, Australia with a level of 1.83, Denmark with 1.80, New Zealand with 1.80, Netherlands with 1.75, Sweden with 1.75, Switzerland with 1.73, Norway with a level of 1.63. In the middle of the ranking there are the following countries i.e. Turkiye with a level of − 0.0819, Trinidad and Tobago with − 0.0854, Brazil with − 0.1108, Morocco − 0.1217, Vanuatu with − 0.1228, Samoa with a level of − 0.1668, Bosnia and Herzegovina with a level of − 0.1786, Ghana with a level of -0.2003, Paraguay with a level of − 0.2077, Mongolia with a level of − 0.2086, Mexico with a level of − 0.2307. In the final part of the ranking there are the following countries i.e. Iran with − 1.6223, Syrian Arab Republic with − 1.6289, Equatorial Guinea with − 1.7128, Somalia with − 1.8172, Libya with − 1,9512, South Sudan with − 1.9846, Yemen with − 2.0079, Turkmenistan with − 2.0188, Venezuela RB with a level of − 2.1957, Eritrea with − 2.2687, North Korea with -2.3274. Only 84 countries over 191 have a positive value of RQ. This means that the vast majority of countries i.e. the 53% of world countries have negative values of RQ i.e. miss an institutional and legal framework able to promote the development of the private sector. This result counterfactual since it contrast with the idea of diffusion of capitalism and market society as a unique institutional framework for the global economy. There more than 100 countries in the world economy that have a legislative order that is inefficient in promoting the private sector and property rights (Fig. 1).

Fig. 1
figure 1

Mean value of RQ for 191 countries in the period 2010–2021

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Considering the percentage change in the RQ value between 2010 and 2021 it is possible to verify the following order: Montenegro is in first place with a change equal to 6037% of the RQ value, followed by Cabo Verde with + 286.86%, United Arab Emirates with 218.27, Seychelles with 211.47%, Serbia with 179.39%, Indonesia with 178.29%, Dominican Republic with 176.81%, Nauru with 137.22%, Philippines with 135.52% and Kazakhstan with 131.75%. The mid-ranking countries in terms of percentage change in RQ between 2010 and 2021 are: Bangladesh with 1.39%, Netherlands with + 1.36%, Finland with + 1.33%, Liechtenstein with + 0.66%, United States with + 0.55%m and New Zealand with − 0.23%, Israel with − 0.48%, Andorra with − 1.94%, Denmark and Ireland with − 3.47%, Micronesia Fed Sts with − 4.24%. Closing the ranking are Uganda with − 136.86%, Brazil with − 144.93%, Nicaragua with − 176.44%, El Salvador with − 201.97%, Yemen Rep with − 226.08%, Kenya with − 226.56%, Egypt with − 243.22%, Mexico with − 247.58%, Tunisia with − 345.03%, Ghana with − 473.97%, Lebanon with − 4,056.57%. We can note that among the countries that have seen the value of RQ grow significantly there are important economies such as the United Arab Emirates, Indonesia and Kazakhstan. Especially relevant is the case of Indonesia which is now one of the largest economies in the world in terms of absolute GDP. Also relevant is the case of Kazakhstan which will probably become an increasingly important country due to its supply of energy-related raw materials. Among the countries that have lost ranks in terms of RQ there are significant economies such as Brazil, Egypt and Mexico. Particularly relevant is the case of Brazil, a country which is part of the group Brazil, Russia, India, China, South Africa-BRICS and which has fairly high GDP growth rates. These data could suggest that not alles link GDP growth to the growth of the RQ value and that there are individual trajectories for some countries (Table 3).

Table 3 Top ten, mid-table and last places by RQ value between 2010 and 2021
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However. Western countries remain leaders in terms of RQ even in the presence of significant growth in RQ in many Asian countries (Fig. 2).

Fig. 2
figure 2

The map of RQ at world level in the 2021

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Considering the average value for 191 countries in the period 2010–2021 it is possible to verify a worsening of the RQ level in the period 2018–2021. The reduction of the level of RQ started before Covid-19 in 2018 and continued in the period 2020–2021. The level of RQ in 2021 during the Covid-19 pandemic reached a low level close to the absolute minimum of the entire period that was − 0.093 in 2015. This result is coherent with the choices of many governments to improve the public spending and increase the public control on the private market.

Furthermore, an unsupervised machine learning technique was applied to verify the presence of clusters among the data, i.e. k-Means algorithms optimized with the Elbow method (Fig. 3).

