**1. Introduction**

In recent years, hydrogen production and fuel cell technologies have attracted the attention of the authorities in many countries. Moreover, the number of research studies related to these technologies increases significantly every year. Such technologies are perceived as breakthrough solutions with the potential to become clean and sustainable energy carriers [1]. Hence, many countries include the possibility of supporting the development of hydrogen and fuel cell vehicle production (along with the necessary infrastructure) in their energy policy scenarios for the coming years. These policies are connected to the national net-zero emissions target declarations in European [2–7] and Asian [8–10] countries, as well as the USA [11] and Australia [12], among others. Hydrogen is predicted to play a significant role in the energy transformation of global economies [13].

The demand for hydrogen is mainly linked to oil refining and chemical industries [14,15]. Despite the limited consumption of hydrogen in other sectors of the economy, it has significant potential in the power industry through its use in fuel cells. Currently, most hydrogen applications are focused on generator cooling and hydrogen burning in boilers or CHP units onsite. In transport, hydrogen can be used as a fuel, both directly (fuel cells, internal combustion engines) or indirectly (complex synthetic fuels) [16].

Various technologies are involved in hydrogen production [17,18]. Hydrogen can be produced by electrolysis using nuclear or renewable electricity (green hydrogen). The proportion of hydrogen produced from renewable energy is still insignificant, mainly due to cost. Hydrogen can also be produced using fossil fuels, e.g., hard or lignite coal and natural gas, with CO2 emissions reduced via carbon capture storage (blue hydrogen). Fossil fuels are still the main source of fuel for hydrogen production (natural gas, approximately 75%; coal, approximately 23%) [18]. Hydrogen production is also possible without using the CCS method of Steam Methane Reforming (SMR) or the gasification method (grey or

**Citation:** Cader, J.; Koneczna, R.; Olczak, P. The Impact of Economic, Energy, and Environmental Factors on the Development of the Hydrogen Economy. *Energies* **2021**, *14*, 4811. https://doi.org/10.3390/en14164811

Academic Editor: Bahman Shabani

Received: 8 July 2021 Accepted: 4 August 2021 Published: 7 August 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/).

brown hydrogen). The pyrolysis process of methane is an alternative production method (turquoise hydrogen).

The development of hydrogen energy is currently related to the search for ways to implement economic production of green hydrogen by reducing the cost of large-scale production [1,19]. Moreover, the implementation of hydrogen technology is particularly important in transport since a continuous increase in road traffic is expected [20]. Transport is predicted to be the main target for the application of hydrogen energy in the near future [21].

The implementation of new hydrogen energy technologies depends, inter alia, on the state of the economy of individual countries and the long-term goals and scenarios included in their national strategies, policies, research and development (R&D) programs, and roadmaps [14,22]. The processes of decarbonization of the economy and energy transformation are also associated with many socio-economic, environmental, and legal factors [23,24]. Most of the studies of the hydrogen economy involve prognostic analyses. Such analyses consider the production and demand for hydrogen together with the development of fuel cell vehicles and the accompanying infrastructure.

Current policies for a hydrogen economy based on a Romanian example were described by Iordache et al. [25]. They referred to energy (energy dependency, RES, net import of electricity, combined heat and power electricity production), transport (road density, roads fuel consumption, motor vehicles), and environmental indicators (CO2 emissions). Xu et al. [26] studied the influence of factors such as CO2 emissions, per capita income, the scale of the labor input, the added value in the industry, and European governmental mechanisms for the production of renewable energy based on hydrogen. National economic variables have been found to have a positive impact on hydrogen-based renewable energy. The number and type of patents in selected countries were used as tools to map the development of the hydrogen economy by Sinigaglia et al. [27]. In terms of technological progress, Japan and the United States were found to be the most advanced. The level of application of hydrogen technologies in selected economies for 2008 was analyzed by Leben and Hoˇcevar (2008) [28]. They used correlations of national development indicators (gross domestic product, public expenditure on education, R&D expenditure, number of researchers, science and technology doctorates, general patents, greenhouse gas emissions, total final energy consumption) together with a group of hydrogen indicators (number of hydrogen refueling stations, fuel cell vehicles, and hydrogen production). The study supported the hypothesis that the implementation of hydrogen technologies was dependent on selected national development indicators.

