Although the above optimization algorithms have proved the availability in the forecasting application, more improvements can be added to achieve better modeling performance. The traditional time series method requires stable time series data in the forecast model, but it has poor fitting ability to complex nonlinear systems, and the forecast accuracy of GDP growth is not accurate enough [30]. To further improve the forecasting accuracy for GDP growth trends, novel deep learning models are gradually investigated and applied, which are getting better at fitting complex systems. Sa'adah and Wibowo used two learning models for the prediction of GDP in Indonesia: the long short-term memory (LSTM) and recurrent neural network (RNN), resulting in an accuracy of over 80% [31]. Liu et al. applied the gated recurrent unit (GRU) network in the prediction of Chinese energy consumption [32]. In the comparison with the multiple linear regression (MLR) and the support vector regression (SVR) models, the GRU proved the superiority of complex nonlinear sequence data processing with lower prediction errors. In the research work of Wang et al., the temporal convolutional network (TCN) is employed for the short-term prediction of power system load, the TCN displayed faster speed and less storage demand by the specific structure, which leads to the best performance compared with SVR and LSTM [33]. It is meaningful to analyze the performance of TCN in the prediction study. Therefore, the TCN is applied as the main predictor in the paper.

In economic forecasting, a reasonable forecast should be selected according to the characteristics of the data and application scenarios. In the analysis of various influencing factors of GDP, the feature cross-validation can accurately measure the effect of the proposed model used on the actual datasets, which helps to select the suitable parameters [34,35]. The multi-feature modeling can sort the importance of variables that affect GDP, then complete the steps of feature extraction and feature filtering, and select important variables for calculation [36]. Ortega-Bastida et al. used an autoencoder (AE) to simultaneously reduce the reconstruction errors and data redundancy of the impacts with the corresponding GDP values to guarantee precision in forecasting [37]. Nahil and Lyhyaoui proposed the kernel principal component analysis (KPCA) to raise generalization performance and provide effective input variables for the predictor SVR [38]. The hybrid framework performed significantly better than the single SVR. Wang and Li utilized several feature extraction methods, which contained variational mode decomposition, Kullback-Leibler divergence (KLD), energy measure (EM), and sample entropy (SE) to extract the best features of raw time-series data [39]. The experimental results showed that the feature extraction method can optimize the predictor. Kosana et al. applied Q-learning as the selection method for time series prediction, which could dynamically select the best approach to increase the total model accuracy [40]. The hybrid model was regarded as the online model selection with Q-learning (OMS-QL). Xu et al. also chose Q-learning to conduct feature selection that outperformed other feature selection algorithms in the comparative experiments [41]. Maeda-Gutiérrez et al. combined the Boruta algorithm with a random forest algorithm as a hybrid BorutaRF framework that contains the function of feature selection and classification using the cross-validation strategy [42].

Based on the above literature survey, the existing excellent feature selection and prediction framework can be summarized in Table 1.

Based on the above literature research, it is sinnvoll to research the application of multi-feature analysis methods with the validation process to optimize the parameters in the forecasting model. Considering the excellent feature analysis ability of feature crossing, BorutaRF, and Q-learning algorithm, this study proposed a new three-stage feature selection to optimize the input of TCN and establish a multi-data-driven GDP prediction model. The innovation and contribution of the paper are presented as follows:

**Table 1.** Basic information about these GDP forecasting models.

The structure of this study is listed as follows: Section 2 introduces the technical details of deep learning and feature engineering commonly used in current mainstream GDP forecasting models. Section 3 mainly introduces in detail the applied data information, the proposed methods, and the total framework of the paper. In Section 4, comparative experiments are conducted to verify the performance improvement of the proposed model. Section 5 concludes the main contributions of this paper and prospects the research direction of GDP prediction application.

#### **3. Methodology**

#### *3.1. Framework of the Proposed Regional GDP Forecasting Model*

The influencing factors of regional GDP are complex, and the prediction accuracy of simple single series is not satisfactory enough under the circumstance. This paper proposes a regional GDP forecasting method based on the integration of economic, educational, employment, and industrial data. The accuracy of the prediction model can be improved greatly through feature analysis of the multivariate data. Moreover, a three-step feature selection method is proposed to better obtain the features that are helpful to GDP prediction. TCN network can deeply explore the nonlinear relationship between features and target prediction. In this paper, the TCN model is used to predict regional GDP in combination with selected features. The specific model framework is shown in Figure 1.

#### *3.2. Multivariate Economic Characteristic Data*

Regional economic forecasting is a typical time series forecasting problem, but it is different from traditional single time series forecasting. The regional economy is affected by education, industrial structure, transportation and logistics, geographical location, and other factors. Therefore, multivariate data analysis is indispensable to realizing accurate regional economic forecasts. In this paper, education, industry, historical economic data, population, and other factors that have a great impact on regional economic forecast are taken as the prediction features. Historical information is the first place to be considered. The historical economic information like real GDP, real consumption, and so on can reflect quite a few laws in economic development, which is instructive for GDP forecasting [43]. Employment and population decide the purchasing power of the public and further influence the market circulation and the improvement of GDP [44]. As for education and technology, positive education can promote employment, and science and technology is the basement of productivity-increasing [45]. Thus, education data is also in need to improve the accuracy of GDP prediction. Finally, industrial information is directly associated with GDP. For example, industrial output, energy consumption, the transportation efficiency are all crucial parts of the economy [46]. The stability and accuracy of the regional economic forecasting model can be greatly improved through multivariate data fusion. As shown in Figure 2, there are 20 features, which are mainly divided into four categories: historical economic indicators, employment and population, educational scale, and industrial structure.

**Figure 1.** The core structure of the proposed GDP prediction model.

#### *3.3. Three-Stage Feature Selection*

#### 3.3.1. Stage I: Feature Crossing

The 20-dimensional initial features used are divided into four groups according to different domains. The degree of correlation of features within and between groups is different, and the amount of useful information contained in the features is also different. Directly applying feature selection is easy to cause the loss of useful information, and the data cannot be exploited to the full [47]. Thus, feature crossing is utilized to solve the problems. On the one hand, the different information contained in the feature can be combined effectively by applying feature cross, which is able to improve the performance of feature selection. On the other hand, it also allows models to learn more complex nonlinear features. In this part, four feature crossing schemes are proposed. According to whether features belong to the same category, different statistical aggregation or simple calculating methods are carried out on features. Then, the new features are obtained. As shown in Figure 3, distinguishing the feature class by color and the detailed feature crossing method are illustrated below.

**Figure 2.** Initial features for regional GDP forecasting.

Scheme 1: Traverse features. The 20-dimensional features are added, subtracted, multiplied, and divided.

Scheme 2: Intra-group features. If two sets of features belong to the same class, addition and subtraction are carried on each pairwise feature; otherwise, multiply and divide.

Scheme 3: Group aggregation features. For all features that belong to the same class, calculate the mean, standard deviation, maximum, minimum, and range of them to generate new features.

Scheme 4: Intra-group feature and group aggregation features. Namely, the new feature splicing obtained by Schemes 2 and 3.

#### 3.3.2. Stage II: Feature Filtering Based on Boruta-RF

Through feature crossing, the input feature dimension is greatly increased. Among all features, some of them have no correction with the dependent variables. If all the crossed features were taken as the inputs of the feature selection part, the efficiency would be impacted. As a result, a feature filter method is adopted before feature selection. Boruta is an important feature filtering algorithm proposed by M. Kursa and R. Rudnicki [48]. The application of this method as a feature selection method belongs to filter feature selection. Different from most feature screening methods, which aim at the maximization of the evaluation function index or the optimization of the model loss function, this method aims to filter out features unrelated to dependent variables and get all feature sets related to dependent variables. Generally, it is believed that if a feature is added or deleted and the model performance does not change, then the feature is not important. However, it is not completely true. When the feature only has no or little effect on the improvement of model performance, it is not necessarily irrelevant to the dependent variable. Boruta can retain all the features related to the target value, so it is of great significance to use this algorithm as a preliminary feature filtering algorithm for feature selection.

The core idea of Boruta is to Shuffle each feature to generate its shadow feature. The shadow features are chaotic and do not correspond to the original samples. All the features and shadows are utilized to train models. Then, the shadow features with the highest importance scores are taken as the baseline, and the feature sets related to the dependent variable are selected from the crossed features according to the baseline. The specific steps are clarified as follows.

Step 1: shuffle each feature Xi in the feature matrix X and combine the shuffled features and original features [49].

$$
\lambda \mathbf{s} = \text{shuffle}(\lambda) \tag{1}
$$

$$
\lambda \mathbf{\dot{n}} = [\mathbf{\dot{\chi}}; \mathbf{\dot{\chi}} \mathbf{s}] \tag{2}
$$

where Xs and Xn are the shadow feature matrix and newly generated feature matrix respectively.

Step 2: Train the Random Forest model using the new generated features and calculate the average relative entropy of each feature. Then, calculate Zscore [50], which is given below for all features including the shadow features, and take the highest Z score value of shadow features as the baseline, named Zbase.

$$\text{Zscore} = \frac{\text{G}}{\text{g}\_{\text{G}}} \tag{3}$$

where Gis the related entropy of features, Gis themean value of G, and σG is the standard deviation.

Step 3: Set a percentage parameter perc, compare Zscore values of the crossed features with perc•Zbase and get rid of the features whose Zscore value is lower than perc•Zbase. In the process, Benjamini Hochberg FDR and Bonferroni are adopted to guarantee the stability of the algorithm.

Step 4: Delete all shadow features and repeat the above steps until all features are marked as important or unimportant.

#### 3.3.3. Stage III: Feature Selection Based on Reinforcement Learning

Reinforcement learning is a real-time learning method that focuses on online learning and environmental feedback [51]. It is an algorithm used to describe and solve the problem that agents maximize returns or achieve specific goals through Learning strategies during their interaction with the environment. Different from the traditional evolutionary algorithms, it can realize dynamic optimization and is inclusive of the error path optimization [52]. As a classic reinforcement learning algorithm with excellent decisionmaking, Q-learning is widely used in decision-making and optimization problems. In this part, a feature selection method based on Q-learning is proposed. The filtered features are

further screened to avoid over-fitting the model due to excessively high feature dimensions. The specific steps are given as follows:

Step 1: Initialize the core parameters of Q-learning (the state matrix S and the action matrix a). The state matrix S represents the selection of these features. The action matrix a is the action to keep or leave these features [53].

$$\mathbf{S} = [\mathbf{s}\_1, \mathbf{s}\_2, \dots, \mathbf{s}\_m] \tag{4}$$

$$\mathbf{a} = [\Delta \mathbf{s}\_1, \Delta \mathbf{s}\_2, \Delta \mathbf{s}\_3, \dots, \Delta \mathbf{s}\_m] \tag{5}$$

where sm represents the selection of these features, and sm is 0 or 1 (0 represents that the feature is not required, and 1 represents that the feature is retained). Δsm is the action of adding or deleting the m-th feature.

Action a: Select an action strategy according to ε-greedy.

$$\mathbf{a}\_{\mathbf{n}} = \begin{cases} \text{Action based on } \max \mathbf{Q}(\mathbf{S}, \mathbf{a}) (probability \text{ of } 1 - \varepsilon) \\ \text{Random action} (probability \text{ of } \varepsilon) \end{cases} \tag{6}$$

$$
\varepsilon \in (0,1)\tag{7}
$$

where ε is the exploration probability.

Step 2: Establish the reward R, which will affect the agent's action. In this part, the MAPE of the TCN is taken as a reward.

Step 3: The agent performs an action based on a comprehensive analysis of the current environment and the state S.

Step 4: Calculate the evaluation function Q and update the Q table. Based on the reward R received from the environment, the agent updates the state and Q table by adjusting the action of input feature changes. The calculation formula of the Q value is shown as follows [54]:

$$\mathbf{Q\_{n+1}}(\mathbf{S\_{n\prime}}\mathbf{a\_{n}}) = \mathbf{Q\_{n}}(\mathbf{S\_{n\prime}}\mathbf{a\_{n}}) + \beta\_{\mathrm{n}}(\mathbf{R}(\mathbf{S\_{n\prime}}a\_{\mathrm{n}}) + \gamma \max \mathbf{Q\_{n}}(\mathbf{S\_{n+1}}a\_{\mathrm{n}+1}) - \mathbf{Q\_{n}}(\mathbf{S\_{n\prime}}a\_{\mathrm{n}})) \tag{8}$$

where a represents the agent's behavior; S stands for the current status of an agent; R is the immediate return; *γ* is the discount parameter; *β* represents learning speed.

