The Impacts of Non-Fossil Energy, Economic Growth, Energy Consumption, and Oil Price on Carbon Intensity: Evidence from a Panel Quantile Regression Analysis of EU 28

: This study investigates some determinants of carbon intensity in 28 countries in the European Union (EU), including non-fossil energy, economic growth, energy consumption, and oil price. A panel quantile regression method, which considers both individual heterogeneity and distributional heterogeneity, is applied in this paper. The empirical results imply that the inﬂuences of these determinants on carbon intensity are heterogeneous and asymmetric across different quantiles. Speciﬁcally, non-fossil energy can signiﬁcantly decrease carbon intensity, but shows a U-shaped relationship. Economic growth has a negative impact on carbon intensity, especially for medium-emission and high-emission countries. The effects of heating degree days on carbon intensity are positive, although the coefﬁcients are not signiﬁcant at low quantiles, they become signiﬁcant from medium quantiles. Besides, we ﬁnd an inverse U-shaped relationship between crude oil price and carbon intensity. Finally, several relevant policy recommendations are proposed based on the empirical results.


Introduction
Carbon emissions have been a hot topic all over the world because it is one of the primary drivers for the climate change and global warming which are perceived as great threats to human beings and sustainable development since 1992 [1]. From 1990 to 2014, CO 2 emissions in the world increased by about 63% and reached 36.14 billion tons in 2014 [2]. CO 2 emissions cause the rise of sea surface height and many extreme weathers, like the rainstorm and hyperthermia. Moreover, it is estimated that carbon dioxide caused massive damage to Chinese economics in 2016, reaching 0.35 trillion US dollars [2]. Therefore, many governments and global organizations attempt to propose climate policies to control CO 2 emissions, and to develop a low-carbon and sustainable economy.
The determinants of carbon intensity need to be first recognized before these climate policies are recommended. Therefore, we aim to discover the decisive factors of carbon intensity in this paper. Economic growth and energy consumption are proved as the two most important variables than EU countries. Besides, non-fossil energy, especially renewable energy, is widely adopted in EU countries, and EU announced several energy policies to accelerate the development of non-fossil energy and to improve energy efficiency [22]. An investigation of the relationship between carbon intensity and non-fossil energy in EU countries can provide useful information for other countries.
In summary, this paper aims at investigating the main determinants of carbon intensity of EU countries. In our panel quantile model, carbon intensity is determined by economic growth, energy consumption (denoted by heating degree days and petroleum products in the transportation sector), non-fossil energy use and crude oil price.
Compared with previous studies, this paper contributes to the existing literature in two ways: (1) it applies the panel quantile regression model, which can provide a complete relationship between carbon intensity and all the variables. (2) it employs heating degree days and petroleum products in the transportation sector as two variables to avoid endogeneity problems caused by energy consumption.
This paper is organized as follows. Section 2 presents a brief review of the relevant literature. Section 3 describes the data and the panel quantile econometric model applied in this paper. Section 4 presents and discusses the corresponding estimation results. Section 5 concludes the paper and provides related policy recommendations.

Literature Review
Recently, many studies have applied econometric approaches to investigate factors influencing CO 2 emissions (related studies are summarized in Table 1, Table 1 in [11] also provides the related literature). The two most relevant strands of research are: (1) Examining the impacts of economic growth, energy consumption on carbon emissions. In this strand, the scholars mainly focused on two independent variables, namely the economic growth and energy consumption. These two variables are widely recognized to have impacts on carbon intensity and carbon emissions. Apart from the two common variables, different scholars would include other variables into their model according to their research objectives-e.g., Zhu et al. aimed to investigate the impacts of foreign direct investment (FDI) on CO 2 emissions, so Zhu et al. included FDI in their model [3]. (2) Analyzing the effects of economic growth and non-fossil energy consumption on carbon emissions. This strand originates from strand (1) because many scholars want to discover the impacts of renewable energy on CO 2 emissions. The main differences among these studies are the samples, the regression methods and the control variables. Therefore, we will analyze the existing literature from these two aspects.

