Economic growth and energy consumption in 12 European countries : a panel data approach

Q e paper investigates the relationships between energy consumption and economic growth for 12 European countries over 13 years using data for the sample period of 2000 to 2012. Understanding the relationships of energy consumption in relation to the economy is very important task to ensure a stable economic development. Q e hypothesis of the study says that there is a positive relationship between energy use and economic growth. Q e estimation of GDP equation indicated that that the energy consumption is positive related to the economic growth. Q e evaluated regression model includes growth rates of Energy Consumption and growth rates of Gross Fixed Capital in real prices. Q e analysis let to state that in the analyzed countries energy consumption is not neutral to economic growth. Furthermore, the applied modeling pointed the individual growth rate e[ ect of GDP for every country, that was not captured by the estimated model.


INTRODUCTION
e relationship between energy consumption and economic growth has been an area of interest in the energy economics literature over the past two decades.Most empirical studies conclude that there is a strong relationship between the two variables and energy consumption can be very helpful by estimating economic growth.Ferguson in 1997, in a research program on the bene ts of electricity generation showed that for the G7 group of countries as a whole (USA, Japan, Germany, France, UK, Italy and Canada), constituting two-thirds of the global economy, there was a well correlated relationship between electricity use and wealth creation.Ferguson, Wilkinson and Hill (2000) found correlation between wealth creation and electricity use in 100 developing countries.e correlation was even stronger between wealth and electricity use then between total energy consumption and wealth.Ayres and Voudouris (2014) demonstrated nonlinear relationships between capital, labor, useful energy and economic growth by examining the economic growth of UK, Japan and US during the 20th century.e major conclusion of their study was quite simple that an increasing supply of a ordable useful energy is a precondition for continued growth.is means that future economic growth presupposes the availability of increasing quantities of useful energy.So they concluded that traditional computable general equilibrium models make unwarranted assum ptions that economic growth is driven only by the accumulation of capital per worker.
e ndings stay strong opposite to the neo-classical economic worldview, where the economy is seen as a closed system within which goods are produced only by inputs of capital and labor, and then exchanged between consumers and rms.e economic growth is achieved by increasing inputs of labor or human capital (Hall, Cleveland, Kaufmann, 1986).e aim of this paper is to empirically investigate the relationships between energy consumption and economic growth for 12 countries of Europe over 13 years, using data from the Eurostat databases for the sample period of 2000 to 2012.Understanding the relationships of energy consumption in relation to the economy is very important task to ensure a stable economic development.e hypothesis of the study is: there is positive relationship between energy use and economic growth, what is typical for modern human economies (Sha ee and Topal 2008, Smil 2008, Payne 2010).So, the energy consumption is a signi cant explanatory variable in GDP equation.
e remainder of the paper is organized as follows.Section 2 describes the model and the econometric methodology used in the analysis.Section 3 reports the data employed in this study and the empirical results.Finally, conclusions are made in Section 4.

THE METHOD AND THE MODEL
In the present study, we use the panel data approach to investigate the relationship between energy consumption and economic growth.We propose a framework based on the conventional neo-classical onesector aggregate production function, where we treat Energy Consumption (E), Capital (K) and Total Employment (L), as separate inputs in GDP equation.at is: where:

GDP= ln of Gross Domestic Product K= ln of Gross Fixed Capital E= ln of Total Energy Consumption L= ln of Total Employment
e methodology adopted in this study uses a two-step procedure.First, panel unit root tests are applied to test the degree of integration of economic growth and energy consumption.Second, panel least squares method is applied to determine the signi cant relationships between energy consumption and GDP. e empirical study was made using EViews software.EViews provides convenient tools for computing panel unit root tests.We computed the following tests: Levin, Lin and Chu (2002), Im, Pesaran and Shin (2003), Fisher-type tests using ADF and PP tests- Maddala and Wu (1999), Choi (2001).

Data and variables defi nitions
e data for calculation was taken from Eurostat databases.e nancial data was adapted to reality with the use of Eurostat price indices.en data were converted to their logarithms which allowed to present the relationships between variables in an additive equation.e research covers the period from the 2000 to 2012 for 12 European countries given in table 1.
Table 1 Countries under investigation e variables' notations are as follows: GDP -Gross Domestic Product in real prices, E -Total Energy Consumption, K -Gross Fixed Capital in real prices, L -Total employment.

Test results for unit roots
Before conducting any further analysis, the applied time series were examined by unit root tests.e tests are needed because the applied panel least squares method assumes the stationarity of the analyzed time series.Table 2 reports the results of testing for unit roots in the level variables as well as in their rst di erence.
In the rst half of the table the null hypothesis that each variable has a unit root cannot be rejected.However, after applying the rst di erence, three of the variables meet the requirements of the study.So, we can acknowledge their stationarity for the 95% con dence interval.Only in the case of Total Employment (L) is there no con dence about the lack of unit root, which results in applying the second di erence.After applying the second di erence we can acknowledge the stationarity for Total Employment, but the economic interpretation of the two times di erenced variable is problematic.