Fig. 3
figure 3

Optimal number of clusters using the Elbow Method. The number of k is equal to 5

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The results show the presence of five clusters as follows:

  • Cluster 1: Haiti, Yemen Rep., Myanmar, Comoros, Guinea-Bissau, Afghanistan, Algeria, Central African Republic, Uzbekistan, Congo rep., South Sudan, Iran, Syrian Arab Republic, Congo Dem. Rep., North Korea, Cuba, Sudan, Libya, Venezuela, Somalia, Zimbabwe, Eritrea, Turkmenistan, Equatorial Guinea;

  • Cluster 2: Italy, Uruguay, Slovenia, Hungary, Botswana, Qatar, Portugal, Malaysia, Bahrain, Bulgaria, Costa Rica, Georgia, St. Kittis and Nevis, Slovak Republic, Romania, United Arab Emirates, Brunei Darussalam, Span, Poland, Barbados, Antigua and Barbuda, Panama, Peru, Mauritius, Oman, Greece, South Korea, Cyprus, Latvia, Croatia, North Macedonia, Lithuania;

  • Cluster 3: Nepal, Mauritania, Togo, Lao DPR, Malawi, Cameroon, Sierra Leone, Sao Tome and Principe, Nigeria, Bangladesh, Madagascar, Pakistan, Niger, Djibouti, Timor-Leste, Guinea, Gabon, Angola, Burundi, Ecuador, Tuvalu, Suriname, Micronesia Fed Sts., Bhutan, Liberia, Solomon Islands, Mozambique, Mali, Guyana, Papua New Guinea, Ethiopia, Argentina, Egypt Arab Rep., Kiribati, Cote d’Ivoire, Nauru, Zambia, Belarus, Tajikistan, Lesotho, Gambia The, Vietnam, Cambodia, Tanzania, Palau, Vanuatu, Belize, Benin, Nicaragua, Tonga, Marshall Islands, Iraq, Chad, Maldives, Ukraine, Russian Federation.

  • Cluster 4: Dominican Republic, Moldova, Seychelles, Bosnia and Herzegovina, Rwanda, Ghana, Kuwait, Cabo Verde, Brazil, Serbia, Saudi Arabia, Philippines, Morocco, Namibia, Thailand, Sri Lanka, Indonesia, Grenada, Jamaica, Kazakhstan, El Salvador, Mongolia, Senegal, Samoa, Jordan, Paraguay, Trinidad and Tobago, Guatemala, China, Mexico, Uganda, South Africa, Dominica, Montenegro, the Bahamas, Fiji, Albania, Turkiye, Armenia, Kenya, Armenia, Kenya, Tunisia, Lebanon, Burkina Faso, Eswatini, India, Azerbaijan, Kyrgyz Republic, Honduras, Colombia, St. Vincent and the Grenadines, St. Lucia;

  • Cluster 5: Canada, Switzerland, Germany, Norway, United Kingdom, Luxembourg, Australia, Ireland, Sweden, Finland, Netherlands, Denmark, Estonia, New Zealand, Liechtenstein, Austria, Singapore, United States, Chile, Belgium, Israel, Iceland, Malta, Japan, Andorra, France, Czechia.

Essentially RQ coincides with the western civilization in the Anglo-Saxon, Scandinavian, European and Japanese-Korean version (Fig. 4).

Fig. 4
figure 4

Clusterization with the k-Means algorithm optimized with the Elbow Method with the indication of the Silhouette Coefficient

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The clusters can be sorted based on the median value. Taking into consideration the value of the median of the clusters it is possible to identify the following ordering of the clusters: C5 = 1.5591 > C2 = 0.7225 > C4 = − 0.0596 > C3 = − 0.7619 > C1 = − 1.4779. In the C5 there are countries that have a highest level of per capita income. The vast majority of countries in C5 are European countries and in general western countries. In C5, there is also a subset of countries with high per capita income such as Andorra, Singapore, Liechtenstein, Luxembourg, Switzerland, Ireland that have developed a specifically legal order that is favourable to the development of the private sector. RQ can be considered as the output of a set of elements that capture the ability of a country to promote either political either economic freedom i.e. a mix of market society and democracy. In this sense, a comparison between RQ and the Index of Economic Freedom-IEF is proposedThe index of Economic Freedom is realized by the Heritage Foundation. An index varies in a range between 0 and 100. The IEF considers at country level the following macro-variables i.e. “Rule of Law”, “Government Size”, “Regulatory Efficiency” and “Market Openness”. It is possible to indicate the expression of the Index of Economic Freedom in the following form:

$$Index\,Of\,Economic\,Freedom=f\left(Rule\,Of\,Law\,Government\,Size\,Regulatory\,Efficiency\,Market\,Openness\right)$$

