Introduction

The literature on the stationary (or unit root) tests for energy market indicators has developed as a new research field in the energy since 2006 (Ozturk and Aslan 2011).Footnote 1 Since then, the variety of studies has been performed by using different country data, subcomponents of energy sources, time periods, and unit root test techniques. It is important to understand the stochastic properties of energy consumption in order to propose and maintain effective energy policies. Indeed, whether the energy variables are stationary or not is important for the effectiveness of a policy implication to decrease consumption of fossil fuels or support the consumption of renewable energy. For instance, if renewable energy consumption follows a unit root process, permanent policy implications (e.g., portfolio standards) will be more useful than temporary policy implications (e.g., investment and tax incentives) (Smyth and Narayan, 2015). Therefore, analyzing the stochastic properties of renewable energy consumption is vital to develop effective energy policies to increase the level of renewable energy consumption.

Moreover, if renewable energy usage follows a stationary process, the historical data on renewable energy can be considered in forecasts; otherwise, it is not possible to forecast future value of renewable energy consumption. Depending on the integration of the renewable energy sector in the whole economy, permanent shocks to renewable energy may be transmitted to other industries (Barros et al. 2013). Indeed, renewable energy sources are becoming more important in all around the world, and this has attracted the attention of scientists and policymakers (Apergis and Tsoumas 2011). However, in terms of the stationary patterns of renewable and alternative energy sources, there is limited evidence. This is a noteworthy issue since the renewable energy sources are considered as the important factor to decrease the level of carbon emissions and to promote the global green economy.

Our paper analyzes whether there is a unit root in the consumption of renewable energy in 54 countries for the period from 1971 to 2016. To this end, the unit root test of Narayan and Popp (2010) with two structural breaks was applied. A unit root test with one break can be inadequate to model stochastic properties of renewable energy consumption for the period from 1971 to 2016, due to the evidence that there are at least two incidents to provide structural breaks in energy consumption: the Energy Crises in the 1970s and the Global Recession of 2008–2009 (Smyth 2013; Smyth and Narayan 2015). On the other hand, the sample size is small for energy variables, and this fact can lead to bias empirical results if more than two structural breaks in the renewable energy consumption are considered (Omri 2014). In addition, Narayan and Popp (2013) illustrate that the Narayan–Popp unit root test is more powerful than the Lagrange Multiplier (LM) unit root test of Lee and Strazicich (2003) with two structural breaks in general and in the case of the small sample in particular. Based on this evidence, we consider the Narayan–Popp unit root test with two breaks.Footnote 2

To the best of our knowledge, this is the first paper in the literature that directly analyzes the stochastic properties of renewable energy consumption series in the literature by using the robust unit root test of Narayan and Popp (2010). As we discussed in the literature review, the stochastic properties of renewable energy consumption are highly neglected at the aggregated level and most papers focus on renewable energy consumption on the disaggregated level. Focusing on the aggregated level data on renewable energy consumption in 54 countries for the period from 1971 to 2016, our paper observes that renewable energy consumption follows a unit root process in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. Our paper also finds that renewable energy consumption series are stationary around both the level and the time trend in 45 of 54 countries when two structural breaks were considered. In short, our paper uses a robust unit root test of Narayan and Popp (2010) and enhances the current knowledge of the unit root characteristics in the renewable energy consumption to the highest number of countries (54) and the coverage time (1971–2016).

The remaining parts of the paper are organized as follows. The “Literature review” section briefly reviews the previous papers on the unit root findings for energy consumption. The “Data and econometric methodology” section expresses the data and the unit root methodology. The “Empirical findings” discusses the empirical findings and the policy implications. The “Conclusion” section concludes the paper.