Studies Examining the Impacts of Economic Growth and Energy Consumption on Carbon Emission
There are plenty of studies concerning the relationship between CO 2 emission, economic growth and energy consumption, see details in Table 1 in [11]. The method and variables are similar in these studies; therefore, we select four recent studies here. There are three methodologies in these studies, namely OLS, panel VAR (PVAR), and panel quantile regression. To be specific, Begum et al. applied DOLS to investigate the relationship among carbon emissions, economic growth, and energy consumption in Malaysia, and concluded both energy consumption and economic growth raise carbon emissions [23]. Wang et al. used FMOLS to study the nexus in China from the provinces' perspective, and concluded that both energy consumption and economic growth enhance carbon emissions. Moreover, there are bidirectional causal links between economic growth and energy consumption, and between energy consumption and carbon emissions, and there is a unidirectional causal link from economic growth to carbon emissions [21]. Antonakakis et al. employed PVAR to research the nexus from a panel of 106 countries, and concluded that economic growth increase CO 2 emissions, and they also proved that there is a bidirectional causal link between economic growth and CO 2 emissions [24]. Zhu et al. applied panel quantile regression to study the nexus by using the data of five ASEAN countries, and discovered the impacts of the different determinants on CO 2 emissions shows a clear heterogeneity along with all quantiles [3].

Studies Examining the Influences of Economic Growth and Non-Fossil Energy Consumption on CO 2 Emissions
With regard to this issue, there are also many studies to research the interactions between carbon emissions, economic growth, and non-fossil energy consumption (see [10,11,18,19]). The method they used is similar, including OLS, FMOLS, DOLS, panel regression, and so on. However, the empirical results are not consistent with each other.
Second, the impacts of economic growth on carbon emissions are mixed.  [10,14].
Several reasons may explain the mixed results, like the data are different, the model and method used are different, and control variables are different [25]. However, we argue that the neglect of individual heterogeneity and distributional heterogeneity is the main reason for the different conclusions. As discussed above, most of existing literature applied common regression technique to investigating the influencing variables of CO 2 emissions, but they overlook the individual heterogeneity and distributional heterogeneity, which has been proven to have great influence on the regression results [3]. Therefore, in order to discover more details and to obtain more useful information about the influencing factors of CO 2 emissions, we apply panel quantile regression technique in this paper, which constitutes an important contribution to the existing literature. Besides, unlike general studies, we use heating degree days and petroleum products in the transportation sector as explanatory variables for energy consumption, aiming to avoid the impacts of share data. Moreover, many studies neglect the competition relationship between non-fossil energy and fossil energy, so in order to find this relationship's impact on CO 2 emission, we use crude oil price as a control variable.
In short, compared with previous studies, especially [10,11] in which EU are analyzed, this paper has two contributions: (1) It applied panel quantile regression method, which may be more suitable than OLS method because both individual heterogeneity and distributional heterogeneity are considered. It can provide a complete picture of the relationship between the explanatory variables and CO 2 emissions. (2) Unlike previous studies, it used heating degree days and petroleum productions in the transportation sector as explanatory variables, rather than employed energy consumption as an independent variable. In this way, we can avoid a possible endogeneity problem.

Date
The data we use consist of panel data of carbon intensity of GDP (ton CO 2 /trillion €), GDP per Capita at 2010 market prices (€), gross electricity generation by nuclear and renewable (100 GWh), heating and cooling degree days, final consumption of petroleum products in transportation sector (kilo tonne of oil equivalent, ktoe), and Brent oil price in 28 European countries. The data are obtained from the European Commission. Our data covers the period from 1990 to 2015.
Carbon intensity of GDP (CDEI) is the dependent variable, and GDP per capita (GDPC), gross electricity generation by non-fossil energy (GEG), heating degree days (HDD), and petroleum products in the transportation sector (PPT) are the independent variables. The GDP per capita is measured in terms of 2010 market prices. To make patterns in the data more interpretable, we transform the data into natural logarithms before empirical analysis. The specific definition of each variable is provided here: (1) Carbon intensity of GDP is calculated as CO 2 emissions divided by GDP; it is measured as CO 2 emissions per unit GDP. Carbon intensity of GDP for different EU countries during 1990-2015 is illustrated in Figure 1. For most of the EU countries, the carbon intensity of GDP decreases slightly over time (see details in Figure 1), because most of them are developed countries. However, a minor increase in carbon intensity can be observed in some less-developed EU countries.