Due to this characteristic, the IEF is able to represent either democratic issues either the presence of a pro-market society at country level. The analysis conducted shows the existence of a positive relationship between RQ and IEF for countries in C5. Specifically, it is possible to verify that the best countries for RQ also have the highest IEF valuesFor example, Singapore as a RQ of 2.23 and an IEF of 89.70, the same value for New Zealand are 1.80 and 83.90, Australia 1.83 and 82.40, Switzerland with 1.73 and 81.90, Ireland with 1.56 and 81.40 and United Kingdom with 1.45 and 78.40. The positive relationship between RQ and IEF shows that the ability of countries to orient the institutional framework towards the development of the private sectors is not independent from the level of democracy and the degree of economic freedom. Economic freedom is a synthesis between democracy and the market society oriented to entrepreneurship, innovation and property rights. Furthermore, economic freedoms and rights have a special role in promoting either democracy either the production of value added in a market society creating the conditions for the empowerment of individuals, groups and communities (Fig. 5).

Fig. 5
figure 5

The positive relationship between RQ and IEF for countries in C5

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By analyzing the relationship between RQ and IEF for the year 2021 for countries in C2, it is possible to find that there is a positive connection.The increase in the level of economic freedom is positively associated to the improvement of RQ at national level for the countries in C2. Countries in C2 are in large part European Countries with a middle level of per capita income. Furthermore, there are also other countries that are heterogeneous in the sense of geography among which there is a sub-group of central and southern American countries such as: Uruguay, Peru, Panama and Costa Rica. In addition, other countries have not any geographical connection i.e. Botswana, Oman and South Korea. In these countries, the increase in the level of economic freedom is positively associated to an increase in the RQ i.e. an improvement in the ability to generate a political and institutional framework that is favourable to the private sector and the empowerment of the market society. It should be considered that the C2 countries are essentially democratic countries. This means that for countries that have a middle income per capita, and that are already functioning democracies, there is a chance to improve the level of RQ and economic freedom in the same set of policies. But, it is largely possible that the presence of a culture that is essentially oriented towards democracy can boost the ability to generate institutional reforms that can deepen economic freedoms (Fig. 6).

Fig. 6
figure 6

Relationship between RQ and IEF in C2

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Similar results hold in the relationship between RQ and IEF for the other clusters as showed in the appendix. This means that essentially countries that develop deeper economic freedom also tend to develop an orientation toward the market society generating a positive effect in promoting property rights.

5 Machine learning and predictions for the prediction of the future value of RQ

In the following part, a comparison between eight different machine learning algorithms for predicting the future value of RQ is proposed. The 70% of the data have been used as learning rate for the algorithms, while the remaining 30% are used for the prediction. The performance of algorithms is evaluated through the maximization of R-squared and the minimization of Mean Squared Error, Root Mean Squared Error, mean Absolute Error. The results show the following order of algorithms in terms of performance:

  • Polynomial Regression with a payoff equal to 5;

  • Linear Regression with a payoff equal to 7;

  • Random Forest Regression with a payoff equal to 12;

  • Simple Regression Tree with a payoff equal to 16;

  • Gradient Boosted Tree with a payoff equal to 20;

  • ANN-Artificial Neural Network with a payoff equal to 29;

  • Tree Ensemble Regression with a payoff equal to 29;

  • PNN-Probabilistic Neural Network with a payoff equal to 30.

Polynomial Regression is the best predictive algorithm based on the minimization of the statistical errors and the maximization of R-Squared.

Through the application of Polynomial Regression, it is possible to find that 17 countries are “winners” in the sense that they experience an increase in the expected value of RQ, while, on the contrary, there are 37 countries that are “losers”, i.e. countries that have a negative predictive value in terms of RQ. Among the winners, the best ten performers are: Iran with + 53.15, Myanmar + 41.58%, Kyrgyz Republic with 17.11%, Malta with 17.02%, Papua New Guinea with 13.92%, Italy with 11.08%, Ethiopia with + 10.15%, Guinea Bissau with 8.17%, Bulgaria with 5.97%, Tunisia with 5.69%. Among the losers, the top performers are: Bahrain with − 17.00%, Costa Rica with 13.42%, India − 10.51%, Azerbaijan -9.63%, Fiji with − 8.78%, Vanuatu with − 8.72%, Bangladesh − 8.02%, Georgia − 7.36%, Singapore − 7.30%, Luxembourg − 7.02%. Considering the average value of the countries for which the prediction was obtained, it is possible to calculate that the RQ level should reduce by − 1.29%. (Fig. 7).