In addition, the analysis of environmental (CO2 emissions) and economic (GDP, oil prices) factors in relation to renewable energy sources was applied by Sadorsky [29], showing a significant impact of emissions and GDP on the consumption of renewable energy. Similar conclusions were reported by Wang et al. [30], describing the significant impact of GDP on RES consumption. Marques and Fuinhas [31] showed that market dependencies such as fossil fuel prices and incomes were not significant for the development of RES at the turn of the 20th and 21st centuries. Mendonça et al. [32] demonstrated the positive impact of GDP and population on CO2 emissions and renewable energy production as a way to reduce emissions.

This research attempts to correlate the following factors:


Using Spearman's correlation and a linear regression approach, the relationship between indicators was examined in this research. These methods were previously used in

various studies related to the analysis of environmental, economic, and energy factors in the areas of renewable energy. Directly in the field of the hydrogen economy, Spearman's method for national development and hydrogen was used by Leben and Hoˇcevar [28]. Spearman's rank correlation was also used by Durmu¸so ˘glu et al. [33] to visualize the factors that influence environmental performance. The correlations were sought for the variables of GDP, CO2 emissions, and renewable energy consumption as well as for environmental, energy, and economic indexes. Spearman's correlation was also used to search for indicators covering the economy, society, and the environment to present the level of sustainable development [34]. The linear regression approach was applied by Asumadu-Sarkodie and Owusu [35], showing a positive correlation between CO2 emissions, energy use, GDP, and population. Menz and Vachon [36] discussed the contribution of various policies and systems in US states to the development of wind energy. For this purpose, they used linear regression equations.

In this article the comparison was made for the following nine countries: China, the United States, Japan, the Republic of Korea, the Netherlands, France, the United Kingdom, Germany, Australia. These countries were selected because of their commitment to implementation of hydrogen strategies and overall progress towards a hydrogen economy (see Section 1.1). Time-series data from 2008 to 2018 were analyzed.

Multiple factors, such as socio-economic, energy, and environmental ones, strongly influence the development of the countries with zero-emission policies. Because of that, there is a need to distinguish which specific indicators affect the development of the hydrogen economy in order to create better and more effective strategies in the coming years. The presented methodology, as well as multidimensional factors, will confirm the hypothesis:

*"There is a correlation between selected economic, energy, and environmental indicators and the development of the hydrogen economy in countries involved in the implementation of hydrogen technologies".*

This study adds value to the extant literature in two novel ways. The first is the analysis of the possibilities for the development of hydrogen technologies and modeling interdependencies between chosen indicators. This is considered by monitoring the number of subsidies and the number of patents dedicated to these solutions, as well as observations of the hydrogen market in the country (through the volume of hydrogen production and consumption) concerning a selected group of indicators essential to strategic policy creation. Secondly, the study improves the global debate on the steps taken so far to evolve the low-carbon economy and the energy transition associated with the vision of the future of hydrogen.

#### *1.1. Hydrogen Strategy in Chosen Countries*

Hydrogen is a crucial factor in most strategies employed by 75 countries to achieve net-zero greenhouse gas emissions. By the beginning of 2021, over 30 countries had created hydrogen roadmaps or strategies at a national level. An additional six are currently drafting their strategies. Among the countries analyzed, four have hydrogen strategies and the rest have hydrogen roadmaps (Figure 1). The main focus of these policies is transport and industry.

The United States is the world leader in stocks of FCEVs, with approximately one in three FCEVs on USA roads. The USA is closely followed by China, Japan, Korea [37], Germany, and France [38]. The situation in China and Korea is particularly dynamic, with new sales climbing from a few units in 2017 to almost 4400 in China and 4100 in Korea, in 2019. The global forecast is for 4.5 million FCEVs by 2030 [37].