Step 5: When the termination condition is met, the agent stops its action. At this point, the state matrix S is the final selection result of model input features. Otherwise, repeat steps 3 to 4.

#### *3.4. TCN for Regional GDP Forecasting*

TCN is a neural network model which integrates extended causal convolution and residual connection and can be used for time series prediction [55]. TCN is composed of multiple TCN residual blocks stacked. Each TCN residual block has an important parameter pair (k, d) which represents the convolution kernel size and expansion coefficient respectively [56]. The final output of the TCN residual block is the sum of the outputs of the two paths. One path takes the input values through two levels of the same DCC and outputs them. Firstly, the input value enters the DCC after the weight initialization of layer 1. Then, the output is nonlinear transformed by the ReLU activation function. Finally, the nonlinear outputs are regularized to reduce the overfitting of the model and are input to layer 2 DCC for the same transformation again. The other path is for the input value to reach the output directly through the one-dimensional convolution layer. The path is RC, which is derived from the residual neural network. It can alleviate the problems of gradient disappearance and gradient explosion existing in the deep neural network and contribute to the construction of the deep neural network.

The core component of TCN is DCC. DCC increases the value of expansion coefficient d based on causal convolution, thus expanding the receptive field of the network, that is, accepting longer historical data [57]. The first is the application of causal convolution, which means that there is no leakage of information in the past. In the network applied in this paper, the convolution kernel is 2, the expansion coefficient is 1, and the receptive field is 3. And the yt GDP sequences are calculated from input sequences ˆ [xt − 2, xt − 1, xt] and have nothing to do with the input sequences [xt + 1, xt + 2, ...]. Therefore, the application of causal convolution in TCN will not give rise to information leakage. However, causal convolution has the problem of a small receptive field. Therefore, DCC expands the network receptive field by increasing the expansion coefficient. The receptive field of DCC in the same layer can be expanded to 4. The extended convolution operation can be obtained by the following equation [58]:

$$\text{TCN}(\mathbf{t}) = \sum\_{\mathbf{l}=0}^{\mathbf{p}-1} \mathbf{f}(\mathbf{l}) \chi\_{\mathbf{t}-\mathbf{dl}} \tag{9}$$

where TCN(t) is the extended convolution operation, X represents the time series data, f is the filter function, p is the length of the data, l is the element in X.

#### **4. Case Study**

#### *4.1. GDP Dataset*

The case study is the key to evaluating the performance of different GDP prediction frameworks. In order to select valuable regional GDP data sets, based on the analysis of GDP data in the references [59], this paper adopts the data of three Provinces in China to construct the experimental analysis. The data comes from the National Statistical Yearbook, which contains GDP data and other features data for each quarter from 2005 to 2021. Table 2 gives the basic information and input features of these three data. Figures 4–6 show the temporal fluctuation characteristics of three sets of GDP data. It is necessary to ensure the stability and robustness of the proposed model. To fully prove the stability and validity of the GDP prediction model, the proposed model and other benchmark models are evaluated by the ten-fold cross-validation method. In addition, ten repeated tests were used to evaluate the performance of the model. The average value of the evaluation index of the ten predicted results was used to analyze the effect of the model. This paper mainly constructs the single-step forecasting model, that is, the model predicts the GDP of the next quarter through the current moment and historical data. The key software platform used for experiments and modeling in this paper is the Python 3.8.5 platform, mainly using TensorFlow 2.3 to build the neural network. The Python was designed by Guido van Rossum, who works in Google. The version of python used in this paper is 3.8.5. The TensorFlow was created by Google open source, the version used in this paper is 2.3.

#### *4.2. Performance Evaluation Indexes*

The regression analysis index is the key to evaluating the performance of the model proposed in this paper. To fully analyze the modeling performance of each model, three classic indexes, which are the MAE (Mean Absolute Error), the MAPE (Mean Absolute Percentage Error), and the RMSE (Root Mean Square Error), are used in all case studies. These indexes can be obtained by the following Equation (10) [60]:

$$\begin{cases} \text{MAE} = \left(\sum\_{\mathbf{T}=1}^{\mathbf{n}} \left| \mathbf{Y}(\mathbf{T}) - \widehat{\mathbf{Y}}(\mathbf{T}) \right| \right) / \text{n} \\\\ \text{MAPE} = \left(\sum\_{\mathbf{T}=1}^{\mathbf{n}} \left| \mathbf{Y}(\mathbf{T}) - \widehat{\mathbf{Y}}(\mathbf{T}) \right| / \mathbf{y}(\mathbf{T}) \right) / \text{n} \\\\ \text{RMSE} = \sqrt{\left(\sum\_{\mathbf{T}=1}^{\mathbf{n}} \left[ \mathbf{Y}(\mathbf{T}) - \widehat{\mathbf{Y}}(\mathbf{T}) \right]^2 \right) / \text{n}} \end{cases} \tag{10}$$

where Y (T) represents true GDP data. - Y(T) represents the GDP data calculated by the proposed model. N means the number of samples.

**Figure 4.** Raw GDP Data 1.

**Figure 5.** Raw GDP Data 2.

**Figure 6.** Raw GDP Data 3.

**Table 2.** Basic information about this GDP dataset.

At the same time, it is necessary to select appropriate indicators to evaluate the performance differences between different models. This study utilized the Promoting percentages of the MAE (PMAE), the Promoting percentages of the MAPE (PMAPE), and the Promoting percentages of the RMSE (PRMSE) to evaluate the performance differences between different algorithms. These indexes can be obtained by the following Equation (11) [61]:

$$\begin{cases} \text{P}\_{\text{MAE}} = \frac{(\text{MAE}\_{\text{a}} - \text{MAE}\_{\text{b}})}{\text{MAE}\_{\text{a}}} \\\\ \text{P}\_{\text{MAPE}} = \frac{(\text{MAPE}\_{\text{a}} - \text{MAPE}\_{\text{b}})}{\text{MAPE}\_{\text{a}}} \\\\ \text{P}\_{\text{RMSE}} = \frac{(\text{RMSE}\_{\text{a}} - \text{RMSE}\_{\text{b}})}{\text{RMSE}\_{\text{a}}} \end{cases} \tag{11}$$

#### *4.3. Contrast Experiment with Benchmark Algorithms*

4.3.1. Experimental Results and Analysis of Different Predictors

To fully compare and analyze the modeling effects of different predictors and prove the superiority of the TCN algorithm, this paper adopts TCN, GRU, LSTM, RNN, ELM, and RBF models to construct comparative experiments. The experiment includes a classical deep learning model and a traditional shallow neural network. Table 3 gives the regression analysis indexes of the prediction results of these algorithms. From Table 3, the following conclusions can be drawn:

#### 4.3.2. Experimental Results and Analysis of Different Hybrid Models

In order to fully verify the application value of the GDP prediction model proposed in this paper, two parts of comparative experiments are set up in this section.

Part I: To prove that the three-stage feature selection method adopted in this paper can effectively optimize the prediction performance of the TCN algorithm, the proposed FC-BorutaRF-Q-TCN algorithm is compared with FC-BorutaRF-TCN, FC-Q-TCN, and TCN respectively.

Part II: To fully prove that the feature selection model based on reinforcement learning adopted in this paper has excellent feature selection ability, the Q-learning algorithm is compared with classical GA and PSO.

**Table 3.** The regression analysis indexes of several predictors.

Table 4 gives the regression analysis indexes of the prediction results of these algorithms. Tables 5 and 6 show the promoting percentages of FC-Borutarf-Q-TCN by other models. Figure 7 gives the loss of different feature selection algorithms during iteration. Table 7 shows the results of feature selection. From Tables 4–7 and Figure 7, the following conclusions can be drawn:

educational features and population features are less reserved. It proves that historical GDP data and industrial features play a paramount role in the composition of regional GDP. Based on the feature selection results, a more accurate prediction framework can be constructed in the process of establishing a GDP prediction model in the future.

**Table 4.** The indexes evaluation results of several forecasting models.

**Table 5.** The promoting percentages of FC-BorutaRF-Q-TCN by other models.

**Table 6.** The promoting percentages of the Q-learning by heuristic algorithms.

#### *4.4. Contrast Experiment with Existing Algorithms*

To prove that the FC-BorutarRF-Q-TCN model proposed in this paper is an advanced GDP forecasting model with excellent research prospects, it is compared with the four existing models. The four existing models include the classical time series model (ARIMA), the traditional machine learning model (SVM), and the two most advanced models (Yan's model [62] and Dong's model [63]). Figures 8–10 show the MAE, MAPE, and RMSE values of the proposed model and those of four existing models. Figures 11–13 show the prediction results of all the comparison models. Based on Figures 8–13, the following conclusions can be drawn:

**Figure 7.** Loss of different feature selection algorithms during iteration.

**Figure 8.** MAE values of the proposed model and existing models.

**Figure 9.** MAPE values of the proposed model and existing models.

**Figure 10.** RMSE values of the proposed model and existing models.

**Figure 11.** Predicted results of all algorithms (Data 1).

**Figure 12.** Predicted results of all algorithms (Data 2).

**Figure 13.** Predicted results of all algorithms (Data 3).

#### *4.5. Discussion*

Based on the above analysis of all experimental results, the following discussion and analysis are carried out in this section:

(1) The FC-BorutarRF-Q-TCN model proposed in this paper can achieve the best prediction accuracy in all cases. In addition, the stability and effectiveness of the model are fully proved by the results of ten-fold cross-validation and ten repeated experiments.

#### **5. Conclusions and Future Work**

As a comprehensive signal of the future economic situation, GDP forecasting technology provides technical support for national macro-economic regulation. In the paper, a new multi-data-driven GDP prediction model based on three-stage feature selection and a TCN network is proposed. The main contributions of this paper are summarized from the following perspectives:

that the FC-BorutarRF-Q-TCN model is a GDP forecasting framework with excellent research prospects. The MAPE values are all less than 5%.

The proposed multi-factor data-driven GDP prediction framework provides a meaningful reference for regional economic development strategy. In the future, the model proposed can be further improved from the following perspectives to enhance its practical value:

**Author Contributions:** Conceptualization, G.Y. and C.Y.; methodology, C.Y.; software, G.Y. and C.Y.; validation, C.Y., G.Y. and Q.L.; formal analysis, Q.L.; investigation, Q.L.; resources, Q.L.; data curation, Q.L. and C.Y.; writing—original draft preparation, Q.L.; writing—review and editing, Q.L., G.Y. and C.Y.; visualization, Q.L.; supervision, G.Y.; project administration, G.Y.; funding acquisition, Q.L. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This study is fully supported by the Natural Science Foundation of Hunan Province (Grant No. 2021JJ60003).

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

#### **References**

## *Article* **Toward Sustainability: Dynamics of Total Carbon Dioxide Emissions, Aggregate Income, Non-Renewable Energy, and Renewable Power**

**Wan-Jiun Chen**

Department of Economics, Chinese Culture University, No. 55, Hwa-Kang Rd., Taipei 11114, Taiwan<EMAIL_ADDRESS>Tel.: +886-2861-0511

**Abstract:** The purpose of energy sustainability policy is to support both economic growth and environmental quality. With climate change accelerating, economies must reduce carbon emissions. Low-carbon economics can balance the oft-contradictory policy aims of income growth and carbon reduction. Carbon pricing and renewable substitutes can pave the way. This analysis probes the dynamics of the adjustments toward the ideals of low-carbon economics through Granger causality testing of total carbon emissions, income, nonrenewable energy consumption, and renewable power. Cointegration regressions and a panel data vector error correction model are used to demonstrate the aforementioned variables' long-term balance and short-term adjustment, respectively. Two panels of countries, namely 18 European Union and 32 Organization of Economic Co-operation and Development countries, are investigated with 1990–2021 data. Determinants for the success of low-carbon development and the implications of border regulations and taxation of carbon footprint are also discussed. Economic competitiveness, as well as increases in commodity prices, would initially emerge as interferences and then induce carbon reduction and accelerate the adoption and development of green technology.

**Keywords:** innovations; renewable power; rebound effect; low-carbon economy; carbon pricing policy; border carbon tax

#### **1. Introduction**

Since the industrial revolution, increasing amounts of carbon-based fuels have been used, with the combustion of fossil fuels first powering factories and later providing energy for electric power plants, transportation, and other uses. Carbon dioxide emissions naturally accompany the burning of these fuels. The carbon dioxide concentrates in the atmosphere and traps heat, causing climate change. This has become problematic for worldwide economic growth, as income and carbon emissions are positively correlated. Under the global warming emergency, strategies are required to mitigate climate change.