Panel least squares estimation results
In studying relationships between energy consumption and GDP we applied panel least squares method.ere were estimated equations of GDP, taking into consideration one way models with xed or random cross-section e ects.e nal form of estimated equation is as follows: e results of modeling the equation are reported in Table 3, which presents the econometrical tests of the estimated models as well.Results were obtained using EViews software.e results of the estimation of GDP equation appears to be a little confusing.Notice that there are two sets of tests made by modeling.e rst set consists of two tests -Cross-section F and Cross-section Chi-square -that evaluate the joint signi cance of the cross-section e ects using sums-of-squares (F-test) and the likelihood function (Chi-square test).e two statistic values (3.743511 and 39.804727) and the associated p-values strongly reject the null hypothesis that the cross-section e ects are redundant.On the other hand the second test was Hausman test.A central assumption in case of random e ects estimation is the assumption that the random e ects are uncorrelated with the explanatory variables.One common method for testing this assumption is to employ a test to compare the xed and random e ects estimates of coe cients (Hausman, 1978).e statistic provides evidence that there is no reason to reject the null hypothesis that there is no misspeci cation.
After testing it appears that we have here a situation, where the cross-section e ects could be treated as xed e ects as well as random e ects.e good practices in such situations says that when we have a model, where we are seeking some dependences in countries level then we should choose xed cross-section effects.Second we should take the statistics of evaluated models into account.When we do this it becomes obvious that the rst equation of GDP is the right one.

Diagram 1. Residuals, actual and fi tted data by ∆GDP Model 1
Source: Own calculation.
e adjusted R-squared is higher than in second equation (0.804 > 0.784), so the rst model better ts the actual data.e estimated DW test statistic for the model is 1.828, so we can state that the residuals are uncorrelated and the heteroscedasticity of residuals is not present.Furthermore, the residual PAC correlogram was made taking 4 quarters lag into consideration.e results are presented in Table 4. e analysis con rms that the residuals are uncorrelated.e calculation of con dence intervals and various signi cance tests for coe cients are all based on the assumptions of normally distributed residuals.Sometimes, the residual distribution is distorted by the presence of a few large outliers.Since the parameter estimation is based on the minimization of squared error, a few extreme observations can exert a disproportionate in uence on parameter estimates.If the error distribution is signi cantly non-normal, con dence intervals may be too wide or too narrow.For this reason, we conducted a test for the normality of residuals (Diagram 2).

Diagram 2. Normality of residuals
Source: Own calculation.
e the Jarque-Bera statistic rejects the hypothesis of normal distribution.e p-value is low, so it indicates that there is no reason to con rm the null hypothesis.So we have recalculated the equation using panel EGLS (Cross-section weights) to meet the assumptions of regression.e equation is given in table 4. e estimated DW test statistic for the model is 1.877, so we can state that the residuals are uncorrelated and the heteroscedasticity of residuals is not present.Furthermore, the residual PAC correlogram was made taking 4 quarters lag into consideration.e results are presented in Table 5. e analysis con rms that the residuals are uncorrelated.We conducted a test for the normality of residuals as well.e results are presented on diagram 3. e modeling we carried out meets all the requirements of a proper estimation.e residuals of the model have normal distribution with the expected value 0. In addition, we used stationary variables for the estimation of the equation .e estimated model of economic growth with the application of energy consumption as one of the explanatory variables meets all the conditions of proper estimation, so it undoubtedly has reliable economic interpretation.

CONCLUSIONS
In the study, we attempted to analyze the relationships between energy consumption and economic growth for 12 European countries.e analysis was based on panel least squares modeling.e estimation of GDP equation indicated that that the energy consumption is positive related to the economic growth.
e nal GDP equation excludes Total Employment, what stands in line with the previous studies in the subject (Kasperowicz, 2013).
e evaluated regression model includes growth rates of Energy Consumption and growth rates of Gross Fixed Capital in real prices.e analysis let us to state that in the analyzed countries energy consumption is not neutral to economic growth.e Energy Consumption is a pro-growth variable, which means that the increase of the energy consumption causes the increase of economic growth.e conclusion stands in contradiction to the neo-classical argument that energy is neutral to output growth.e second signi cant variable -Gross Fixed Capital is a pro-growth variable as well.e increase of the capital causes the increase of economic growth in the analyzed countries.e above-mentioned variables make up a regression equation, which explains about 86% of the variability of the economic growth in analyzed countries.e applied panel modeling with cross-section xed e ects let to point the individual e ect for every country, that was not captured by the estimated model (the e ects are given in table 6).e individual e ects show the part of growth rate of economic growth of a country that is not calibrated in the model.So we have here some other information about the results.For example -the characteristics of Polish economy that was not included in the model a ected the Polish economic growth rate so that the Polish economic growth rate was about 0.01 (0.009718) higher than the average economic growth rate in analyzed countries.Analogously can be interpreted xed e ect for other countries.
To sum up, the empirical results of the study show that the economic growth of analyzed European countries is energy-dependent, so one can state that energy consumption is a limiting factor to economic growth.However, the results obtained should be considered very carefully, because the results have been achieved on the basis of a limited, small number of observations of independent variables.e studies should be counted as a preliminary study for further re ection on the subject.

Table 2
Test results for unit roots Source: Own calculation.

Table 4 Autocorrelation testing
Source: Own calculation.