Index

Abstract

Besides traditional production factors, such as labor and capital, one of the inputs used in the production process is energy. Although the use of fossil fuels is more common in many production processes renewable energy sources are increasingly important in ensuring sustainable development. In many countries in the world, the share of renewable energy is the total energy consumption is very high, including in European Union (EU) countries. The purpose of this study is the investigate the output elasticity coefficients of capital and renewable energy in 12 EU countries by using the Cobb–Douglas production function approach. In this study, the Gross domestic Product these countries from 2000 to 2017, was examined using a generalized method of moments estimation, which used labor, capital, and renewable energy data. As a result of the study, the output elasticity coefficient in the Cobb–Douglas production function was found to be 1.147. This indicates that a 1% increase in labor, capital, and renewable energy increased GDP by 0.598%, 0.446%, and 0.093%, respectively. Among the findings, the relationship between GDP and explanatory variables is statistically significant and economically significant. It is understood that there is a positive relationship between the variables.

Keywords: Labor, Cobb–Douglas production function, Capital renewable energy, Generalized moments method (GMM).

Received: 20 July 2020 / Revised: 24 August 2020 / Accepted: 14 October 2020/ Published: 16 November 2020

Contribution/ Originality

This study contributes to existing literature by investigating the output elasticity coefficients of capital and renewable energy using the Cobb–Douglas production function approach.


1. INTRODUCTION

Along with traditional production factors such as labor and capital, energy is one of the indispensable inputs of production. Fossil fuels, such as oil, natural gas, and coal, are widely used in production processes. However, the use of renewable energy sources has become increasingly widespread in order to ensure energy supply security and to protect the environment based on sustainable development. Today, the share of renewable energy of the total energy consumption is continuously increasing in EU countries. These countries, which do not have sufficient oil, gas, or coal resources, import the energy that they need. Therefore, EU countries have become foreign-dependent on energy, and various energy policies have been established in order to reduce this dependency. Today, the scope of the EU's energy policies can be listed as ensuring effective energy consumption, seeking alternative energy sources, and increasing the production of new and renewable energy sources.

The inputs used in production have an impact on the output. In economic theory, the effect of inputs on the outputs is explained by the concept of output flexibility. Output flexibility is defined as the sensitivity of production to the proportional changes that occur to the inputs used in production and the coefficients are equal to the total and show the return according to the scale (Kurumu, 2011).

The relationship between GDP and energy consumption has attracted the attention of many economists. In literature from various countries around the world, numerous studies have been carried out in EU However, the common features of these studies are the long-term causality relationships between energy sources and economic growth. As explained in the literature review, the results of these studies indicated that the two parameters mentioned had the right or opposite relationships with each other. The conclusion drawn from the examination of these studies on the analysis of the impact of the change in inputs on the outputs was that the work was inadequate.

In countries that are dependent on foreign energy, the trend towards renewable energy sources is quite high. In production processes, renewable energy use has become as important as labor and capital. The purpose of this study is the investigate the output elasticity coefficients of capital and renewable energy in 12 EU countries by using the Cobb–Douglas production function approach. In this study, the Gross domestic Product  these countries from 2000 to 2017, was examined using a generalized method of moments estimation, which used labor, capital, and renewable energy data.

In the first section, renewable energy sources and policies of the EU are mentioned; in the second section, empirical studies examining the relations between GDP, labor, capital, and renewable energy are included; in the third section, econometrics with the dataset used in the analysis methodology are introduced; the fourth section shows the results of the econometric analysis; and the final section comprises the conclusion and policy suggestions based on the results.