**Figure 1.** The latest hydrogen-related government documents cited in this paper.

In 2019, there were 470 hydrogen refueling stations in the world. Compared to 2018, there was a significant increase in their number by over 20%. Most of these stations are located in Japan (113). Germany has 81, the United States has 64, and China has 61 [37]. The number of FCEVs is projected to continue to increase, e.g., in China to one million by 2030 [39], in Korea, to 800,000 by 2030 [8], in the Netherlands to 15,000 by 2030 [5], in France to 22,500 by 2028 [40], and in Japan to 800,000 by 2030 [9].

Much attention has also been given to buses, trains, inland and coastal navigation, car fleets, and airplanes. For example, the EU indicated that around 45,000 fuel cell trucks and buses could be put on the road by 2030. Fuel cell trains could also replace approximately 570 diesel trains by 2030 [41]. The French National Railway Company has already taken the first step in this direction by ordering 15 hydrogen trains [40]. Japan and China are also developing hydrogen railway technology [42].

Germany will allocate EUR 0.6 billion for the purchase of buses with an alternative drive system as part of the H2 Mobility program [43]. Japan plans to purchase 1200 hydrogen buses by 2030 [9]. Since air traffic will continue to run on liquid fuel, it makes sense to require suppliers to use electric jet fuel, the production of which uses green hydrogen. In the interest of an ambitious market ramp-up, a 2% minimum for 2030 is being discussed [2].

The priorities of hydrogen strategies also include the need to decarbonize construction, industry (e.g., steel, chemical), and the power system. Korea is already a leader in hydrogenbased micro-CHP plants (mCHP) in new buildings. It is predicted that by 2030, there will be 20,000 mCHP in buildings, consuming 150,000 tons of hydrogen per year. In addition, as much as 3.5 GW of power generated from hydrogen fuel cells will be installed [8]. Japan forecasts that there will be 5.3 million stationary fuel cells in households by 2030 [9].

In the EU, clusters can play a major role in helping countries in the decarbonizing industry. Their goal is to facilitate cooperation and help create an energy-saving industry, e.g., the Rotterdam cluster [3]. In the Netherlands, the chemical industry can play an important role in capturing and utilizing carbon dioxide with green hydrogen. In Germany, attention is focused on the steel industry. Planned investments will focus on alternative processes, i.e., hydrogen injection into blast furnaces and direct hydrogen reduction in dedicated installations. Such solutions are also promoted by Posco, the dominant steel producer in South Korea [44].

Another priority for hydrogen strategies is the power system. For example, Japan is promoting the installation of gas supply systems to store surplus electricity from renewable energy as part of the Fukushima demonstration project [9].

Certain international initiatives should also be mentioned. In Germany, the coalition committee's package for the future provides EUR 2.0 billion to intensify international cooperation in the field of hydrogen at all levels [2]. Globally, there are 228 hydrogen projects across the value chain which result from the assumed strategic goals [38]. Europe is the global leader in the number of proposed hydrogen projects, with Australia, Japan, and Korea. China and the USA are following as additional hubs [45]. Over half of the announced projects (55%) are located in Europe [38]. One of the most active EU member states in expanding hydrogen technologies is Germany [2].

If all projects are successful, the total investment will exceed USD 300 billion in hydrogen spending by 2030 [38]. Particular attention is given to R&D projects. Several countries are developing ambitious research programs as part of their national hydrogen strategy (e.g., Australia, South Korea, and several EU member states) [46]. In 2019, significant funding was allocated to these projects by Japan (USD 281.7 million), the USA (USD 120 million), and Germany (USD 50.7 million) according to an IEA estimation [47]. Germany has launched a research campaign called 'Hydrogen Technologies 2030'. Its key elements are technologies dedicated to the transport sector, steel and chemical industries, the green hydrogen production industry, technologies for export, and the creation of a new research network.