Nobel Laureate William Nordhaus [1] argued that carbon pricing and green technology progress are among the most effective approaches to reducing carbon emissions; a lowcarbon economy is the goal for contemporary economic development. The contemporary economic reality is characterized by fast growth in renewable energy and renewable power, and carbon pricing policy variations locally within nations and expanding globally through border carbon price adjustment. Politics is focused on pursuing a low-carbon economy through energy transition [2]. Total carbon emissions contribute directly to the concentrations of atmospheric carbon dioxide and to the effects of climate change. Total carbon dioxide emissions is one of the key elements in climate change mitigation.

Sustainability of energy supports income and environmental quality. Energy securities and resilience are main governmental policies. Per capita income is widely used as a proxy to reflect the average standard of living in an economy. Researchers have affirmed the environmental Kuznets curve hypothesis in plotting per capita carbon emissions against

**Citation:** Chen, W.-J. Toward Sustainability: Dynamics of Total Carbon Dioxide Emissions, Aggregate Income, Non-Renewable Energy, and Renewable Power. *Sustainability* **2022**, *14*, 2712. https://doi.org/10.3390/su14052712

Academic Editors: Elkhan Richard Sadik-Zada and Andrea Gatto

Received: 19 January 2022 Accepted: 22 February 2022 Published: 25 February 2022

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

**Copyright:** © 2022 by the author. 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/).

per capita income [3,4]. The slope of the environmental Kuznets curve shares the same definition of the carbon intensity, namely the ratio of carbon emissions to income. The decreasing slope, as well as declining carbon intensity, has exhibited decreasing amounts of carbon emissions associated with one unit of income since the beginning of industrialization [3,4]. That the technology progress since then is a driving force to this declination verifies the insights of Nordhaus' argument that green technology progress is among one of the most effective approaches to reducing carbon emissions [1].

However, per capita carbon emissions cannot directly reflect the contribution of emissions to atmospheric concentrations. Actual observations indicate that the total amount of carbon emissions is rapidly increasing, and that induced effects of climate change from the total amount of carbon emissions are extremely severe. To reflect the pursuit of sustainability along the ongoing energy transition, the present study investigated the dynamics of total carbon dioxide emissions and its nexus with aggregate income, nonrenewable energy consumption, and renewable power.

The benign approach of carbon pricing policy, green technology development, and lowcarbon economic development might mitigate climate change. To elucidate the mechanisms of this approach, the nexus and dynamics of key aggregate variables are investigated in this study. The variables included in the investigation are total carbon emissions, aggregate income, nonrenewable energy consumption, and renewable power. Their long-run relationships and short-run adjustment mechanisms are investigated by estimating cointegration equations and with a panel vector error correction model (PVECM).

Two carbon pricing measures are typically applied to reduce carbon emissions: carbon taxation, and emissions trading schemes (ETSs). A carbon tax is a tax on carbon emissions. With a tax, emitting carbon is no longer free, and it incentivizes firms to reduce emissions. The second policy is an ETS. With this policy, a country sets a maximum cap for carbon emissions, issues permits that match the cap, and restricts firms to trading emissions on a market. The permits are tradable, and the price of permits is set to reduce emissions to the cap level. In economic theory, these pricing systems are equivalent, although in their empirical implementations, a carbon tax is regarded as a stringent punishment of firms and emitters, whereas an ETS trading system allows emission flexibility.

After the climate issue drew attention and became recognized, the first international mitigation treaty, the Kyoto protocol, was adopted in 1997. Since then, many countries have adopted pricing measures, either carbon taxes or ETSs, in addition to developing environmental regulations through command-and-control policy. The commitment to and implementation of carbon taxes and ETSs can be observed at various spatial scales, such as cities, states, countries, and regions, throughout the world.

Asen [5] published a summary report on the European Union (EU) carbon taxation and the EU ETS. The information herein is based on Asen's report. Europe has the world's highest carbon tax coverage and its largest trading system [5]. Most European countries that levy a carbon tax are also part of the EU ETS. Finland was the first country worldwide to introduce a carbon tax, in 1990. Most European countries have followed suit and implemented carbon taxes, ranging from US\$0.08 (Poland) to US\$137 (Sweden) (USD 1 = EUR 0.84913 on 1 April 2021). All member states of the EU are part of the EU ETS. With the exception of Switzerland, Ukraine, and the United Kingdom (UK), European countries that levy a carbon tax are also part of the EU ETS (Switzerland has its own emissions trading system, which has been tied to the EU ETS since January 2020. Following Brexit, the UK implemented its own UK ETS as of January 2021).

Additionally, the EU Taxation and Customs Union announced the proposal of the world's first border carbon tax in 2021 [6]. An announced European Green Deal goal was to become "climate neutral" by 2050. International trade closely links the global economy. Hundreds of cities and private companies have already pledged to reach "net zero" removing carbon emissions, thus following the EU's long-term strategy of achieving carbon neutrality by 2050. The decrease of carbon emissions outside EU countries is, hopefully, to be accelerated under the incentives of a border carbon tax [7].

In addition to carbon pricing policies, a strategy that Nordhaus [1] proposed is the development of green technology. Novel low-carbon, renewable-energy technologies, such as hydrological, wind, and solar power, are currently being implemented. They have been introduced on a relatively small scale but are flourishing in most developed and some developing countries. These technologies are part of a long-term plan for low-carbon energy development. Renewable energy is bounded by a series of challenges to address low generation capacity, unreliability, inefficiency, enormous capital requirements, large spaces for installation, expensive storage costs, lack of commercial viability, and pollution generation. Research into and applications of renewable-energy technology will take time.

Renewable energy can be used to ensure local energy abundance. However, the location of renewable energy generation is highly geographically restricted. Fortunately, renewable energy in the form of power can be connected with a power grid and transported without geographical restriction. Many countries aim to develop a power sector based largely on the renewable sources provided by European Commission [8], and the number of patents involving green energy is increasing. Carbon pricing policy and the promotion of renewable power as incentives and substitutes are applied to pave the way toward low-carbon economic patterns. Two questions present themselves here: whether renewable power is the ideal potential substitute for nonrenewable energy, and whether the availability of substitutes is the key determinant of the success of an extensive and intensive carbon pricing policy.

The objectives of this investigation are to demonstrate the long-run balance relationship and short-term adjustment patterns for the dynamic connections among (1) total carbon dioxide emissions, (2) aggregate income, (3) nonrenewable energy as represented by the sum of coal, gas, and oil consumption, and (4) renewable power. Policy implications for carbon and border taxes are addressed. The article aimed to investigate two groups of countries to obtain common empirical evidence. A panel of 18 countries in the EU (EU-18) and a panel of 32 countries in the Organization for Economic Co-operation and Development (OECD-32) were investigated over 1990–2021. The countries of EU-18 are Austria, Belgium, Czech Republic, Demark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Luxembourg, Netherlands, Poland, Portugal, Spain, Sweden, and the United Kingdom. The United Kingdom ended its membership on 31 January 2020. The countries of OECD-32 are Australia, Austria, Belgium, Canada, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, South Korea, Spain, Sweden, Switzerland, Turkey, the US, and the United Kingdom. Various different new technologies have been initiated and adopted in different countries. Renewable power is of high heterogeneity between countries. Renewable energy has gradually become an effective source of electricity but remaining a small proportion. The EU countries are the most devoted countries to mitigating climate change. The dynamics of the selected variables in EU countries are of importance for climate mitigation policy. The wealthy OECD economies were also investigated for their higher propensity to develop advanced green technology for renewable power. Some countries overlap in the two groups. The abundance and availability of renewable power data in these two groups are relative high compared to other groups of less developed countries. Since common reliable data of renewable power in the data sources are highly available after 1990, the study year starts from 1990.

The goal of this study is to investigate linkages between total carbon emissions, income, nonrenewable energy consumption (coal, gas, and oil consumption), and renewable power in EU-18 and OECD-32 countries through cointegration regressions and Granger causality based on a PVECM. Studies employing a PVECM [9–12] have focused more on the relationship between renewable energies and income and have typically included the income nexus and ignored the carbon emissions nexus. The goal of carbon pricing and low-carbon development is to mitigate climate change without hindering income. Hence, in the present study, the nexus with carbon dioxide, as well as that with aggregate income, are investigated.

Most renewable energies provide energy for local use. However, the variable of renewable power is not adequately addressed in the literature [9–12]. In the context of severe climate change effects, adjustments in carbon emissions should be investigated; thus, renewable power is included in this study as a variable representing progress in energy efficiency.

The study also addresses questions regarding global carbon pricing policy, as well as the dynamics of adopting and developing energy-efficient technology, taking renewable power as an example. The contemporaneous dynamic responses of the variables in reacting to changes should be investigated, as should how a short-run adjustment moves back toward the long-run cointegration equilibrium and whether deviations disturb balanced long-run patterns.

This study also addresses the implication of rebound effects regarding energy efficiency increases and the carbon leakages of an economy through international trading. Technological progress should improve energy efficiency. However, empirical research, such as Greening et al. [13], has reported an increase in energy consumption associated with improvements in coal-firing efficiency. With rebound effects, a reduction in consumption cannot be expected when relevant technology progresses. Improved energy efficiency cannot reduce energy consumption if the rebound effect occurs. Questions thus surround the reasonability of expecting climate change mitigation with a reliance on technological progress.

Finally, carbon leakage frequently occurs in developed countries, especially in the aspect of consumption-based emissions [14]. These countries import and consume commodities produced (with carbon emitted) elsewhere, especially in developing or industrializing countries [14]. How carbon border adjustment affects international competition and carbon leakage merits investigation.

#### **2. Literature Review**

The energy driving the engine of growth is a vital component in economic development. Issues of energy security [15–18] and the resilience to energy vulnerability [19–21] are usually targets of concentrated policy efforts of a country, being undertaken to ensure economic sustainability. Both non-renewable and renewable energy sources are subjects of prudent policy and intensive research to strengthen the path of energy security to support the economy. However, energy services are essential for sustainable development as well. Three pillars are the foci of energy policy for sustainability: the economy, society, and the environment. Energy generation and use are strongly linked to all elements of sustainable development, including the sustainability of the economy, living standards, and the environment [22–26].

In fact, energy is one of the most important issues for human development. To review human history, human development closely relies on energy utilization and availability [24]. Over the energy transition history [27], the early use of biofuels and animal power that improved lives transformed to the present world with use of fossil fuels, electricity, and cleaner fuels. That large amounts of fossil fuel combustion produce carbon dioxide emissions has drawn much attention and concerns about the effects on global climate. International agreements, domestic policy, and local actions have been committed to reducing these emissions. Potential solutions to current environmental problems have been identified, along with the development of renewable energy technologies. Innovations promote energy transitions to the exploitation and promotion of renewable energy resources [28]. Kaygusuz [22,24,26] argued that innovations in renewable energy use may alleviate the growing concerns over energy security and climate change. These innovations are regarded as solutions to the challenges of global warming in the argument of Dincer [23]. Climate policies anticipate a transition to renewable energy, potentially achieving solutions to environmental problems that we face today. Green transitions to renewable sources for the purpose of reducing total

greenhouse gas emissions requires long-term potential actions for the path of sustainable development [23]. In this regard, renewable energy and sustainable development are intimately connected, and the innovations of renewable energy resources appear to be some of the efficient and effective solutions [23].

Green innovations transform energy use in the energy transition [29]. Not only can renewable energy provide a clean, flexible power source at the micro-to-medium scales [24], but innovative technology progress has allowed electricity generated from renewable sources, and it has huge potential to create a multitude of meaningful uses. Rather than renewable energy, the present paper investigates the dynamic effects of electricity generated through the renewable sources. It is believed that the conclusions and recommendations drawn in the present study are useful for energy scientists and engineers and policy makers.

The energy transition patterns from wood to fossil fuels, and then to renewable energy are widely addressed in the literature [30,31]. Facing global climate change and scarce petroleum supplies, the world must switch to sustainable energy systems for the purpose of energy security [15]. Under threat of serious climate change crises over the world, a rapid renewable energy transition to renewable energy and renewable power provides an opportunity and is most often met with calls for innovation. Leach [31] suggested that human beings need a sustainable energy transition to avoid, first, a major crisis in energy supplies and, secondly, climate change with catastrophic consequences. The paths should be taken to ensure success in meeting these two goals of energy transition [31]. Hence, important studies are on the nexus and the dynamics of energy uses, along the energy transition, with income and carbon dioxide emissions. These issues are the aims that the present research is devoted to.

