Carbon dioxide emissions, urbanization level, and industrial structure: empirical evidence from North China

This paper aims to examine the nexus among carbon dioxide (CO2) emissions, urbanization level and industrial structure in North China over the period 2004–2019, according to an expanded Cobb-Douglas production function. The panel econometric techniques are employed to complete the empirical analysis, including cross-sectional correlation test, panel unit root test, panel co-integration test, and panel Granger causality test. The empirical results support the long-term equilibrium relationship among CO2 emissions, urbanization level and industrial structure in North China, and the urbanization level contributes most to CO2 emissions, followed by fossil energy consumption. Furthermore, the bidirectional causality between CO2 emissions and urbanization level and unidirectional causality from industrial structure to CO2 emissions are found in North China, indicating that urbanization level and industrial structure have significant impacts on CO2 emissions. Finally, according to the empirical findings, several policy suggestions are proposed for the purpose of reducing CO2 emissions in North China.


Introduction
In recent years, the increasing use of fossil fuels has led to the rapid growth of global carbon emissions, which has brought serious crisis to human beings. Firstly, excessive concentrations of carbon dioxide in the atmosphere may have negative effects on human health, including but not limited to reduced cognitive levels (Karnauskas et al. 2020), greater fatigue during brainwork (Snow et al. 2019), and increased anxiety (Savulich et al. 2019). Second, excessive carbon emissions are making the climate problem even worse. According to the fourth Assessment Report released by the IPCC (Intergovernmental Panel on Climate Change), carbon dioxide is the biggest contributor to climate change among the greenhouse gases emitted by human activities, accounting for 63% of the total warming effect of all greenhouse gases. Excessive carbon emissions promote the process of climate warming, leading to a series of environmental problems, such as the frequent occurrence of various extreme weather (Gasparrini et al. 2017), the accelerated melting of glaciers (Giersch et al. 2017), and the habitat loss of animals (Sedighkia et al. 2019;Stirling and Derocher 2012). According to NOAA (National Oceanic and Atmospheric Administration), average global monthly carbon dioxide concentrations have hit record highs several times in recent years (exceeding 400 ppm in March 2015 and 410 ppm in April 2018, well above the roughly 280 ppm before the start of the industrial revolution), meaning that global carbon dioxide levels have entered the dangerous range and something need to be done to control further increases in carbon dioxide emissions. In addition, some commonly used measures to reduce carbon dioxide emissions, such as increasing the proportion of renewable energy in primary energy consumption (Kahia et al. 2019), also plays a role in promoting sustainable economic growth to a limited extent in some specific situations (Pao et al. 2014), which makes carbon dioxide emission reduction more important.
According to the Global Carbon Budget 2017 released at UN Climate Change Conference 2017 (COP23) by GCP (the Global Carbon Project), China is the country with the largest carbon emission in the world and its total carbon emission reached 27% of the world in 2017, which is more than the sum of the USA and the European Union (Le Quéré C et al. 2017). At the same time, China is facing the pressure of international public opinion and domestic environmental problems, as a result, the demand for energy conservation and emission reduction is increasingly urgent. China is deeply aware of the importance and urgency of reducing CO 2 emissions, in order to achieve the goal of low-carbon economic development, China submitted "strengthening action on climate change-China's national independent contribution" (hereinafter referred to as "national independent contribution") in 2015, publicly committed that its CO 2 emissions will reach the peak around 2030, and strive to reach the peak as soon as possible. On 22 September 2020, at the general debate of the 75th UN General Assembly, China proposed to enhance the national independent contribution, adopt more powerful policies and measures, strive to reach the peak of CO 2 emissions by 2030, and strive to achieve carbon neutrality by 2060. The research on CO 2 peaking in China is becoming more and more important and urgent. North china, including Beijing, Tianjin, Hebei, Shanxi, and Inner Mongolia, is an important part of China's economy. In 2019, North China's GDP accounted for 13.85% of the total GDP of China, while carbon emissions in North China accounted for 21.78% of China's total. With the increase of CO 2 emissions, reducing the carbon emissions intensity in North China is very important for low-carbon development. Based on this, researching the relationship among carbon emissions and economic growth in the North of China can promote a benign transformation of economic growth patterns in this region. The early realization of a low-carbon economic development path will eliminate the link between carbon emissions and economic growth, and is of positive significance to China's energy conservation and emission reduction.
With the continuous expansion of global warming, extensive economic development mode is no longer applicable, which requires us to reduce energy consumption and improve utilization rate. Therefore, low-carbon economic development path has become the focus of the world. Regions such as Beijing, Tianjin, and Hebei not only play an important role in the geographical location but also a major impact on China's economic development. The integration of Beijing, Tianjin, and Hebei has made this region more and more important. The planning of lowcarbon economy for the whole region can truly solve the carbon emissions problems and make the region achieve sustainable development. It is worth noting that North China is a key area of China's urbanization and industrial restructuring, revealing that the urbanization and industrial restructuring in this region can significantly change China's economic development mode, improve the quality of economic development, and provide a demonstration effect for other regions to achieve low-carbon development. Therefore, this article explores the relationship between carbon emissions, urbanization levels and industrial structure in North China, and aims to provide a reference for formulating carbon emission reduction policies from the perspective of urbanization and industrial structure.
In general, the main contributions of this article are the following: (1) In previous studies on the link among carbon emissions and economic growth, the absolute value of each variable was often used as the research object, so that the results could only reflect the overall trend and could not further describe the internal relationship between variables. Therefore, this paper introduces relative variables such as carbon emission intensity, energy consumption structure and GDP per capita, and expands the traditional Cobb-Douglas production function, which can reveal the internal connection between carbon emissions, economic growth, and energy consumption.
(2) According to panel data of five provinces in North China, this paper studies the relationship among the above three variables. At the same time, considering the relevant industrial and economic development status, this paper add industrial structure and urbanization rate into the model, which can truly reflect the relationship between carbon emissions, energy consumption and economic growth under the background of China's new normal economic development. Meanwhile, the empirical results provide a reference for the development of carbon reduction policy of urbanization and industrial structure perspective.
The rest of this article is organized as follows. The related literature is introduced in "Literature review" section. "Methodology" section introduces the methods that this paper needs. "Data and empirical analysis" section reports the data sources and empirical analysis. Finally, we summarize the conclusions and propose some policy proposes in "Conclusion and policy implications" section.

