*Article* **Non-Renewable and Renewable Energies, and COVID-19 Pandemic: Do They Matter for China's Environmental Sustainability?**

**Yugang He 1,\* and Ziqian Zhang <sup>2</sup>**


**\*** Correspondence: 1293647581@sejong.ac.kr

**Abstract:** Since the emergence of the COVID-19 pandemic, people all around the globe have seen its effects, including city closures, travel restrictions, and stringent security measures. However, the effects of the COVID-19 pandemic extend beyond people's everyday lives. It impacts the air, water, soil, and carbon emissions as well. This article examines the effect of energy and the COVID-19 pandemic on China's carbon dioxide emissions in light of the aforementioned context, using the daily data from 20 January 2020 and ending on 20 April 2022. Using the nonlinear autoregressive distributed lag model for empirical analysis, the findings indicate that COVID-19 pandemic confirmed cases and renewable energy advance environmental sustainability due to their negative effects on carbon dioxide emissions, whereas fossil fuel energy hinders environmental sustainability due to its positive effect on carbon dioxide emissions. Moreover, these results are also supported by the results of the frequency domain causality test and the Markow switching regression. In light of these results, there are several policy implications, such as vaccination, renewable energy utilization, and non-renewable energy alternative policies, which have been proposed in this paper.

**Keywords:** COVID-19 pandemic; renewable energy; fossil fuel energy; carbon dioxide emissions; nonlinear autoregressive distributed lag model; frequency domain causality test; Markow switching regression

### **1. Introduction**

The fast rise in global carbon dioxide emissions may be traced directly back to the over-reliance on the use of fossil fuels to fuel economic expansion. According to Our World in Data, worldwide carbon dioxide emissions reached 34.05 billion tons in 2018, up 617 million tons from 2017 and 1.85% from the previous year. Due to the constant increase in carbon dioxide emissions, the climate has become more variable, resulting in an increase in natural disasters. In recent years, countries throughout the globe have given increasing attention to the issue of carbon dioxide emissions. Since 2019, worldwide carbon dioxide emissions have begun to fall. Due to the effect of the COVID-19 outbreak in 2020, the majority of countries enacted preventative and control measures by halting work and production and isolating citizens at home. Some governments or areas also adopted efforts to "close off the country" and "shut off the city" to avoid and contain the outbreak, resulting in a significant decrease in global carbon dioxide emissions. Another piece of data from Our World in The data revealed that global carbon dioxide emissions totaled 31.98 billion tons in 2020, a decrease of 2.056 billion tons from 2019 and a decrease of 6.04 percent from the previous year.

The World Resources Institute stated that China, the world's biggest developing country, had the highest level of carbon dioxide emissions in the world in the year 2020, with 9893.5 million tons. The emissions of carbon dioxide that are produced in China account for 30.93% of the total world emissions of carbon dioxide. One of the most

**Citation:** He, Y.; Zhang, Z. Non-Renewable and Renewable Energies, and COVID-19 Pandemic: Do They Matter for China's Environmental Sustainability? *Energies* **2022**, *15*, 7143. https://doi.org/10.3390/en15197143

Academic Editors: Sebastian Saniuk, Piotr Bórawski and Tomasz Rokicki

Received: 28 August 2022 Accepted: 27 September 2022 Published: 28 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

important considerations is the fact that China has, for a very long time, been driving fast economic expansion by increasing its use of fossil fuels. As a result, figuring out how to lower emissions of carbon dioxide is a challenging problem that China is now experiencing. In addition to this, this has been quite effective in attracting many academics to investigate this subject. Using novel dynamic autoregressive distributed lag and frequency domain causality methods, Abbasi et al. [1] discovered that, from 1980 to 2018, fossil fuel energy significantly increased carbon dioxide emissions over the long and short term. In addition, He [2] pointed out that by using data from 1971 to 2017 and the auto-regressive distributed lag method to undertake an empirical study, fossil fuel usage was placing rising pressure on environmental sustainability because of its beneficial effects on carbon dioxide emissions. Meanwhile, similar results were reported by Li and Haneklaus [3], He and Huang [4], Wang et al. [5], and He et al. [6]. Moreover, China's carbon dioxide emissions have also surfaced in a new scenario as a result of the emergence of COVID-19 and the conflict between Russia and Ukraine. This presents a new possibility for this study, which also offers an opportunity for further research.

Considering the aforementioned examination of the current circumstances, three kinds of hypotheses were proposed. Hypothesis 1 (H1) is that the COVID-19 pandemic negatively affects carbon dioxide emissions. Hypothesis 2 (H2) is that renewable energy negatively affects carbon dioxide emissions. Hypothesis 3 (H3) is that non-renewable energy positively affects carbon dioxide emissions. Based on this background, this article investigates the impacts of energy and the COVID-19 pandemic on China's carbon dioxide emissions (a proxy for environmental sustainability) from 20 January 2020 to 20 April 2022. The results of this empirical study that used a nonlinear autoregressive distributed lag model highlight that COVID-19 pandemic confirmed cases and renewable energy advance environmental sustainability with negative effects on carbon dioxide emissions, whereas fossil fuel energy precludes environmental sustainability, which has positive impacts on carbon dioxide emissions. Furthermore, these findings have confirmed the results of the frequency domain causality test and the Markow switching regression.