2. RENEWABLE ENERGY SOURCES IN EUROPEAN UNION COUNTRIES

The main objective of energy policies is to ensure sustainability. Environmental protection to ensure energy sustainability and combat climate change is constantly being observed. One of the most important steps in this regard was taken in 2007 with the decision of the energy and climate change package led by the European Commission. The 2020 energy strategy, published in 2010, set out three important energy-related targets to reach the reduce greenhouse gas emissions by at least 20% compared to 1990, increase the share of renewable energy sources of the total energy supply to 20%, and increase the share of renewable energy used in vehicles to 10%. The overall aim is to save 20% in primary energy resource consumption (European commission, 2019a; TR Ministry of Foreign Affairs, 2017). These targets were revised in 2014 and are due to be reviewed again in 2030. The energy strategy for the year was announced, and according to this strategy, renewable energy increased its share in the total energy consumption to 27%. It aims to reduce greenhouse gas emissions by 40% and increase energy efficiency to 27% (Bonn, Heitmann, Reichert, & Voßwinkel, 2015). In addition, 2030 targets were revised in 2018, and the decision was made to increase the share of renewable energy to 32% and effective energy consumption to 32.5% (European commission, 2019a). Production and consumption of renewable energy are the main energy policies of the EU, and the provision is based on contributing to the protection of the environment based on competition and sustainable development (European Commission, 2019bc).

The common energy policy of all member states could not be established across the EU. The European Commission, therefore, seeks to harmonize the goals of each member country to increase the share of renewable energy use of their total energy consumption. The obligation to calculate the consumption of these resources according to GDP was requested from the member countries. Accordingly, priority was given to environmental protection to ensure sustainable development in EU countries. Elements related to the green economy, such as environmental protection, resource efficiency, social integration, and creating new business areas are integrated into various EU policies (Yılmaz, 2014) and are the main aspects regarding renewable energy sources in the EU.

Each country in the EU has different energy consumption patterns according to its economic growth rate and economic structure. Table 1 shows the data of 12 selected countries with high renewable energy production capacity in the EU.

Table 1. Total renewable energy resource production capacity (MW).

 
2010
2011
2012
2013
2014
2015
2016
2017
2018
EU Country
322 521
361 475
395 655
420 261
440 680
465 132
489 206
513 360
536 719
Germany
56 546
67 424
78 164
83 766
90 320
98 013
104 746
112 719
119 388
Italy
29 507
40 822
46 721
48 857
49 526
50 417
51 195
52 128
53 290
France
31 717
34 903
37 126
38 773
40 424
42 759
44 921
47 972
50 504
Sweden
22 707
23 469
24 293
24 645
25 528
26 869
27 805
28 337
29 178
Spain
42 246
43 920
46 413
47 676
47 711
47 742
47 776
47 899
48 277
England
9 627
12 783
15 902
20 027
24 895
30 822
35 488
40 311
43 460
Finland
5 127
5 282
5 329
5 632
5 863
6 256
6 858
7 618
7 867
Austria
44 980
44 980
40 866
51 210
50 410
49 977
47 369
50 922
50 854
Poland
2 178
3 019
4 094
5 116
5 638
6 919
7 881
7 982
8 236
Romania
6 791
7 410
8 354
10 098
11 152
11 212
11 162
11 145
11 148
Netherlands
3 562
3 748
4 038
4 547
4 837
5 808
7 185
7 942
9 753
Portugal
9 607
10 548
10 955
11 143
11 573
12 153
13 208
13 541
13 787

Source: IRENA (2019).

As seen in Table 1, the capacity related to these resources increased from 3.2 GW to 5.4 GW between 2010 and 2018 thanks to technological progress throughout the EU. The highest capacity increases in this period were realized by Poland, England, Holland, Germany, Italy, and France, respectively. With the increase in capacity across the EU, renewable energy production has increased economically. In addition, the fact that Germany has approximately 20% of the total capacity indicates that this country has an important share in the production of renewable energy. The relationship between renewable energy use and economic growth is no different from the relationship between general energy consumption and economic growth.

3. LITERATURE REVIEW

Studies that investigated the causality relationship between renewable energy and economic growth, as well as studies that analyzed flexibility coefficients in a production function, are summarized below.