Literature review
Before studying the relationship between fossil energy consumption, industrial structure, urbanization rate, per capita GDP and carbon dioxide emissions in China, it is necessary to use the previous research results as references. A large amount of literature has analyzed the relationship between energy consumption and economic growth, depicting the nature character and the causal relationship. Kraft and Kraft (1978) were the earliest to study the relationship between economic growth and energy consumption and found a unidirectional causal link between GNP and energy consumption. However, Akarca and Long (1980), by changing the data interval to two years in the same date, found that no causation between GNP and energy consumption. Later, more and more scholars have begun to study the relationship between these two variables, the mainstream views can be divided into four hypotheses as shown in the table below Table 1 According to the research above, it can be found that the relationship between energy consumption and economic growth in different countries and regions is completely different. With the deepening of research, even in the same country, the corresponding direction and causal relationship quit diversity. The main reasons are (1) different economic development methods and different industrial structures are significantly different in different countries or regions. (2) different stages of development in the same country adopt different energy and economic intervention measures, such as adjusting energy consumption structure and adopting measures to reduce emissions and save energy. Therefore, the conclusions of different periods are also different; and (3) different techniques in modeling will also produce various conclusions.
In studying the long-term relationship between energy consumption and economic growth, Pedroni panel co-integration method (Pedroni 1999(Pedroni , 2004) is a tool widely used by scholars, its typical application is shown in Table 2, Nos. 1-8. Li et al. (2018) used panel co-integration to study the relationship between investment demand, gross domestic product, population scale, electricity consumption, and installed electrical capacity for China during the 2004-2016 periods. Farhani et al. (2013) studied the relationship between carbon dioxide emissions, urbanization, GDP, and energy consumption of 11 MENA countries using panel data method, and he found that more the sources of energy use and greater trade opening to the outside tend to cause more carbon dioxide emissions, and the improvement in the level of urbanization in environmental functions has a positive impact on reducing pollution levels. Cialani (2017) using the panel unit root, co-integration, and Granger causality to study Table 1 Four hypotheses about the relationship between economic growth and energy consumption Hypothesis Viewpoint Inference supporter Growth hypothesis Energy consumption has one-way causal relationship with economic growth Increasing energy consumption will promote real GDP growth and more aggressive energy policies should be adopted to drive economic development Wang et al. 2011Vafaeirad et al. 2015Chaudhry et al. 2015 Conservation hypothesis Economic growth has one-way causality with energy consumption The government issuance of energy conservation policies at the right moment can reduce energy consumption, but it will not affect the growth of real GDP Ozturk and Acaravci 2010 Narayan and Popp 2012 Li et al. 2020Qazi et al. 2021 Neutrality hypothesis The change of energy consumption has little or no impact on economic growth, and economic development will not affect energy consumption The policy of saving energy has no unfavorable impact on economic development Oyaromade et al. 2014 Destek M A 2015 Faisal andResatoglu 2016 Yakubu et al. 2017 Feedback hypothesis There is a two-way causal relationship between energy consumption and economic growth the government should actively improve the efficiency of energy utilization, which is conducive to both economic growth and resource conservation Wang et al. 2016bKahia et al. 2017Amri 2017Etokakpan et al. 2020 (2017) used cross-sectionally dependent heterogeneous panel estimation techniques to explore the link between carbon dioxide emissions, GDP, energy consumption and tourism in the EU and candidate countries during the period of 1995-2011. Al-Mulali (2014) studied the relationship between consumption and GDP growth of nuclear energy and carbon dioxide emissions of 30 major consumer of nuclear energy using Granger causality test and panel data methods, and employing Granger causality test and panel data method. The results showed that the consumption of nuclear energy plays a significant role in the growth of GDP but has make no difference on carbon dioxide emissions. Esfahani and Rasoulinezhad (2015) used group cointegration, FMOLS and DOLS groups and studied the relationship between oil consumption, GDP, and CO 2 emissions in the next 11 (N-11) countries from 1980 to 2013, and the results showed that there is a long-term twoway relationship between GDP per capita oil consumption and CO 2 emissions. Saleh and Abedi (2014) studied the link among carbon dioxide emissions and GDP using panel date and the vector auto-regression model and found that a bidirectional causality relationship among carbon dioxide emissions and GDP for three groups of countries. Saidi and Mbarek (2016) studied the relationship between factors such as carbon dioxide emissions and GDP per capita during 1990-2013 period using Pedroni's method in nine developed countries. In recent years, because of the problem of global warming is becoming more and more serious, many researchers in the study of the relationship between energy consumption and economic growth has begun to consider carbon dioxide emissions, some experts also conducted more in-depth studies by examining the relationship among industrial structure. As shown in Table 2, nos. 9-14, researchers differ on the relationship between carbon dioxide emissions and energy consumption, and they do not reach a universal conclusion. For instance, Wang et al. (2016a) studied the link between carbon dioxide emissions, energy use, and urbanization in the Association of Southeast Asian Nations countries BRICS, and Bhat et al. (2021) studied the link between saving and economic growth, using panel co-integration, etc. These papers show that the results of causality between different countries are different, so a unified energy policy will not be a good strategy for widespread implementation. Moreover, JLS Lim (2017) and Sulaiman and Abdulrahim (2017) employed different methods to analyze the relationship in Malaysia and reached a similar conclusion: there is a one-way relationship in CO 2 emissions to economic growth in the long run. In addition, for new EU member states and candidate countries, the results show that there is a oneway causality from trade openness, energy consumption and urbanization to carbon dioxide emissions, from energy consumption, urbanization, and GDP to trade (Kasman and Duman 2015). Finally, for 14 MENA countries, Salari et al. (2021) used simultaneous-equation models for testing the relationship among carbon dioxide emissions and energy consumption and found that there is a bidirectional causal relationship among these variables.
To better understand the relationship among industrial structure, energy consumption structure, urbanization rate, per capita GDP, and CO 2 emissions, the production function of Cobb-Douglas is introduced in Cobb and Douglas (1928). This production function is used as a department model, with the research object as the department and the department output as the explanatory variable. The major control variables are energy consumption, industrial structure and population density playing an important role in the output. It also introduces other variables in the model that may affect the output. Based on the estimation of the model, the contribution of these input variables to output is analyzed, and the purpose of the study is achieved (Van 2021). As shown in Table 2, nos. 15-21, many factors were analyzed when researchers explored the factors that affect carbon dioxide emissions and their mechanisms, such as energy consumption, urbanization, tourism activities, and international tread. Ouyang and Lin (2017), Wang et al. (2014), and Xu and Zhang (2016) analyzed the influences of urbanization on carbon dioxide emissions and found a bidirectional causal relationship among carbon dioxide emissions, urbanization, and energy consumption: specifically. There is a two-way positive causal link between urbanization and carbon dioxide emissions exists, and a same correlation exists in them. Zaman et al. (2016) and Margarita et al. (2016) explored the relationship among carbon dioxide emissions and tourism of Portuguese during 2000-2008 and found that tourism activity has an important effect to carbon intensity. Boamah et al. (2017) employed Johansen co-integration model for China during 1970-2014 period. The results show that there is a long-term N-shaped relationship between economic growth, carbon dioxide emissions, and international tread under the estimated Kuznet curve framework. The effects of land finance and land urbanization on CO 2 emissions were studied by Zhang and Xu (2017) and the literature found that the two variables significantly affect carbon dioxide emissions.
Through the observation of previous research findings, it can be found that there are many factors that affect CO2 emissions, such as industrial structure, energy consumption structure, urbanization rate, and per capita GDP. However, most of the existing studies involve only a few of factors, which are not comprehensive. Moreover, there is not much research on the causality relationship between these variables. Therefore, a multivariable model based on Cobb Douglas production function is proposed in this paper. Because the panel data model can effectively solve the problem of sample shortage and consider time series data and cross-sectional data, it helps to correctly estimate the relationship between variables and improve the importance of model estimation (Zhang et al. 2012). For accurate comparison of the contribution of each variable to carbon dioxide emissions in the five provinces, including Hebei, Shanxi, Beijing, Inner Mongolia, and Tianjin, we analyze causality and co-integration relationship between those variables in different provinces panel data model.

