1 Introduction

The nexus between urbanization, coal consumption, and CO2 emissions has attracted the attention of many studies in the literature, especially for developing countries where rates of urbanization change drastically. However, there is no consensus reached in the literature on the direction and size of the impact, as well as the significance in different stages of development. Table 1 summarize the previous studies. Urbanization is regarded as the other engine to deal with sluggish economic growth in China. As the second largest economy, China was an agricultural powerhouse in the past decades. The rural population takes the proportion of 88.82% of total population in the year of 1950. However, the proportion decreases to 36.16% in 2019 (National Bureau of Statistics of China, 2017–2019). In contrast, the urbanization rate represented by the ratio of urban population to total population peaks on 60.09% in 2019. There are significant achievements in encouraging the population to relocate to urban cities by government policy especially after the implementation of the 11th 5-Year Plan. In 1985, the coal consumption was 1966.55 million tons, but increase to 9017.98 million tons in next 30 years (see Wang et al. 2016; Lin and Xu 2018; and National Bureau of Statistics of China). Besides, developed countries always blame China and other developing countries for high pollutant emission (see Lu and Huang 2011; Wang et al. 2016; Chen et al. 2017; Lin and Xu, 2018; and Chen et al. 2019). To balance urbanization and pollution, the causality among coal consumption, CO2 emission and urbanization should be figured out beforehand. For this, many scholars contribute their efforts to test whether there are some causal relations among urbanization, coal consumption, and CO2 emissions.

Table 1 Summary of Previous Literature
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Knowledge of the causal relationship and the direction among urbanization, coal consumption and CO2 emissions are of particular importance to policy makers from China to make an appropriate urbanization and energy strategy. This study revisits urbanization, coal consumption and CO2 emissions nexus in China using a novel Granger causality namely Bootstrap Fourier Granger Causality in Quantiles (BFGC-Q, hereafter). In fact, we extended the Nazlioglu et al. (2016)’s Fourier Toda-Yamamoto Granger causality test and rather than focusing on a single part of the conditional distribution, the causality is tested in all conditional quantiles. The BFGC-Q test has two main properties more than Toda-Yamamoto GC test. First, the smooth breaks in the deterministic parts (intercept/trend function) are controlled by Fourier expansions. Second, the GC is tested within each conditional quantiles and this property allows us to identify which part of distribution of dependent variables are predicted by covariates. Empirical results indicate ne-way Granger causality running from urbanization rates to both CO2 emissions (within quantile 0.2) and coal consumption (within quantiles 0.4, 0.6 and 0.8) in China. Our empirical results have important policy implications for the government conducting urbanization and effective energy polices in China. We hope the current research can fill the existing gap in the literature.

This study is organized as follows. Section 2 discusses the proposed new Bootstrap Fourier Granger Causality in Quantiles test. Section 3 describes the data used in our study. Section 4 presents the empirical results and some policy implications of these empirical finings. Section 5 offers the conclusions of this study.

2 Methodology

While the causality definition of Granger causality test (Granger 1969) cannot provide information about a tail causal relation or nonlinear causalities, the quantile causality approach evaluates causal relationships in a more detailed and flexible way. In this paper, we propose the Fourier Toda-Yamamoto Granger causality test of Nazlioglu et al. (2016) based on quantile autoregression approach, call Bootstrap Fourier Granger causality in quantiles (BFGC-Q), and apply it to examine the nexus among urbanization, CO2 emissions and coal consumption for China. Following Nazlioglu et al. (2016), to allow for the structural breaks in the deterministic parts of Granger causality equation, the Fourier expansion in the Eq. (1) is included instead of using dummy variables in the Granger causality equationFootnote 1:

$$d\left( t \right) = \gamma_{0} + \gamma_{1} \sin \left( {\frac{2\pi kt}{T}} \right) + \gamma_{2} { \cos }\left( {\frac{2\pi kt}{T}} \right)$$
(1)

where \(d\left( t \right)\) is the Fourier function to capture the smooth breaks, \({\text{k}}\) represents the frequency of the Fourier function. \(\gamma\) is the coefficients’ vector and measures the amplitude and displacement of the frequency component (sin(.) and cosine(.) terms), and \({\text{t}}\) and \({\text{T}}\), are the linear trend and number of observations respectively. The sin(.) and cosine(.) terms are included to control for smooth breaks in the deterministic terms of GC equation.