Sustainability 2018, 10, x FOR PEER REVIEW 7 of 20 transform the data into natural logarithms before empirical analysis. The specific definition of each variable is provided here: (1) Carbon intensity of GDP is calculated as CO2 emissions divided by GDP; it is measured as CO2 emissions per unit GDP. Carbon intensity of GDP for different EU countries during 1990-2015 is illustrated in Figure 1. For most of the EU countries, the carbon intensity of GDP decreases slightly over time (see details in Figure 1), because most of them are developed countries. However, a minor increase in carbon intensity can be observed in some less-developed EU countries. (2) GDP per capita at 2010 market prices equals to the gross domestic product divided by the population. The GDP per capita reflects the economic growth in one country and is considered a crucial factor for the carbon intensity in previous research [26,27]. Besides, other scholars also proved that economic growth affects carbon intensity by applying decoupling methods and convergence analysis [28][29][30]. GDP per capita for different EU countries during 1990-2015 is shown in Figure 2. We find an increasing trend in the GDP per capita for almost all EU countries by observing Figure 2. The trends for the carbon intensity of GDP and economic growth are opposite; this finding indicates that GDP may reduce the carbon intensity.  (2) GDP per capita at 2010 market prices equals to the gross domestic product divided by the population. The GDP per capita reflects the economic growth in one country and is considered a crucial factor for the carbon intensity in previous research [26,27]. Besides, other scholars also proved that economic growth affects carbon intensity by applying decoupling methods and convergence analysis [28][29][30]. GDP per capita for different EU countries during 1990-2015 is shown in Figure 2. We find an increasing trend in the GDP per capita for almost all EU countries by observing Figure 2. The trends for the carbon intensity of GDP and economic growth are opposite; this finding indicates that GDP may reduce the carbon intensity. transform the data into natural logarithms before empirical analysis. The specific definition of each variable is provided here: (1) Carbon intensity of GDP is calculated as CO2 emissions divided by GDP; it is measured as CO2 emissions per unit GDP. Carbon intensity of GDP for different EU countries during 1990-2015 is illustrated in Figure 1. For most of the EU countries, the carbon intensity of GDP decreases slightly over time (see details in Figure 1), because most of them are developed countries. However, a minor increase in carbon intensity can be observed in some less-developed EU countries. (2) GDP per capita at 2010 market prices equals to the gross domestic product divided by the population. The GDP per capita reflects the economic growth in one country and is considered a crucial factor for the carbon intensity in previous research [26,27]. Besides, other scholars also proved that economic growth affects carbon intensity by applying decoupling methods and convergence analysis [28][29][30]. GDP per capita for different EU countries during 1990-2015 is shown in Figure 2. We find an increasing trend in the GDP per capita for almost all EU countries by observing Figure 2. The trends for the carbon intensity of GDP and economic growth are opposite; this finding indicates that GDP may reduce the carbon intensity.   (3) Gross electricity generation by non-fossil energy is denoted by the gross electricity generated by nuclear and renewable energy. More precisely, renewable energy includes hydro energy, geothermal energy, solar energy, wind energy, and tide/wave/ocean energy. Figure 3 describes different time series of gross electricity generation by non-fossil energy in EU countries. Overall, continued growth is observed in most EU countries. The trends for the carbon intensity of GDP and non-fossil energy are different, which implies that the use of non-fossil energy may decrease the carbon intensity of GDP. (3) Gross electricity generation by non-fossil energy is denoted by the gross electricity generated by nuclear and renewable energy. More precisely, renewable energy includes hydro energy, geothermal energy, solar energy, wind energy, and tide/wave/ocean energy. Figure 3 describes different time series of gross electricity generation by non-fossil energy in EU countries. Overall, continued growth is observed in most EU countries. The trends for the carbon intensity of GDP and non-fossil energy are different, which implies that the use of non-fossil energy may decrease the carbon intensity of GDP. (4) Heating degree days are used to measure the energy demand which is incurred by heating buildings. To be specific, there is a benchmark temperature (such as 18° Celsius) below which the buildings need to be heated. Heating degree days refer to the accumulated degree which is below the benchmark temperature. Heating degree days are not only related to the location, but also related to incomes, building design, energy systems, and human behaviors. As we know, energy is consumed by industry use (including power generation), the transportation sector, and commercial/residential use. Heating degree days is a useful variable as it can reflect the activity of industry use and commercial/residential use. Figure 4 shows the time series of heating degree days in the EU countries. Overall, an intensive fluctuation is observed in most EU countries.  (4) Heating degree days are used to measure the energy demand which is incurred by heating buildings. To be specific, there is a benchmark temperature (such as 18 • Celsius) below which the buildings need to be heated. Heating degree days refer to the accumulated degree which is below the benchmark temperature. Heating degree days are not only related to the location, but also related to incomes, building design, energy systems, and human behaviors. As we know, energy is consumed by industry use (including power generation), the transportation sector, and commercial/residential use. Heating degree days is a useful variable as it can reflect the activity of industry use and commercial/residential use. Figure 4 shows the time series of heating degree days in the EU countries. Overall, an intensive fluctuation is observed in most EU countries. (3) Gross electricity generation by non-fossil energy is denoted by the gross electricity generated by nuclear and renewable energy. More precisely, renewable energy includes hydro energy, geothermal energy, solar energy, wind energy, and tide/wave/ocean energy. Figure 3 describes different time series of gross electricity generation by non-fossil energy in EU countries. Overall, continued growth is observed in most EU countries. The trends for the carbon intensity of GDP and non-fossil energy are different, which implies that the use of non-fossil energy may decrease the carbon intensity of GDP. (4) Heating degree days are used to measure the energy demand which is incurred by heating buildings. To be specific, there is a benchmark temperature (such as 18° Celsius) below which the buildings need to be heated. Heating degree days refer to the accumulated degree which is below the benchmark temperature. Heating degree days are not only related to the location, but also related to incomes, building design, energy systems, and human behaviors. As we know, energy is consumed by industry use (including power generation), the transportation sector, and commercial/residential use. Heating degree days is a useful variable as it can reflect the activity of industry use and commercial/residential use. Figure 4 shows the time series of heating degree days in the EU countries. Overall, an intensive fluctuation is observed in most EU countries.   to reflect the energy consumption in the transportation sector because most of the energy used in the transportation sector belongs to the products of crude oil. Figure 5 describes the time series of petroleum production in the transportation sector in EU countries. As we can see, there is a small fluctuation for most of the EU countries.
Sustainability 2018, 10, x FOR PEER REVIEW 9 of 20 (5) Petroleum products in the transportation sector are denoted by the total consumption of the LPG, motor gasoline and gas/diesel oil in the transportation sector of each country. It is used to reflect the energy consumption in the transportation sector because most of the energy used in the transportation sector belongs to the products of crude oil. Figure 5 describes the time series of petroleum production in the transportation sector in EU countries. As we can see, there is a small fluctuation for most of the EU countries. Besides, we use Brent oil prices as a control variable, because there is a competition between fossil and non-fossil energy. Table 2 presents the descriptive statistics for all variables. As we can see in Table 2, the skewness and kurtosis values of all variables indicate that the six distributions have long tails, and are not normally distributed. Besides, the Jarque-Bera test clearly shows that all series depart from normality.

Panel Quantile Regression
In this study, a panel quantile regression model is used to analyze the effects of GDP per capita, gross electricity generation by non-fossil energy, heating degree days, petroleum products in the transportation sector, and Brent oil price on the carbon intensity of GDP in EU countries. By using this model, we can examine the driven factors of carbon intensity of GDP at different quantile levels. Much previous empirical research considered traditional conditional mean regression [26,31,32]. Besides, we use Brent oil prices as a control variable, because there is a competition between fossil and non-fossil energy. Table 2 presents the descriptive statistics for all variables. As we can see in Table 2, the skewness and kurtosis values of all variables indicate that the six distributions have long tails, and are not normally distributed. Besides, the Jarque-Bera test clearly shows that all series depart from normality.