In a study by Sari and Soytas (2007), an analysis was made within the scope of the Cobb–Douglas production function using labor, capital, and energy inputs from ten ountries between 1971 and 2002. As a result of this study using VAR analysis, it was determined that energy may be a more important input than labor and capital in some countries. However, Sadorsky (2009)  in this study, general renewable energy data was used a cointegration analysis to examine the relationship between renewable energy consumption and per capita income in developing countries. The results showed an increase in real income per capita, which increased renewable energy consumption per capita in the long term. The relationship between economic growth and renewable energy sources was studied by differentiating the period and country using renewable energy, GDP, labor, and fixed capital formation variables (Apergis & Payne, 2010a, 2010b, 2011a, 2011b, 2012). In their studies, panel cointegration and panel causality were investigated, and a two-way causality relationship was found between Renewable energy consumption and GDP. Menegaki (2011) investigated the relationship between economic growth and renewable energy sources in 27 EU countries from 1997 to 2007. As a result of the study conducted in the framework of multivariate panel data, it was determined that there was no causal relationship between the two variables.

Ocal and Aslan (2013) examined relations between renewable energy consumption and economic growth in Turkey from 1990 to 2010. This study used the Toda–Yamamoto and ARDL causality tests; it was found that there is an inverse relationship between renewable energy consumption and economic growth and that economic growth affects renewable energy consumption. Apergis and Dănuleţiu (2014) investigated the relationship between renewable energy and economic growth in 80 developed and developing countries. The study used the panel data analysis method, and the Canning–Pedroni causality test was applied using data from 1990 to 2012. It was determined that a causality relationship exists between economic growth and renewable energy consumption.  

Kula (2014) examined the relationship between economic growth and renewable energy per capita using the dynamic panel data method in 19 OECD countries from 1980 to 2008, and a causality relationship between economic growth and renewable energy consumption was found. In studies by Salim, Hassan, and Shafiei (2014), the relationships between energy sources, industrial sector production, and economic growth in 29 OECD countries between 1980 and 2011 were analyzed. In studies that used Westerlund cointegration and panel Granger causality analysis, it was found that there was a bidirectional causality relationship between the variables in the long term. In studies by Çermikli and Tokatlıoğlu (2015), the Cobb–Douglas production function, which used labor, capital, and energy inputs for 44 countries (27 high-income and 17 middle-income) was estimated between 1990 and 2011. In this study, the effect of development in different technologies on energy intensity was investigated. As a result of the study using the panel data analysis method, it was found that energy savings of 1.25% in high-income countries and 1.65% in middle-income countries were achieved due to advances in technology.

In the works of Shahbaz, Loganathan, Zeshan, and Zaman (2015), the relationship between renewable energy and economic growth in Pakistan was examined for the period between January 1972 to April 2011.In the study in which the ARDL method and vector error correction model were used, it was concluded that the variables cointegrated in the long term, the use of renewable energy increases economic growth, and there is a bidirectional causality relationship between the variables. In studies by Aslan and Ocal (2016), the relationship between renewable energy use, capital and labor, and economic growth in countries that were new to the EU between 1990 and 2009 was investigated. As a result of the study using the ARDL and Hatemi-J causality tests, it was found that there is a one-way effect from renewable energy use to economic growth in the countries included in the study. In studies by Bhattacharya, Paramati, Ozturk, and Bhattacharya (2016), the relationship between renewable energy consumption and economic growth was investigated in 38 countries with the most renewable energy resources in the world from 1991 to 2012. In the study that used the Pedroni panel cointegration test, panel dynamic ordinary least square (DOLS) estimation and panel Granger causality test, renewable energy is economical, and it was concluded that it has a positive effect on growth. Dogan (2016) studied data from 1988 to 2012 on economic growth and energy consumption in Turkey. As a result of the study, which used the ARDL method, and the Johansen and Gregory–Hansen cointegration tests, the use of fossil fuel energy was determined to have a positive effect on economic growth, but that renewable energy does not affect economic growth.