Production function model
A single-sector economic model that considers CO 2 emissions, it is assumed that society as a whole has only one production department and one production function. On the basis of the traditional production function, the CO 2 emissions are introduced into the production function, and the concrete form of the model is expressed as follows: where Y is the output value that is CO 2 emissions, L t , H t , R t and W t are the fossil energy consumption structure, industrial structure, urbanization rate, per capita GDP, respectively, and A, α, β, γ and ε are the constant values.
By changing the original variable in Eq.
(1) to the following logarithmic equation, the effect of heteroscedasticity on the regression result can be prevented: where lnY is the natural logarithm of the output, and lnA means the logarithm of total factor CO 2 emissions productivity, L t is energy consumption structure, H t stands for the logarithm industrial structure, R t represent the urbanization rate, lnW t is the logarithm of per capita GDP, and α, β, γ, ε are the output elasticities.
If Eq.
(2) considers individual factors and time series factors, the panel data model for each factor of production under the framework of the production function model can be derived from Eq. (3).
where μ it is the random error term. It is independent, satisfying the null hypothesis mean value and has the same variance of 2 means the number of cross-section, and t stands for time period. (1) There will be two cases. First, the Eq. (3) is a fixed effect model when the individual non-observation effects presented by lnA i is the individual characteristics and do not change with time; Second, the Eq. (3) is a random effect model, when lnA i is a random variable and conforms to a specific distribution.