To test the null hypothesis of non-Granger causality using BFGC-Q approach, we design a two steps procedure. In the first step, to control for smooth breaks of deterministic terms, the Fourier expansions \(d\left( t \right)\) is included in the following Granger causality equation:

$$Y_{t} = \gamma_{0} + \gamma_{1} \sin \left( {\frac{2\pi kt}{T}} \right) + \gamma_{2} { \cos }\left( {\frac{2\pi kt}{T}} \right) + \mathop \sum \limits_{i = 1}^{p + h} \theta_{i} Y_{t - i} + \mathop \sum \limits_{j = 1}^{m} \mathop \sum \limits_{i = 1}^{p + h} \vartheta_{j,i} X_{j,t - i} + \varepsilon_{t}$$
(2)

where Y and X are the dependent and independent variables, respectively, p is lag lengths, h is the maximum integration degree of the variables, and m is number of covariates. To estimate the Eq. (2), we should select the optimal value of k, say \(k^{*}\) and optimal value of lag(s), say \(p^{*} .\) To this end, we do a grid search and for each \({\text{i}} \in \left\{ {1,2, \ldots ,{\text{p}}} \right\}\), we select k = k* as optimum frequency when the SSR is minimized and then select the optimal value of lags, \(p^{*}\), using AIC criteria. We apply the standard restricted F test statistics to test the null hypothesis of \(\gamma_{1} = \gamma_{2} = 0\).

By choosing the \(k^{*}\) and \(p^{*}\), we estimate the Eq. (2) by quantile regression rather than OLS estimator:

$$ \begin{aligned}Q_{{Y_{t} }} (\tau |{\text{Z}}) &= \gamma_{0} \left( \tau \right) + \gamma_{1} \left( \tau \right)\sin \left( {\frac{{2\pi k^{*} t}}{T}} \right) + \gamma_{2} \left( \tau \right){ \cos }\left( {\frac{{2\pi k^{*} t}}{T}} \right) \\ &\quad+ \mathop \sum \limits_{i = 1}^{{p^{*} + h}} \theta_{i} \left( \tau \right)Y_{t - i} + \mathop \sum \limits_{i = 1}^{{p^{*} + h}} \vartheta_{j,i} \left( \tau \right)X_{j,t - i} + \varepsilon_{t}\end{aligned} $$
(3)

where Z is a matrix of all covariates in the regression model (3). Estimating the regression model (3) by quantile regression approach allows for testing the null hypothesis of Granger non-causality from X to \({\text{Y }}({\text{X}}{ \nrightarrow \ominus }{\text{Y)}}\) at different qunatiles \(\tau \in \left( {0,1} \right)\) as follows:

$${\text{H}}_{0} : \hat{\vartheta }_{j,1} \left( \tau \right) = \hat{\vartheta }_{j,2} \left( \tau \right) = \ldots = \hat{\vartheta }_{{j,p^{*} }} \left( \tau \right) = 0, \quad \forall \tau \in \left( {0,1} \right)$$
(4)

The null hypothesis of Granger non-causality in the restriction (4) is tested by following Wald test:

$${\text{Wald}} = \left[ {\left. {{\text{T}}\left( {\left. {\left( {\hat{\vartheta }_{j} \left( \tau \right)} \right)^{'} \left( {\left. {\hat{\varOmega }\left( \tau \right)} \right)} \right.^{ - 1} \left( {\hat{\vartheta }_{j} \left( \tau \right)} \right)} \right)} \right.} \right]} \right./\left. {\tau (1 - \tau } \right)$$
(5)

where \(\hat{\vartheta }_{j} \left( \tau \right)\) is the vector of estimated coefficients of \(\tau\) th quantile, \(\hat{\varOmega }\left( \tau \right)\) is the consistence estimator of variance–covariance matrix of the \(\hat{\vartheta }_{j} \left( \tau \right)\). As noted by Hatemi and Uddin (2012), due to the existence of autoregressive conditional heteroskedasticity (ARCH) effects in data, they do not usually follow a normal distribution and hence there is the possibility that the distribution of the Wald statistic substantially deviates from its asymptotic distribution. We thus use the bootstrapping simulation technique based on Hatemi and Uddin (2012) approach for 10,000 iterations to construct the 10%, 5%, and 1% critical values from the empirical distribution. We also computed the critical values of restricted F statistics (to test the null hypothesis of absence of sin(.) and cosine(.) terms in the Eq. (2)) using bootstrapping procedure.

3 Data

We apply annual data covering the period from 1969 to 2019 for China. The variables used in this study include the coal consumption, CO2 emissions and the ratio of urban population to total population used to indicate urbanization. Both urban population and total population are retrieved from National Bureau of Statistics of China and both CO2 emissions and coal consumption are retrieved from BP Statistic Review of World Energy (June, 2019). Table 1 reports the summary statistics for the data series. Jarque–Bera statistics indicate that CO2 emissions, coal consumption, and urbanization are non-normally distributed. By looking at the data series plots that we find that all three variables are trending upwards although urbanization grew slower than both CO2 emissions and coal consumption.