To support research by Aslan and Ocal (2016), the relationship between non-renewable and renewable energy consumption and economic growth was investigated in 17 emerging market economies between 1980 and 2012. The study used a panel causality test, and the results showed a one-way relationship from economic growth to renewable energy consumption in Colombia and Thailand, a one-way relationship from renewable energy consumption to economic growth in Peru, and a mutual causality relationship between renewable energy and economic growth in Greece and South Korea. It was determined that there was no relationship between the variables in other countries. Ito (2017) investigated the relationship between energy consumption and economic growth in 42 developing countries between 2002 and 2011. As a result of using the generalized moment method (GMM), renewable energy consumption in the long term was found to positively affect economic growth. In studies by Kahia, Ben Aissa, and Charfeddine (2017), the relationship between non-renewable and renewable energy consumption and economic growth in the oil-importing MENA countries from 1980 to 2012 was investigated. The study used a panel data analysis and the results showed a bidirectional causality relationship between renewable energy consumption and economic growth. In studies by Koçak and Şarkgüneşi̇ (2017), the relationship between renewable energy and economic growth was investigated in nine Black Sea and Balkan countries from 1990 to 2012. The results of the study using panel data analysis indicated that there is a long-term and right-way relationship between renewable energy and economic growth. Rafindadi and Ozturk (2017) investigated the relationship between renewable energy and economic growth in Germany from January 1970 to April 2013. The study used the ARDL boundary test and Bayer–Hanck cointegration test, and it was determined that renewable energy consumption increased economic growth, and a two-way causality relationship exists between the variables.

Bulut and Muratoglu (2018) investigated the relationship between renewable energy and economic growth in Turkey from 1990 to 2015, and the result of these studies, which were carried out using the ARDL and Khatami–Jan causality tests, indicated economic growth in Turkey.

It has been found that there is no causal relationship between renewable energy and Economic growth Durgün and Durgün (2018) investigated relations between GDP per capita and renewable energy consumption per capita in Turkey from 1980 to 2015. The study was conducted using the ARDL boundary test and cointegrated Toda–Yamamoto causality test, and a one-way causality relationship was found from renewable energy use to economic growth. Alper and Oguz (2016), investigated economic growth and renewable energy relations in Turkey between 1990 and 2017. The study used the Bayer–Hanck cointegration test and the Toda–Yamamoto causality test, and it was determined that there is a one-way causality relationship between variables in the long term from economic growth to renewable energy consumption.

In the study by Marinaș, Dinu, Socol, and Socol (2018), the relationship between economic growth and renewable energy sources in central and eastern Europe was investigated from 1990 to 2014. The results of the study using the ARDL method, both short and long term, determined that there was a significant relationship between the variables. Stamatios et al. (2018) found a positive relationship between economic growth and consumption of renewable energy and other energy in 25 EU member states from 2007 to 2016. Songur (2019) studied GDP in Turkey from 1982 to 2014 using labor, capital, natural gas, oil, and coal translog production function estimated data. In the study conducted using the Ridge regression method, it was found that the elasticity of substitution between inputs remained at same  level, while the output elasticities were positive.

Many studies have been conducted to investigate the relationship between renewable energy consumption and economic growth, and to examine the relationship between output and labor, capital, and energy within the scope of the production function. However, due to the different methods used, the selected sample group, the time intervals examined, and the different data sets, a common conclusion regarding the causality relationships could not be reached. Unlike the studies summarized above, the differences between the countries and the variables considered in this study, as well as the output elasticity coefficients of GDP and variables of labor, capital, and renewable energy are calculated within the scope of the Cobb–Douglas production function. The work carried out is detailed below.

4. METHODOLOGY

4.1. Data Set

Data on GDP, labor (L), capital (K) and renewable energy (RE) from 2000 to 2017 in 12 EU countries with the largest share in the production of renewable energy based on the flexibility of renewable energy, labor, and capital inputs were used. The countries used as examples were Germany, Italy, France, Sweden, Spain, England, Finland, Austria, Poland, Romania, the Netherlands, and Portugal. The definitions and data sources of the variables used in the analysis are given in Table 2.

Table 2. Definitions of variables and data sources.