Cross-sectional dependence test
Neglecting the cross-section data correlation will lead to low efficiency and invalid test statistics. Hence, before a series of empirical analysis is carried out, it is necessary to test whether the cross-sectional is dependence. The spatial error regression model can be expressed as follows: where u it means the regression error perturbation term with random individual effect. According to Anselin (1988) and v t and μ are independent of each other. In formula (6) Cross-sectional dependence test, that is, to check the correlation between the N cross-sections in the panel data. As long as two of the cross-sections are related, it is considered that there is cross-sectional dependence panel date. The null hypothesis of the cross-sectional dependent test can be expressed as below: The alternative hypothesis is shown in Eq. (8): The test statistics based on uncorrelated regression in Breusch and Pagan (1980) is provided by And û it is the residual estimation of (10). Under the null hypothesis, the asymptotic distribution of the LM test statistics is a χ 2 distribution with N(N − 1)/2 degrees of freedom. When N < T, this test is suitable for the case. When N > T, the following two methods can be used for testing. Pesaran (2004) proposed a simple method to test the crosssection error, which is suitable for the case that the crosssection individuals N are relatively large and the time T is relatively small. The test is an average of the correlation coefficients of the residuals that obtained from the OLS regression, and the test statistics are as follows: Under the null hypothesis of uncorrelated, the asymptotic limit distribution of CD statistic is normal distribution. Besides Pesaran confirms the superior performance of this test in small examples and it is very suitable for our research.

Panel unit root test
The unit root test should be carried out before the panel data regression analysis, which can avoid spurious regression. There are many methods of unit root test that including LLC test (Levin et al. 2004), IPS test (Im et al. 2003), Breitung (Breitung 1999), Hadrid (Hadri 2000), and Carrion-i-Silvestre et al. ( Lluís Carrioni-Silvestre et al. 2005). The LCC test method is as below: We assume that ξ it is independent distributed for all i, Δ represents the first order difference operator (1-L). If γ i = 0, then y it contains the unit root, while if γ i < 0, y it is considered to be stationary. The null hypothesis of LLC and the alternative hypothesis of LCC are as follows: To test the null hypothesis H 0 and the alternative hypothesis H 1 , Levin and Lin suggest that we should make a regressing of ∆y it and y i, t − 1 for each i relative to the other variables in Eq. (12) firstly and obtain residuals ê it and v i,t−1 , respectively. Secondly, the regression estimate of Eq. (15) is γ.
The t statistic for test γ = 0 is as follows: Where the ∼ is the least square estimate of Eq. (15), The IPS test sets the alternative hypothesis to the following equation: This hypothesis broadens the strong assumption that Levin and Lin require Eq. (12) to be homogeneity under the alternative hypothesis. Therefore, the IPS test cannot use mixed data, and the ADF unit root test should be performed for each individual in the N cross-sections, respectively.
The Hadri test is similar to time series KPSS test. H 0 : none of the sequences in the panel data contain unit roots. Considering the back-end residual sequence of the original panel data, define the LM statistic, which contains two types of statistics: drift term and trend term. The formula is as follows: where S i (t) = ∑ t s=1û it is the residual accumulated function, f 0 is the residual spectral density when the frequency is 0. Considering cross-section heterogeneity, LM 2 is chosen as a test statistic.
Under the condition of H 0 , the asymptotic distribution of the statistic Z = √ N(LM − )∕ is the normal distribution.