Sustainability issues of energy transition to support income and to mitigate climate change pose extraordinary challenges and opportunities for societies. With climate change intensifying, scientists in the United Nations Environment Programme (UNEP) [32] warned in the 2021 report that humanity is running out of time to limit global warming. With spatial and temporal externalities, the problems related to climate change have a global dimension, confront present and future generations, and are very difficult to solve [33]. The solution may require fundamental changes in consumption practices, lifestyles, technologies, infrastructures, business models, and policies. Energy transition from fossil fuels to renewables and to renewable power is in the focus of the sustainable transition. The present analysis makes contribution in the energy transition path towards sustainability.

Many energy transition studies focus on technical innovations [34], and many social economic studies on energy transition are on issues of income support and energy vulnerability, security, poverty, and justice [35–40]. The adaptation and initiations of renewable energy are often addressed in the aforementioned literature. Recent renewable energy developed in the form of renewable power that relies on much advanced feed-in grids is an example of the current technology innovation.

The motivation for this research is the currently serious crisis of climate change, renewable power as energy innovation technology, and ongoing policy formulation of carbon tax border adjustment for international commodity trade, as it is proposed as an incentive to mitigate climate change globally. There is a large body of research on the nexus of income, energy, and carbon dioxide emissions. The dynamics and nexus of economic growth, energy, renewable energy, carbon dioxide emissions, and carbon intensity have been examined in a variety of contexts. Carbon dioxide emissions have been studied in the scope of country panel groups, individual countries, and economic sectors, with a huge variety of empirical analysis techniques. Narayan and Popp [41] studied the nexus of income and energy consumption; Bilan et al. [42], Dogru et al. [43], and Balcilar et al. [44] studied the nexus of economic growth, renewable energy consumption, and carbon dioxide emissions. Dogru et al. [43] studied the OECD; Balcilar et al. [44] studied the G7 countries; Torvanger [45] studied the manufacturing sector of the OECD; Dogru et al. [43] studied the tourism sectors. These studies were on different economic scales, utilized a huge variation of different empirical analysis techniques, and reported a great variation of findings, accordingly.

Moreover, Cary [46] studied how tariffs impact carbon intensities, carbon dioxide emissions, and the environment under the US–China economic confrontation. Cary [46] indicated that imposing tariffs on other nations does not reduce local carbon dioxide emissions and would increase overall trade inefficiency. Since overall carbon dioxide emissions do not decline over time, concerns over environmental quality and health should be raised [46]. However, a study on carbon intensity can demonstrate the changes in the proportional rate of carbon emissions to income, suitable for analysis on an income basis. The present study is on the mechanisms of climate change mitigation in order to demonstrate the dynamics to environmental sustainability. Total emissions of carbon dioxide, as well as atmospheric carbon dioxide concentrations, contribute directly to climate change. The studies of Apergis and Payne [9,10] and Armeanu et al. [11] have focused more on the dynamics between renewable energies and income, and they found that renewable energy has induced income increases. A complete list tabulated in the study of Armeanu et al. [11] illustrates the previous related studies on renewable energy consumption and economic growth. However, these three analysis ignore the carbon emissions nexus.

The threat of climate change requires an energy transition from fossil fuels towards renewable energies and higher efficiency. The European energy transition includes a highlevel of renewable energy installations. European energy transition policy is used as one tool to encompass both goals of climate change mitigation and economic stimulation, and as well as reducing trade deficits and increasing employment. Creutzig et al. [47] studied the dynamics of renewable energy, income, and carbon dioxide emissions for three categories of relevant countries: the European countries, the European candidate countries, and the potential European candidate countries. Creutzig et al. [47] found that (1) for the European countries, renewable energy has an impact on the GDP, and that (2) for the candidate and potential candidate countries for EU membership, developing affordable and effective instruments and mechanisms to intensify energy transition to renewables is necessary to decrease the impacts of climate change induced particularly from decreasing carbon dioxide emissions without any reduction in economic growth.

According to Wooldridge [48], stationary or non-stationary series can be used to study their cointegration tests, long-run relationships, and error correction mechanisms. Following the principles of panel data analysis [48], the present study investigated the dynamics of total carbon dioxide emissions, aggregate income, non-renewable energy consumption, and renewable power. The variable of renewable power was used to represent the advanced innovation of renewable energy at high energy efficiency. More specifically, through the perspective of energy sustainability, the primary purpose of this research was to estimate the long-run effects and short-run linkages among variables. The long-run balance of how aggregate income and total dioxide emissions are affected by the traditional nonrenewable energy consumption and the advanced innovations of renewable power was probed by adopting cointegration regressions. A Cobb–Douglas functional form was investigated; the data were investigated in their monotonic logarithm transformation [48]. The data are available at open data sources, namely the Penn World Table (PWT10) [49], and British Petroleum Global [50]. Then, the first step of the analysis was to take the logarithm of the original data to test the non-stationarity of the time series and then to test for cointegration. Each series of individual variables and their first difference were tested with panel unit root tests, specifically, the Levin, Lin, and Chu (LLC); Im, Pesaran, and Shin (IPS); Augmented Dickey–Fuller (ADF); and Phillips–Perron (PP) tests. After passing unit root tests, a group test was performed on the datasets of the four variables for their cointegration.

Econometric scholars have developed panel testing methodologies to determine the existence of cointegration. Kao [51] proposed a test for homogeneous cointegration through pooled regression permitting for individual fixed effects. Pedroni's method [52] tests for heterogeneous cointegration. However, the power of these tests remains unclear, as Gutierrez compared these two tests by using the Monte Carlo simulation method and

reported inconclusive advantages over the test power [53]. A panel cointegration estimation technique is applied to estimate the single equation relationship. In the literature, single panel cointegration regression is typically estimated using ordinary least squares (OLS) or fully modified ordinary least squares (FMOLS), as outlined by Pedroni [54], for a heterogeneous cointegration panel, or dynamic ordinary least squares (DOLS), as outlined by Kao and Chiang [55] and Mark and Sul [56], for a homogeneous cointegration panel. If countries are assumed to exhibit heterogeneous cointegration, accordingly the FMOLS estimation is feasible for panel cointegration estimation, and a DOLS, developed especially for homogenous cointegration, is not suitable. The method of FMOLS was adopted in a series of studies [57–61], as was the method of DOLS [62–65]. The data in this investigation were assumed to have heterogeneity, and the model of the long-run relationship was estimated by using the FMOLS technique.

The mechanism of the short-run adjustment was probed by the method of PVECM, which is a capable and reliable econometric technique to estimate the dynamic linkages among variables and which has widely been applied in empirical data studies [66–85]. Granger causality can be adopted in the PVECM method by incorporating a vector of autoregressive model with lagged variables and the residuals of long term balance regressions. Granger causality based on PVECM was also applied to the aforementioned analyses on the dynamics of variables by Apergis and Payne [9,10], Armeanu et al. [11], and Creutzig et al. [47].

The present study estimated the long-run relationships by FMOL as proposed by Pederoni [52,54], with high heterogeneity in the variables across countries. Additionally, the linking effects among variables were probed via the Granger causality test, based on PVECM, by the procedures described in the literature [9–11].

In addition to parametric analysis of PVECM applied in the present study and a series of research in the literature [86–88], research based on nonparametric techniques are used in the analysis of climate change as well [89–97]. A combination of the two techniques has also been applied in the literature [98,99]. In a parametric analysis, the statistical information about the distribution of the population is known and represented based on a fixed set of parameters. On the contrary, in a nonparametric analysis, the statistical information about the distribution of a population is unknown, the parameters are not fixed, and it is necessary to test the hypothesis for the population.

Nonparametric analysis is an alternative technique with its own individual applicability, rather than being superior to others in all circumstances. The often-used time varying nonparametric methods are powerful to detect structure breaks, since they allow for flexibility in parameters over time. Nonparametric method can be used to identify structure breaks [91–94].

Chen et al. [98] used both parametric and nonparametric methods to capture the joint dynamics in their study, and Chen et al. [98] evidenced that parameters seemed to better capture the changes of the impacts than the nonparametric techniques in that study.

#### **3. Methodology**

After retrieving data from reliable sources, the first step was to test for the stationarity for the panel data series of the variables for the country groups under this investigation. If the non-stationarity and cointegration of the data were affirmed, their cointegration was estimated to represent their long-run equilibrium relationships, and the PVECM was applied with Granger causality for short-run patterns to adjust toward the long-run equilibrium relationships.

#### *3.1. Data*

This investigation demonstrated the long-run balance relationship and short-term adjustment patterns for the dynamic connections among (1) total carbon dioxide emissions, (2) aggregate income, (3) nonrenewable energy as represented by the sum of coal, gas, and oil consumption, and (4) renewable power.

The 1990–2021 raw data were retrieved from reliable open-access databases. Real income data of the study countries were retrieved from Penn World Table, PWT10 [49], represented by the output-side real GDP at current PPP (in mil. 2017 US\$). Data for total carbon dioxide emissions and energy variables were retrieved from the Statistical Review of World Energy, British Petroleum Global [50]. The corresponding variable definitions were as follows:

#### *3.2. Long-Run Equilibrium Relationship*

Two specifications were used to represent long-run cointegration relations among the variables. The long-run relationships between the variables were estimated in terms of carbon emissions and income as econometric specifications in Equations (1) and (2), respectively. The coefficient demonstrates the elasticity for a 1% change in the dependent variable to the percentage change of the independent variable, carbon emissions.

Cointegration (equilibrium) relations for carbon dioxide emissions are as follows:

$$\begin{aligned} \text{LOG}(\text{CO2}\_{\text{MTCO2}})\_{\text{it}} &= \pi\_i + \beta\_1 \text{LOG}(\text{RGDPO}\_{\text{PVT}10})\_{\text{it}} + \beta\_2 \text{LOG}(\text{POP})\_{\text{it}} \\ &+ \beta\_3 \text{LOG}\left(\text{COALCONS}\_{\text{El}}\right)\_{\text{it}} + \beta\_4 \text{LOG}\left(\text{GASCON}\_{\text{Ef}}\right)\_{\text{it}} \\ &+ \beta\_5 \text{LOG}\left(\text{OILCONS}\_{\text{Ef}}\right)\_{\text{it}} + \beta\_6 \text{LOG}\left(\text{REN}\_{\text{POWER}}\right)\_{\text{it}} \\ &+ \text{RESID}\_{\text{CO2it}} \end{aligned} \tag{1}$$

Cointegration (equilibrium) relations for income are as follows:

$$\begin{aligned} \text{LOG}(\text{RGDPO}\_{\text{PVT1}})\_{it} &= a\_i + \beta\_1 \text{LOG}(\text{CO2}\_{\text{MTCO2}})\_{it} + \beta\_2 \text{LOG}(\text{POP})\_{it} \\ &+ \beta\_3 \text{LOG}\left(\text{COALCONS}\_{\text{Ef}}\right)\_{it} + \beta\_4 \text{LOG}\left(\text{GASCON}\_{\text{Ef}}\right)\_{it} \\ &+ \beta\_5 \text{LOG}\left(\text{OILCONS}\_{\text{Ef}}\right)\_{it} + \beta\_6 \text{LOG}\left(\text{REN}\_{\text{PONER}\_{\text{Ef}}}\right)\_{it} \\ &+ \text{RESID}\_{\text{GDPit}} \end{aligned} \tag{2}$$

where *t* = 1990, 1991, ... , 2019; the parameter α*i* permits for country-specific fixed effects; subscript *i* denotes the *i*th country in the panel; and *RESID* denotes the estimated residuals, which depict deviations from the long-run relationship.

#### *3.3. Short-Run Dynamics*

The short-run dynamics in the two panels of countries were investigated using a Granger causality test, based on PVECM. The deviations were captured by the residuals of the long-run cointegration regression. Then, this PVECM model was used (1) to demonstrate Granger causality between variables, and (2) as an error correction mechanism illustrating the long-run dynamics.

#### 3.3.1. Vector Autoregression and Granger Causality

Granger causality tests based on vector autoregression (VAR) were adopted as the specifications for the present study. In the VAR method, each variable has an equation modeling its evolution over time. This study included one-period lagged (past) values of the first difference regarding the variable itself, the other variables, and an error term in the regression. VAR models do not require as much information regarding driving forces as structural models with simultaneous equations do. The only information required in a VAR model is a list of variables that can be hypothesized to affect each other over time. Granger "causality" does not measure cause–effect relationships but is a statistical correlation between the current value of one variable and the past values of others (i.e., Granger causality does not directly imply changes in one variable causing changes in another). Granger causality indicates the changes in one variable in response to one-period lagged changes in itself and other variables.