Variables Description Source
GSYH 2011 prices (in millions of dollars) Penn World Table, PWT 9.0
L Million people Penn World Table, PWT 9.0
K Gross fixed at prices in 2011 capital formation (in millions of dollars) World Bank
RE Renewable energy sources, including biofuels Eurostat

4.2. Cobb–Douglas Production Function

In order to show the relationship between inputs and outputs, and to obtain the flexibility coefficient of the production and the output elasticity coefficient according to the inputs, the Cobb–Douglas production function was used. The Cobb–Douglas production function was developed in 1928 by Charles Cobb and Paul Douglas. This production function helps to calculate the flexibility of production for labor and capital, and the flexibility of production for renewable energy. By adding GDP as a dependent variable to be estimated in the Cobb–Douglas production function, labor, capital, and renewable energy were used as independent variables. Therefore, the below three-input Cobb–Douglas production function is created:

In order to express equation 1 in linear form, the natural logarithm of both sides of the equation was taken and arranged in equation 2. Since the growth rate in the period being studied (t-1) affects the overall growth rate (t)  the Cobb–Douglas production function utilized a dynamic panel data analysis. In this context, the Cobb–Douglas production function converted to linear form is shown below.

5. METHOD AND EMPIRICAL FINDINGS

In the first part of the study, the cross-sectional dependence from the dynamic panel data analysis was tested. Horizontal cross-sectional dependence and spatial propagation effects excluded observed or common factors, which may be caused by independence in the error term, and may also arise if these factors are taken into account (Breitung & Pesaran, 2005). In order to avoid deviated results or false inferences, horizontal cross-sectional dependency should be investigated in the panel data analysis (Chudik, Pesaran, & Tosetti, 2011; Pesaran, 2004).

Chudik and Pesaran (2013) assumed that cross-sectional dependence is often used in panel data analyses and they made parameter estimates. One of the main issues encountered in estimating the model is whether a horizontal cross-sectional dependence exists. Therefore, the cross-sectional dependency was tested initially, assuming that the 12 countries being examined would affect each other. Based on the assumption that there is a variance problem in the dynamic panel data analysis, and that the model has a constant effect, it is not necessary to make preliminary estimates on these issues. In his research, Hoechle (2007) proposed Pesaran's cross-sectional dependent estimation method for models with variable variance (variable error term hypothesis and heteroscedastic variance) and fixed-effect models because of the possible dependency issue between units of data (De Hoyos & Sarafidis, 2006). Results related to this test are given in Table 3.

Table 3. Pesaran's cross-sectional dependency test results.

LogGSYH
Coefficient
Standard Error
t-statistic
P-Value
Confidence Interval 95 %
LogL
-0.062962
0.0627163
-1
0.317**
0.186628
0.060705
LogK
0.433462
0.0182117
23.8
0.000**
0.397552
0.469373
LogRE
0.136527
0.0093599
14.59
0.000**
0.118071
0.154983
sigma_u
0.264191
sigma_e
0.017847
rho
0.995457
(fraction of variance due to u_i)
F(11, 201)
44.62
F test that all u_i=0
F(3, 201)
359.11
R Kare
0.8063
Prob>f
0.000*
Pr
0.0316
Pesaran's test of cross-sectional independence
2.149
Average absolute value of the off-diagonal elements
0.577
Fixed effects (regression - within)

Note: *The probability value being zero indicates that the null hypothesis is rejected. In other words, there is a dependency between the size of the cross-sectional units of capital and renewable energy production. ** Since the P value for labor is higher than zero, the null hypothesis is accepted. In other words, there is no cross-sectional dependence between the units of labor datasets. There is a cross-sectional dependence between the units of the other two variables.

As shown in Table 3, Pesaran's cross-sectional dependency test was performed for all logarithmic variables. At the end of this test, except for the labor parameter, the variables with a P value were lower than the error term. Therefore, it was determined that the model demonstrated cross-sectional dependence. After the horizontal cross-sectional dependency test, a unit root test was performed to test the stability of the data sets. There are two types of panel unit root tests in the literature. In the first type, the individual time series in the panel are considered to be distributed cross-sectionally independently (Choi, 2001; Im, Pesaran, & Shin, 2003; Maddala & Wu, 1999), and in the second type, horizontal cross-sectional dependence is permitted (Moon & Perron, 2004; Pesaran, Smith, & Yamagata, 2013).

