of investments into renewable energy sources”

Greening the economy requires green innovations, and innovations require investments. Most countries of the world are still relying on conventional (fossil-based) sources of energy. The transition toward green or renewable energy sources is an effective and innovative way to meet ever-increasing demand as a result of the rising population. Another reason for innovations in the field of green energy is the need to mitigate climate change and avoid pollution, especially in developing countries. The monitored investments into renewable energy sources are usually public. Therefore, this paper aims to determine whether the se- lected countries of the world produced renewable energy efficiently, considering the investments made by public financial institutions and installed electricity capacity for renewable energy sources, for the period 2013–2017 (for a deeper analysis, the year 2017 was chosen). For this purpose, the Stochastic Frontier Analysis model in the logarithmic form of the Cobb-Douglas production function is used, which helps to judge the competitiveness of countries based on effectively transforming the inputs into outputs. Results suggest that the effect of the first variable “installed electricity capacity” on electricity generation was highly statistically significant, and the impact of the second variable “public investments” was characterized as statistically insignificant. The monitored countries were divided into 10 groups according to the different range of estimated output-oriented technical efficiency from 0.00 to 1.00. Most countries should increase the renewable electricity generation approximately by 40-49%, given the level of inputs (16 countries of 6th group with estimated output-oriented technical efficiency 0.51-0.60) for the year 2017. because it comes from natural processes that are constantly re-plenishing. Investing in these innovative solutions can fundamentally change the way energy is produced, stored, and used, thereby gradu-ally ensure moving from fossil fuels to renewable energy. Investments from public financial institutions in 2017 amounted to USD 29,101 million worldwide, 6,190,948 GWh of renewable energy was produced, and devices for the use of renewable energy sources with an output of 2,181,577 MW were installed (International Renewable Energy Agency, 2019). The main objective of the paper is to find out whether the countries of the world under study produce energy from renewable energy sources efficiently with respect to investments provided by public financial institutions and installed electricity capacity for renewable energy sources. To achieve the main objective, the Stochastic Frontier Analysis (SFA) model is used to monitor not only the direct dependence between inputs and outputs but also the efficiency of input to output transformation → output-oriented technical efficiency, which also helps in assessing the competitiveness of the countries.


INTRODUCTION
Renewable energy is derived from renewable sources (water, wind, solar, geothermal, and biomass energy). It is often referred to it as clean energy because it comes from natural processes that are constantly replenishing. Investing in these innovative solutions can fundamentally change the way energy is produced, stored, and used, thereby gradually ensure moving from fossil fuels to renewable energy. Investments from public financial institutions in 2017 amounted to USD 29,101 million worldwide, 6,190,948 GWh of renewable energy was produced, and devices for the use of renewable energy sources with an output of 2,181,577 MW were installed (International Renewable Energy Agency, 2019). The main objective of the paper is to find out whether the countries of the world under study produce energy from renewable energy sources efficiently with respect to investments provided by public financial institutions and installed electricity capacity for renewable energy sources. To achieve the main objective, the Stochastic Frontier Analysis (SFA) model is used to monitor not only the direct dependence between inputs and outputs but also the efficiency of input to output transformation → output-oriented technical efficiency, which also helps in assessing the competitiveness of the countries.

Renewable energy sources
Energy use and its influence on the environment is the one among the foremost important challenges facing humanity in the 21 st century (

Efficiency
According to Karlaftis and Tsamboulas (2012), the term efficiency refers to the comparison between the real or observed values of output/outputs and input/inputs with the optimal values of input/ inputs and output/outputs (p. 393). According to Shumais (2020), there exist two ways of measuring the efficiency, specifically, the output efficiency that measures how far an inefficient unit (e.g., country) can increase its output to reach the frontier with the level of inputs in incorporates, and the input efficiency that determines how far a unit can decrease its input usage for a given level of output it produces (p. 113). Bezat-Jarzębowska and Rembisz (2013) state that the efficiency of input factor use (not the increase of it) is the main factor of producer's competitiveness that is expressed by the ability for a long-term and effective growth and performance (p. 359). Economic efficiency combines technical efficiency (mentioned in this paper) and allocative efficiency, with technical efficiency referring to the increase of output given a fixed level of input, and allocative efficiency allowing adjustment of input to meet consumer preferences (Liu, 2019, p. 114). The area of efficiency and productivity analysis using frontier estimation methodologies has been developing very rapidly in the last four decades -nonparametric approach Data Envelopment Analysis (DEA) and parametric approach Stochastic Frontier Analysis (SFA) (

AIM, DATA, AND METHODS
The main objective of the paper is to determine whether the countries of the world under study produce renewable energy efficiently, considering the investments made by public financial institutions and installed electricity capacity for renewable energy sources.
The research considers countries of the world, which were financed by public financial institutions for the support of renewable energy sources annually, during the monitored period 2013-2017. Countries are examined from the perspective of the renewable energy situation in total for hydropower, wind, solar, biomass, and geothermal energy.