Patents are the result of many R&D projects in this field. In 2019, significant progress was made in the filing of patents for hydrogen technologies and fuel cells: China (1493), Japan (682), and Korea (444) [48]. These three countries account for over 55% of all global fuel cell patents and over 65% of all hydrogen-related patents. EU countries have only issued around 16% of all patents. Among the European countries analyzed, Germany filed the most patents (136 in 2019) [48].

Growing demand for hydrogen in various sectors will depend on innovative solutions to increase hydrogen production. In Europe, Germany is the largest producer of hydrogen with an estimated annual volume of over 2.4 billion m3 in 2019. The secondlargest producer is the Netherlands (2.1 billion m3) [37]. However, China ranks first in the world in the production of hydrogen (4.3 billion m3), which accounts for 18% of the total world production [49]. Second in the world is the USA (2.6 billion m3). These countries produce hydrogen from fossil fuels (natural gas, oil, coal), and to a much lesser extent, via electrolysis. Replacing them with renewable energy sources is a priority.

Australia, California, and the United Kingdom have great potential in the development of renewable energy. However, Germany aims to become the lead supplier of green hydrogen technology to the global market [40]. Geoscience Australia estimates that, based on the quality of its wind, solar, and water resources alone, about 11% (872,000 km2) may be highly suitable for hydrogen production [12]. However, the United Kingdom has one of the largest offshore wind farm markets in the world. The state of California in the USA has large resources of renewable energy (31.7% of the energy mix in 2019 [50], 50% in 2030 [51]). It should also be mentioned that Japan has built a hydrogen plant in Namie, Fukushima, to implement full-scale power-to-gas technology. The facility, called Fukushima Hydrogen Energy Research Field (FH2R), uses a 20 MW solar power plant on a 180,000 m<sup>2</sup> site along with grid energy to electrolyze water in a renewable 10 MW hydrogen production unit, the world's largest [52]. Australia is also planning a project on a similar scale as part of the ARENA program [42].

The development of hydrogen technologies contributes to the establishment of international partnerships by various countries, increasing the prospects of creating a hydrogen economy. The example of such cooperation is The International Partnership for Hydrogen and Fuel Cells in the Economy (IPHE). The intergovernmental organization was created to facilitate the transition to clean energy and mobility systems based on hydrogen technologies. Apart from the analyzed and described countries (China, the United States, Japan, Republic of Korea, the Netherlands, France, the United Kingdom, Germany, Australia), the members of this organization also include Chile, Italy, Austria, Brazil, Costa Rica, Iceland, Canada, India, and European Commission [53]. All member states are obliged to accelerate the development of hydrogen technologies, which directly increases the prospects for the development of the hydrogen economy in these countries. It is visible among others by dominating the global market in terms of the distribution of fuel cell vehicles and the number of hydrogen refueling stations [54].

The contribution of individual countries to the development of the hydrogen economy is also visible through the global collaboration The Hydrogen Valley Platform founded by the Fuel Cells and Hydrogen Joint [55]. The platform collects flagship hydrogen projects. Currently, 36 Hydrogen Valleys in 19 countries are described. In addition to the aforementioned countries, Denmark, French Guiana, Portugal, Romania, Slovakia, Spain, and Thailand stand out in terms of planned investments in hydrogen technology.

The foundations for the creation of hydrogen economies and societies in African countries are established thanks to the pancontinental association The Africa Hydrogen Partnership. Particular efforts in this direction are visible in Morocco (partnership with Germany to develop the first green hydrogen plant in Africa) and in the Republic of South Africa (expanding knowledge and innovation in hydrogen technology via the Hydrogen South Africa—HySA initiative) [56].

#### **2. Data and Methodology**

#### *2.1. Indicators*

The study correlates selected economic, energy, and environmental indicators along with a group of specific factors connected with the development of the hydrogen economy.

#### 2.1.1. Hydrogen Indicators (HyInd)

The group of hydrogen indicators consisted of hydrogen production volume (HPV, in billion m3), the number of patents (PAT, numbers of patents), and energy RD&D budget (RDD, in USD million) in the hydrogen production and fuel cells category. Additionally, data for hydrogen consumption were also compiled (HCV, in billion m3).