Moreover, the results of this research make three significant advances to the existing body of knowledge. Firstly, it has been brought to our notice that there is not a single piece of published research that focuses specifically on China and investigates the relationship between the COVID-19 pandemic, energy, and environmental sustainability. Secondly, there has been a significant amount of scientific input on the subject of energy and environmental sustainability. The COVID-19 pandemic was not included in the vast majority of the studies that were conducted on environmental sustainability and energy. Alternatively, the emphasis is placed on the rise of the economy, as can be observed from the great majority of the articles that were looked at in this context. This study, therefore, addressed the COVID-19 pandemic, environmental sustainability, and energy within the same framework in order to achieve a comprehensive understanding of the subject matter. Thirdly, a quantifiable contribution has been observed in the research that is now being conducted. Even though published works have used methods such as autoregressive distributed lag, the generalized method of moments, and Granger causality to measure the variables of interest, nonlinear models are still not very common. In order to accurately estimate the constraints and features of the COVID-19 pandemic, which is asymmetrical and characterized by unanticipated changes that linear models are unable to capture, nonlinear models, are required. In addition, linear models are incapable of handling the complex and asymmetric high-frequency data dynamics associated with COVID-19 data. As a result, enhanced nonlinear models such as the Fourier autoregressive distributed lag cointegration test, Breitung and Candelon causality test, and Markov switching regression were used to reexamine this subject.

To this end, the remainder of this work is organized as follows: Section 2 summarizes previous studies on this topic. Section 3 discusses the variables and econometric approaches. Section 4 presents the findings and discussions. Section 5 has the conclusion.

### **2. Literature Review**

This section will be subdivided into three subsections, each discussing the paper's highlighted issues. The objective of the first subsection is to investigate the impact of the COVID-19 pandemic on environmental sustainability. The objective of the second subsection is to explore the impact of renewable energy on environmental sustainability. The objective of the third subsection is to examine the impact of non-renewable energy on environmental sustainability. They are presented with the following layout:

### *2.1. Effect of the COVID-19 Pandemic on Environmental Sustainability*

The pandemic caused by COVID-19 is having an effect on human activities, which in turn will have an effect on carbon dioxide emissions. Based on data that was collected in almost real-time, Liu et al. [7] provided daily estimates of carbon dioxide emissions at the national level for a variety of different industries. They discovered that the pandemic's impacts on worldwide emissions decreased as lockdown prohibitions were loosened and several economic activities resumed, particularly in China and a some European countries. However, considerable differences in progress were observed between countries, with emissions tending to decline in the United States, where COVID-19 confirmed cases were still rising significantly. Meanwhile, Nguyen et al. [8] discovered that, as a consequence of the COVID-19 pandemic, the brief lockdown periods led to significant reductions in daily worldwide carbon dioxide emissions. In addition, the favorable effects on the local environment were obvious in the decreased output and global migration between cities and regions. Moreover, Aktar et al. [9] observed that the lockdown had precipitated a worldwide economic shock at an alarming rate, leading to severe recessions in several nations. At the same time, the lockdowns triggered by the COVID-19 pandemic radically altered global patterns of energy use and decreased carbon dioxide emissions. Tan et al. [10] found that carbon dioxide emissions for the globe and Malaysia were reduced substantially by 4.02% (1365.83 Mt carbon dioxide emissions) and 9.7% (225.97 Mt carbon dioxide emissions) in 2020, respectively, compared to 2019. In addition, Le Quéré et al. [11], Peng and Jimenez [12], Andreoni [13], and Bertram et al. [14] all corroborated this conclusion.

### *2.2. Effect of the Effect of Renewable Energy on Environmental Sustainability*

Environmental contamination is one of the most important concerns affecting the contemporary world. Because it impacts billions of people, environmental degradation has attracted a considerable amount of attention from scientists and academics. The use of renewable energy as a viable alternative has garnered the support of a significant number of academics as a potential solution to this issue. Anwar et al. [15] investigated the influence that the usage of renewable energy had on carbon dioxide emissions in fifteen Asian economies from 1990 to 2014. After conducting an empirical investigation using methodologies such as impulse response function and variance decomposition, they came to the conclusion that consuming renewable energy sources resulted in lower levels of carbon dioxide emissions. Lei et al. [16] examined the dynamic effects of energy efficiency and renewable energy consumption on China's carbon dioxide emissions between 1991 and 2019. Using the non-linear autoregressive distributed lag technique, they revealed that renewable energy consumption with a positive shock had a large negative influence on carbon dioxide emissions, but renewable energy consumption with a negative shock resulted in an increase in pollutant emissions in the long term. Furthermore, positive shocks to renewable energy usage had a short-term negative impact on carbon dioxide emissions. Mirziyoyeva and Salahodjaev [17] used panel data methodologies to investigate the link between renewable energy and carbon dioxide emissions intensity in the most carbon-intensive countries from 2000 to 2015. Their findings, which were based on the two-step generalized moment method and fixed effects regression for empirical analysis, demonstrated that the use of renewable energy had a substantial and detrimental impact on carbon dioxide emissions. To be more specific, a reduction in carbon dioxide emissions of 0.98% was achieved for every percentage increase in the use of renewable sources of energy. Furthermore, this result was supported by the research conducted by Rahman et al. [18], Fan and Tahir [19], Qudrat-Ullah [20], and Adebayo et al. [21].