Panel Quantile Regression
In this study, a panel quantile regression model is used to analyze the effects of GDP per capita, gross electricity generation by non-fossil energy, heating degree days, petroleum products in the transportation sector, and Brent oil price on the carbon intensity of GDP in EU countries. By using this model, we can examine the driven factors of carbon intensity of GDP at different quantile levels. Much previous empirical research considered traditional conditional mean regression [26,31,32]. However, this method may get the biased relevant coefficient or without finding important relationships [3,33]. In general, the interpretation of the conditional mean method is consistent with human intuition, and it is easy to calculate. In particular, if the error follows a normal distribution, the results of the least squares method are unbiased and efficient. However, in the area of risk management, people often focus on the tail behavior of distributions. Meanwhile, the data usually is not normally distributed, with an apparent peak or fat tails. In this case, the results of the classic regression will get poor results. In addition, there often exist some abnormal points in the data, which will also affect the accuracy of the estimated results. Therefore, many scholars began to use quantile regression to avoid these issues mentioned above. The τth quantile of a random variable Y is given by a quantile function: where τ ∈ (0, 1) and F Y (y) = P(Y ≤ y). This model captures the fact that the quantile function Q Y (τ) returns the minimum value of y from amongst all those values whose cumulative distribution function (CDF) value exceeds τ. The quantile regression, which was proposed by Koenker and Bassett Jr, has many advantages compared to the OLS regression [34], such as the empirical result of panel quantile regression is more robust [35], and there is no need to design distributional assumptions by using panel quantile regression [36]. Moreover, this method is able to capture the characteristics of the entire conditional distribution of all variables [37]. These are of particular interest in econometric analysis and forecasting (see [38][39][40], for example). The developments of quantile regression, as well as wide applications, has been summarized by Koenker and Hallock [41] and Yu et al. [42].
In order to take the impact effects and unobserved individual heterogeneity into consideration, we apply the model where Y i,t and X i,t represent the carbon intensity and corresponding driven factors in country i at time t, and β i denote the unobserved individual effects. α(τ) denote a vector of estimated parameters in the equation, which are varying on different quantile τ. The main difficulties for solving Equation (2) is that we cannot apply traditional linear approaches in the panel quantile regression model. To solve this problem, Koenker proposed an appropriate method with a L 1 -norm penalty term to eliminate unobserved fixed effects, called the shrinkage method [43]. This method is advantageous in controlling the variability caused by a lot of estimated individual coefficients and effectively reducing the number of estimated parameters. Here, we will apply this method to estimate our model, which is where ρ τ (y) = y τ − 1 y<0 is the traditional check function, 1 A is the indicator function. i and t denote the countries and the time, respectively. K is the indicators for quantiles, and w k = 1/K represent the relative weight on the k-th quantile, which is used to denote the contribution of different quantiles in this estimation (see [3,43]). µ is the tuning parameter, it is used to determine the individual effect. With reference to [3], we assume it is 1. Furthermore, in this paper, we study the effects of GDP per capita, gross electricity generation by non-fossil energy, heating degree days, petroleum products in the transportation sector and Brent oil price on the carbon intensity of GDP in EU countries. In order to enable the specifications in our study to differentiate themselves from previous studies, we conduct our analysis by using the model In Equation (4), the countries and the time is denoted by i and t, respectively.

Panel Unit Root Test
Before applying our model, we first adopt stationarity tests to verify which data we should use in our analysis, the selected level or the first difference. Such tests include Levin-Lin-Chu unit-root test [44], Fisher test [45], Hadri test [46], and modified p-test [47]. The tests results for six variables are listed in Table 3. As we can see, the results indicate that all variables are stationary at 1% significant level. Therefore, we will use the selected level in the later empirical analysis.

Panel Quantile Regression Results
Our empirical results are listed in this section. In order to compare the regression results of OLS and panel quantile regression, the model is also estimated by using two panel OLS models, and the estimation results are presented in Column 1 and 2 in Table 4. Other columns in Table 4 show the results of the estimation results of panel quantile regression with fixed effect at the different quantile levels. As shown in Table 4, we conduct the panel quantile regression at intervals of 10th quantile of the conditional carbon intensity of GDP distribution. The estimation results in Table 4 clearly imply that the influences of different determinants on the carbon intensity of GDP are heterogeneous. The corresponding result is illustrated in Figure 6, which allows us to observe the different change patterns of the coefficients of different variables with respect to different quantiles. In each subfigure of Figure 6, the x-axis denotes the conditional quantiles of carbon intensity of GDP, and the y-axis presents the coefficient values of different variables. Moreover, the black solid line shows the point estimation results at different quantile levels. The red dashed line represents the estimation results of the relevant OLS methods.