The hydrogen production and consumption data could be used to monitor trends in the hydrogen market at national levels. They could also be used to illustrate hydrogen use. The hydrogen volume indicator is the estimated amount of hydrogen produced in a particular market and refers to production in physical terms. The data come from the AI-powered statistical database for market analysis, IndexBox. They are shown after raw and mirror information is combined, and after performing IB AI algorithms to eliminate any anomalies and to complete missing data [57]. To a large extent, the data for hydrogen consumption overlap with production volumes due to the current use of hydrogen and the complexity of hydrogen storage and distribution [17]. Most hydrogen is produced and consumed on-site [58,59]. For this reason, only production data were used in the correlation analysis and modeling.

The process of developing new methods of production and application of hydrogen is associated with its potential funding. Government subsidies support research and development, and further technological changes relevant to the industry, energy, and transport sectors. The allocated subsidies reflect an assessment of the state's efforts to increase competitiveness in a given technology and are important in accelerating the implementation of hydrogen technology [60]. Collective data on RD&D budgets (for hydrogen and fuel cell technology in particular) were used. Collective data were used firstly because different countries use different methodologies to allocate subsidies and secondly because the data are incomplete for several years. These data are compiled by the International Energy Agency (IEA) and include central or federal government budgets and expenditures by state-owned companies. The database reflects the expenditure allocated to basic and applied research, experimental development programs, and energy-related and fundamental research programs in selected countries [45]. The statistics are available only for IEA member countries.

A good indicator of the level of innovation is the number of patents filed [61]. This enables the preferred directions of technological progress for a given country to be determined [62,63]. Patents are considered to be key in accelerating the development of the hydrogen economy [27]. The number of patents per country per year (from 2014 to 2018) in the hydrogen production and fuel cells category according to an established classification

system (the Cooperative Patent Classification—CPC) were obtained from the Fuel Cells and Hydrogen Observatory (FCHO) as extracted from the PatBase database [48].

2.1.2. Economic, Energy, and Environmental Indicators

The following significant national indicators were identified:


The population (POP, in mln) of the country was also taken into account.

Population and GDP are the variables used in the vast majority of the studies related to the environment and energy [26,28,32,64]. GDP is a synthetic and objective measure of economic performance, but it is essential to policy creation [65]. For comparison, data normalization in terms of gross domestic product and population was also used, eliminating the influence of the size of the countries concerned. GDP data were obtained from the Organization for Economic Cooperation and Development (OECD) database. Population statistics were compiled by the World Bank.

Carbon dioxide emissions contribute to climate change and environmental degradation. Currently, hydrogen is produced from fossil fuels, with significant CO2 emissions. Since the 1930s, the vision of a hydrogen economy has been associated with the reduction of emissions [66]. Reducing carbon emissions across the economy is essential to achieve carbon neutrality. The impact of greenhouse gases in the context of a hydrogen economy has been considered by various authors [25,26,28]. The reduction in CO2 emissions is an indicator of the level of decarbonization of a given country. This may contribute to supporting hydrogen technologies.

TFC data help to estimate the environmental impact of energy use. The indicator can be used to monitor and evaluate the success of key policies that have been designed to influence energy consumption and energy efficiency [67]. A significant relationship exists between energy consumption and economic growth in the long term [68,69]. In addition, economic growth drives energy consumption in the end-use sectors of transport and industry. The share of the industry and transport sectors in the total final energy consumption in the selected countries is significant. The statistics reports and database compiled by the IEA were used to provide data for carbon dioxide emissions and total final energy consumption [70,71].

The last factor is renewable energy defined as the proportion of the total primary energy supply that is renewable. The source of the RES indicator was the OECD. The RES indicator illustrates the commitment of a given country to search for clean and ecological energy sources as an effective solution to increasing energy production, taking into account environmental constraints (e.g., greenhouse emissions). Access to clean, modern, and more efficient energy in all countries is also important in the context of sustainable development [72], while the use of renewable energy sources in the hydrogen production process is defined as the long-term goal of a developed hydrogen economy [73]. Interest in green hydrogen production solutions facilitates the development of renewable energy technologies on a large scale [13]. Countries with a large share of RES with the possibility of further renewable-cost reduction, have the potential to develop a clean hydrogen economy [1].