Panel co-integration test
Only after the unit root test indicates that the series is stable can the panel co-integration test be performed by Pedroni co-integration test theory. The theory holds that cross-sectional independence is related to different individual effects. It is used as below: where t = 1, 2, ⋯, T represents the time period, i = 1, 2, ⋯, N represents the country or region in the panel date. The parameter α it is the likelihood of fixed effects and δ i is the deterministic trends in specified-country or specifiedregion, ε it means the estimated residual, which is a departure from long-term relationships. When some variables are expressed in the form of natural logarithms, the parameters γ 1i , γ 2i , γ 3i , γ 4i , γ 5i in Eq. (12) can be interpreted as elastic coefficients. In order to test the null hypothesis that there is no co-integration, that is, ρ i = 1, the later unit root test of the residuals is expressed as follows: Pedroni proposed two co-integration test sets. The method of panel testing based on internal dimension includes panel ρ-statistic, v-statistic, ADF-statistic, and PP-statistic. These statistics use the auto-regressive coefficients of different countries or regions to estimate the unit root test of the residuals. Statistics take the common time and the heterogeneity of countries or regions into account. The group test based on the between dimension method includes group PP-statistic, group ADF-statistic and group ρ-statistic. These statistics based on the average of the auto-regressive coefficients for each group. In the panel, the auto-regressive coefficient is related to the unit root test of the residuals for each country or region. These seven statistics are asymptotically standard distributions. When Pedroni test shows that there is cointegration relation among variables, fixed effect estimation and causality test can be carried out.

Panel estimation method
Differential GMM is a mainstream panel model estimation method, which can effectively deal with individual effects without considering stationarity. According to the differential GMM estimation method, the basic regression model of panel data is: where, y it is the explained variable, y it − 1 is a lag phase variable of the explained variable. α is the elasticity coefficient of the explained variable lagging by one period, β is the elastic coefficient of each explanatory variable. X it is the explanatory variable, μ it is a fixed effect, ε it is the residual of the model. In order to solve the possible individual fixation effect, Arellano-Bond uses the GMM method to carry out the first-order difference processing of formula (24), and obtains: It can be seen from formula (25) that the model after differential treatment solves the individual fixed effect. The GMM method does not consider the stationarity of data, but there is a two-way causal relationship between various variables, also known as endogeneity. In order to solve this endogeneity, Sargan test and Arellano-Bond test can be used to verify the scientificity of the model and variables (Baum et al. 2003).
The differential GMM model eliminates the individual fixed effect through difference, and can get better overall panel estimation results. However, analyzing the differences of different sections is of practical significance to explain the problems studied. In order to further analyze the cross-section difference, based on the overall panel estimation results and the existing literature (Zhao et al. 2016), this paper first judges the form of the cross-section estimation model. Then the section model is estimated, and finally the effectiveness of the section model estimation results is tested.
Therefore, the panel estimation in this paper mainly includes two parts: First, the difference GMM method is used to estimate the overall panel; The second is to consider the cross-section difference, estimate the cross-section model and test its effectiveness.

Panel causality test
Engle and Granger proposed that a unidirectional or a bidirectional Granger Causality will exit in two variables if there is co-integration between the two variables in the long term. Besides, Granger causality test is widely applied in studying causality between variables. In the case of time series, Granger defines the causal relationship between two economic variables X and Y as follows: under the past information contains variables X and Y conditions, the prediction result of variable Y is better than that conducting the past information of Y alone, that is, the variable X can help us explain the future change of the variable Y, so X is considered as the Granger cause of Y. This paper uses Granger model to analyze the causal relationship between time series: The Eq. (28) represents the null hypothesis of the tests, that is, X is not the Granger cause of Y. If Eq. (28) is rejected, we can conclude that X Granger caused Y. Meanwhile, it can be concluded that Y Granger caused X when formula (29) is rejected: H 0 ∶ j = 0, j = 1, 2, ⋯ , n

Data source and descriptive statistics
This paper adopts balanced panel data of North China, including Hebei, Shanxi, Beijing, Tianjin, and Inner Mongolia, over the period of 2004-2019. The model proposed in this paper involves five variables, namely, fossil energy consumption (Fes), industrial structure (S), urbanization rate (Ur), per capita GDP (pcGDP), and per capita CO 2 emissions (pcCE). We obtained CE data from WIND database and other variables data from the website of China National Bureau of Statistics. In order to avoid drastic fluctuations in the data and eliminate the heterodyne phenomenon in the time series, some variables are transformed in the nature logarithmic series, such lnpcGDP. At the same time, the coefficient of the logarithmic model can represent the elasticity of the variable.
The summary statistics of PcCE, Ur, S, lnpcGDP, and Fes are presented in Table 3. The mean of CO 2 emissions ranges from 0.92 in Beijing to 6.37 in Hebei. Beijing is one of the first cities in China to put forward the goal of reaching the peak of carbon emission. At the first Sino US climate smart Low Carbon City Summit held in 2015, Beijing put forward the goal of "achieving the peak of carbon emission around 2020", Hebei Province is a major energy consumption province dominated by heavy industry, In 2002-2011, Hebei Province ranked second in China and fourth in China from 2012 to 2017. As for the per capita GDP, Shanxi has the lowest per capita GDP, whereas Beijing has the highest. Shanxi Province is an industrial system dominated by resource-based industries such as coal and coking. The price of energy raw materials such as coal fell due to traditional overcapacity, and the economy of Shanxi Province began to decline like a cliff. In 2018, the per capita GDP of Shanxi Province was China's ranking fell to 25th. Based on the urbanization rate, which is defined as the ratio of urban population to the total population, Beijing has the highest urbanization rate, while Hebei is the lowest in the panel. Hebei Province is located around the tidal sea in Beijing, Tianjin, and Hebei. Affected by the regional development of Beijing and Tianjin, Hebei Province is subject to Beijing and Tianjin. There are no mega cities in the 11 prefecture level cities in Hebei Province, and its ability to drive the economic welfare of the surrounding areas is not strong. In realizing industrial structure, which is displayed by the proportion of the added value of the secondary industry to GDP, Hebei has the highest industrial structure because there are many heavy industrial enterprises in Shanxi, and Beijing has the lowest industrial structure among five provinces. Regarding the fossil energy consumption, Shanxi has the highest ratio, whereas Beijing has the lowest in North China.
Prior to empirical analysis, a correlations test should be conducted on the panel data. The results of correlations test for the panel data are listed in Table 4. As shown in the table, the test results, at 1% level of significance or 10% level of significance, reject the null hypothesis. Therefore, there is a statistical correlation between variables.

