5.1. Non linearity and stationarity tests
We adopt the Broock–Dechert–Scheinkman (BDS) test developed by Broock et al. (1996) in order to check the nonlinearity in the data series. The null hypothesis is that the data are independently and identically distributed.
The results of the non-linearity BDS test are reported in Table 2. The results attest that for all series, the null hypothesis is rejected, meaning that all variables are not identically and independently distributed which proves the presence of asymmetries.
For this reason, it is necessary to use an asymmetric integration model to analyze the non-linear interactions.
Table 2
Results of BDS nonlinearity test
Variables | BDS statistic at different dimensions |
m = 2 | m = 3 | m = 4 | m = 5 | m = 6 |
lnCO2 | 0.138 * | 0.222* | 0.289* | 0.311* | 0.298* |
lnGDP | 0.199* | 0.332* | 0.426* | 0.496* | 0.549* |
lnGDP2 | 0.196* | 0.329* | 0.423* | 0.493* | 0.546* |
lnNUC | 0.131* | 0.246* | 0.345* | 0.429* | 0.501* |
lnNRE | 0.102* | 0.149* | 0.190* | 0.207* | 0.185* |
lnTR | 0.143* | 0.228* | 0.276* | 0.299* | 0.3001* |
Notes: * indicates the rejection of the null hypothesis at 1% level of significance and “m” designs the embedding dimension. |
We apply the Augmented Dickey Fuller (Dickey and Fuller 1979) and Zivot-Andrews (Zivot and Andrews 1992) tests to examine the order of integration. Concerning, the null hypothesis of the Augmented Dickey Fuller and Zivot-Andrews tests is the existence of unit root which indicates the non-stationarity of the series. Table 3 reports the results of both Augmented Dickey Fuller and Zivot-Andrews tests for all variables in levels and in first differences.
The Augmented Dickey Fuller test reveals that the null assumption is rejected for CO2, NUC and NRE in levels. However, at first difference, the null hypothesis is rejected for all variables, which means that the nuclear energy, the fossil fuel energy and the CO2 emission are I(0), while the economic income and the trade openness are I(1).
Furthermore, previous studies have highlighted that classic unit root tests such as the Augmented Dickey Fuller are unable to detect the structural changes in the series that can lead to a misspecification of the variables’ integration order (Perron 1989). Therefore, we follow Syed et al. (2021) and Lahiani et al. (2019) in adopting the Zivot-Andrews test which is considered appropriate in the presence of non-linearity in the time series.
The Zivot -Andrews test shows that all series are stationary in I(1) except for NRE which is I(0).
The results of the precedent tests showed that all the variables are integrated in order I(0) and I(1), and no variables are I(2). This finding leads us to apply the non-linear ARDL model since the conditions of order of stationarity and linearity are valid.
Table 3
Variables | Augmented Dickey–Fuller | Zivot-Andrews |
Level | First difference | Level | Break year | First difference | Break year |
lnCO2 | -2.194** | -5.716* | -4.544 | 2011 | -6.859 * | 1998 |
lnNUC | -10.009* | -4.731* | -3.475 | 2007 | -7.348* | 1988 |
lnGDP | -1.768 | -4.099* | -3.630 | 2008 | -4.727*** | 2001 |
lnNRE | -2.971** | -7.283* | -4.779*** | 1998 | -8.124* | 2006 |
lnTR | -0.560 | -6.007* | -4.559 | 1986 | -6.433* | 1994 |
Note: *, **,*** represent the rejection of the null assumption at the significance levels of 1%, 5%, and 10%, respectively. Critical values for the Zivot-Andrews test are − 5.34, -4.80 and − 4.58 for the levels of significance 1%, 5%, and 10%, respectively. |
5.2. Results of the NARDL cointegration
The results of the NARDL bounds estimation are presented in Table 4. The results express that the speed of adjustment (-1.507) is negatively significant at the 1% level, meaning that the estimated NARDL model is stable.
Furthermore, the t-statistic (TBDM) suggested by Banerjee et al. (1998), and the F-statistic (FPSS) presented by Pesaran et al. (2001) validate the presence of asymmetric long run cointegration between the selected variables at 1% significance level.
The R2 value indicates that 98.74% of the data fit the regression model. In other terms, it indicates that 98.74% of the variance in CO2 is collectively explained by the independent variables.