#### *2.2. Methods*

The analysis involved two stages. First, Spearman's correlation was used, the second, one-parameter and multi-parameter linear regression models (ordinary least squares method) were used. The basis for choosing Spearman's correlation is that it is more general using than the Pearson correlation (which is only for a linear relationship). Additionally, Spearman's correlation is more resistant to outliers in trials than the Pearson correlation. Spearman's method was used in many articles concerning the area of renewable energy [28,33,34,74–79].

#### 2.2.1. Spearman's Correlation

Spearman's correlation was used to investigate the relationship between the two selected parameters, one from each of the hydrogen indicator groups and one from the economic, energy, and environmental indicator groups—Equation (1).

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

where:

x—parameter y—parameter R(x) and R(y)—ranks of the x and y variables R(x) and R(y)—mean ranks n—total number of observations i—number of observations

#### 2.2.2. The Linear Regression Models

In the second part of the calculation, the regression tool from the RStudio and Analysis ToolPak (MS Excel) was used to perform a linear regression analysis using the least squares method. This enables analysis of the influence of independent variables on the dependent variable. To select parameters potentially best suited to the parameters closely related to the hydrogen economy, a single-parameter regression model was built. A linear regression model has also been used many times in the energy area, for example, in [35,36,80–84].

Linear regression Equation (2) is as follows:

$$\mathbf{y}\_{\rm io}(\mathbf{cn}) = \mathbf{c1}(\mathbf{cn}, \mathbf{y}\_{\rm o}, \mathbf{x}\_{\rm d0}) + \mathbf{c2}(\mathbf{cn}, \mathbf{y}\_{\rm o}, \mathbf{x}\_{\rm d0}) \times \mathbf{x}\_{\rm id0}(\mathbf{cn}) \tag{2}$$

where:

xd0(cn) ∈ DI(cn), yo ∈ DO(cn)

c1, c2—regression coefficients, values depend on the country and parameters used in the calculations, including their values

cn—country

years of analysis: from 2008 to 2018

DI—data input (raw values in Supplementary Data, Table S1)

DO—data output (raw values in Supplementary Data, Table S1)

DO = (HPV, RDD); DI = (POP, GDP, TFC, TFC\_T, TFC\_I, RES, CO2, CO2\_T, CO2 \_I)

The purpose of the analysis of various parameters is to maximize the value of the linear regression coefficient R<sup>2</sup> depending on the country and y0, xd0. For each parameter, the c1 and c2 coefficients were calculated.

An example of the application of Formula (3) is presented below:

$$\text{HPV}\_i(\text{IPN}) = \text{c1}(\text{IPN}, \text{HPV}, \text{GDP}) + \text{c2}(\text{IPN}, \text{HPV}, \text{GDP}) \times \text{GDP}\_i(\text{cn}) \tag{3}$$

where:

JPN—Japan GDP—Gross Domestic Product as parameter GDPi—GDP value in year i

Next, a parametric regression model was built to select a pair of parameters potentially best suited to the parameters closely related to the hydrogen economy (hydrogen

production and share of technology energy research, development, and demonstration (RDD) budget).