### *2.3. Effect of Non-renewable Energy on Environmental Sustainability*

For a very long time, fast economic expansion has been contingent on a large consumption of non-renewable energy. Despite the fact that this has led to an improvement in our quality of life, it has also resulted in significant harm to the environment. As a result of this, a significant number of academics have begun to investigate the effect that non-renewable energy has on the emission of carbon dioxide. Mohsin et al. [22] adopted nonlinear techniques such as causality-in-quantiles, wavelet coherence, and quantile-onquantile regression to investigate the influence of fossil fuel energy consumption on carbon dioxide emissions in European and Central Asian countries from 1989 to 2021. They identified that the use of energy derived from fossil fuels had a beneficial effect on carbon dioxide emissions in the short, medium, and long term; however, the impact varied depending on the periods and frequencies at which it occurred. Tan et al. [23] investigated, via the use of the dynamic autoregressive distributed lag method, how changes in China's nonrenewable energy consumption influenced carbon dioxide emissions from 1990 to 2019. They determined that greater usage of fossil fuels led to higher carbon dioxide emissions. Specifically, carbon dioxide emissions per capita increased by 0.311% for every 1% rise in per capita fossil fuel usage. Similarly, Uzair Ali et al. [24] used yearly data from 1971 to 2014 to evaluate the influence of fossil fuel usage on carbon dioxide emissions in India, Pakistan, and Bangladesh. They unearthed that, in the long run, fossil fuel usage had a positive influence on carbon dioxide emissions using a panel autoregressive distributed lag. Moreover, Rezaei Sadr et al. [25] assessed this issue based on panel data from 1995 to 2019 using fully modified ordinary least squares and dynamic ordinary least squares regression techniques in three Western European countries. They found that crude oil consumption had the greatest influence on both models in terms of carbon dioxide emissions. Additionally, this finding was corroborated by the studies carried out by Vo and Vo [26], Mujtaba et al. [27], Omri and Saidi [28], and Saleem et al. [29].

### **3. Variable Description and Econometric Approach**

### *3.1. Variable Description*

The goal of this study is to identify the effect of energy and the COVID-19 pandemic on environmental sustainability (carbon dioxide emissions are a proxy for environmental sustainability) using a sample from China. The daily dataset covers the time span beginning on 20 January 2020 and ending on 20 April 2022. There are four variables being investigated in this paper. They are the COVID-19 confirmed cases, renewable energy, fossil fuel energy, and carbon dioxide emissions. Because the daily data on renewable energy and fossil fuel energy cannot be available, the stock prices of the two most representative renewable energy companies and fossil energy companies in China are considered proxy variables for renewable energy and non-renewable energy, respectively. The basic idea behind this concept is that changes in the price of energy may almost instantaneously be reflected in both supply and demand for energy. To put it another way, the ebb and flow of energy prices may, to a certain degree, mirror the state of affairs regarding energy consumption. These highlighted variables are sourced from Johns Hopkins University, the Chinese Center for Disease Control and Prevention, Carbon Monitor, and Invest.com. The forms and definitions of these four investigated variables are provided in Table 1, which is required for gaining an in-depth understanding of them for the whole work.


**Table 1.** Results of variable description.

### *3.2. Econometric Approach*

### 3.2.1. Unit Root Test

In this study, we investigate the stationary characteristics of these four highlighted variables by using the Augmented Dicky–Fuller test and the Fourier-Augmented Dicky– Fuller test. The expression of the Augmented Dicky–Fuller test is shown as follows:

$$
\Delta \mathbf{y}\_{\text{t}} = \rho \mathbf{y}\_{\text{t}-1} + \rho\_1 \Delta \mathbf{y}\_{\text{t}-1} + \rho\_2 \Delta \mathbf{y}\_{\text{t}-2} + \dots + \rho\_n \Delta \mathbf{y}\_{\text{t}-n} + \delta \chi\_{\text{t}} + \mu\_{\text{t}} \tag{1}
$$

where ∆ denotes the difference operator; µ<sup>t</sup> denote the white noise. The introduction of the lagged term was undertaken so as to solve the problem of autocorrelation. It is well known that the Augmented Dicky–Fuller test does not have the capacity to identify the structural breakpoints of these investigated variables. It is possible that these investigated variables went through certain structural modifications, which might lead to a variety of different kinds of nonlinearity. Omay [30], Tsong et al. [31], and Narayan and Popp [32] improved the Augmented Dicky–Fuller test for a nonlinear framework by using a Fourier function that was made up of a variety of frequency components. The following equation provides a definition of a Fourier function:

$$\mathbf{y}\_{\mathbf{t}} = \rho\_0 + \rho\_1 \mathbf{t} + \sum\_{i=1}^{\mathbf{p}} \gamma\_i \sin\left(\frac{2\pi \mathbf{i} \mathbf{t}}{\mathbf{n}}\right) + \sum\_{\mathbf{j}}^{\mathbf{p}} \beta\_{\mathbf{i}} \cos\left(\frac{2\pi \mathbf{j} \mathbf{t}}{\mathbf{n}}\right) \tag{2}$$

where ρ<sup>0</sup> denotes the coefficient of intercept; ρ<sup>1</sup> denotes the coefficient of trend; γ<sup>i</sup> denotes the dynamics displacement; β<sup>i</sup> denotes the amplitude; p is less than half of n; t belongs to one and two; i and j denote the nonlinear parameters. Nonlinearity occurs when either i or j is significant in statistic. However, the highlighted variable will be linear when i and j are zero.

### 3.2.2. Fourier Autoregressive Distributed Lag Cointegration Test

The cointegration test was carried out so that we could identify these highlighted variables that were responsible for the study's long-term connection. In order to achieve cointegration, all these four highlighted variables must be integrated using the same sequence. The Fourier autoregressive distributed lag cointegration developed by Güri¸s [33], Yilanci and Tunali [34], and Westerlund and Edgerton [35] is used in this paper. When compared with conventional cointegration tests developed by Kremers et al. [36], Doornik [37], and MacKinnon [38], the Fourier autoregressive distributed lag cointegration test is superior because of its ability to identify a series of nonlinear long-run associations. This test removes the need to determine the duration of the breaks and prevents power loss that may occur when using dummies for an excessive amount of time. For this test, the formula is shown as follows:

$$
\Delta \mathbf{y}\_{1t} = \mathbf{d}\_t + \Delta \mathbf{y}\_{1,t-1} + \tau \Delta \mathbf{y}\_{2,t-1} + \mu\_t \tag{3}
$$

where the null hypothesis is that there is no cointegration while the alternative hypothesis is that there is a cointegration.