Literature review

According to Ozcan (2013), the motivation for analyzing stationarity in energy market indicators was firstly based on the findings by Narayan and Smyth (2007). They use the Augmented Dickey–Fuller (ADF) unit root test in 182 countries, and the evidence indicates that energy consumption is stationary in almost 30% of countries. Chen and Lee (2007) use the Panel Unit Root (PUR) test of Carrion-i Silvestre et al. (2005) (henceforth CBL) that allows for structural breaks to investigate the stationary of energy consumption per capita for seven regions over the period 1971–2002. They find that all regional-based panels of energy consumption are stationary when multiple breaks are incorporated. Following Chen and Lee (2007), Hsu et al. (2008) reanalyze the stationary properties of energy consumption by implementing the Panel Seemingly Unrelated Regressions Augmented Dickey–Fuller (SURADF) test in 84 countries over the period 1971–2003. They report the mixed evidence of stationarity depending on the regions. Narayan et al. (2010) employ the Lee–Strazicich unit root test with two breaks to examine the energy consumption in Australia in the industry and the regional levels. In most cases, they observe that energy consumption is stationary. Hasanov and Telatar (2011) illustrate that most of the countries have stationary energy consumption series. After applying one break LM unit root test for each sector, Ozturk and Aslan (2011) show that energy consumption in all industries is stationary in Turkey over the period 1970–2006. Aslan and Kum (2011) also provide the further evidence from Turkey by showing that the energy consumption in four of seven energy sector follows a unit root process. Ozcan (2013) confirms the stationarity for most of the Middle Eastern countries for the period from 1980 to 2009. According to the results of the CBL test, energy consumption in 8 of the 13 countries is stationary. Ozturk and Aslan (2015) firstly apply a linearity test to understand the path of electricity consumption in 23 Organization for Economic Co-operation and Development (OECD) countries over the period 1960–2005. Then, they run the LM unit root test in six countries with the linear path and the Kruse test in 17 countries with the nonlinear path. It is found that electricity consumption follows a unit root process in 12 countries. Using panel unit root tests, Magazzino (2016) examines the stationary properties of per capita energy consumption in 19 Eurozone member countries for the period from 1960 to 2013 and observes the mixed empirical results.

Several papers analyze the unit root properties of energy consumption at the disaggregated level. For instance, the first study examining the unit root properties of the nuclear energy consumption per capita is performed by Zhu and Guo (2016). The paper finds that nuclear energy consumption follows a stationary process for a panel data sample of 27 countries, but the findings are not robust to different sub-samples. A similar finding for nuclear energy consumption is obtained by Gozgor and Demir (2017) that indicates there is a significant unit root only in France. In terms of the coal consumption, Apergis et al. (2010) find that the coal consumption in the United States (U.S.) is stationary for the period of 1982–2007. Shahbaz et al. (2014) also confirm that the coal consumption is stationary in almost all of 47 developed and developing countries over the period 1965–2010. Our paper is similar to those papers for analyzing the cases of various countries around the globe, but it focuses on the renewable energy, which is neglected by the previous papers.

There are also several papers for examining the case of the renewable energy consumption. For instance, Apergis and Tsoumas (2011) examine the integration properties of disaggregated (solar, geothermal, and biomass) energy consumption in the U.S., and the results are sensitive to the inclusion of structural breaks. Barros et al. (2012) perform the fractional integration techniques for renewable energy consumption that capture the effects of the persistence and the seasonality to examine the degrees of persistence in the U.S. by using monthly data from 1981 to 2010. According to the findings, the degree of integration shows non-stationarity with the mean-reverting behavior. Using a similar methodology, Barros et al. (2013) examine whether shocks to the various components of the renewable energy consumption have permanent or temporary effects. The findings imply non-stationarity, but the mean-reverting process is obtained in the consumption of hydropower, solar, wind, and biofuels. By considering the LM unit root test with one break and two breaks models, Gozgor (2016) examines the presence of unit roots in the renewable energy in Brazil, China, and India for the period from 1971 to 2014. The findings of the paper indicate that renewable energy is a unit root process in Brazil, but it is a mean-reverting process in China and India. Finally, Tiwari and Albulescu (2016) analyze whether there is a unit root in the share of renewables in the electricity consumption ratio in 90 countries for the period from 1980 to 2011 by proposing the Fourier Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test. Their findings indicate the presence of stationarity in most of the countries. They also suggest that more detailed country-based analysis is needed (especially in the developed countries) to consider the share of renewables in the electricity consumption. Following this suggestion of Tiwari and Albulescu (2016), our paper looks at the stochastic properties of the renewable energy consumption in detail in 54 developing and developed countries.