Since the model has a horizontal cross-sectional dependence, in many studies it is recommended to use the second-generation test method to perform unit root testing. In the study, the unit root test subject was tested using the horizontal cross-sectional Dickey–Fuller (cross-sectionally augmented Dickey–Fuller or CADF) test. In this study, Dickey–Fuller regressions were expanded by taking the first and second differences of the cross-sectional units and the horizontal cross-sectional averages of the lagged values, however, cross-sectional dependence and variable variance problems were found. The most appropriate unit root test was the estimation method by Pesaran (2007), so this method was used in the model as it was developed based on both cross-sectional dependence and variable variance assumption (Lewandowski, 2007). Pesaran’s CADF testing is also recommended for heterogeneous models, including macro panels and time series for 20- to 30-year periods. Within the scope of this test, the exact stationarity of the variables was tested, and the variables with unit roots should be made stationarity. The results of the test are detailed in Table 4.

Table 4. CADF unit root test.

Variables
P-Value
t-bar
cv10
cv5
cv1
z[t-bar]
Log RE
0.090*
-2.668
-2.67
-2.78
-3.01
-1.343*
D1.LogRE
0.000**
D2.LogRE
0.000***
LogK
0.167*
-2.559
-2.67
-2.78
-3.01
-0.965*
D1.LogK
0.021**
D2.LogK
0.000***
LogGSYH
0.164*
-2.563
-2.67
-2.78
-3.01
-0.979*
D1.LogGSYH
0.366**
D2.LogGSYH
0.000***
LogL
0.158*
-2.569
-2.67
-2.66
-3.01
-1.002*
D1.LogL
0.245**
D2.LogL
0.000***

Note: * Both P-values and z-bar values indicate that the null hypothesis is rejected. This result shows that logarithm variables contain unit roots. ** Stationarity efforts were made by taking the first difference of the series, however, not all of the series have been made stationary. *** By taking the second difference of the series, the stagnation process was realized in all series.

According to the CADF test results in Table 4, when only the second differences were taken for all series, the null hypothesis was strongly rejected at a 1% probability level. In other words, the related series became stationary in the second difference. Since all the variables could not be made stationary after the first difference of the series was taken, the second difference was taken and a stabilization process of all variables was carried out. In other words, the series are integrated in the second order. Therefore, based on the panel unit root test findings, it was concluded that all the variables subjected to the analysis were integrated in the second order I (2). As a result, considering the cross-sectional dependency in the model, variables were stabilized in the second order by the Pesaran CADF test on logarithm variables.

To select the appropriate final estimation method in the dynamic panel models, the two most important assumptions in the series must be tested. The first test is to determine if the explanatory variables are completely external (internality problem test; the correlation between the error term and the lagged variables), and the second is to test whether the error terms are autocorrelated or not. Anderson and Hsiao (1982) tried to solve this problem by using the tool variables method in their research to solve the problem of internality in the series. In this context, the effect resulting from the correlation between the error term and delayed variables can be kept under control. It should determine whether there is autocorrelation in the error terms in order to solve the problem of internality. However, this test method does not include autocorrelation in the model, and it is assumed that it was not preferred in the final parameter estimation. The results related to the internality problem test conducted in the context of the tool variable method are given in Table 5.

Table 5. Internality test results.

 
Coefficients
Standard    Errors
Z-Value
P-Value
Confidence Interval 95%
D2.LogGSYH
D2.LogRE
0.086259
0.010971
7.86
0.000*
0.064756
0.107762
D2. LogL
0.541478
0.016815
32.2
0.000*
0.508522
0.574434
D2.LogK
0.529451
0.015506
34.15
0.000*
0.49906
0.559842
Prob > Chi2
0.0000*
Number of Observations
214
R-Kare
0.9795
Root MSE
0.02498
Wald chi2(3)
10218.6

Note: * The null hypothesis was rejected because the P value and probability value were lower than the critical value (0.05%). In other words, there is a correlation between the error term and delayed variables of all series. However, this method is considered invalid because autocorrelation was not considered.