### 3.2.3. Markov Switching Approach

The Markov switching approach, which was developed by Hamilton [39] and is a superior alternative in comparison to other statistical procedures, was used on the variables of research because of the nonlinearity characteristic of the variables as well as a quick shift in the variation in the variables of the study. This technique is an option that does not follow a linear progression. The fundamental ideas behind this approach are very malleable and may be modified in response to changes in regime transitions. In fact, this method is applicable in situations in which the variables are not stationary. Nonlinearity happens when a process passes through discrete changes in regimes, which are occurrences in which the dynamic behavior of a certain series behaves differently, as described by Hamilton [40]. This is when nonlinearity arises. The following is an expression that may be used to describe the Markov switching regression with two different regimes:

$$\mathbf{y}\_t = \mathbf{a}\_1 + \sum\_{i=1}^p \mathbf{b}\_{1,i} \mathbf{y}\_{t-1} + \mathbf{a}\_{1,t} \text{ with } \mathbf{s}\_t = 1 \tag{4}$$

$$\mathbf{b}\_{\mathbf{t}} = \mathbf{a}\_{2} + \sum\_{i=1}^{p} \mathbf{b}\_{2,i} \mathbf{y}\_{t-1} + \mathbf{a}\_{2,t} \text{ with } \mathbf{s}\_{\mathbf{t}} = \mathbf{2} \tag{5}$$

where a1,t ∼ N 0, σ 2 i ; s<sup>t</sup> denotes the state variable constrained by the first-order Markov chain. In order to represent the different probabilities of transition, the following matrix structure may be utilized:

$$\mathbf{P} = \begin{bmatrix} \mathfrak{e}\_{11} \ \mathfrak{e}\_{12} \\ \mathfrak{e}\_{21} \ \mathfrak{e}\_{22} \end{bmatrix} \tag{6}$$

if the ρij value is quite small, the structure will continue to be in state i for a considerable amount of time. The expected state duration is <sup>1</sup> ρij , and the number of regime (r) is greater than two.

### 3.2.4. Non-Linear Autoregressive Distributed Lag Approach

In order to investigate the connection between the highlighted variables, the nonlinear autoregressive distributed lag approach is employed in this article. The asymmetric autoregressive distributed lag approach can be applied in situations in which the highlighted variables are either I(0) or I(1), or both I(0) and I(1). The non-linear autoregressive distributed lag approach requires efficient lag selection, and endogeneity problems may be alleviated by choosing an appropriate lag length. Following Shin et al. [41] and Katrakilidis and Trachanas [42], having an appropriate lag can also be helpful in tackling the challenges posed by probable multicollinearity in the non-linear autoregressive distributed lag approach. The non-linear autoregressive distributed lag approach is used to segregate variables based on the positive and negative shifts that each variable exhibits. In the model, fossil fuel energy, renewable energy, and the number of COVID-19 confirmed cases are reduced to positive and negative movements. The variables are transformed into shocks as rene+, rene−, foss+, foss−, covid+, and covid−. Furthermore, the partial sum of the movements for rene, foss, and covid is presented as follows:

$$\text{(rene}^+ = \sum\_{i=1}^t \Delta \text{rene}^+ + \sum\_{i=1}^t \max(\text{rene}\_{\text{i}}, \bullet) \tag{7}$$

$$\text{(rene}^{-} = \sum\_{i=1}^{t} \Delta \text{rene}^{-} + \sum\_{i=1}^{t} \min(\text{rene}\_{\text{i}} \text{ o}) \tag{8}$$

$$\text{foss}^+ = \sum\_{i=1}^t \Delta \text{foss}^+ + \sum\_{i=1}^t \max(\text{foss}\_{\text{i}}, \text{o}) \tag{9}$$

$$\text{foss}^{-} = \sum\_{\mathbf{i}=1}^{\mathbf{t}} \Delta \text{foss}^{-} + \sum\_{\mathbf{i}=1}^{\mathbf{t}} \min(\text{foss}\_{\mathbf{i}\prime} \text{ o}) \tag{10}$$

$$\mathbf{c}\,\mathbf{c}\,\mathbf{v}\mathbf{d}^+ = \sum\_{i=1}^t \mathbf{A}\mathbf{c}\mathbf{v}\mathbf{i}\mathbf{d}^+ + \sum\_{i=1}^t \mathbf{max}(\mathbf{c}\mathbf{v}\mathbf{i}\mathbf{d}\_{i\prime}\mathbf{o})\tag{11}$$

$$\text{covid}^{-} = \sum\_{i=1}^{t} \Delta \text{covid}^{-} + \sum\_{i=1}^{t} \min(\text{covid}\_{i}, \mathbf{o}) \tag{12}$$

the basic model used in this paper is shown as follows:

$$\mathbf{a}\mathbf{c}\mathbf{b}\_{\mathbf{l}} = \mathbf{a}\_{0} + \mathbf{a}\_{1}\mathbf{r}\mathbf{e}\mathbf{e}\_{\mathbf{l}} + \mathbf{a}\_{2}\mathbf{f}\mathbf{s}\mathbf{s}\_{\mathbf{l}} + \mathbf{a}\_{3}\mathbf{c}\mathbf{v}\mathbf{i}\mathbf{d}\_{\mathbf{l}} + \boldsymbol{\mu}\_{\mathbf{t}}\tag{13}$$

where a<sup>0</sup> denotes the constant; [a1, a3] denote the estimated coefficients; µ<sup>t</sup> denotes the white noise. Moreover, the following equation can be used to combine both long-run and short-run dynamics in the non-linear autoregressive distributed lag model.