Data and econometric methodology

Data

This paper uses renewable energy consumption (million tons oil equivalent) in 54 countriesFootnote 3 over the period 1971–2016. The frequency of the data is annual. The renewable energy consumption data are obtained from the Statistical Review of World Energy of the British Petroleum in 2017. A summary of the descriptive statistics is reported in Table 1 over the period 1971–2016.

Table 1 Descriptive Summary Statistics for the Renewable Energy Consumption (Million Tonnes Oil Equivalent, 1971–2016)
Full size table

According to Table 1, the largest renewable energy consumers over the period 1971–2016 are the U.S., China, and Germany, respectively. When the standard deviations of the renewable energy consumption are analyzed, again, it can be seen that the largest numbers are in the U.S., China, and Germany, respectively. In short, these three countries are the most important renewable energy consumers around the globe. In addition, there are also rapidly growing renewable energy consumers over the period under concern, such as Brazil, India, and Spain.

Methodology: the Narayan–Popp unit root test

The Narayan–Popp unit root test that takes two endogenous (unknown) structural breaks into account. This unit root test is implemented to the renewable energy consumption in our paper. However, umpteen numbers of papers have applied the Lee–Strazicich unit root test with two structural breaks in energy consumption. As a matter of fact, Lee and Strazicich (2003) showed that the usage of two structural breaks in their unit root test can provide a “substantial deviations in size and power” in the case of the small samples. In addition, Narayan and Popp (2013) illustrated that the Narayan–Popp unit root test is more powerful than the Lee–Strazicich unit root test with two structural breaks in general and in the case of the small sample in particular. Furthermore, the Narayan–Popp unit root test can accurately set the structural breaks than the Lee–Strazicich unit root test (Narayan and Popp 2013). That is why the Narayan–Popp unit root test is considered in our paper. Another issue in the unit root test methodology for the renewable energy consumption is that to model structural breaks in the constant and the time trend terms (Smyth and Narayan 2015).

After explaining these issues in the literature, the Narayan–Popp unit root test can be expressed as follows. Let us assume that an unobserved components model is defined as the data generation process (DGP). DGP (y t ) has two components: the deterministic component (d t ) and the stochastic component (μ t ), and they can be represented as such

$$ {y}_t={d}_t+{\mu}_t $$
(1)
$$ {\mu}_t={\rho \mu}_{t-1}+{\varepsilon}_t $$
(2)
$$ {\varepsilon}_t={\psi}^{\ast }(L){e}_t={A}^{\ast }{(L)}^{-1}B(L){e}_t $$
(3)

where \( {e}_t\sim id\left(0,{\sigma}_{\varepsilon}^2\right) \) and it is assumed that the roots of lag polynomials A ∗(L)andB(L)are with order p and q, respectively. These lag polynomials are outside the unit circle.

Two different specifications for both the trending data are also defined: (i) allows for two structural breaks in the level (this will be defined as the Model 1 (M1)) and (ii) allows for structural two breaks in the level as well as the slope (this will be defined as the Model 2 or (M2)). The deterministic component (d t ) of the model can be represented as such

$$ {d}_t^{M1}=\alpha +\beta t+{\psi}^{\ast }(L)\left({\theta}_1{DU}_{1,t}^{\hbox{'}}+{\theta}_2{DU}_{2,t}^{\hbox{'}}\right) $$
(4)
$$ {d}_t^{M2}=\alpha +\beta t+{\psi}^{\ast }(L)\left({\theta}_1{DU}_{1,t}^{\hbox{'}}+{\theta}_2{DU}_{2,t}^{\hbox{'}}+{\gamma}_1{DT}_{1,t}^{\hbox{'}}+{\gamma}_2{DT}_{2,t}^{\hbox{'}}\right) $$
(5)

with \( {DU}_{i,t}^{\hbox{'}}=1\left(t>{TB}_{B,i}^{\hbox{'}}\right){DT}_{i,t}^{\hbox{'}}=1\left(t>{TB}_{B,i}^{\hbox{'}}\right)\left(t-{TB}_{B,i}^{\hbox{'}}\right),i=1,2.{TB}_{B,i}^{\hbox{'}},i=1,2. \) as the correct structural break dates. θand γ represent the magnitude of the level and the slope of breaks, respectively. ψ ∗(L) captures the effect that “the series responds to shocks to the trend function the way it reacts to shocks to the innovation process (e t )” (Narayan and Popp 2010: 1427). These models can be used in the unit root hypothesis and are derived by combining the structural models from Eq. (1) to Eq. (5). See also Narayan and Popp (2010: 1427–32) for the derivation of the unit root test statistics by combining the structural models and the results of the Monte Carlo simulations for generating the critical values both in the small and the finite sample sizes.