Fig. 7
figure 7

Structures of Network Analysis with the Euclidean distance

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6 Network analysis with predicted values in the application of the Euclidean distance

Below, Euclidean distance is applied in a network analysis framework to find the presence of connection between countries with the estimated values generated in the application of polynomial regression. Network analysis does not determine causal relationships between RQ values in the analyzed countries. However, it implies the presence of similar characteristics in the historical dataset augmented with the predicted data. Our analysis led us to the identification of a set of six complex network structures and a simplified network structure (Fig. 7).

There is a network structure composed as follows:

  • Bahrain has a connection with Costa Rica in the amount of 0.35 units;

  • Costa Rica has a connection with Bahrain with an amount of 0.35 units, with Bulgaria with an amount of 0.3 units, and with Antigua and Barbuda with an amount of 0.35 units;

  • Bulgaria has a connection with Costa Rica amounting to 0.3 units;

  • Antigua and Barbuda have a connection with Costa Rica in the amount of 0.35 units and with Croatia in the amount of 0.38 units;

  • Croatia has a connection with Antigua and Barbuda in the amount of 0.38 units, with North Macedonia in the amount of 0.34 units and with Vincent and the Grenadines in the amount of 0.31 units;

  • North Macedonia has a connection with Croatia amounting to 0.34 units and with Vincent and the Grenadines amounting to 0.31 units;

  • St. Vincent and the Grenadines have a connection with North Macedonia for the amount of 0.3 units, with Croatia for the amount of 0.31 units and with Armenia for the amount of 0.24 units;

  • Armenia has a connection with St. Vincent and the Grenadines for the amount of 0.24 units and with Jamaica for the amount of 0.32 units;

  • Jamaica has a connection with Armenia amounting to 0.32 units and with Saudi Arabia amounting to 0.32 units.

There is a complex network structure between the following countries namely:

  • Estonia has a connection with Ireland in the amount of 0.29 units and with Germany in the amount of 0.3 units;

  • Ireland has a connection with Estonia in the amount of 0.29 units and with Germany in the amount of 0.23 units;

  • Germany has a connection with Estonia for 0.3 units and with Ireland for 0.23 units.

There is a complex network structure between the following countries namely:

  • Sao Tome and Principe has a connection with Algeria for an amount of 0.15 units, with Cameroon for an amount of 0.23 units with Bangladesh for an amount of 0.2 units;

  • Algeria has a connection with Sao Tome and Principe for an amount of 0.15 units, with Cameroon for an amount of 0.31 units and with Bangladesh for an amount of 0.31 units;

  • Cameroon has a connection with Sao Tome and Principe for a value of 0.23 units, with Algeria for an amount of 0.31 units and with Bangladesh for an amount of 0.14 units;

  • Bangladesh has a connection with Sao Tome and Principe for the amount of 0.2 units, with Algeria for the amount of 0.31 units and with Cameroon for the amount of 0.14 units and with Ethiopia for an amount of 0.3;

  • Ethiopia have a connection with Bangladesh equal to an amount of 0.3 units, with Iraq an amount of 0.36 units, with Chad an amount of 0.37 units;

  • Chad has a connection with Ethiopia in the amount of 0.37 units, with Iraq in the amount of 0.25 and with Guinea Bissau in the amount of 0.3 units;

  • Guinea Bissau has a connection with Chad in the amount of 0.3 units and with Iraq in the amount of 0.33 units;

  • Iraq has a connection with Guinea Bissau amounting to 0.33 units, with Chad amounting to 0.25 units and with Ethiopia amounting to 0.36 units.

There is a complex network structure between the following countries namely:

  • Senegal has a connection with Paraguay in the amount of 0.23 units;

  • Paraguay has a connection with Senegal in the amount of 0.23 units, with Azerbaijan in the amount of 0.36 units, and with India in the amount of 0.35 units;

  • Azerbaijan has a connection with Paraguay in the amount of 0.36 units and with India in the amount of 0.25 units;

  • India has a connection with Paraguay amounting to 0.35 units and with Azerbaijan amounting to 0.25 units.

There is a complex network structure made up of the following countries:

  • Turkmenistan has a connection with Somalia in the amount of 0.36 units, and with Eritrea in the amount of 0.32 units;

  • Eritrea has a connection with Turkmenistan in the amount of 0.32 units and with Somalia in the amount of 0.38 units;

  • Somalia has a connection with Eritrea amounting to 0.38 units and with Turkmenistan amounting to 0.36 units.