Concerning the sensitivity analysis of the model, the Durbin-Watson statistic (2.431) specifies the non-existence of autocorrelation. In addition, the Breusch-Godfrey serial correlation test (2.088) confirms the null assumption of the absence of serial correlation of error terms, since the p-value of the serial correlation test is insignificant at the different levels of significance.
On the other hand, the Autoregressive Conditional Heteroskedasticity (ARCH) test denies the existence of any conditional heteroskedasticity. Furthermore, the functional form is well-conceived and verified by the Ramsey Regression Equation Specification Error Test (RESET), at the different levels of significance.
Finally, we perform the CUSUM and CUSUMSQ tests in order to check the model stability. Figure 4 presents the CUSUM and CUSUMSQ tests, and indicates that the estimated lines are between the critical bounds at the 5% threshold. This means that the estimated parameters in the model are stable over the period 1980–2019.
Table 4 provides also the long-run and short run coefficients estimated by applying the NARDL cointegration for the determinants of CO2 emissions. In our case, nuclear energy, nonrenewable energy and trade are decomposed into positive and negative changes, while the income and the square of GDP are non-decomposed in order to test the EKC model.
The first long-term result to be retained from this model is the following: the impact of income on CO2 is positive (49.252). This implies that a 1% increase in the level of economic growth increases CO2 emissions by 49.252%. Concerning the squared real GDP per capita, it decreases the level of pollution by about 2.334%.
The significant positive and negative signs of the coefficients of lnGDP and (lnGDP)2, respectively, confirm the existence of an inverted U-shaped curve relying income with CO2 emissions. Accordingly, the EKC hypothesis is supported in our case, which means that over the earliest phases of development, an increase in economic growth is accompanied with a rise of pollutant emissions till a specific threshold level of GDP is reached when an increase of growth is followed by a decrease of pollutant emissions.
These results are consistent with divers researches dealing with the case of France and confirming the EKC hypothesis, such as Iwata et al. (2010), Can and Gozgor (2016), Shahbaz et al. (2018), Ang (2007), and Shahbaz et al. (2017b), Ma et al. (2021). Concerning other countries, the EKC is validated by Malik et al. (2020) and Zhang et al. (2021) for the case of Pakistan, Salari et al., (2021) in the USA.
However, our results are inconsistent with those of Ben Jebli and Ben Youssef (2015) and Amri et al. (2019) which rejected the EKC hypothesis for the case of Tunisia and Pata and Caglar (2021) for the case of China.
Based on the coefficients related to the variable GDP and its square, we can extract the turning point of the EKC curve and the turning year. The calculated turning point value is of the order of 40473.292 (US constant) which corresponds to the logarithm value equal to 10.608. This value is lower than the highest real value over the sample period.
In fact, Ang (2007) and Iwata et al. (2010) have supported this result for the case of France. This value is included in our sample. Indeed, by calculating the turning point, we can further extract the turning year which corresponds to the year 2012. Practically these results are not surprising since France is a developed country and its growth is mature. This result is inconsistent with the work of Dong et al. (2018) which consider that after the year 2028, which corresponds to the turning point, China will realize its mature economic growth.
We have also focused on the potential role of nuclear energy on the environment quality. The results reveal that a favorable variation in generated nuclear energy has a negative influence on carbon emissions. In other words, a 1% upturn in nuclear energy decreases CO2 emissions by 0.12%. Moreover, a 1% decline in nuclear energy drops the CO2 emissions by 0.322%. The negative change in nuclear energy has a more important effect than a positive change in declining the level of CO2 emissions into the atmosphere.
Our findings support the argument that nuclear energy as a green technology can help in reducing CO2 emissions in the long run, confirming the findings of IEA (2019) which points out that nuclear energy makes a substantial contribution to enhancing the global fight against climate change.
Our results are in harmony with the findings of Iwata et al. (2010) and Marques et al. (2016) who stipulated the positive role of nuclear energy in reducing the pollutant emissions for the case of France. Our results are also consistent with Nathaniel et al. (2021) for the group of seven and Hassan et al. (2020) for the BRICS countries, and Syed et al. (2021) for the case of India.
However, results are in contradiction with those of Mahmoud et al. (2020) for the case of Pakistan, Pan and Zhang (2020) for the case of the USA, and Sarkodie and Adams (2018) for the case of South Africa.