Empirical findings

The Narayan–Popp unit root test with two unknown structural breaks is implemented in the renewable energy consumption series in 54 countries over the period 1971–2016 and the results are reported in Table 2.

Table 2 Results of the Narayan–Popp Unit Root Test for renewable energy consumption (1971–2016)
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The findings in Table 2 illustrate that the renewable energy consumption series are stationary in 36 of 54 countries when two structural breaks are modeled. In addition, the renewable energy consumption follows a unit root process in 18 countries when the structural breaks in the level are considered.

The findings in Table 2 illustrate that renewable energy consumption series are stationary in 45 of 54 countries when two structural breaks in both the level and the time trend terms are modeled. These findings are in line with the results of Tiwari and Albulescu (2016). In addition, the renewable energy consumption follows a unit root process in nine countries (Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey) when the structural breaks in both the level and the time trend terms are considered. The findings for Brazil are in line with the findings of Gozgor (2016). However, we find that both China and India are also effective for promoting renewable energy policies since there is a significant unit root in the renewable energy consumption in the related countries. Following Smyth and Narayan (2015), the results of the structural breaks in the level as well as in both the level and the trend terms are considered as the “benchmark results”.Footnote 4

In addition, we analyze the unit root properties of the renewable energy consumption in the panel data of 54 developed and developing countries using the second-generation cross-sectional dependence PUR test. After showing the cross-sectional dependence among the renewable energy consumption series by implementing the cross-section independence (CD) test of Pesaran (2004), we apply the cross-sectional augmented panel unit root (CIPS) test of Pesaran (2007). We report the results of the CIPS test using only a constant term as well as both constant and trend terms in Table 2. According to the results from the CIPS test, the renewable energy consumption is a stationary process. Since the findings of individual time-series analysis illustrate that the renewable energy consumption in most countries (45 of 54) is a stationary process, the findings from the CIPS test of Pesaran (2007) can be considered as the statistically robust.

Conclusion

This paper analyzed whether there is a unit root in renewable energy consumption in 54 countries over the period 1971–2016. To this end, Narayan–Popp unit root test with two breaks was applied. To the best of our knowledge, this is the first paper in the literature that directly analyzes the stochastic properties of the renewable energy consumption series in the literature by using the robust unit root test of Narayan and Popp (2010). As we discussed, the stochastic properties of renewable energy consumption have been widely neglected at the aggregated level. We observed that renewable energy consumption at the aggregated level follows a unit root process in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. We also found that renewable energy consumption series are stationary around both level and the time trend in 45 of 54 countries when two structural breaks were considered.

The empirical results in the paper provide important policy implications. First, policy changes have temporary effects on the renewable energy consumption in 45 countries, but they will persistently affect the renewable energy consumption in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. In other words, permanent policy implications (e.g., portfolio standard) would be a more effective tool than temporary policy stances (e.g., investment and tax incentives) in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. Temporary policy stances can be more successful in other 45 countries. Second, there could be potential for shock spillover from the renewable energy consumption to macroeconomic variables (e.g., economic growth, inflation, and real exchange rates) in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. Similarly, these possible relationships between renewable energy consumption and the related macroeconomic variables can be analyzed with the co-integration techniques in the related nine countries. Third, since renewable energy consumption follows a unit root process, it is impossible to forecast the future path of the renewable energy consumption in Brazil, China, Colombia, India, Israel, Japan, the Netherlands, Spain, and Turkey. However, this issue can be achieved in other 45 countries, which are considered in the paper.

Future papers on this subject can investigate the unit root properties of the energy consumption series (including the renewable energy and its sub-components) using the recent GARCH-based unit root test of Narayan and Liu (2015).