Granger causality relationships were verified between the following variables: (1) total carbon dioxide emissions, (2) aggregate income, (3) nonrenewable energy consumption (energy use measured by the sum of coal, gas, and oil consumption), and (4) green energy technology represented by the use of renewable power. The Granger causality model is a time series model of first differences that includes current values on the left-hand side and the past values of their first differences on the right-hand side. The Granger causality relationships between variables are indicated by the magnitudes and significance of the estimated coefficients.

#### 3.3.2. Error Correction Mechanism

The error correction mechanism is an adjustment response to deviations from the long-term equilibrium [48]. The adjustment is indicated by how the contemporary changes of one variable responds to past deviations from the long-term equilibrium.

The error correction model is a time series model in first differences that also contains an error correction term, which works to bring the (1) series back into long-run equilibrium. This study assumed that the adjustment would occur as a response to deviations from the long-run equilibrium levels of carbon emissions and income. The aforementioned cointegration regression Equations (1) and (2) represent long-run balances. The forecasted residuals of these two regressions represent the deviations of actual carbon emissions and actual income from their balance equilibrium levels. Past values (one-period backward) of both forecasted residuals, as the error correction terms (ECTs), were simultaneously introduced into the Granger VAR model, which became a PVECM.

A two-step procedure was adopted. The first step was to estimate and forecast residuals of Equations (1) and (2) by using FMOLS for the EU and OECD countries. Subsequently, one-period lagged values of the residuals were included simultaneously as two ECTs in the PVECM. The estimated coefficients of ECTs demonstrate the adjustment backward (with a negative sign) or outward (with a positive sign) to the long-run equilibrium levels of carbon emissions and income.

#### 3.3.3. PVECM Specification and Short-Run Dynamics

Briefly, this PVECM can demonstrate Granger causality by including the first differences of the included variables in a VAR system, as well as long-term adjustment patterns by including ECTs. The described long-run models are estimated by FMOLS for both panels. One-period lags of the deviation from equilibrium, represented by the error terms of Equations (1) and (2) and denoted as *RESIDCO*2*it*−1 and *RESIDGDPit*−1, are introduced into the PVECM as the ECTs. The coefficients of the ECTs reveal the dynamic adjustment patterns toward equilibrium.

The PVECM is set by including a one-period lagged VAR system with two ECTs. The PVECM equations are as follows:

For j = 1 (used to represent how current changes of total carbon dioxide emissions are affected by lagged changes (lagged first difference) of all selected variables and lagged residuals of the long-run system equilibrium),

$$\begin{split} \triangle LOG(CO2\_{MTCO2})\_{it} &= a\_{1j} + \gamma\_{11i} \triangle LOG(CO2\_{MTCO2})\_{it-1} \\ &+ \gamma\_{12i} \triangle LOG(RGDPO\_{WT10})\_{it-1} + \gamma\_{13i} \triangle LOG(NEN\_{El})\_{it-1} \\ &+ \gamma\_{14i} \triangle LOG(REN\_{POWER})\_{it-1} + \varrho\_{11i} RESID\_{CO2it-1} \\ &+ \varrho\_{12i} RESID\_{GDPit-1} + \varepsilon\_{1it} \end{split} \tag{3}$$

For j = 2 (used to represent how current changes of national aggregate income are affected by lagged changes (lagged first difference) of all selected variables and lagged residuals of the long-run system equilibrium),

$$\begin{aligned} \triangle LOG(\text{RGDPO}\_{\text{PWM}})\_{it} &= a\_{2j} + \gamma\_{21i} \triangle LOG(\text{CO2}\_{\text{MTCO2}})\_{it-1} \\ + \gamma\_{22i} \triangle LOG(\text{RGDPO}\_{\text{PWM}})\_{it-1} &+ \gamma\_{23i} \triangle LOG(\text{NEN}\_{\text{EI}})\_{it-1} \\ + \gamma\_{24i} \triangle LOG(\text{REN}\_{\text{POWER}})\_{it-1} &+ \varrho\_{21i} \text{RESID}\_{\text{CO2}i-1} \\ + \varrho\_{22i} \text{RESID}\_{\text{GDPit}-1} &+ c\_{2it} \end{aligned} \tag{4}$$

For j = 3 (used to represent how current changes of nonrenewable energy consumption by lagged changes (lagged first difference) of all chosen variables and lagged residuals of the long-run system equilibrium),

$$\begin{aligned} \triangle LOG \left( NREN\_{\mathrm{E}} \right)\_{it} &= \mathfrak{a}\_{3\circ} + \gamma\_{31i} \triangle LOG \left( CO2\_{MTCO2} \right)\_{it-1} \\ + + \gamma\_{32i} \triangle LOG \left( RGDPO\_{PVT10} \right)\_{it-1} &+ \gamma\_{33i} \triangle LOG \left( NREN\_{\mathrm{E}} \right)\_{it-1} \\ + \gamma\_{34i} \triangle LOG \left( REN\_{\mathrm{POWER}} \right)\_{it} &+ \mathfrak{e}\_{31i} RESID\_{CO2it-1} \\ + \mathfrak{e}\_{32i} &ESID\_{\mathrm{GDPit-1}} + \mathfrak{e}\_{3it} \end{aligned} \tag{5}$$

For j = 4 (used to represent how current changes in renewable power are affected by lagged changes (lagged first difference) of all selected variables and lagged residuals of the long-run system equilibrium),

$$\begin{split} \triangle LOG \Big( \text{REN}\_{\text{POWER}\_{\text{EI}}} \Big)\_{it} &= \mathfrak{a}\_{4j} + \gamma\_{41i} \triangle LOG \big( \text{CO2}\_{\text{MTCO2}} \big)\_{it-1} \\ &+ \gamma\_{42i} \triangle LOG \big( \text{RGDPO}\_{\text{PVT}10} \big)\_{it-1} + \gamma\_{43i} \triangle LOG \big( \text{NEN}\_{\text{EI}} \big)\_{it-1} \\ &+ \gamma\_{44i} \triangle LOG \big( \text{REN}\_{\text{POWER}\_{\text{EI}}} \big)\_{it-1} + \uprho\_{41i} \text{RESID}\_{\text{CO2}i-1} \\ &+ \uprho\_{42i} \text{RESID}\_{\text{GDPit}-1} + \iota\_{4it} \end{split} \tag{6}$$

where the notation denotes the first difference of the variable; the subscript *j* denotes the *j*th equations that represent the mechanism of the *j*th variable; and *j* = 1, 2, . . . , and 4.

#### **4. Analysis**

The analysis was based on aggregate country-level annual data of two panels of countries, EU-18 and OECD-32, from 1990 to 2019. The data were investigated in their monotonic logarithm transformation, as the original long-run relationship was specified as a Cobb–Douglas functional form. The data were tested for their individual panel stationarity and group cointegration. After affirmation of their non-stationarity and cointegration, their cointegration relationships were estimated to represent their long-run equilibrium relationships, and the PVECM was applied with Granger causality for short-run patterns to adjust the long-run equilibrium relationships.

#### *4.1. Data Descriptive Statistics*

Data definitions are as shown in Table 1 and descriptive statistics of the raw data are presented in the following Table 2.

**Table 1.** Definitions of variables.

**Table 2.** Descriptive statistics of variables as raw data (1990–2021).

#### *4.2. Testing for Non-Stationarity and Cointegration*

The first step of the analysis was to take the logarithm of the original data to test the non-stationarity of the time series and to test for cointegration.

Each series of individual variables and their first difference were tested with panel unit root tests, including LLC, IPS, ADF, and PP tests, according to Wooldridge [48]. The results are listed in Tables 3 and 4. The results indicated that the individual variables were stationary in their first difference. The results for the level data were mixed, but most were nonstationary.

Both Kao's [51] and Pedroni's [52] tests were applied in this study to investigate cointegration in EU-18 (Table 3) and OECD-32 (Table 4). On the basis of the results of Kao's test, the variables were cointegrated, as the null of no cointegration was rejected.

A long-term equilibrium was observed for the aforementioned variables, as the hypothesis of the presence of a long-run relationship was confirmed. Then, the next step was to estimate this relationship with regressions.

**Table 4.** Panel unit root and cointegration tests for OECD-32 (1990–2019).

and PP assume individual unit root process. The cointegration tests have a null hypothesis of no cointegration.

**Table 4.** *Cont.*

Source: Author's computation. Notes: Data are log transformed. denotes the first difference. \* *p* < 0.1, \*\* *p* < 0.01, \*\*\* *p* < 0.001. LLC, IPS, ADF, PP respectively denote Levin, Lin, and Chu t\* stat.; Im, Pesaran, and Shin W-stat.; ADF Fisher chi-square; and PP Fisher chi-square. LLC assumes common unit root process. IPS, ADF, and PP assume individual unit root process. The cointegration tests have a null hypothesis of no cointegration.

#### *4.3. Estimating the Long-Run Relationships*

After the hypothesis of the presence of a long-run relationship among variables was affirmed, the estimated results of Equations (1) and (2) revealed the long-run equilibrium patterns for carbon emissions and income. A panel cointegration estimation technique was applied to estimate the single equation relationship. In the literature, single panel cointegration regression is typically estimated using OLS, FMOLS, or DOLS. The model of the long-run relationship in present study was estimated by using the FMOLS technique, as we assumed heterogeneity among countries. The estimated results of Equations (1) and (2) are presented in Table 5.

**Table 5.** Results of long-run cointegration relationship by FMOLS for EU-18 and OECD-32.

Source: Author's computation. \* *p* < 0.1, \*\* *p* < 0.01, and \*\*\* *p* < 0.001.

Carbon emission patterns emerged in the estimates of Equation (1). The findings for the EU-18 group were as follows. (1) Weak statistical significance and a small margin were present in the relation between income change and carbon emissions change (significant at 10% level). A 1% income increase would reduce aggregate country-level total

carbon emissions by 0.0244%. (2) Carbon dioxide emissions in the EU were found to be closely connected with nonrenewable energy use. The magnitudes were large, and the coefficient was strongly statistically significant. The empirical estimate indicated that a 1.0366% increase in carbon emissions corresponds to a 1% increase in nonrenewable energy use in EU countries. Hence, if nonrenewable energy consumption were reduced in EU countries, carbon emissions would be reduced accordingly. Tremendous reductions in carbon emissions would be achieved if EU countries could promote and maintain decreasing trends in nonrenewable energy use. In this respect, countries face both profound challenges and numerous opportunities. (3) A slightly negative but strongly significant margin was reflected in the relationship between renewable power and carbon emissions. A 1% increase in renewable power use in the EU would reduce country-level total carbon emissions by 0.0113%. The elasticity magnitude was small, but the statistical significance was quite strong. With a sharply increasing trend in the use of renewable power, this evidence of the relationships between renewable power and carbon emissions in the EU is welcome news.

The empirical results for the OECD-32 group were similar to those for the EU-18 group.

Three key findings were revealed in the evidence from the estimates in Equation (2).

#### *4.4. PVECM and Short-Run Dynamics*

The PVECM was estimated by allowing heterogeneous intercepts and no trend in each equation. The results revealed Granger causality between variables and adjustment to the balance equilibrium.

#### 4.4.1. Findings in Granger Causality Test

The estimated coefficients of the lagged variables shown in Table 6 demonstrated short-run Granger causality. The value of the coefficient revealed the extent of the variable's impact in the contemporary period by 1% changes of itself ("self-causality") and other variables from the past. The Granger nexuses between variables are depicted in Figures 1 and 2 for the EU-18 and OECD-32 groups, respectively. The findings are summarized in the following text.

**Table 6.** Granger causality (based on PVECM) for EU-18 and OECD-32 (1990–2019).

**Figure 1.** Granger nexus between selected variables in the EU-18.

**Figure 2.** Granger nexus between selected variables in the OECD-32.

The lack of self-Granger causality in the EU's nonrenewable energy consumption and total carbon emissions during the study period merits attention. After strict carbon abatement policies have eliminated most of the emissions that may be removed, policymakers must determine what areas the EU should continue to work on.

(4) The EU's carbon emissions significantly Granger-caused renewable power (with a positive sign) at the 10% significance level. A 1% change in lagged nonrenewable energy would Granger-cause 1.5469% changes in renewable power use. Furthermore, the EU's nonrenewable energy consumption significantly Granger-caused renewable power (with a negative sign) at a 10% significance level. A 1% decrease in lagged nonrenewable energy would Granger-cause a 1.4551% increase in the use of renewable energy. This finding affirmed that nonrenewable energy can be substituted by renewable power in the EU. However, this substitution effect was not significant in the OECD. Even in the EU, the substitution effect (between nonrenewable energy consumption and renewable power) had significance only at the 10% level. The evidence was statistically weak. Therefore, people have not strongly moved to use renewable power in response to carbon emissions, particularly in the OECD.