Results of cross-sectional dependence test
The results of Pesaran cross-sectional dependence test are listed in Table 5. As shown in the table, the test results, at 5% level of significance, accept a null hypothesis with no cross-sectional dependence. Therefore, the first-generation unit root tests including Im, Pesaran and Shin W-stat (IPS) test, Levin, Lin, and Chu (L.L&C) t test, Phillips-Perron Fisher (PP-Fisher) test and Augmented Dickey Fuller-Fisher (ADF-Fisher) test can be used to test the stationary of different variables.

Results of panel unit root test
It is necessary to check the stationary of these variables before the panel co-integration is used to test the long-term relationship between the fossil energy consumption, industrial structure, urbanization rate, per capita GDP in the five provinces of North China. The commonly used methods of unit root test are Im, Pesaran, and Shin W-stat (IPS) test, Levin, Lin, and Chu (L.L&C) t test, Phillips-Perron Fisher (PP-Fisher) test, and Augmented Dickey Fuller-Fisher (ADF-Fisher) test. Obviously, from the results of the unit test in Table 6, it can be seen that these variables are not stationary in level forms.
In general, differenced methods can be further used for non-stationary sequences to determine the stationary of those variables. ΔPcCE', ΔLnpcGDP', ΔS', ΔUr', and ΔFes' represent those variables at the second difference. From Table 4, it can be seen that the unit root test statistic of all variables exceeds the critical value at 1% level and all these variables are stationary at the first difference, indicating that the null hypothesis that there is a unit root is rejected.

Panel co-integration test results
Because all variables are stationary in the first difference, the Pedroni [22] test can be used to test the panel co-integration. The Pedroni method constructs seven statistics to test the residuals for each province in the group based on the mean value of the single auto-regressive coefficient related to the unit root. From the results in Table 7, among the seven statistics, four are significant at the level of 5%, revealing that the co-integration relationship exists among the examined variables. Moreover, Kao test and Johansen test are employed to test the co-integration relationship for robust, and the results also support the conclusion that there is a co-integration relationship among the examined variables.

Panel estimation result
Empirical analysis is carried out according to the above measurement models and estimation methods. In the estimation of the equation, the first-order lag term of the explained variable is introduced as the explanatory variable, which is difficult to make the difference of the disturbance term have no second-order autocorrelation. Therefore, we continue to introduce the lag term of order 2-4 as the explanatory variable. The estimation results show that the perturbation term difference of the equation has first-order autocorrelation, but there is no second-order autocorrelation, which shows that the estimation is effective. At the same time, the coefficient joint significance test of difference GMM estimation is significant. Sargan test results show that the equation accepts the original assumption that all instrumental variables are valid, and it can be considered that the selection of instrumental variables is reasonable, as showed in Table 8. According to the estimation results, the following conclusions can be drawn: first, the lag coefficient of per capita carbon dioxide emission (pcCE) is a positive number less than 1, and the rejection coefficient is 0 at the significance level of 1%, which shows that per capita carbon dioxide emission is subject to obvious inertia. Second, the increase of per capita GDP (pcGDP) and urbanization rate (Ur) will negatively and significantly affect per capita carbon dioxide emissions (pcCE), which shows that the development of urbanization is conducive to reducing carbon dioxide emissions. Third, the improvement of industrial structure (S) and fossil energy consumption (Fes) will positively and significantly affect the per capita carbon dioxide emission (pcCE), which shows that in the future development, we should pay attention to the development of the tertiary industry and gradually reduce the consumption of fossil energy.