On the other hand, the estimated coefficients related to fossil fuel energy appear positive and significant. Specifically, a 1% increase of fossil fuel production leads to an increase of the CO2 emissions by 1.409%, similarly a decrease of 1% of this variable increases CO2 emissions by 1.381%. The results support the fact that CO2 emissions are driven by fossil fuel production in France.
These results are in accordance with the reported results of Ma et al. (2021) study comparing between France and Germany and Martins et al. (2021) for the case of G7 countries. Likewise, Kartal (2022) for the case of the top 5 carbon emitting countries and Lawson (2020) for the case of 41 Sub-Saharan African countries are confirming these results.
The results also attest that the estimated coefficients for trade openness are positive. More specifically, the results reveal that the downside variations in trade openness have a positive impact (0.363), while the positive variations in the trade openness have no significant impact in controlling CO2 emissions in France. Consequently, we can consider the positive effect of the flows of international trade in France for both exports and imports on CO2 emissions. In this regard, policy makers in France should enhance the use of clean technologies, by implementing incentive policies toward environmentally friendly industries and it should also penalize polluting industries by involving taxes and norms.
This finding is analogous to Mutascu (2018) for the case of France, and Aslam et al. (2021) for the case of Malaysia. However, it is inconsistent with the results of Iwata et al. (2010) in the case of France, who found that trade has an insignificant impact on CO2 emissions.
The short run estimation in Table 4 confirms the EKC hypothesis. The income per capita increases the CO2 emissions by 41.944% at 10% of significance level, and its squared curtails the level of CO2 by -1.979% at 10% of significance level.
Regarding nuclear energy, its positive and negative changes have no significant impact on the CO2 emissions in the short run.
The positive and negative changes in fossil fuels have positive repercussions on CO2 emissions. Besides, both positive and negative changes of trade openness have no significant impacts, in the short run.
The next step is to analyze the long-term asymmetric responses of CO2 emissions to positive and negative variations in nuclear, fossil fuel and trade openness, while the GDP per capita and its squared followed a symmetrical approach.
Table 4 also details these asymmetric long term parameters. We conclude that a 1% increase of nuclear energy leads to a decrease of CO2 emissions by 0.080%. Similarly, a 1% decrease of nuclear energy eases off CO2 emissions by 0.214%.
However, a 1% increase of non-renewable energy leads to a significant increase of CO2 emissions by 0.935%. Likewise, a 1% decrease of this variable has the same impact on the environment quality (0.917%).
The trade openness has a negative effect on CO2 emission in the case of positive shock (-0.113%). However, it leads to a raise on CO2 emissions by 0.241% in the case of a negative shock.
Table 4
NARDL long-run and short-run estimations
Long term analysis | t-Statistics | P-value |
Variables | coefficients |
\({\text{l}\text{n}\text{C}\text{O}2}_{\text{t}-1}\) | -1.507 * | -5.08 | 0.000 |
\({\text{l}\text{n}\text{G}\text{D}\text{P}}_{\text{t}-1}\) | 49.252* | 3.95 | 0.002 |
\({\left(\text{l}\text{n}\text{G}\text{D}\text{P}\right)}_{\text{t}-1}^{2}\) | -2.334* | -3.93 | 0.002 |
\(\text{l}{\text{n}\text{N}\text{U}\text{C}}_{\text{t}-1}^{+}\) | -0.120*** | -2.07 | 0.063 |
\({\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}-1}^{-}\) | -0.322*** | -1.93 | 0.080 |
\({\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}-1}^{+}\) | 1.409* | 4.54 | 0.001 |
\({\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}-1}^{-}\) | 1.381* | 5.48 | 0.000 |
\({\text{l}\text{n}\text{T}\text{R}}_{\text{t}-1}^{+}\) | -0.170 | -1.59 | 0.139 |