Thus, the Granger causality (from past changes of carbon emissions to contemporary renewable power) was not strong in the two panels of countries included in this study. Climate mitigation policies are expected to promote the development of renewable energy sources and thus curb the consumption of nonrenewable energy, help reduce carbon emissions, and ultimately counter climate change. However, these outcomes are not always realistic. In fact, renewable power would contribute to carbon emissions in the OECD with Granger causality at the 10% significance level.

(5) In the OECD, carbon emissions would inversely Granger-cause nonrenewable energy consumption. The response elasticity was found to be 0.2799% in the OECD. If a 1% increase in total carbon emissions occurred in the previous period, nonrenewable energy use would decrease by 0.27998% in the contemporary period. However, the effects in the EU were statistically insignificant.

Because none of the four variables Granger-caused the EU's reductions in carbon emissions, the EU may already be approaching its carrying capacity in carbon reduction through the reduction of nonrenewable energy use.

#### 4.4.2. Findings from ECT

The direction and magnitude of the error correction toward long-run equilibrium can be indexed by the estimated coefficients of ECTs. This study included two ECTs, *RESIDCO*2*it*−1 and *RESIDGDPit*−1. The estimated coefficients of these two series of lagged residuals in PVECM captured how their deviations from the equilibria were adjusted. The value of the coefficient revealed how much of the adjustment in the contemporary period responded to 1% of the deviation of the actual values from their forecasted equilibrium level; that is, the corresponding adjustment in current changes toward the long-run equilibrium. A negative sign demonstrates an adjustment back toward the carbon cointegration equilibrium or toward the income cointegration equilibrium, or both. A positive sign demonstrates an outward movement that breaks the equilibrium. Several findings were evidence of short-run adjustments as deviations to the long-run equilibrium.

#### **5. Discussion**

(1) Long-run equilibrium relationships between variables

The results regarding long-run cointegration relationships indicate that the cointegrated linkage of carbon dioxide and income is not strong either in the EU or the OECD. Additionally, both renewable power and nonrenewable energy play central roles in supporting income in EU countries. Most importantly, renewable power has especially strong effects in alleviating carbon emissions and increasing income in both panels.

(2) Short-run Granger causality and equilibrium adjustment

After the long-term relationship is affirmed, the next question to be answered is how the variables adjust in response to changes. The PVECM provided evidence. The ECT results (Table 6) reveal that long-run adjustments statistically occur in the time series of all the variables and bring the series back to both equilibria; renewable power is the exception. Increases in renewable power use would be triggered by a positive deviation, as the value for actual renewable power is greater than that of the estimated equilibrium level.

Policy intended to decrease carbon emissions must be effectively devised because a reduction of emissions is not triggered by the variables included in the short-run PVECM used in this study. For EU carbon emissions, short-run causality from the included variables is not significant, and systematic adjustments are only noted in response to deviations in the long-run equilibrium of carbon emissions and income. For OECD carbon emissions, renewable power would mildly stimulate an increase of carbon emissions, and shortrun adjustments would occur in response to deviation in carbon emissions; however, no significant adjustment is made in response to deviation in income equilibrium.

(3) Substitution effects between energies

Nonrenewable energy can be substituted by renewable power in the EU, while this substitution effect is not significant in the OECD.

(4) Role of renewable power

Renewable power in the EU and OECD demonstrates a strong, significant self-Granger causality in its evolution over time. Progress in green technology, indicated by renewable power in this study, would promote further progress over time. Accumulation effects would result in strong increasing trends.

Additionally, changes in contemporary renewable power strongly push deviations outward in response to past deviations from the long-run equilibrium of carbon emissions and income, as evidenced by the significant positive ECTs of emissions and income growth. Renewable power is capable of breaking long-run linkages among the selected variables. Renewable power has a lively role in its self-increase and in its response to the deviation from the long-run equilibrium. The outbreak of renewable power would indicate rebound effects with progress in green technology. Progress that improves energy efficiency would readily support income increases and further increase the demand for such power.

Potential carbon reduction arising from technological progress may be reduced by the rebound effect. Technological improvement and increases in its efficiency would increase the consumption of energy as discussed by Greening et al. [13]. This rebound effect (the Jevons paradox) was first proposed in 1865 in William Stanley Jevons's book *The Coal Question* [100], as he observed coal consumption in the United Kingdom soaring with coal-fired engine efficiency improvement [13].

The modern world is experiencing the problems associated with carbon-based energy. The problems have intensified as the world population's increasing needs are met. Humanity has long ignored the carrying capacity of the environment. Renewable energy is said to be limitless, but negative impacts might emerge when it is used on enlarged scales. Learning from our experiences, if it is time to develop a low-carbon economy, we should prepare for any negative impacts.

#### (5) Carbon pricing policy

Carbon pricing policies, such as carbon taxation, ETSs, and border carbon pricing adjustment, have been proposed to place a price on carbon emissions associated with commodities. Border carbon taxes, a measure of border carbon price adjustment, have been proposed in regional and global economic integration. The EU has proposed a border carbon tax that places a fee on global warming emissions embedded in goods produced outside the EU. The policy is aimed at incentivizing a reduction in carbon emissions beyond the EU.

According to the long-run connection patterns evidenced by Equations (1) and (2), an increase in renewable power use would suppress carbon emissions and support income increases. Renewable energy is limitless, and hopefully advances in technology will be triggered and inspired when the new demand emerges.

EU income exhibits short-run Granger causality one period ahead as a response to income changes. The same is true for the OECD. This is evidence that with an increasing trend, wealth in EU and OECD countries grew with the increase of prior wealth and not renewable power nor nonrenewable energy use. This is a noteworthy finding. These countries seem to insist on pursuing year-on-year income growth. However, income usually represents people's physical living standards.

The pollution haven hypothesis seems to hold, with emissions triggered in heavily industrialized developing countries. Because global production and consumption systems are closely integrated, the EU's border carbon pricing would be an effective remedy against pollution havens and carbon leakage by effectively imposing prices on emissions at each stage of supply and consumption chains. In addition to the explicated purposes of carbon reduction and climate change mitigation, the border carbon pricing policy can greatly increase the EU's international competitiveness. Stringent carbon reduction schemes might already have somewhat exhausted the carrying capacity of the EU's reduction without hindering its income. Implementing a border carbon pricing adjustment to drive dual advantages is reasonable. In this scenario, the price of imported commodities would increase. Whether the policy will lead to more application of local-made high-carbon products is another question.

The current results reveal that the adjustment of nonrenewable energy is barely significant in its connection to the prior-period changes of the included variables in the EU and OECD. Moreover, the long-run adjustment to deviations in income and carbon emissions (ECT) in the EU and OECD are not strongly significant. Indeed, nonrenewable energy is irresponsive to its own previous changes. "The dogs bark, but the caravan moves on." This appears to be unfortunate news for the mitigation of climate change. Persistent inertia is evidenced in nonrenewable energy consumption.

The expansion of carbon pricing, from local or regional carbon pricing to border adjustments to exert pricing effects on a global scale, will initially affect international competitiveness and result in changes in local consumer prices, even if the explicit goal is to mitigate climate change. Carbon pricing policy is also likely to have monetary effects. No matter how high the tax rates imposed, the effects on income may be greater than those on carbon reduction. Total carbon emissions is immovable. The current results indicate that the short-run Granger causality is such that (1) none of the four variables Granger-causes EU carbon emissions; and (2) renewable power even (weakly) Granger-causes OECD carbon emissions.

Questions remain regarding the types of policy most effective in combating climate change. An integration of current green technology into the designs of regulations would be effective in reducing total carbon emissions and mitigating climate change. However, recent policies of carbon pricing and the pursuit of net-zero emissions will have financial and trade impacts.

(6) Current carbon tax and border adjustment policy

Under current globalization and its interconnected international trade system, the proposed EU carbon border tax is intended to provide carbon reduction incentives to slash emissions far beyond Europe. Currently, the EU, South Korea, Singapore, Japan, and China have country-wide carbon pricing schemes, and the United States, Canada, and several other countries have local carbon pricing regulations. EU and OECD countries have enjoyed benefits from carbon leakage (emission outside and consumption inside). With the self-adjustment of renewable power continually increasing, as evidenced in the empirics of EU-18 and OECD-32 in this study, carbon pricing policy, including local, national, and border policy, would provide continuous and powerful reinforcement of the development of renewable power.

Border carbon taxation increases the price of imports and exports. International competitiveness is affected in the pursuit of explicit policy aims—climate mitigation. The study's finding of short-run adjustment to long-run equilibrium, occurring with respect to income and carbon emissions, indicates that governments, for international cooperation with global supply and demand chains, would react to increase competitiveness by seeking to reduce carbon emissions. Governments will, hopefully, outline the necessary steps for limiting global warming at the upcoming international climate meetings.

Taxing imported goods produced by high-carbon manufacturers could compel countries of production and the manufacturers to enact more aggressive climate rules. But is this fair to poor nations? This question remains unanswered. Furthermore, environmental capacity is also an important issue along with the expansion of renewable energy and renewable power. Rebound effects are affirmed to be embedded in the development of renewable power by their self-Granger causality. Our pursuit of income growth can trigger the rebound effects of renewable power. As the on-going green technology progress to meet needs of energy and pursuits of income increases, the related carrying capacity and environmental costs should also be addressed. The effects of tariffs were proposed by Carry [46], that tariffs would reduce trade deficits rather than promote sustainability, and tariffs would decrease economic efficiency and have no effects on reducing domestic total carbon dioxide emissions.

#### **6. Conclusions**

Nordhaus [1] posited that carbon pricing and green technology are the two most effective approaches for reducing carbon dioxide emissions to mitigate climate change. A decreasing in carbon intensity driven by the technology progress since industrial revolution in the study of Stefanski [3] is consistent with the insights of Nordhaus' argument that green technology progress is among one of the most effective approaches to reducing carbon emissions [1]. A low-carbon economy is the goal for contemporary economic development. Total carbon dioxide emissions is a direct key variable in determining climate change mitigation. Along the contemporary energy transition path, rapid technological progress promotes renewable energy, renewable power development, and energy efficiency boosting technology. Renewable power is promoted with high innovations, and of high heterogeneity between countries. Various different new technologies have been initiated and adopted in different countries. The current share of renewable energy, or renewable power, remains lower than that of nonrenewable energy, mostly fossil fuels. Renewable power is convenient when it is ready to feed into existing power grids. With progress in green technology and policies of carbon pricing triggering its advances, renewable power, as well as renewable energy, may have an opportunity to replace fossil fuels.

To probe the dynamics of key variables toward the low carbon development along the energy transition, this study investigates the long-run relationships and short-run linkages of total carbon emissions, aggregate output, nonrenewable energy consumption, and renewable power with a cointegration regression and Granger causality based on the PVECM model. The common dynamic empirics of the European Union countries and the Organization of Economic Co-operation and Development countries are addressed.

The Pedroni [52] heterogeneous panel cointegration tests reveal a long-run equilibrium relationship between the variables. Several findings are revealed regarding the long-term equilibrium and short-run adjustment linkage among variables.

Firstly, there is no strong long-term relation between aggregate income and total carbon dioxide emissions in both groups of countries, consistent with the evidences in the literature [101]. A negative but low significance relationship in the European Union countries is shown in Table 5, and it indicates a reversal in the directionality of the effects between income and total carbon dioxide emissions. The European Union countries, which are actively working on total carbon mitigations, appear to have approached a status where increases in income can be approached with decreasing total carbon dioxide emissions. For the group of the Organization of Economic Co-operation and Development countries, no linkage is presented at a low significance level (*p*-value < 0.1). This result states a week but bright vision for sustainable economic development of human beings to develop towards a low-carbon economy in the European Union countries.

According to this first finding in the long-run equilibrium, the loose long-term linkages between carbon dioxide emissions in its relationship to income, the viability of a carbon tax border adjustment policy might not be strong, especially to reduce carbon emissions by driven forces for the income effects of the policy. The feasible parts of the border regulation might generate from its mandatory effects of border regulation. Cary [46] argued that tariffs could be a viable political tool designed to reduce trade deficits rather than promote sustainability. Extending border taxation adjustment policy would, at first, have more effects on price changes and economic competition for the European Union countries, definitely.