$$\begin{array}{c} \mathsf{Acorb}\_{\mathtt{l}} = \mathsf{b}\_{0} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{l}} \mathsf{Acorb}\_{\mathtt{l}-\mathtt{i}} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{l}} \mathsf{Arende}\_{\mathtt{t}-\mathtt{i}}^{+} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{b}} \mathsf{Arende}\_{\mathtt{t}-\mathtt{i}}^{-} +\\ \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{d}} \mathsf{Aros}\_{\mathtt{t}-\mathtt{i}}^{+} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{b}} \mathsf{Aros}\_{\mathtt{t}-\mathtt{i}}^{-} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{b}} \mathsf{Acorid}\_{\mathtt{t}-\mathtt{i}}^{+} + \sum\_{\mathtt{i}=1}^{t} \mathsf{b}\_{\mathtt{b}} \mathsf{Acorid}\_{\mathtt{t}-\mathtt{i}}^{-} + \mu\_{\mathtt{t}} \end{array} \tag{14}$$

where b<sup>0</sup> denotes the constant; [b1, b7] denote the estimated coefficients; µ<sup>t</sup> denotes the white noise. By simply adding an error correction term to Equation (14), it is possible to convert Equation (14) into an error correction model.

$$\begin{array}{c} \mathsf{\dot{\Delta}} \mathsf{corb}\_{\mathsf{t}} = \mathsf{c}\_{0} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{1} \mathsf{\dot{\Delta}} \mathsf{corb}\_{\mathsf{t}-\mathsf{i}} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{2} \mathsf{\dot{\Delta}} \mathsf{rece}\_{\mathsf{t}-\mathsf{i}}^{+} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{3} \mathsf{\dot{\Delta}} \mathsf{rece}\_{\mathsf{t}-\mathsf{i}}^{-} +\\ \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{4} \mathsf{\dot{\Delta}} \mathsf{f} \mathsf{oss}\_{\mathsf{t}-\mathsf{i}}^{+} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{5} \mathsf{\dot{\Delta}} \mathsf{f} \mathsf{oss}\_{\mathsf{t}-\mathsf{i}}^{-} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{6} \mathsf{Accvid}\_{\mathsf{t}-\mathsf{i}}^{+} + \sum\_{\mathsf{i}=1}^{t} \mathsf{c}\_{7} \mathsf{\dot{\Delta}} \mathsf{cov} \mathsf{id}\_{\mathsf{t}-\mathsf{i}}^{-} +\\ \lambda \mathsf{ect}\_{\mathsf{t}-1} + \mu\_{\mathsf{t}} \end{array} (15)$$

where c<sup>0</sup> denotes the constant; [c1, λ] denote the estimated coefficients; ect denotes the error correction term; µ<sup>t</sup> denotes the white noise.

### 3.2.5. Frequency Domain Causality Test

This approach is inspired by the work that was undertaken by Geweke [43], and Hosoya [44], who developed measurements of causality in the frequency domain. First, assume that z<sup>t</sup> = [x<sup>t</sup> , y<sup>t</sup> ] ' is an observing time series's two-dimensional vector at t ∈ [1, T]. Let z<sup>t</sup> be a vector autoregressive representation with a finite order:

$$
\Theta(\mathcal{L})\mathbf{z}\_{\mathsf{t}} = \mathfrak{u}\_{\mathsf{t}} \tag{16}
$$

where Θ(L) = I − Θ1L − ... − ΘpL p is a 2 × 2 lag polynomial with L k <sup>z</sup><sup>t</sup> = <sup>z</sup>t−k. Let the error vector (µ<sup>t</sup> ) be the white noise that has E(µ<sup>t</sup> ) = 0 and E µtµ ' t = ∑, where ∑ denotes the positive definite. For the sake of clarity, we disregard any deterministic components in Equation (1), despite the fact that empirical applications frequently contain constants, trends, or dummy variables. Assume that G denotes the lower triangular matrix of the Cholesky decomposition G ' <sup>t</sup>G<sup>t</sup> = ∑ −1 such that E ηtη ' t = I and η<sup>t</sup> = Gµ<sup>t</sup> . Under the assumption that the system is stationary, the MA representation of the system appears as follows:

$$\mathbf{z}\_{\mathbf{t}} = \boldsymbol{\Phi}(\mathbf{L})\boldsymbol{\mu}\_{\mathbf{t}} = \begin{bmatrix} \boldsymbol{\Phi}\_{11}(\mathbf{L}) & \boldsymbol{\Phi}\_{12}(\mathbf{L}) \\ \boldsymbol{\Phi}\_{21}(\mathbf{L}) & \boldsymbol{\Phi}\_{22}(\mathbf{L}) \end{bmatrix} \begin{bmatrix} \boldsymbol{\mu}\_{\mathbf{t}\mathbf{t}} \\ \boldsymbol{\mu}\_{\mathbf{2t}} \end{bmatrix} = \boldsymbol{\Psi}(\mathbf{L})\boldsymbol{\eta}\_{\mathbf{t}} = \begin{bmatrix} \boldsymbol{\Psi}\_{11}(\mathbf{L}) & \boldsymbol{\Psi}\_{12}(\mathbf{L}) \\ \boldsymbol{\Psi}\_{21}(\mathbf{L}) & \boldsymbol{\Psi}\_{22}(\mathbf{L}) \end{bmatrix} \begin{bmatrix} \varepsilon\_{\mathbf{1t}} \\ \varepsilon\_{\mathbf{2t}} \end{bmatrix} \tag{17}$$