The appropriate test method is the Arellano–Bond GMM (generalized method of moments). However, in order to use this method, the second order in the model autocorrelation should be absent (Roodman, 2009). First and second-degree autocorrelation tests should be conducted. In this context, models without second-degree autocorrelation are considered appropriate. The autocorrelation test results are given in Table 6.

Table 6. Arellano–Bond autocorrelation test.

Degree
z
Prob>z
1
-4.5319
0.0000*
2
-0.51498
0.6066*

Note: * P values indicate that there is no second-degree autocorrelation.

Table 7. Two-stage Arellano–Bond GMM * dynamic panel data test results.

LogGSYH
Coefficient
Standard Errors
Z-Value
P-Value
95% c.i
D2.L1.LogGSYH
-0.016207
0.000738
-21.97
0
-0.017653
-0.014761
D2.LogL***
0.598481
0.022674
26.4
0.000**
0.554041
0.642921
D2.LogRE***
0.092941
0.005769
16.11
0.000**
0.081635
0.104248
D2.LogK***
0.456092
0.012082
37.75
0.000**
0.432413
0.479772
GMM türü L(2/.).D2.LogGSYH
Standard D2.LogL D2.LogK D2.LogRE
Wald chi2(4) 74325.05
Prob > chi2 0

Note: * In the generalized moments method (GMM), normally the first differences are estimated in the context of the generalized least squares method by converting the dynamic fixed effect model vehicle with variables. However, since the variables are stationary from the second difference in the unit root test, the second difference variables are used. Making the model robust error is not preferred because this causes deviation in standard error amounts and decreases the reliability of the final results. ** P values and probability values mean that the final test result is significant and positive because these values are lower than the critical value (0.05%). *** The second difference of logarithm independent variables was taken and included in the test.

As shown in Table 6, since the second order P value is higher than the error margin (0.05%) according to the probability results and (z) statistics, the model was not autocorrelated from the second order (P = 0.1483 > 0.05). Therefore, using the Arellano–Bond GMM method was considered to be appropriate to generate consistent results in the research. In this context, the relationship between independent variables and the dependent variable was examined using the Arellano–Bond test for the final parameter estimation, and Table 7 shows the results. The statistically significant and positive values of P of L, K and RE indicate that labor, capital and renewablenergy are related to GDP. The relationship between renewable energy and GDP is meaningful and positive, and this shows that the policies regarding renewable energy sources play an active role in the selected EU countries, and the factor elasticity coefficients of production were shown to be positive, which is economically consistent and significant.

6. CONCLUSION

The Cobb–Douglas production function of output flexibility coefficients for renewable energy consumption and labor and capital inputs in EU countries selected from 2000 to 2017,  it was estimated within the scope of the coefficients obtained as a result of the analysis were found to be statistically and economically significant. The Cobb–Douglas production was converted to linear to form the coefficients of the variables in the function and express the production factor elasticity coefficients. The sum of these coefficients constitutes the output elasticity coefficient, and the findings are summarized as follows. The coefficients estimated as a result of the analysis have received positive values. The elasticity coefficient of production was estimated to be 0.598 for labor, 0.4456 for capital, and 0.093 for renewable energy. The sum of these flexibility coefficients is 1.147, and in the 12 selected EU countries there was an increased yield by scale within the Cobb–Douglas production function. In addition, the largest factor flexibility coefficient among the inputs in the case of explanatory variables belongs to the labor factor, which is followed by capital and renewable energy, respectively.

The flexibility of labor, capital, and renewable energy inputs in the production function between 0 and 1 means that the average product of these inputs is larger than the marginal product. In this context, all of the inputs are located in the second region of production, which is the region where the law of decreasing yields operates. The positive values of the factor flexibility coefficients of the products show that there is a functional complementarity relation between the inputs. An increase in the amount increases the marginal efficiency of the other inputs. The Cobb–Douglas production function estimated by this state produced results compatible with the theory. It would be beneficial for the selected EU countries that produce the most renewable energy to increase their support policies for renewable energy use.

Funding: This study received no specific financial support.  

Competing Interests: The authors declare that they have no competing interests.

Acknowledgement: All authors contributed equally to the conception and design of the study.

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