The second findings evidenced the long-run relationships of the consumption of nonrenewable energy and carbon dioxide emissions. For European Union countries in 1990–2021, the consumption of non-renewable energy still remains its significant role in determining income, while this role has been sloughed off in the Organization of Economic Co-operation and Development countries. The European Union countries, which are actively working on CO2 reduction, appear to have encountered a stringent reliance on non-renewable energy consumption to support income.

The third finding is regarding the connections of nonrenewable energy consumption and carbon dioxide emissions. Not surprisingly, nonrenewable energy consumption performs a strong intimate relation with total carbon dioxide emissions, since the combustion of fossil fuels directly emits carbon dioxides.

The fourth finding is related to the advanced innovation of renewable energy, represented by the renewable power. Renewable power seems important in both perspectives of supporting income and mitigating carbon dioxide emissions, in both groups of countries. This finding can answer a fundamental question: Will green technology progress allow us to see and to go for the dawn of mitigating climate change? Nowadays, renewable power, and also renewable energy, is in composite a very small part in people's energy use in most countries. However, the vision for the future will be full of opportunities. More investigations should be conducted on individual model countries that initiate and develop renewable power, as well as renewable energy.

Five findings are evidenced by the estimated results of Equations (3)–(6) as probing short-run adjustments with Granger causality tests based on a PVECM.

Firstly, strong self-causality of income and renewable power is evidenced along the short-run adjustment, in both country groups. An increase in income or renewable power would promote their own further increase. We can expect that spontaneous growth itself will create a quantum leap. In addition to the aforementioned strong self-causality of income and renewable power, some weak adjustments are evidenced at the 0.1 level. There are two folds for the European Union countries and another two for the Organization of Economic Co-operation and Development countries. In the European Union countries, (1) carbon dioxide emissions weakly Granger cause renewable power, and (2) consumption of nonrenewable energy have weak and negative effects on renewable power. In the Organization of Economic Co-operation and Development countries, (1) renewable power weakly Granger causes carbon dioxide emissions and (2) carbon dioxide emissions negatively, and renewable energy consumption itself positively Granger causes nonrenewable energy consumption. The European Union countries have actively adopted various methods to reduce carbon emissions and have achieved remarkable results, but it is also seen from their PVECM short-term adjustment estimates that they have been unable to adjust the nonrenewable energy consumption that causes carbon emissions through any variables.

In the Organization of Economic Co-operation and Development countries, nonrenewable energy consumption would still statistical weakly be Granger caused by total carbon dioxide emissions and nonrenewable energy consumption itself. Nonrenewable energy efficiency improvement is still possible, and renewable power is still a carbon dioxide generator in the Organization of Economic Co-operation and Development countries.

The long-run dynamics can be captured by the statistical significance of error correction terms in Equations (3)–(6), as seen by the estimates of the error correction term in the PVEVMs shown in Table 6. For the European Union countries, carbon dioxide emissions, nonrenewable energy consumption, and renewable power would response to a deviation of carbon dioxide equilibrium, while carbon dioxide emissions, income, nonrenewable energy consumption, and renewable power would response to a deviation of income equilibrium. For the Organization of Economic Co-operation and Development countries, the carbon dioxide emissions, income, nonrenewable energy consumption, and renewable power would response to a deviation of carbon dioxide emission equilibrium, while income and renewable power would respond to a deviation of income equilibrium. (1) The study on the European Union countries evidenced that a deviation of carbon dioxide emissions from its balanced equilibrium would move backward through adjustment of carbon dioxide emissions, nonrenewable energy consumption, and the use of renewable power. The adjustment speed of renewable power is especially high, and the adjustment of income is not significant. At the same time, a deviation from income equilibrium will be adjusted via all variables. However, the adjustment of renewable power pushes this deviation away from the balance. (2) The study of the Organization of Economic Co-operation and Development evidenced that deviations of carbon dioxide emissions from their equilibrium would be brought back through the adjustment of all variables, while a deviation from income equilibrium would only be adjusted back via income, and brought away by the adjustment of renewable power. However, the adjustment of carbon dioxide emissions and nonrenewable energy are insignificant.

The evidences of the aforementioned empirics indicated by income ECT in the European Union and the Organization of Economic Co-operation and Development affirm that only renewable power can break down the long-run equilibrium of income. The development of renewable power is adjusted for income supporting and expansion, rather than combating carbon dioxide emissions and rather than alleviating climate change. Green technology development supports income but has no effect on the reduction of domestic total carbon dioxide emissions. This is a sad story! The approach low carbon development through development of green technology leaves unfulfilled ideals and slogans. The question of what is the effective policy to break down the balance of carbon dioxide emissions for mitigating climate change remains barely answered by the development of renewable power to combat total carbon dioxide emissions. Policy recommendations work to bind and integrate current low carbon technology into income earnings, so as to develop prudent detailed government regulations. The study of carbon intensity and energy intensity already present declination trends due to technological innovations in the literature [2,4]. The internal reduction response effects of the enterprises and lifestyles of people would be another important issues to be probed.

Based upon the aforementioned dynamics of the selected variables, recent policies of carbon pricing and net-zero carbon emissions, which have intended to pursue suppressing the persistent increase of carbon dioxide emissions for combating climate change, have more role in terms of monetary effects rather than to increase the declination of total carbon dioxide emissions. As suggested by Cary [46], when it comes to extending carbon pricing to border adjustment from various local or regional carbon pricing to take effects globally, the effects would go to changes in international competitions and local consumption prices, even though the explicit goal is set to mitigate climate. Overall carbon dioxide emissions do not decline over time. The present study has evidenced a lack of connections to incentivize their reduction with the included aggregate variables. The concerns over climate changes should be raised.

The evidence in the present research is based on panel vector error correction model techniques and 1990–2021 data of 18 European Union countries and 32 Organization of Economic Co-operation and Development countries. The implementations of the study would represent the temporal and spatial scopes of the panel data applied. Renewable power is used to represent one advanced example of green technology progress. More important findings might be generated from extant studies by utilizing different empirical techniques on other economic scales by extending the research time frame. In order to find effective ways to mitigate climate change, more research is worthwhile on the dynamics of individual countries, on carbon intensity analysis, on the incentive effects of carbon pricing and carbon tax border adjustment, and on carbon reduction in enterprises and lifestyles. We would like to conclude this paper by outlining some further developments. The parametric estimation approach, which is used in the present study, can provide estimated value of a parameter to demonstrate the patterns for the linkages between variables. However, a time-varying nonparametric model would be suitable to detect the structural breaks as the changes in the parameter are captured [93]. The present study applies a parameter technique, and the parameters are fixed over time. The present paper would conclude further developments on the time varying techniques to detect the structure changes in the linkages of the variables.

**Funding:** This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data were retrieved from Penn World Table and BP statistics.

**Acknowledgments:** The author wants to thank the anonymous reviewers and the editor that contributed to the quality of the paper with their insights.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**

## *Article* **Does the Sino–US Trade Friction Promote Firm Innovation? The Role of the Export Grab Effect**

**Zhen Xu 1, Xin Zhong 1,\* and Zhongyan Zhang 2**

**Abstract:** We examine and explain changes of firm innovation following the Sino–US trade frictions. Specifically, we use the unique microdata of Chinese technology and innovation firms from 2016 to 2019 to identify the response of firm innovation to the shock of the Sino–US trade friction and investigate the changes in firm innovation before and after the outbreak of the Sino–US trade friction. We found that, on average, export firms significantly increased innovation after the Sino–US trade friction. In particular, firms in the advanced manufacturing industry perform significantly better than firms in other technical fields. To explain this phenomenon, we compare firms' export performance in different technical fields and conduct a detailed mechanism test. It is found that the Sino–US trade friction has led to the export grab phenomenon in some technical fields, and the export grab effect is the reason for the significant increase in the innovation of export firms. The direct effect of export grab promotes the innovation of sustainable export firms, and the indirect effect of export grab leads to an increase in innovation by reducing the threshold of the export market. We verified the direct and indirect effects of export grab on firm innovation following the Sino–US trade frictions.

**Keywords:** Sino–US trade friction; export grab effect; firm innovation

**1. Introduction**

Innovation is a sustainable driving force for economic development [1], but the current international economic situation poses great challenges to innovative firms. Since the beginning of 2018, a series of adjustments of import tariffs by China and the United States have exposed the global economy to the great risks of trade policy uncertainty [2]. According to recent advances in trade policy uncertainty literature, the elimination of trade policy uncertainty benefits innovation [3–5]. Previous empirical studies have verified this using Chinese data at both the firm level and industry level [6,7]. Obviously, the theory reveals that there is an inverse linear relationship between trade policy uncertainty and innovation, which means that the rise of trade policy uncertainty will impair innovation. Therefore, does this indicate that the Sino–US trade frictions will damage the innovation of Chinese firms?

We find that trade policy uncertainty literature does not explain changes in Chinese firms' innovation following the Sino–US trade frictions, at least in the comparatively short term. By using the unique microdata of Chinese technology and innovation firms from 2016 to 2019, we find that export firms have significantly increased innovation after the outbreak of the Sino–US trade friction, which is evidently not in line with the internal logic of trade policy uncertainty literature. Further research also found that although the high-tech field is the focus of the Sino–US trade friction, the innovation performance of export firms in the advanced manufacturing industry shows an unusually prominent growth after the Sino–US trade friction. However, it seems difficult for the existing literature to make a reasonable explanation for such a phenomenon. The literature on competitive pressure in export

**Citation:** Xu, Z.; Zhong, X.; Zhang, Z. Does the Sino–US Trade Friction Promote Firm Innovation? The Role of the Export Grab Effect. *Sustainability* **2022**, *14*, 2709. https:// doi.org/10.3390/su14052709

Academic Editors: Elkhan Richard Sadik-Zada and Andrea Gatto

Received: 29 January 2022 Accepted: 23 February 2022 Published: 25 February 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/).

markets may possibly explain this: the Sino–US trade friction intensifies the competitive pressure of export firms facing external markets [8], and escaping the competition effect may make such firms increase research and development (R&D) investment and innovation activities [9–11] to obtain greater market share and profits in the future [12].

However, the dataset used in this paper fails to reveal the competitive pressure in the export market faced by firms; in contrast, it shows that export firms in some technical fields have exceptionally prominent export performance after the Sino–US trade friction. For example, in the advanced manufacturing industry, which has outstanding innovation performance after the trade friction, the annual average export volume of its firms has increased by approximately twice as much as that before the trade friction, and the export share of total income has also increased significantly. Obviously, these indicators are not sufficient to help us obtain a sense of the pressure in the export market when firms are facing adverse shocks. However, by comparing the differences in exports of firms in different technical fields before and after the Sino–US trade friction, we find that those technical fields that have significantly increased innovation after the Sino–US trade friction are often accompanied by comparatively more prominent export business growth, while exports in the technical fields that do not have increased innovation after the Sino–US trade friction are generally not well performing and even have negative growth. Therefore, is this a coincidence?

In fact, after the outbreak of the Sino–US trade friction, Chinese firms have an obvious phenomenon of export grab. According to the annual statistics of China's National Bureau of Statistics, China's exports increased by 7.05% in 2018. Additionally, at the press conference in December 2018, a spokesman for China's Ministry of Commerce said that China's imports and exports achieved rapid growth in 2018. Empirical studies in the literature also reveal the existence of the export grab effect of the Sino–US trade frictions. For example, Xie and Wang [13] found that the Sino–US trade friction can promote the short-term export of products by using monthly data at the product level. Zhang et al. [14] verified the existence of the export grab effect of the Sino–US trade friction by using product-level custom data. Cavallo et al. [15] compared the commodity data of importers and retailers in the United States and found that after the Sino–US trade friction, importers increased their imports from China in the short term and expanded their inventory as much as possible to cope with the risk of further tariff increases in the future.

Export grab is a manifestation of the reallocation effect of the Sino–US trade friction on export firms. By probing into the export behaviour of firms in different technical fields, we find that firms in certain technical fields show an obvious export-grab phenomenon after the outbreak of the Sino–US trade friction, while others do not, and they even suffer a great export shrinkage. Theoretically, the export grab effect comes from the demand shock in the international commodity market. Foreign buyers overdraw their future demand to avoid the risk of future market uncertainty, resulting in a sharp rise in the demand for Chinese products in the short term, which may have two effects. The first is the direct effect. For firms that continue to export, due to the effect of economies of scale, the increase in output caused by demand expansion in the short term will reduce their marginal cost, and then the increased productivity will enable capable firms to carry out innovation activities [16,17]. The second is called the indirect effect. The shock of foreign demand leads to an insufficient supply of domestic sustainable exporters. As a result, export grab reduces the threshold for domestic firms to enter the export market, which will affect firms' entry and exit, export decision making and innovation [16]. The empirical study of this paper verifies that the direct effect and indirect effect of export grab are the mechanism of the increase in innovation of export firms after the Sino–US trade friction and explains the phenomenon that export firms increase innovation after the Sino–US trade friction.