where Φ(L) = Θ(L) −1 and ψ(L) = ψ(L)G −1 . The spectral density x<sup>t</sup> can be described employing this representation as follows:

$$f\_{\mathbf{x}}(\omega) = \frac{\left\{ \left| \psi\_{11} \left( \mathbf{e}^{-i\omega} \right) \right|^{2} + \left| \psi\_{12} \left( \mathbf{e}^{-i\omega} \right) \right|^{2} \right\}}{2\pi} \tag{18}$$

Following Hosoya [44] and Geweke [43], the measure of causality is defined as follows:

$$\mathbf{M}\_{\mathbf{y}\to\mathbf{x}}(\omega) = \log\left[\frac{2\pi\mathbf{f}\_{\mathbf{x}}(\omega)}{\left|\psi\_{11}(\mathbf{e}^{-i\omega})\right|^{2}}\right] = \log\left[1 + \frac{\left|\psi\_{12}(\mathbf{e}^{-i\omega})\right|^{2}}{\left|\psi\_{11}(\mathbf{e}^{-i\omega})\right|^{2}}\right] \tag{19}$$

When ψ12 e −iω is zero, the measure is zero, in which situation we claim that y does not cause x at frequency ω. When the elements of z<sup>t</sup> is cointegrated at I(1), Θ(L) has a unit root. The remaining roots are not included inside the unit circle. Taking zt−<sup>1</sup> away from both sides, Equation (15) yields:

$$\Delta \mathbf{z}\_{t} = (\Theta\_{1} - \mathbf{I})\mathbf{z}\_{t-1} + \Theta\_{2}\mathbf{z}\_{t-2} + \dots + \Theta\_{\mathbf{P}}\mathbf{z}\_{t-\mathbf{P}} + \mu\_{t} = \Theta(\mathbf{L})\mathbf{z}\_{t-1} + \mu\_{t} \tag{20}$$

where Θe (L) = Θ<sup>1</sup> − I + Θ2L + ... + ΘpL p . when y is not a cause of x in the usual Granger sense, following Toda and Phillips (1994), the [1, 2]-element of Θ(L) or Θe (L) is zero. The orthogonalized MA representation can be used to determine the measure of causality in the frequency domain:

$$
\Delta \mathbf{z}\_{\mathbf{t}} = \Phi(\mathbf{L}) \boldsymbol{\mu}\_{\mathbf{t}} = \Psi(\mathbf{L}) \boldsymbol{\eta}\_{\mathbf{t}} \tag{21}
$$

where Ψe(L) is equal to Φe (L)G −1 ; η<sup>t</sup> is equal to Gµ<sup>t</sup> ; G denotes a lower triangular matrix such that E ηtη ' t is equal to I. Following Engle and Granger [45], β 'Ψe(1) is equal to zero in a bivariate cointegrated system. When β is a cointegration vector, β ' z<sup>t</sup> will be stationary. Similar to the situation of stationarity, the resultant causality measure is shown as follows:

$$\mathbf{M}\_{\mathbf{y}\to\mathbf{x}}(\omega) = \log \left[ 1 + \frac{\left| \tilde{\Psi}\_{12} (\mathbf{e}^{-i\omega}) \right|^2}{\left| \tilde{\Psi}\_{11} (\mathbf{e}^{-i\omega}) \right|^2} \right] \tag{22}$$

There is potential for the causality measure to be used in systems with a higher dimension. The approach proposed by Hosoya [46] is predicated on the bivariate causality measure that is obtained by "conditioning out" the third variable. Assume that the causal effect of y1t on y2t in a three-dimensional system with y<sup>t</sup> = - <sup>y</sup>1t, y2t, y3t' is measured. Meanwhile, assume that w<sup>t</sup> denotes the projection residual from a projection of y3t onto the Hilbert space H ∈ - <sup>y</sup>1t, yt−<sup>n</sup> . In addition, *e*t(νt) denotes the projection residual from a projection of y1t(y2t) on H ∈ [w<sup>t</sup> , wt−n]. The form is shown as follows:

$$
\begin{bmatrix}
\Delta \mathbf{y}\_{1t} \\
\Delta \mathbf{y}\_{2t} \\
\Delta \mathbf{y}\_{3t}
\end{bmatrix} = \begin{bmatrix}
\boldsymbol{\Psi}\_{11}(\mathbf{L})\,\boldsymbol{\Psi}\_{12}(\mathbf{L})\,\boldsymbol{\Psi}\_{13}(\mathbf{L}) \\
\boldsymbol{\Psi}\_{21}(\mathbf{L})\,\boldsymbol{\Psi}\_{22}(\mathbf{L})\,\boldsymbol{\Psi}\_{23}(\mathbf{L}) \\
\boldsymbol{\Psi}\_{31}(\mathbf{L})\,\boldsymbol{\Psi}\_{32}(\mathbf{L})\,\boldsymbol{\Psi}\_{33}(\mathbf{L})
\end{bmatrix} \begin{bmatrix}
\boldsymbol{\eta}\_{1t} \\
\boldsymbol{\eta}\_{2t} \\
\boldsymbol{\eta}\_{3t}
\end{bmatrix} \tag{23}
$$