Model form determination
There are two main methods to detect the fixed effect and the random effect, named likelihood ratio (LR) test and Hausman test. The LR test is used to test the fixed effect, and the Hausman test is used to test the random effect. Before estimating the contributions of the fossil energy consumption, industrial structure, urbanization rate, and per capita GDP to CO 2 emissions, LR test and Hausman test are used to determine the model is the random effect or fixed effect. Table 9 is the effect test results, from which it can be seen that the cross-section F statistic is larger than the critical value, revealing that the null hypothesis that the fixed effect is redundant can be reject, that is, it is reasonable to introduce the fixed effect. Because the cross-section random statistic of Hausman test is larger than the critical value, it can reject the null hypothesis that the random effect is irrelevant to explanatory variables at the 5% level of significance. In the same way, the model should be a fixed effect model based on the estimation coefficient of the fixed effect and the random effect as well as the variance values after the difference. Then an F test will be used to select model, including the variable parameter model, the variable intercept model and the contest parameter model. From these models, we can get three different values of the sum squared residual values, which are set to S 1 , S 2 , and S 3 . The F test value can be obtained by calculating the Eq. (30) and Eq. (31). If F 1 > F 1, α , the null hypothesis is rejected, which means that the panel data model is not a variable intercept model. If F 2 > F 2, α , the null hypothesis is rejected, which means that the panel data model is not a constant parameter model: where S 1 is the variable parameter model residual sum of squares, S 2 is the variable intercept model residual sum of squares, S 3 is the sum of the residual squares of the invariant parametric model, N is the number of sections, K is the number of variables, and T is the number of periods. In this paper, N = 5, K = 4, T = 16, so (N − 1) × K = 16, (N − 1) × (K + 1) = 20, N × T -N × (K + 1) = 55. Table 10 is the results of F test. F 1 rejects the null hypothesis, indicating that the panel model is not a variable intercept model, and F 2 rejects the null hypothesis, indicating that the panel model is not a constant parameter model. In summary, the panel model should be a variable-parameter model, that is, a fixed effect variable parameter model.

Panel data model estimation
According to the above results, we can set up a variable parameter model with fixed effect involving the fossil energy consumption, industrial structure, urbanization rate, per capita GDP in the five provinces of North China. Table 11 is the estimated results of the model. From which it can be seen that the R 2 and the adjusted R 2 are 0.9939 and 0.9913, respectively. Besides, the F statistic is significant and each coefficient is positive and significant at the 10% significance level. Therefore, this model has the advantages of significant, high goodness of fit and good model effect. From the estimated results of the model, we can know that: (1). In five provinces of North China, except for Inner Mongolia, the urbanization rate makes the largest contributed to CO 2 emissions, followed by the industrial structure. The level of urbanization in Inner Mongolia has a negative impact on CO 2 emissions, mainly because of the reduction of the negative environmental impacts through the improvement of technology and the reform of industrial structure. The per capita GDP variable is the natural logarithm, and its coefficient can be interpreted as elasticity. The results showed that a 1% increase in GDP per capita actually increased CO 2 emissions in Beijing, Tianjin, Hebei, Shanxi, and Inner Mongolia by − 0.45%, 0.25%, 1.57%, − 0.28%, 0.47%, respectively. It can be seen from the data that the economic development in Beijing and Tianjin can help reduce CO 2 emissions. It is because Beijing and Tianjin are mainly developing low-carbon economies such as tertiary industry. In other provinces, especially Inner Mongolia, the economy is relatively backward, and in order to develop the economy, more fossil fuels with high carbon emissions are consumed. From the impact of industrial structure on CO 2 emissions, expect Beijing, other provinces are positive, among which Hebei is the highest, and Inner Mongolia is the lowest, because Hebei mainly relies on the secondary industry to develop economy, while Inner Mongolia's economy is underdeveloped, resulting that the proportion of the added value of the secondary industry to GDP is low. (2). In general, in the provinces where economic growth relies on heavy industry or underdeveloped provinces, the contribution of fossil energy consumption to the growth of CO 2 emissions is relatively large. Among them, the contribution rates of Shanxi and Hebei are the highest, because Shanxi and Hebei mainly use fossil energy to develop the economy. A 1% increase of the fossil energy consumption in these two province increases CO 2 emissions by 3.21% and 7.45%, respectively.
In order to verify the effectiveness of establishing panel data model, the autocorrelation and heteroscedasticity tests need to be performed. In this study, the Wooldridge test is used to test whether there is a correlation between different variable, and the modified Wald test method is used to check the heteroscedasticity of the different variables. The results are listed in Table 12, showing that there is no sequence correlation and heteroscedasticity, indicating that the model's estimation results are valid. Table 13 reports the panel Granger causality test results. The contents of which contain asterisks means that the null hypothesis should be rejected at a specified level of significance. In Tianjin, for example, when the null hypothesis is  Table 13, we can get the following findings:

Panel Granger causality test results
(1). From the results of the Granger causality test in the relationship between per capita CO 2 emissions and urbanization rate, there is a unidirectional causality running from urbanization rate to per capita CO 2 emissions in the five provinces, meaning that urbanization rate does Granger cause CO 2 emissions. Therefore, the change of urbanization rate will have an impact on CO 2 emissions. Besides, there exists bidirectional causal relationship between per capita CO 2 emissions and urbanization rate in Beijing and Tianjin.
(2). From the results of the Granger causality test in the relationship between per capita CO 2 emissions and per capita GDP, there is a bidirectional causality between per capita GDP to per capita CO 2 emissions in the Tianjin and Shanxi, indicating that the feedback hypothesis that per capita CO 2 emissions and per capita GDP are interrelated and mutually complementary emerges. Therefore, the policy of developing the economy and increasing the per capita GDP will have an impact on the emissions of CO 2 , and the management of CO 2 emissions will also have an impact on economic development. In Hebei, there is a unidirectional causality running from per capita GDP to CO 2 emissions, supporting the growth hypothesis, that is to say, with the increase of per capita GDP in Hebei, CO 2 emissions will increase. (3). Except for Hebei and Beijing, there is a unidirectional relationship between fossil energy consumption and CO 2 emissions. Because Beijing as a developed area with more service industries, its development is mainly based on electric power, and fossil energy consumption is relatively low. Therefore, there is no causal relationship between fossil energy consumption and CO 2 emissions in Beijing. In Tianjin, Inner Mongolia, and Shanxi, there is a unidirectional relationship from CO 2 emissions to industrial structure, which means CO 2 emissions can promote the adjustment of industrial structure in these provinces. (4). From the whole region of North China, there are bidirection causalities between per capita CO 2 emissions and per capita GDP, and between CO 2 emissions and urbanization rate. Besides, the unidirectional causal relationships from fossil energy consumption to CO 2 emissions and from industrial structure to CO 2 emissions are found, revealing that fossil energy consumption and industrial structure have significant influences on CO 2 emissions in North China.

Conclusion and policy implications
China has made great achievements in economic development over the past decades, but the CO 2 emissions are becoming more and more serious. Under such circumstances, China has promised to substantially reduce carbon emissions in the next 30 years. Therefore, it's necessary exploring the nexus between per capita CO 2 emissions, fossil energy consumption, industrial structure, urbanization rate and per capita GDP in North China, including Beijing, Tianjin, Hebei, Shanxi, and Inner Mongolia. In this article, The results of the cross-sectional dependence test suggested that there was no cross-sectional dependence across the panel. The unit root test and co-integration test have been done. The results show that all variables are non-stationary at the level, but stationary at the first different level. And it is co-integration in the long run. Then, panel estimation is carried out from two parts: overall estimation (GMM) and cross-section estimation. According to the model estimation results, the urbanization rate contributed most to CO2 emissions, followed by the fossil energy consumption. Finally, the panel Granger causality test revealed that there existed bidirectional causal relationships between CO2 emissions and urbanization rates in Beijing and Tianjin, and unidirectional causal relationships from CO2 emissions to urbanization rates in other regions. In addition, there existed unidirectional causal relationship from industrial structure to CO2 emissions in North China, reverse causalities in Tianjin, Hebei, and Shanxi and no causality in Beijing and Inner Mongolia. Based on the empirical results, several policy recommendations on how to reduce China's total carbon emissions are put forward, the highest priority is to reduce the use of fossil energy. According to the Granger causality results, it is known that the problem of excessive carbon dioxide emissions caused by fossil energy combustion should be paid attention in North China, especially in Shanxi. In this case, new energy power has become an ideal alternative to coalfired power generation, increasing the proportion of renewable energy in primary energy consumption will help reduce the use of fossil energy. Although China has been ranked as the largest country in the production and use of new energy power for many years, due to some objective factors such as the anti-peak regulation characteristics of new energy power generation, the high unit cost of new energy power generation and the insufficient regulation capacity of the power system, many provinces in China still suffer from severe wind and light abandonment. Based on the past policies and their effects, China can take the following measures to improve the utilization efficiency of new energy resources, so as to reduce the use of fossil energy: (1) In terms of power market construction: (1) reform the power trading mechanism, such as deepening the construction of power spot market and allowing power generation enterprises and electricity enterprises to conduct direct bilateral transactions conditionally; (2) the difference between peak and valley electricity prices should be appropriately enlarged to guide users to adjust the time period of electricity consumption or build the user-side energy storage system, so as to absorb the overflow power during the time when the new energy power supply exceeds the demand; (3) promote the construction of new energy units connected to the grid and enhance the power system's regulatory capacity by transforming idle thermal power units; (2) We can not only reduce CO 2 emissions in North China, but also achieve green GDP growth and weaken the causality between the per capita GDP and per capita CO 2 emissions in North China, so as to make the economy develop sustainably. Under the goals of carbon peak and carbon neutralization, the power industry is an important government regulatory industry, subsidies should be provided by the government to reduce the on-grid price and make grid enterprises willing to accept electricity from new energy power generation enterprises.
In China, which is still a developing country, many provinces, such as Hebei and Shanxi, mainly rely on heavy industry with high carbon emission to develop their economy, causing serious environmental pollution. In this case, speeding up the elimination of outdated production facilities and increasing the proportion of the tertiary industry will help to reduce the emission of CO 2. (4) Finally, in the five provinces of North China, we should reasonably increase the urbanization rate on the basis of fully considering the actual carrying capacity of the region, so as to achieve the goal of energy saving and emission reduction.