Firstly, we can observe that the impact of GDP per-capita is clearly heterogeneous and significantly asymmetric in Figure 6b because the coefficients of different quantile levels change greatly with respect to different conditional distributional of carbon intensity of GDP. Overall, from a statistical perspective, the impact of GDPC is significant at 1% significance level and negative at all quantiles. To be specific, the coefficient initially decreases from −0.5851 at the 10th quantile to −0.7259 at the 30th quantile, and then slowly increases to −0.6889 at the 90th quantile. The negative coefficient means that an increase in GDP per capita will reduce the carbon intensity, which is reported in the earlier empirical study [10,11,27]. This finding implies that promotion of economic development may decrease carbon intensity. The main reason is that most EU countries are developed countries, and achieve a desired level of income. According to the EKC hypothesis, once the level of income exceeds the desired level (namely the turning point), the economic growth is useful to reduce carbon emissions. Moreover, the development policy of "inclusive and sustainable growth" is widely applied in the EU, which pays more attention to reducing carbon emissions. Overall, compared with OLS regression results, these results provide a complete picture about the influences of economic growth on CO 2 emissions, which provide support for our statement that OLS method overlooks the individual and distributional heterogeneity, and provide incomplete information about the impacts of economic growth on carbon intensity. Secondly, Figure 6c reveals that the impact of gross electricity generation by non-fossil energy on carbon emission intensity is also statistically significant and heterogeneous. There is significant asymmetry in the response of carbon intensity to gross electricity generation by non-fossil energy at different quantiles, which is similar to the impact of GDP per-capita. Overall, from a statistical perspective, the impact of GEG is significant at 1% significance level and negative at all quantiles. Specifically, the coefficient of GEG has a U-shaped curve trend at different quantiles, which initially decreases from −0.1427 at the 10th quantile to −0.1611 at the 30th quantile, and then increases to −0.1275 at the 80th quantile. The result indicates that the impact is less in the higher or lower quantiles of carbon emission intensity. The negative coefficient implies that an increase in non-fossil production will reduce the carbon intensity, which is also proven in [10,11]. This finding implies the promotion of non-fossil energy is helpful for the reduction of carbon intensity. Compared with fossil energy, non-fossil energy produces less CO 2 emissions in both the production and consumption process. Moreover, the estimation results prove that OLS regression can only present part of information about the impact of gross electricity generation by non-fossil energy on the carbon intensity of GDP.
Thirdly, the coefficient of heating degree days is insignificant at lower quantile levels of carbon intensity of GDP (specifically, the 10th and 20th quantile), but is significant at higher quantile levels (see Figure 6d). Meanwhile, the coefficient of heating degree days is significant in pooled OLS mean regression. Therefore, OLS mean regression may bias the real coefficient, and it is not suitable to apply panel OLS method to investigate the impact of heating degree days on the carbon intensity of GDP. Overall, the coefficient of different quantile level increase from 0.0041 to 0.4854, indicating an apparent increasing trend with respect to the quantile levels of carbon intensity of GDP. The result indicates that when carbon intensity is relatively large, the carbon intensity may be significantly influenced by heating degree days. Compared with high carbon intensity countries, low carbon intensity countries are more developed. Correspondingly, the technology and residents' consumption habits in low carbon intensity countries are better than the counterparts in high carbon intensity countries. High technologies are helpful to improve the thermal insulation performance of buildings and develop more sophisticated technology, such as ecological housing community or residential energy circulation system. Besides, residents' good consumption habits can eliminate waste of energy. Therefore, the impacts of heating degree days on carbon intensity are more significant for medium and high quantiles.