where *e*<sup>t</sup> = ψ11(L)η1t + ψ12(L)η2t; ν<sup>t</sup> = ψ21(L)η1t + ψ22(L)η2t. The causality measure developed by Hosoya [46] is equal to the bivariate causality measure between *e*<sup>t</sup> and ν<sup>t</sup> :

$$\mathbf{M}\_{\mathbf{y}\_1 \rightarrow \mathbf{y}\_2 | \mathbf{y}\_3}(\mathbf{w}) = \mathbf{M}\_{\varepsilon \rightarrow \mathbf{v}}(\mathbf{w}) \tag{24}$$

consequently, the causality measure in higher-dimensional systems may be stated as a bivariate causality measure as long as the variables are correctly converted.

### **4. Results and Discussions**

### *4.1. Unit Root Test*

In this article, two distinct types of unit root tests are used in order to validate the stationarity of the four variables that were under investigation. They are the Augmented Dicky–Fuller test and the Fourier-Augmented Dicky–Fuller test. The results are shown in Table 2.

The results of the Augmented Dicky–Fuller test are shown in Panel A of Table 2. It is found that carbon emissions and renewable energy are not stationary, while COVID-19 confirmed cases and fossil energy are stationary at levels. However, after taking the first difference, these four investigated variables become stationary. Moreover, the Fourier-Augmented Dicky–Fuller test is used to confirm these four investigated variables. The reason is that the Fourier-Augmented Dicky–Fuller test has the benefit of identifying the stationarity features of a nonlinear series. The results of the Fourier-Augmented Dicky– Fuller test are shown in Panel B of Table 2. Carbon emissions are seen to be nonstationary, whereas the other three variables are stationary at their levels. However, these four variables under consideration are stationary in their first differences.


**Table 2.** Results of unit root test.

Note: frequency shown in the parentheses; critical value of F-statistic shown in the bracket; \*\*\* 1% significant level; \*\* 5% significant level; \* 10% significant level.

### *4.2. Fourier Autoregressive Distributed Lag Cointegration Test*

The objective of this subsection is to investigate the link between these four examined variables in the long run. In contrast to previous research such as Aruga et al. [47] and Iqbal et al. [48], the Fourier autoregressive distributed lag cointegration test is utilized to determine the long-term relationship between carbon emissions, renewable energy, fossil energy, and COVID-19 confirmed cases. The Fourier autoregressive distributed lag cointegration test has the advantage of capturing long-run associations between series, even if the series is nonlinear and has unknown structural breakpoints. The results of the Fourier autoregressive distributed lag cointegration test are shown in Table 3.

**Table 3.** Results of Fourier autoregressive distributed lag cointegration test.


Note: Akaike information criterion selects the minimum value; \*\*\* 1% significant level.

The findings in Table 3 suggest that the absolute value of the F-statistics (9.892) is greater than the absolute value of the 1% critical value (4.66). As a result, it is concluded that the null hypothesis of no cointegration is rejected at a 1% significant level. In other words, the long-term association between carbon emissions and the three other variables under study can be validated.

### *4.3. Effects of Energy and COVID-19 Pandemic on Environmental Sustainability*

This subsection takes the nonlinear auto-regressive distributed lag technique to look at how energy and the COVID-19 pandemic affect carbon dioxide emissions, which are a proxy for environmental sustainability. The results are shown in Table 4.


**Table 4.** Results of effects of energy and COVID-19 pandemic on environmental sustainability.

Note: c constant; the value of t-statistics shown in the parentheses; \*\* 5% significant level; \*\*\* 1% significant level; ect error correction term.

According to Table 4, a negative variation in COVID-19 confirmed cases is associated with a reduction in carbon dioxide emissions, while a positive variation in COVID-19 confirmed cases is associated with an increase in carbon dioxide emissions. One probable explanation for this discovery is that, in order to slow the spread of COVID-19, the Chinese government has implemented related rules requiring the reduction or closure of some factories' production. At the same time, travel and transit constraints are one of the factors that may contribute to this result. Of course, this finding was also supported by Li et al. [49] and Habib et al. [50]. Meanwhile, this finding corroborates the validity of Hypothesis 1 (H1). Equally, in China, a positive movement in renewable energy consumption reduces carbon dioxide emissions, while a negative movement in renewable energy usage raises carbon dioxide emissions. These findings were consistent with Radmehr et al. [51], who studied this topic in European Union countries. Similarly, with a sample of India, Qayyum et al. [52] also verified these findings. However, these results contradict those of Kirikkaleli and Adebayo [53] and Sinha and Shahbaz [54], who discovered a positive correlation between the two variables. This is probably because of the fact that renewable technologies focus on clean energy. It is devoted to satisfying present and future demands and is a source of pollution reduction. These findings in China are achievable, as the country has undertaken a number of policies to increase the use of renewable energy and decrease the use of polluting fossil fuels. This conclusion also demonstrates that the rationale behind Hypothesis 2 (H2) is correct. Moreover, the shocks from fossil fuels have a favorable impact on carbon dioxide emissions. Farhani and Shahbaz [55] validated similar results using data from ten countries in the Middle East and North Africa from 1980 to 2009. One probable explanation is that China's economic progress over the last 30 years has been fueled by the substantial use of fossil fuels. This finding further substantiates support for Hypothesis 3 (H3).

### *4.4. Robustness Test*

The Markow switching regression model is used to reevaluate the impact of energy and the COVID-19 pandemic on carbon dioxide emissions. This is implemented to maintain the accuracy and reliability of the results in Table 4. The results are shown in Table 5.