Overall multiple (two-parameter) linear regression Equation (4):

$$\mathbf{y}\_{\rm inj}(\mathbf{cn}) = \mathbf{c1}(\mathbf{cn}, \mathbf{y}\_{\rm op}, \mathbf{x}\_{\rm d1}, \mathbf{x}\_{\rm d2}) + \mathbf{c2}(\mathbf{cn}, \mathbf{y}\_{\rm op}, \mathbf{x}\_{\rm d1}, \mathbf{x}\_{\rm d2}) \times \mathbf{x}\_{\rm id1}(\mathbf{cn}) + \mathbf{c3}(\mathbf{cn}, \mathbf{y}\_{\rm op}, \mathbf{x}\_{\rm d1}, \mathbf{x}\_{\rm d2}) \times \mathbf{x}\_{\rm id2}(\mathbf{cn}) \tag{4}$$

where:

xd1(cn), xd2(cn) ∈ DI(cn), xd1 = xd2 yo ∈ DO(cn) c1, c2, c3—regression coefficients; values depend on the country and parameters used in the calculations, including their values cn—country i—years of analysis: from 2008 to 2018 DI—data input (raw values in Supplementary Data, Table S1) DO—data output (raw values in Supplementary Data, Table S1) Analyzed combinations in terms of DO and DI: DO = (HPV, RDD); DI = (POP, GDP, TFC, TFC\_T, TFC\_I, RES, CO2, CO2\_T, CO2 \_I) DO = (HPV, RDD); DI = POP GDP , TFC GDP , TFC\_T GDP , TFC\_I GDP , RES, CO2 GDP , CO2 \_T GDP , CO2 \_I GDP DO = (HPV, RDD); DI = GDP POP , TFC POP , TFC\_T POP , TFC\_I POP , RES, CO2 POP , CO2 \_T POP , CO2 \_I POP DO = (HPV, RDD); DI = log(POP, GDP, TFC, TFC\_T, TFC\_I, RES, CO2, CO2\_T, CO2 \_I) DO = log(HPV, RDD); DI = log POP GDP , TFC GDP , TFC\_T GDP , TFC\_I GDP , RES, CO2 GDP , CO2 \_T GDP , CO2 \_I GDP DO = log(HPV, RDD); DI = log GDP POP , TFC POP , TFC\_T POP , TFC\_I POP , RES, CO2 POP , CO2 \_T POP , CO2 \_I POP DO = (HPV, RDD); DI = sqrt(POP, GDP, TFC, TFC\_T, TFC\_I, RES, CO2, CO2\_T, CO2 \_I) DO = (HPV, RDD); DI = sqrt POP GDP , TFC GDP , TFC\_T GDP , TFC\_I GDP , RES, CO2 GDP , CO2 \_T GDP , CO2 \_I GDP DO = (HPV, RDD); DI = sqrt GDP POP , TFC POP , TFC\_T POP , TFC\_I POP , RES, CO2 POP , CO2 \_T POP , CO2 \_I POP DO = (HPV, RDD); DI = (POP, GDP, TFC, TFC\_T, TFC\_I, RES, CO2, CO2\_T, CO2 \_I) 2 DO = (HPV, RDD); DI = POP GDP , TFC GDP , TFC\_T GDP , TFC\_I GDP , RES, CO2 GDP , CO2 \_T GDP , CO2 \_I GDP <sup>2</sup> DO = (HPV, RDD); DI = GDP POP , TFC POP , TFC\_T POP , TFC\_I POP , RES, CO2 POP , CO2 \_T POP , CO2 \_I POP <sup>2</sup>

> The purpose of the analysis of the combination of different pairs of parameters is to maximize the value of the linear regression coefficient of determination R<sup>2</sup> depending on the country and selected cn, y0, xd1, xd2. For each selected combination, the following coefficients were calculated: c1, c2, and c3 (using the least squares method). An example of the application of Formula (5) is presented below:

$$\text{HPV}\_{\text{l}}(\text{lPN}) = \text{c1}(\text{lPN}, \text{HPV}, \text{GDP}, \text{TFC}) + \text{c2}(\text{lPN}, \text{HPV}, \text{GDP}, \text{TFC}) \times \text{GDP}\_{\text{l}}(\text{cm}) + \text{c3}(\text{lPN}, \text{HPV}, \text{GDP}, \text{TFC}) \times \text{TFC}\_{\text{l}}(\text{cm}) \tag{5}$$

where:

JPN—Japan GDP—Gross Domestic Product as parameter GDPi—GDP value in year i

### **3. Results and Discussion**