Region Country
The Statistical Department of the International Renewable Energy Agency provided the data used for the research part of the article to achieve the main objective.
SFA model is applied when examining the efficiency of converting inputs in the field of renewable energy sources (investments from public financial institutions, installed electricity capacity for renewable energy sources) to output (energy generation from renewable energy sources). There is used the general SFA model in the logarithmic form of the Cobb-Douglas production function, which is based on panel data corresponding to the period 2013-2017:
The production function is in the following form: The values of the production function coefficients can be interpreted as the percentage change in output caused by the percentage increase in in-put. In the case of the above production function, should the amount of installed electricity capacity for renewable energy sources increase by 1%, an increase in electricity generation from renewable energy sources by 0.921% is expected. The effect of the interpreted variable is highly statistically significant (Table 2 -p > |z| = 0.000 (0.05 > 0.000) statistically significant). In case the countries under study would invest 1% of the funds provided by public financial institutions, there would be an increase of only 0.0004% in electricity generation from renewable energy sources. The impact of investments can be characterized as statistically insignificant ( From the viewpoint of monitoring the situation in selected countries of the world, it is not only important to interpret the relationship between selected inputs and outputs but also estimate whether the conversion of inputs to output in the renewable energy sector is effective. For this reason, output-oriented technical efficiency was estimated through the SFA model. For a deeper analysis, the year 2017 was chosen. The monitored countries were divided into 10 groups. Each group represents a different range of estimated output-oriented technical efficiency from 0.00 to 1.00 (Table 3). One considers the model country to be the one whose estimated technical efficiency is equal to 1.00, i.e., a country would not have to change its electricity generation from renewable energy sources in terms of inputs to be considered efficient.
In the first group (with an estimated output-oriented technical efficiency of 0.00-0.10), there is no country included out of the monitored countries of the world that invested money from public financial institutions in renewable energy sources. It can, therefore, be concluded that none of the countries uses its inputs inadequately. The biggest group is 6 th group with an estimated output-oriented technical efficiency of 0.51-0.60. In case countries increase electricity generation from renewable energy sources by the above percentages, one would consider them to be efficient in terms of converting inputs to output in the renewable energy sector.
In the last (10 th ) group, some countries are the most efficient out of 89 monitored countries in 1 Given the data for the whole country.
terms of output-oriented technical efficiency. These include Mozambique (Africa), Peru (South America), Cameroon (Africa), Zambia (Africa), Brazil (South America), and Norway (Europe). Their output-oriented technical efficiencies range from 0.91 to 1.00. For unchanged inputs, an increase of 9% in electricity generation from renewable energy sources is needed in Norway, 8% in Brazil and Zambia, 7% in Cameroon and Peru, and only 3% in Mozambique 1 . Following this percentage increase, countries would achieve an output-oriented technical efficiency value of 1.00 and would be considered model countries, which do not need to change electricity generation from renewable energy sources in terms of inputs and still be efficient.
The figure shows the output-oriented technical efficiency of the countries under study in 2017 compared to the technical efficiency that belongs to the model countries, i.e., their output-oriented technical efficiency = 1.00.

CONCLUSION
Energy plays an important role in economic and social development. Globally, countries heavily depend on fossil fuels like coal, oil, and natural gas to meet their energy demands. Renewable energy and biofuels are now on the top of innovations list with the greatest impact on society and business. The main objective of the paper was to determine the effect of investments made by public financial institutions and installed electricity capacity for renewable energy sources in terms of the efficiency of renewable energy generation. Renewable energy is considered as the alternative to current fossil-based energy. Global investments poured into renewable energy usually flow from public resources. The efficiency of production depends on many factors, among others, these investment flows and the installed electricity capacity for renewable energy sources. The SFA model was employed to estimate the efficiency of converting inputs in the field of renewable energy sources (investments from public financial institutions, installed electricity capacity for renewable energy sources) to output (energy generation from renewable energy sources). The monitored countries were divided into 10 groups, and each group represented a different range of estimated output-oriented technical efficiency. The biggest group was 6 th group with an estimated output-oriented technical efficiency of 0.51-0.60. In this group, 16 out of 89 countries in the world were identified. Therefore, given the level of inputs, most countries should increase the production of renewable energy by approximately 40-49%. However, it is important to note that the results might be improved if one could employ the data on private investments as well. Private investments are mentioned, e.g., in Ragosa and Warren's (2019) research. They tested the effects that a variety of factors had on foreign investment in renewable power generation in developing countries.