The results in Table 5 show that in the first and second regimes, the COVID-19 pandemic confirmed cases and renewable energy have a negative impact on carbon dioxide emissions, whereas fossil fuel energy has a favorable impact. These findings are basically congruent with those provided in Table 4. In other words, the findings in Table 4 are reliable and accurate.


**Table 5.** Results of robustness test.

Note: c constant; the value of z-statistics shown in the parentheses; \*\*\* 1% significant level.

### *4.5. Frequency Domain Causality Test*

In this subsection, the frequency domain casualty test is used to explore the causal relationship between the COVID-19 pandemic confirmed cases, renewable energy, fossil fuel energy, and carbon dioxide emissions. An advantage of this method is that the causal link between carbon dioxide emissions and the investigated variables can be captured at different frequencies. The results are shown in Table 6.

**Table 6.** Results of frequency domain causality test.


Note: *p*-value shown in the parentheses; \* 10% significant level; \*\* 5% significant level; \*\*\* 1% significant level.

The results of Table 6 demonstrate that at all frequencies, COVID-19 pandemic confirmed cases cause carbon dioxide emissions. This suggests that COVID-19 pandemic confirmed cases are a reliable assessment of China's carbon dioxide emissions. Meanwhile, fossil fuel energy causes carbon dioxide emissions at all frequencies. This indicates that it is capable of accurately predicting carbon dioxide emissions. Renewable energy, however, cannot cause carbon dioxide emissions in the short run, but it can cause carbon dioxide emissions in the long run. In addition, it is possible to consider these findings to be supplementary to the results presented in Table 4.

### **5. Conclusions**

Every facet of society has been impacted as a result of the combined effects of the COVID-19 pandemic and the conflict that is now going on between Russia and Ukraine. Therefore, this paper examines the effects of energy and the COVID-19 pandemic on China's carbon dioxide emissions (a proxy for environmental sustainability) from 20 January 2020 to 20 April 2022. By using a nonlinear autoregressive distributed lag model for empirical study, the results demonstrate that the COVID-19 pandemic confirmed cases and renewable energy promote environmental sustainability with negative consequences on carbon dioxide emissions, while fossil fuel energy inhibits environmental sustainability, resulting in positive consequences on carbon dioxide emissions. In addition, the outcomes of the frequency domain causality test and the Markow switching regression confirm these findings.

In light of the empirical results discussed in this paper, several policy implications have been presented. First, it is advantageous to environmental sustainability for the government to adopt relevant actions, such as boosting the vaccination rate and enhancing the early warning level of COVID-19, to reduce the rising trend of the number of confirmed cases of COVID-19. Second, the government needs to put more effort into the production of renewable energy and its usage. The rationale for this is that these actions could help the environment remain healthy in the long run. Third, as is well known, the consumption of fossil fuels has been the primary driver of China's economic expansion and the leading cause of environmental degradation for a very long time. In order to achieve both environmental and economic sustainability, the government should expedite the development of alternatives to fossil fuels.

This paper's findings provide three noteworthy contributions to the current body of knowledge. First, it has come to our attention that no piece of literature that investigated the connection between the COVID-19 pandemic, energy, and environmental sustainability was targeted at China. Second, there is an extensive research contribution in the field of environmental sustainability and energy. The majority of investigations into environmental sustainability and energy did not include the COVID-19 pandemic. Instead, the focus is on economic progress, as seen by the vast majority of papers examined in this context. This research thus examined the COVID-19 pandemic, environmental sustainability, and energy in the same framework in order to gain an in-depth understanding of the topic. Third, in the current studies, a quantitative contribution has been found. Nonlinear models are unusual, despite the fact that a number of techniques, including autoregressive distributed lag, generalized method of moments, and Granger causality, have been used in publications to evaluate the variables of interest. Nonlinear models are essential for estimating the limitations and characteristics of the COVID-19 pandemic, which are asymmetrical and marked by unexpected changes that linear models can not represent. Furthermore, linear models cannot deal with the complicated and asymmetric high-frequency data dynamics linked with COVID-19 data. Consequently, improved nonlinear models such as the Fourier autoregressive distributed lag cointegration test, nonlinear autoregressive distributed lag, Breitung and Candelon causality test, and Markov switching regression were used to re-investigate this topic.

Lastly, both the limitations of this study as well as possible future directions that this line of inquiry may go are noted in this paper. First, due to China's vast area, the extent of the COVID-19 outbreak in various regions varies substantially. Future scholars may split China into three regions, namely the eastern region, the central region, and the western region, and conduct a separate examination of this topic, which may result in more intriguing discoveries. Second, this article only uses China as a sample, so the findings may be biased. Future researchers may thus add the United States, the United Kingdom, India, and other countries to the sample and re-analyze this issue using the panel technique, which may result in more trustworthy and robust conclusions. Third, using the prices of renewable energy and nonrenewable energy to replace the usage of renewable energy and nonrenewable energy may be contentious. Future researchers may re-conduct empirical studies on this issue using other proxy variables or daily data on energy usage, which may lead to more credible and intriguing findings.

**Author Contributions:** Conceptualization, Y.H.; methodology, Y.H.; software, Z.Z.; validation, Y.H.; formal analysis, Z.Z.; investigation, Y.H.; resources, Y.H.; data curation, Z.Z.; writing—original draft preparation, Z.Z.; writing—review and editing, Y.H.; visualization, Z.Z.; supervision, Y.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data presented in this study are available from the authors upon request.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