There is a complex network structure composed as follows:

  • The Gambia has a connection with Papua New Guinea equal to an amount of 0.32 units and with Mali for an amount of 0.28 units;

  • Papua New Guinea has a connection with Gambia for the amount of 0.32 units with Mali for the amount of 0.29 units and with the Maldives for the amount of 0.37 units;

  • Maldives has a connection with Papua New Guinea equal to 0.37 units, with Mali with an amount of 0.34 units with Belize equal to 0.19 units, with Kyrgyz Republic with an amount of 0.34, with Honduras for an amount of 0.29 units and with Tunisia for an amount of 0.34 units;

  • Tunisia has a connection with Maldives amounting to 0.34 units with Kyrgyz Republic amounting to 0.27 units and with Honduras amounting to 0.25 units;

  • Honduras has a connection with Tunisia for an amount of 0.25 units, with the Maldives for an amount of 0.29 units, with Belize for an amount of 0.34 units, and with Kyrgyz Republic for an amount by 0.24 units;

  • Kyrgyz Republic has a connection with Tunisia for the amount of 0.27 units, with Honduras for the amount of 0.24 units, with Belize for the amount of 0.37 units and with the Maldives for the amount of 0.26 units;

  • Belize has a connection Maldives amounting to 0.19 units with Honduras amounting to 0.34 units, Kyrgyz Republic having 0.37 units to Mali amounting to 0.3 unit;

  • Mali has connections with Gambia amounting to 0.38 units, with Papua New Guinea amounting to 0.29 units, with Maldives amounting to 0.34 units and with Belize amounting to by 0.3 units.

There is also a simplified network structure as indicated below, namely:

  • Georgia and Portugal have a connection amounting to 0.34 units.

Applying a network analysis shows the cross-country propagation effects of increasing RQ in a country. For example, considering one of the most connected countries, namely the Maldives, it is possible to find that increasing or decreasing RQ has positive or negative effects on Papua New Guinea, Mali, Belize, Kyrgyz Republic, Honduras and Tunisia. Once again it is necessary to underline the fact that causal relationships do not exist but simply identify a series of connections that represent some similarities in the data of the countries analyzed.

7 Conclusions

In the article, an RQ analysis was conducted against a set of variables from the World Bank ESG dataset. The results show that the countries that have high levels of RQ are also countries that suffer for environmental issues with the growth of GHG Emissions, the increase of drought and temperatures. Furthermore, the fact of developing RQ does not sufficiently help countries in the transition to the use of renewable energy, despite the privatization of energy markets, and the development of technologies for energy sustainability. Finally, contrary to current opinion, RQ is negatively associated both with the exercise of civil and political rights and also with the rule of law. A complex picture therefore emerges. Certainly, the development of the market and the private sector is a precious ally for the implementation of technologies that can guide the economy towards environmental sustainability. In addition, the private sector offers many jobs that help workers and families to access better life opportunities by overcoming poverty and social inequality. However, evidently the development of RQ is not sufficient to guarantee the application of ESG models. Furthermore, the private sector has been hit, worldwide, by a set of adverse factors of a macro-economic nature, which have reduced the productivity of companies, disrupted supply chains and cracked trade relations among countries. While on the one hand the growth of companies and the market would be desirable from an ESG perspective, on the other hand macro-economic fragility is causing investment to retreat and could delay the processes of energy transition, social inclusion and good governance.

Originality. Our article is original as it analyzes the relationship between RQ and environmental, social and governance variables within the ESG model. Originality is also given by the set of analytical techniques used. In fact, alongside the econometric analyses, further metric insights were also carried out, i.e. clustering, prediction with machine learning algorithms and network analysis, to verify the presence of groups among the analyzed countries and estimate future RQ trends. The empirical and data driven approach increases the originality of the article which offers new elements on the general RQ scenarios.

Limitations. The limitations of the article refer to the difficulty of taking into consideration cultural, legal, anthropological, social and institutional elements that can have a significant impact in determining RQ levels. Furthermore, sufficient checks were not carried out to verify the presence of opposing blocs in terms of RQ that could somehow predict international frictions between countries.

Future research. In the future it will be necessary to continue analyzing the variables relating to the governance of countries in relation to ESG models, aiming to highlight the counterfactual elements suggested by the data, through the use of artificial intelligence algorithms and econometric models.

The findings of the article are relevant in the field of economics and international economics.