**4. Results**

After analysing the properties of the data, and since the pre-tests supported our choice for the estimations procedures, we proceeded to the presentation of estimation results, as well as their interpretation. Table 5 discloses the results and diagnostic tests.


*Exclusion tests for VOLGDPPCct and LCRESct-1*


Notes: OLS - Ordinary Least Squares. PCSE – Panel Corrected Standard Errors. The F-test is normally distributed N(0,1) and tests the null hypothesis of non-significance as a whole of the estimated parameters. The Wald test has <sup>2</sup> distribution. It tests the null hypothesis of non-significance of all coefficients of explanatory variables; JST - Joint Significance Test. JST is a Wald ( <sup>2</sup> ) test with the null hypothesis of *HO k* : 0 , with and *<sup>k</sup>* the coefficients of LCRESct-1 and the other explanatory variables, respectively. LRT - Linear Restriction Test has the null hypothesis of *HO k* : 0 . All estimates were controlled to include the time effects, although not reported for simplicity. Standard errors are reported in brackets. \*\*\*, \*\*, \*, denote significance at 1, 5 and 10% significance levels, respectively.

Table 5. Results

14 Renewable Energy – Trends and Applications

In order to dispel any doubt we proceed as follows: i) we estimate the models excluding the variable volatility, concluding that there is no change in the coefficients' signals; ii) we compute the Variance Inflation Factor (VIF) test for multicollinearity (see table 3). The mean VIF is only 2.35 and the largest individual VIF is 4.21. From all this we conclude that

Once the first inspection of the data had been made, we proceeded by testing the intrinsic characteristics of the data, namely by assessing the presence of the phenomena previously reported, i.e., heteroskedasticity, panel autocorrelation, and contemporaneous correlation.

*Modified Wald test (χ2)* 4885.68\*\*\*

*Pesaran's test* 8.592\*\*\* 8.069\*\*\* *Frees' test* 5.525\*\*\* 5.749\*\*\* *Friedman's test* 62.200\*\*\* 59.514\*\*\*

From table 2, the null hypothesis of no first-order autocorrelation is rejected, as suggested by the Wooldridge test. From the Modified Wald statistic, we observe that the errors exhibit groupwise heteroskedasticity. As far as the contemporaneous correlation is concerned, all the tests are unanimous in their conclusions. They support the rejection of the null of crosssectional independence, and thus the residuals do not appear to be spatially independent.

After analysing the properties of the data, and since the pre-tests supported our choice for the estimations procedures, we proceeded to the presentation of estimation results, as well

as their interpretation. Table 5 discloses the results and diagnostic tests.

*Pooled Random Effects Fixed Effects* 

Variables *VIF 1/VIF SCOALEGct* 4.21 0.237790 *SNUCLEGct* 3.12 0.321027 *SGASEGct* 2.79 0.358631 *SOILEGct* 2.25 0.444951 *ENERGPCct* 1.98 0.504358 *LCRESct-1* 1.69 0.592946 *IMPTDPct* 1.65 0.604563 *VOLGDPPCct* 1.15 0.867271

collinearity is not a concern.

*Mean VIF* 2.35

Table 4 reveals the specification tests we computed.

*Note:* \*\*\* denotes 1% significance level.

The use of the PCSE is therefore sustained.

Table 4. Specification tests

**4. Results** 

*Wooldridge test F(N(0,1))* 371.271\*\*\*

Table 3. Variance Inflation Factor

Globally, results reveal great consistency and they are not dependent on the assumptions we made about variances across panels and serial correlations. There are no signal changes and, in general, the explanatory variables prove to be consistently statistically significant throughout the models.

The impact of both energy consumption *per capita* and import dependency on energy on economic growth is negative and statistically significant. The effect of the volatility on economic growth is negative and statistically highly significant. This result supports the assumption that higher volatility contributes to reducing economic growth. Results also provide strong evidence that the impact of energy on economic growth is dissimilar, varying according to the source of energy. While oil and nuclear reveal a positive and statistically highly significant effect on economic growth, it seems that renewables are hampering economic growth. This negative and statistically significant relationship is consistent throughout the several models. The effect of the fossil source natural gas on economic growth is positive and statistically significant, albeit at a lower level of significance (5% and 10%). This probably comes from the fact that this source is playing a recent role as a transition source from heavily polluting sources towards cleaner ones. The effect of coal on economic growth is not always statistically significant and, when significant, it is negative.

We deepen the adequacy of use of the variables *LCRESct-1* and VOLGDPPCct since their use is not widespread in the literature. Additionally, we test the simultaneous use of *SCOALEGct, SOILEGct, SGASEGct,* and *SNUCLEGct*. For that purpose, we provide two exclusion tests: i) Joint Significant Test - JST; and ii) Linear Restriction Test -LRT. The variables *LCRESct-1* and VOLGDPPCct, together, must be retained as explanatory variables. Nevertheless, the sum of the estimated coefficients could not be statistically significant in explaining economic growth. From the LRT we reject the null hypothesis and then the sum of their coefficients is different from zero. The same conclusion is reached when we test the adequacy of the simultaneous control for the variables *SCOALEGct, SOILEGct, SGASEGct,*  and *SNUCLEGct*. These variables must belong to the models. Together with the appropriateness of the use of PCSE, these tests corroborate the relevance of the explanatory variables, other than energy consumption per capita and import dependency on energy, since these are well described in the literature.