Fourthly, as illustrated in Figure 6e, the coefficient of petroleum products in the transportation sector on carbon intensity has a positive side but is insignificant at most quantile levels except for low quantiles (0.1, 0.2, 0.3, 0.4). To be specific, the impact is initially stable around 0.15 and then decrease from 0.1600 to 0.0426. However, the coefficient is significant in OLS panel data model at 5% significance level, implying that it is not suitable to apply OLS panel model to investigate the influence of petroleum products in the transportation sector on carbon emissions intensity of GDP. Overall, the coefficient is positively significant at low quantiles, but not significant in medium and high quantiles. This finding indicates that petroleum products in the transportation sector have more impact on carbon emission intensity when carbon emission intensity is relatively small. As the share energy use by transportation sector is small in the mix of total end-use energy in most of Europe countries, the share is about 31% in 2016 as reported in Exxon-Mobil's 2018 outlook for energy. As for low carbon intensity EU countries, the percentage is even smaller than 31%. Besides, more non-fossil energy is used in the transportation sector in these countries. Therefore, an increase in petroleum products in the transportation sector may incur a substantial increase in carbon emissions, which in return raise the carbon intensity. This effect may not be that obvious for high carbon intensity EU countries because their energy use share of the transportation sector in total end-use is larger and they consume more fossil energy in the transportation sector.  Fifthly, the coefficient of Brent crude oil price is insignificant and quite symmetric around its median, but significant at other quantiles (as shown in Figure 6f). The impact of Brent crude oil price on carbon intensity has an inverted U-shaped curve trend, which increases from −0.0978 at the 10th quantile to −0.0330 at the 50th quantile and then decreases to −0.0800 at the 70th quantile. These results indicate that the Brent crude oil has a significantly negative influence on carbon emission intensity of GDP in both high and low carbon intensity countries. One possible explanation is that the motivation of medium emission countries to reduce carbon intensity is not as strong as those of low and high emission countries. Therefore, they are not hurrying to cut down the use of fossil energy to change their consumption structure. Correspondingly, the impact of an increase of crude oil price is not very significant on their energy consumption structure, which in return has no significant impact on carbon intensity.
Finally, to verify the heterogeneity of the coefficients, we consider using Wald tests (see [48]) to compare the estimated coefficients of the 0.1 quantile and some higher quantiles (0.3, 0.5, 0.7, and 0.9 quantiles) and to verify whether they are significantly heterogeneous. Table 5 shows the results of the Wald test, which implies that the null hypothesis for GDP per capita, heating degree days and Brent oil price should be rejected, namely the effects of GDP per capita at 2010 market prices, heating degree days and Brent oil price on carbon dioxide emission intensity of GDP are not homogeneous at different quantiles. Therefore, it is important to consider the heterogeneous impacts of the influence factors on the carbon intensity of GDP at different quantile levels. To summarize, after comparing the estimation results of OLS and quantile panel data models, we can determine that fixed-effect panel quantile model provides a much richer and more comprehensive information of the effects of GDP per capita at 2010 market prices, gross electricity generation by non-fossil energy, heating degree days, petroleum products in transportation sector and Brent oil price on carbon intensity in the EU countries. In addition, these findings also help us to better understand the heterogeneity in the influence variables.

Robustness Check
To verify the robustness and the validity of our model, a robustness check which considers different values for µ is conducted. To be specific, we assume that µ equals to 0.1, 0.9, and 2 respectively, and conduct the panel quantile regression again. The estimation results for main variables are listed in Table 6. As shown in Table 6, the results for different µ broadly conform to the main results in Table 4. In addition, we also perform two additional robustness checks by dropping variables. To be specific, we drop PPT and HDD respectively in the two additional robustness checks, and the corresponding results are listed in Tables 7 and 8, respectively. As we can see, the estimation results for CDPC, GEG, and oil are roughly consistent with the results in Section 4.2, which confirm the robustness of the results outlined in this paper. Note: Numbers in the parentheses represent p-value. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.

Conclusions and Suggestions
The key purpose of this paper is to research the influences of non-fossil energy, economic growth and energy consumption on the CO 2 intensity in EU 28 countries. In order to do so, we collect the annual samples of six variables from 1990 to 2015 of 28 EU countries. Considering that there are some limitations of OLS regression, and in order to find more useful information in limited data, we apply panel quantile regression method, which provides more details by taking unobserved individual heterogeneity and distributional heterogeneity into consideration. Moreover, in order to avoid the impact of shared data between CO 2 intensity and energy consumption, we use heating degree days and petroleum products in the transportation sector as explanatory variables in our model. Compared with traditional OLS method, we think panel quantile regression method could discover more information by considering the impacts of various factors on CO 2 intensity at different quantiles.