4 Empirical results and policy implications

In this study, we apply BFGC-Q approach to test the causal relationship among urbanization, coal consumption, and CO2 emissions in China over 1969–2019. Firs we go for traditional unit root tests and then BFGC-Q test.

  1. (1)

    Results from the Unit Root Test

We first apply several conventional unit root tests such as the ADF, PP, and KPSS and results are reported in Table 2. We find that CO2 emissions, coal consumption, and urbanization are all non-stationary and becomes stationarity (I(0)) after taking the first differenced (Table 3).

Table 2 Descriptive Statistics
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Table 3 Unit Root Test Results
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  1. (2)

    Granger non-Causality Test Results based on Bootstrap Fourier Quantile Model

To test the Granger causality, first we test the absence of Fourier expansion in the Eq. (2) using the conventional restricted F statistics. Before estimating our model, we set the maximum lag lengths (p = 6) and Frequency (k = 4) respectively. The results from Table 4 indicate the value of F statistics equals 10.932 and greater than its bootstrap critical values at 5% (which equals 9.725). The results indicate the null hypothesis of absence of Fourier components i.e. \(\gamma_{1} = \gamma_{2} = 0\) strongly reject at 5% level of significance. From this Table 4 that we also demonstrate the optimal Frequency (p*) and optimal lag lengths (q*) for Eq. (2) are 2.2 and 4, respectively, based on Akaike Information Criteria (AIC). Table 5 report the results of BFGC-Q test and we find a one-way Granger causality running from urbanization to both CO2 emissions (within quantile 0.2) and coal consumption (within quantiles 0.4, 0.6, and 0.8). By looking at the sign of the coefficients of the independent variables that we find urbanization cause coal consumption going up but CO2 emissions going down. Apparently that when urbanization increases, people are provided with energy in a more centralised manner, in addition, people in urban areas tend to belong in higher income and education levels and hence be more conscious about their energy and environmental behaviours, causing thus CO2 emissions to reduce (see Table 5 and Fig. 1). This means that when urbanization causes coal consumption to go up, coal consumption used in more efficient way in urban area, therefore CO2 emissions further goes down. Since urbanization would effectively reduce the CO2 emission, the Chinese government should encourage peasants relocate to urban cities to remove air pollution pressure from dependence of coal consumption in the past and then use coal consumption in more efficient way. The empirical results shed new light on the issues of climate change, the previous suggestions are mainly focused on improving coal utilization efficiency, exploit new energy including solar, nuclear and wind energy, another novel way is urbanization which is also able to reduce CO2 emissions in China.

Table 4 Fourier Test
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Table 5 Quantile Granger Causality Test among Urbanization, CO2 Emissions and Coal Consumption
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Fig. 1
figure 1

Granger Causality Test Direction

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5 Conclusions

China is coming under increasing pressure from its local population and the rest of the world to pay more attention to reducing their contribution to the emission of local air pollutants and greenhouse gases to mitigate the effects of pollution on health and climate change respectively. In this empirical note, we revisit the causal links among urbanization, coal consumption and CO2 emissions nexus in China using a newly developed Bootstrap Fourier Quantile model over the period of 1969–2019. Empirical results indicate urbanization Granger causes both coal consumption and CO2 emissions in China. By looking at the sign of coefficients of the independent variable we find urbanization reduce CO2 emissions but increase coal consumption. Apparently, cities can play an increasingly important role in helping China meet its future energy and CO2 intensity reduction targets (Khanna et al. 2013 and 2016).

Our empirical results have important policy implications for Chinese government conducting both urban and efficient-energy polices to reduce CO2 emissions. A research done by Liu (IEA 2019) suggests that enhancement of energy efficiency coupled with the acceleration of the process of urbanization could help in sustainable development. Figure 1 demonstrates the causal relationship among these three variables (i.e., urbanization, coal consumption and CO2 emissions). This figure further confirms our empirical findings. Apparently our empirical results are not consistent with that of Wang et al. (2014) and Fan et al. (2017) found that urbanization increases energy consumption and CO2 emissions in all 30 Chinese provinces but its specific impact varies depending on the province’s geographical location and economic structure. Results are also not consistent with those of Jones (1989), Shen et al. (2005), Liu (2009), Peters et al. (2011), Jiang and Lin (2012), Zhang and Lin (2012), Khanna et al. (2013) and Zhou et al. (2015) fund urbanization increases both energy consumption and CO2 emissions in China. On the other hand, our results are consistent with those of Fan et al. (2006), Wei et al. (2007), Zhu et al. (2012) and Wang et al. (2014) found that urbanization affected different economies in opposite directions for nine Pacific Island countries and China, respectively.