\({\text{l}\text{n}\text{T}\text{R}}_{\text{t}-1}^{-}\) | 0.363* | 3.84 | 0.003 |
Short term analysis |
\({{\Delta }\text{l}\text{n}\text{G}\text{D}\text{P}}_{\text{t}}\) | 41.944*** | 1.85 | 0.091 |
\({{\Delta }\text{l}\text{n}\text{G}\text{D}\text{P}}_{\text{t}-1}\) | -74.00** | -2.70 | 0.020 |
\({{\Delta }\left(\text{l}\text{n}\text{G}\text{D}\text{P}\right)}_{\text{t}}^{2}\) | -1.979*** | -1.84 | 0.093 |
\({{\Delta }\left(\text{l}\text{n}\text{G}\text{D}\text{P}\right)}_{\text{t}-1}^{2}\) | 3.507** | 2.70 | 0.021 |
\({{\Delta }\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}}^{+}\) | 0.003 | 0.04 | 0.966 |
\({{\Delta }\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}-1}^{+}\) | -0.050 | -0.99 | 0.343 |
\({{\Delta }\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}}^{-}\) | 0.067 | 0.39 | 0.703 |
\({{\Delta }\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}-1}^{-}\) | 0.031 | 0.20 | 0.848 |
\({{\Delta }\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}}^{+}\) | 0.688* | 4.17 | 0.002 |
\({{\Delta }\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}-1}^{+}\) | -0.248 | -1.05 | 0.318 |
\({{\Delta }\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}}^{-}\) | 0.977* | 7.16 | 0.000 |
\({{\Delta }\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}-1}^{-}\) | -0.187 | -0.88 | 0.400 |
\({{\Delta }\text{l}\text{n}\text{T}\text{R}}_{\text{t}}^{+}\) | 0.054 | 0.45 | 0.660 |
\({{\Delta }\text{l}\text{n}\text{T}\text{R}}_{\text{t}-1}^{+}\) | 0.146 | 1.17 | 0.266 |
\({{\Delta }\text{l}\text{n}\text{T}\text{R}}_{\text{t}}^{-}\) | -0.028 | -0.29 | 0.775 |
\({{\Delta }\text{l}\text{n}\text{T}\text{R}}_{\text{t}-1}^{-}\) | -0.229*** | -2.06 | 0.064 |
\(\text{c}\text{o}\text{n}\text{s}\text{t}\text{a}\text{n}\text{t}\) | 9.366* | 5.08 | 0.000 |
\({R}^{2}\) | 0.9874 | | |
Bound Testing for Asymmetric cointegration |
FPSS | 4.1206* | | |
TBDM | -5.0776 * | | |
Long-run parameters | | |
\({{\rho }}_{\text{l}\text{n}\text{G}\text{D}\text{P}}\) | 32.679* | 27.96 | 0.000 |
\({{\rho }}_{(\text{l}\text{n}\text{G}\text{D}{\text{P})}^{2}}\) | -1.549* | 27.31 | 0.000 |
\({{\rho }}_{{\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}}^{+}}\) | -0.080** | 6.559 | 0.026 |
\({{\rho }}_{{\text{l}\text{n}\text{N}\text{U}\text{C}}_{\text{t}}^{-}}\) | -0.214*** | 3.221 | 0.100 |
\({{\rho }}_{{\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}}^{+}}\) | 0.935* | 84.21 | 0.000 |
\({{\rho }}_{{\text{l}\text{n}\text{N}\text{R}\text{E}}_{\text{t}}^{-}}\) | 0.917* | 66.33 | 0.000 |
\({{\rho }}_{{\text{l}\text{n}\text{T}\text{R}}_{\text{t}}^{+}}\) | -0.113*** | 3.342 | 0.095 |
\({{\rho }}_{\text{l}\text{n}{\text{T}\text{R}}_{\text{t}}^{-}}\) | 0.241* | 14.42 | 0.003 |
Sensitivity analysis |
D.W | 2.431 | | |
SERIAL | 2.088 | | 0.148 |
ARCH | 1.249 | | 0.1008 |
RESET | 1.39 | | 0.268 |
CUSUM | Stable | | |
CUSUMQ | Stable | | |
Note: The asterisks (*), (**), and (***) refer to 1%, 5%, and 10% significance levels, sequentially. |
Figure 5 presents the results of the dynamic asymmetric multiplier, which characterizes the dynamic adjustment process between the variables in the model, except for the case of real GDP per capita, and its square which are selected to have a linear reaction during the whole period in order to test the EKC hypothesis.
Clearly, it designs the asymmetric adjustment path of CO2 emissions following one unit change of nuclear energy, nonrenewable energy, and trade openness. The analysis of this step allows French policy makers to integrate and design effective strategies to accomplish their objectives concerning the protection of the environment through the control of CO2 emissions.
It can be observed from Fig. 5 that negative shocks on both nuclear energy and trade openness have a deeper effect on CO2 emissions than positive ones in the long run.
Controversially, the impact of non-renewable energy on CO2 emissions is equivalent in the case of positive and negative changes.