The possible contributions of this paper are as follows: First, we use unique microdata of Chinese technology and innovation firms to provide new evidence that the Sino–US trade friction stimulates firms' innovation. Although previous studies have discussed trade friction and innovation [18,19], they have not yet formed a unified conclusion. In contrast to these studies, we use more detailed microdata of technology and innovative firms and take the outbreak of the Sino–US trade friction in 2018 as an exogenous shock. It is found that, on average, export firms increase innovation after the Sino–US trade friction. Second, we explain a new mechanism of trade friction affecting firm innovation, which is also the most important innovation of this paper. Wei and Liu [18] believe that trade friction has a compelling effect, which leads to an increase in firm innovation. We creatively find that the export grab effect is the reason for the increase in export firm innovation after the Sino–US trade friction. Third, this paper enriches the research on the relationship between exports and firm innovation. Studies in the field of trade have shown that exports could benefit firm innovation and technological upgrading [16,17,20,21]. We verify the significance of exports to firm innovation again.

The structure of the rest of the text is arranged as follows after the introduction part: the second part reviews the relevant literature; the third part introduces the empirical design and data; the fourth part reports the empirical benchmark results, the effectiveness test and robustness test of identification; the fifth part shows the results of the heterogeneity test and tests the export grab mechanism; the sixth part summarizes the entire text.

#### **2. Literature Review**

Since the purpose of this article is to test the response of firm innovation to the Sino–US trade friction, and explain the increase in firm innovation following the Sino–US trade friction from the perspective of export grab, we arrange our literature review as follows: We first review the relevant theories of trade friction and literatures evaluating the effects of trade friction in Section 2.1. We then summarize the main theoretical literature on the relationship between export and innovation in Section 2.2.

#### *2.1. Related Economic Effects of the Sino–US Trade Frictions*

The Sino–US trade friction represents the return of the United States to trade protectionism [22]. Discussions on trade protectionism in international economics have a long tradition and form a series of rich theories, but trade protectionism theories from different periods have different policy objectives due to the different economic contexts. According to the development context of trade protectionism theory, early mercantilism believed that primitive wealth could be accumulated by restricting imports and expanding exports, while List's infant industrial protection theory believed that trade policy did not need to restrict the import of all industries, and restrictions on agricultural products should be relaxed, while policies should be protected for promising industries [23]. However, when trade protection theory developed in the 1980s, technology transfer and technology restriction became an important part of the theory [24,25]. New trade protection theory and strategic trade protection theory believe that developed countries need to intervene in trade behaviour and restrict the trade of high-tech products by using policies such as technical barriers and intellectual property protection to reduce technology transfer from developed countries to developing countries and safeguard their international competitive advantage and interests [26,27].

However, free trade theory holds that large-scale trade frictions will hurt both sides. Quantitative studies based on this Sino–US trade friction have also verified this point. For example, in Chinese literature, the research of Li et al. shows that the increase in US tariffs will damage the welfare level of both China and the United States. In addition, the employment, import and export of the two countries will be damaged to a certain extent [28]. Lv et al. compared the economic effects of the strategic adjustment on both China and the United States. The study found that the Sino–US trade friction will reduce the scale of the Sino–US trade on a large scale, especially imports of the United States from China, which will be greatly damaged. However, compared to the United States, China's welfare loss will be more serious in trade frictions [29]. Cui et al. also confirmed the above view. Furthermore, they believe that China's retaliatory tariff will aggravate China's welfare loss in trade frictions [30]. In the United States, Amiti et al. studied the

price mechanism of the impact of tariff increases on welfare in the United States and found that tariffs in the United States increase the pricing level and mark-ups of the American manufacturing industry and reduce the variety of products consumed by consumers, and that retaliatory tariffs from other countries will make American consumers face serious welfare losses [31]. Similarly, the research of Fajgelbaum et al. shows that the impact of tariff increases in the Sino–US trade frictions will fully penetrate the United States through the import price effect and will be absorbed by American consumers and import firms. In general, the United States will face serious welfare losses [22]. Cavallo et al. once again verified the price effect of tariffs on U.S. welfare with U.S. product level data. From the analysis of Chinese and American economists, it can be found that trade frictions will damage the overall welfare of China and the United States [15].

In addition to the macrolevel analysis of the Sino–US trade friction, the microlevel investigation in the literature also reveals that there is an obvious export grab effect following the Sino–US trade friction. For example, Xie and Wang verified that trade frictions have the effect of export grabbing by using monthly data at the product level, and that the Sino–US trade frictions can promote the short-term export of products [13]. Zhang et al. verified the existence of the export grab effect of trade friction by using data on customs products before and after the Sino–US trade friction [14]. Moreover, data from the United States also prove that trade frictions have an export grab effect in at least some specific industries. Cavallo et al. found that after the Sino–US trade friction, importers have increased their imports from China in the short term and expanded their inventory as much as possible to cope with the risk of further tariff increases in the future. Moreover, compared with Chinese firms exporting to the United States, American firms exporting to China have obvious price reduction behaviour in the face of China's retaliatory tariffs [15].

Therefore, what is the impact of trade friction on firm innovation? No clear and unified conclusion has been reached for this problem in the literature. For example, Wei and Liu used the data of China's listed companies from 2003 to 2016 to measure the trade environment uncertainty faced by firms by the number of trade frictions in the industry and studied the relationship between trade environment uncertainty and firm innovation [18]. The conclusion shows that trade environment uncertainty has a positive effect on firm innovation. The greater the uncertainty of the trade environment is, the higher the innovation of firms in the industry. In contrast, the research of Wan et al. shows that the Sino–US trade frictions will reduce the international R&D level of Chinese firms [19]. Therefore, the effect of trade friction on innovation is not generalized and should be analysed in detail.

#### *2.2. Export Grab Effect and Firm Innovation*

However, the export grab induced by the Sino–US trade friction may potentially lead to firm innovation. Although the relationship between export grab and firm innovation has not been addressed in the literature, there have been many discussions on the relationship between exports and innovation in the field of trade in recent years. First, exports have a learning effect. Export firms can improve technology and promote innovation through export learning. Many studies have verified the export learning effect [21,32,33]. On the one hand, the export learning effect affects firm innovation through economies of scale. Exports help in expanding firms' production, and then the role of economies of scale can be further brought into play, which will reduce the marginal cost of firms [20], and promote firm performance [32], and is reflected as productivity gains [34]. Therefore, with increasing performance, firms have an incentive to upgrade their technology, generating an export promotion technological upgrading effect [17]. On the other hand, the export learning effect can be improved through communication with foreign customers. This effect is particularly obvious for export firms in developing countries. Export firms learn from customers or competitors through export behaviour so that their productivity or technical level can be improved [10,21,35–38]. Second, exports have a selective effect. Engaging in innovation is conducive to increasing the productivity level of firms, allowing them to self-select in export

markets [34,39]. Indeed, some firms that prefer to enter export markets will undertake ex ante R&D to achieve access to export markets [40], while sustainable exporters will also engage in innovative activities due to competitive pressures in international markets [8] to avoid being eliminated or losing market share in competitive markets [12]. Moreover, the shock of export demand will have a reallocation effect on export firms [11]. On the one hand, the demand expansion in foreign markets will increase the innovation rent of firms and stimulate the innovation investment behaviour of firms; on the other hand, the expansion of foreign demand reduces the threshold of the export market, and new export firms improve the competitive atmosphere of the export market, which also encourages firms' innovation behaviour. However, the shock of foreign demand tends to affect larger firms at the forefront of technology and may play a smaller role in promoting the innovation of new firms.

In fact, the phenomenon of export grabbing following the Sino–US trade friction is a reflection of the impact of foreign demand shocks. To hedge against the risk of further increases in future trade costs, foreign buyers overdrew future demand, which manifested itself in a sharp short-term rise in Chinese export volumes. Based on the above literature review, this paper theoretically argues that this will have two effects on exporters' innovation [11,16]. The first is the direct effect. The expanded export demand reduces the marginal cost of firms, promotes firm productivity and expands firm performance. Firms have the ability and motivation to carry out innovation activities and upgrade technology to obtain more market share and innovation rent in the future. The second is the indirect effect. The shock of foreign demand will change the distribution of firms and have a reallocation effect on domestic export firms, allowing new exporters to enter the export market and generate an export learning effect. Exports will be reallocated to larger firms, and innovation will converge with exporters at the technological frontier, thus leading to an overall increase in the level of innovation among exporters. This paper uses unique data on national technology and innovation firms from 2016 to 2019 to study the impact of the Sino– US trade frictions on firm innovation and verifies the direct and indirect effect mechanisms of firm innovation caused by export grabs following the Sino–US trade frictions.

#### **3. Identification Strategy and Data**

#### *3.1. Identification Strategy*

In this paper, the treatment group and the control group are divided according to whether the firm is an exporter or not. The control group is non-exporters, and the treatment group is exporters; that is, firms with exports in any period of the sample are defined as export firms in all periods to identify the differential responses of firms in different groups to the shock of the Sino–US trade friction, comparing the changes in firm innovation before and after the Sino–US trade friction. The specific identification equation is as follows:

$$\ln(Innovation)\_{fit} = \alpha + \beta\_1 \ast EXP\_{fi} \ast Post18\_l + X\_{ft} \ast \beta\_2 + X\_{it} \ast \beta\_3 + \nu\_f + \text{Year}\_l + \varepsilon\_{fit} \tag{1}$$

where subscript *f* means firm, *i* indicates the industry to which the enterprise belongs, and *t* indicates the year. The explained variable *ln*(*Innovation*)*fit* indicates the innovation level of firms. The explanatory variable *EXPf i* ∗ *Post*18*t* is the interaction of a firm's export status *EXPf i* and the 2018 Sino–US trade friction shock variables *Post*18*t*. *EXPf i* takes 1 as exporters and 0 as non-exporters. *Post*18*t* takes 1 indicates years after the outbreak of the 2018 Sino–US trade friction and takes 0 otherwise. The coefficient of primary interest to us is *β*1, which measures the innovation performance difference between export firms and non-export firms after being impacted by the Sino–US trade friction. *Xf t* and *Xit* represent the firm-level and industry-level control variables, respectively, which are used to control the firm characteristics and industry characteristics over time; *νf* is a firm-level fixed effect, which is used to control firm heterogeneity that does not change over time; *Yeart* is the year fixed effect, which is used to control the interference of time factors on identification; and *εfit* is the error term. In addition, we also cluster the standard error according to the four-digit code of the Chinese industry.

It should be noted that, first, we divide the treatment group and the control group because we consider the selective effect of the export market. The Sino–US trade friction may affect the choice of firms to enter and exit the export market. The way we divide the treatment and control groups can fix the impact of the effect of firms entering and exiting the export market based on the results to a certain extent. Second, although export firms are intuitively more likely to be impacted by the Sino–US trade frictions, we cannot deny that non-export firms are not affected during the process of the Sino–US trade frictions. In identifying the effect of Sino–US trade friction on the innovation of exporting firms, using non-exporting firms as a control group requires an examination of whether exporting and non-exporting firms are comparable; therefore, we will verify in the identification validity below that there is a parallel trend between the two after controlling for as many potential influences as possible. Third, this paper chooses the beginning of 2018 as the shock time node of the Sino–US trade friction because the first import tariff increase of the United States was in January 2018; however, the "301" survey of the United States in 2017 may have had an impact on Chinese innovative firms. Therefore, setting 2018 as the shock node may only underestimate the effect of the Sino–US trade friction on firm innovation. In other words, if setting 2018 as the impact node can identify the effect of the Sino–US trade friction on firm innovation, we have reasons to believe that the real effect may be greater.

#### *3.2. Data and Indicators*

The empirical research mainly uses our unique mircodata of Chinese technology and innovation firms. This dataset is jointly investigated and recorded by China's National Bureau of Statistics and China's Ministry of Science and Technology. The respondents are technological and innovative firms in most cities of mainland China. The variables involved cover four categories of information: basic information of firms, economic overview of firms, employees of firms and intellectual property rights of firms. The data cover a wide range of industries, including many subindustries under agriculture, manufacturing and service industries. We select subsamples of tradable sectors of the manufacturing industry in the dataset. The sample year is 2016–2019, just two years before and after the Sino–US trade friction in 2018, which can be used to identify the changes in firm innovation before and after the Sino–US trade friction.