Conclusions
(1) The regression results indicate that there exist heterogeneity and asymmetry effects at different quantiles with regards to the impacts of the determinants on carbon intensity. It implies that the panel regression method may be more suitable than OLS method because it can provide more details about the relationship between CO 2 emissions and the decisive factors, such as non-fossil energy, economic growth, heating degree days, and so on. It is meaningful for policy makers because the impacts of determinate variables are different for different countries. Therefore, policy makers could adjust their policies according to their own characteristics.
(2) The impact of non-fossil energy on carbon intensity is negative, which conforms to [9,11,13,14,[17][18][19]. In particular, [11] also proved that non-fossil energy is helpful for the reduction of carbon emissions in EU countries by applying panel OLS method. However, our results indicate that the impact of non-fossil energy on carbon intensity is negative and significant at all quantiles, especially in the 0.3 quantile, which exhibits a U-shaped curve. It indicates that non-fossil energy is helpful for reduction of CO 2 emissions, but the impacts are different for different countries. Therefore, it proves that the traditional OLS regression method only provides the mean results, which is not the comprehensive relationship between variables and independent variables.
(3) As for economic growth, we find that economic growth has negative and significant impacts on carbon intensity, which is also proved in [10,13,20]. Particularly, [10] also demonstrated that economic growth mitigates CO 2 emissions in EU countries. However, [10,13,20] applied the OLS method, which provided the same results for all countries. Nevertheless, we find that economic growth decreases carbon intensity, and its decreasing power is enhanced at medium and high quantiles.
(4) With regards to energy consumption, the effect of energy consumption is different for heating degree days and petroleum products consumption in transportation sectors: (1) the impact of heating degree days on carbon intensity is positive and becomes significant at higher quantiles. High carbon intensity countries are less developed; therefore, their technology and residents' energy consumption habits may not be as good as low carbon intensity countries. Thus, heating degree days have a significant positive impact on high carbon intensity countries. (2) the effect of petroleum products consumption for the transportation sector is positive but not significant, except for low quantile. The energy consumption structure for low carbon intensity countries is cleaner than high carbon intensity countries; therefore, an increase in the petroleum products of the transportation sector has a more apparent impact for low carbon intensity countries.
(5) We find that the crude oil price' impacts on carbon intensity present an inverted U-shaped curve with respect to different quantiles. The willing to reduce the carbon intensity of the medium carbon intensity countries may not be as strong as high and low carbon intensity countries; therefore, they are reluctant to change their energy consumption structure. Thus, the impact of an increase in crude oil price in medium carbon intensity countries is not as huge as the counterparts in high and low carbon intensity countries.
In summary, the contribution of this paper to the existing literature is that it applied the panel quantile regression method, and provide more details about the relationship between carton intensity and its decisive factors. Therefore, policy makers can make more suitable policies according to the countries' own characteristics.

Suggestions
Based on the empirical results and our analysis, severval policy recommendations are proposed to further improve the environment in EU countries. (1) In terms of non-fossil energy, as non-fossil energy is helpful for the reduction of carbon intensity of GDP. Therefore, both high-carbon-intensity countries and low-carbon-intensity countries need to promote the development and consumption of non-fossil energy, such as the government can encourage the application of renewable energy in the public sector. The city government in Baeza (Spain) has applied biomass energy to public lighting [49]. Moreover, the government can provide green finance to support the development of non-fossil energy [50]. (2) With regards to energy consumption, EU countries should further improve the energy efficiency in heating, use the more energy-saving material and apply circular economy in building sector, which will effectively reduce the energy consumption caused by heating demand [51]. EU countries also should reduce fossil fuel energy in the transportation sector, especially for low-carbon-intensity countries. This policy recommendation is consistent with the current EU policies as many EU government announced they would stop producing gasoline-fueled cars in the future. IPCC also suggests that improvement in energy efficiency and modification of energy structure are useful methods to mitigate carbon emissions [52]. (3) As for economic growth, our results suggest that medium-carbon-intensity and high-carbon-intensity countries would obtain a lot of benefits if their GDP per capita raised, compared with the counterparties of low-carbon-intensity countries. Therefore, medium-carbon-intensity and high-carbon-intensity countries should develop their economy. Nevertheless, the low-carbon-intensity countries should also try their best to promote their economy because economic growth in EU countries helps to reduce carbon intensity.