Kaya Equation

The Kaya Equation [27] is a simple mathematical formula that relates CO₂ emissions from human activities to economic, policy, and demographic factors. In this paper, the Kaya carbon constancy equation is broken down into the corresponding CO₂ emission influencing factors and expressed as:

Where C is CO₂ emissions, C_i is the CO₂ emissions of the energy source, TE is the total consumption of energy, GDP is gross domestic product GDP, and P is population size. CI stands for CO₂ intensity, which is the ratio of carbon emissions to total energy. EI stands for energy intensity, which is the ratio of total energy consumption to GDP, and PGDP is per capita GDP.

From this, Equation (1) can be rewritten as:

The right side of Equation (2) divides the main CO₂ emission drivers into multiplicative factors, while the left side corresponds to CO₂ emissions. According to the equation and the corresponding literature analysis, CO₂ emissions are mainly determined by influencing factors: population, economic development level, energy intensity, and CO₂ emission intensity.

Data and Descriptive Statistics

So the following variables have been selected as the main research variables in this paper:

CO₂ emissions: Since the consumption of fossil and other energy sources is the main source of CO₂ emissions, the total CO₂ emissions are mainly measured on the basis of three energy sources with large CO₂ emissions, namely coal, oil, and natural gas; according to the measurement method provided by the IPCC, CO₂ emissions = Σ consumption of energy i* carbon emission factor of energy i (i is the type of energy source), and energy consumption must be converted into standard coal in a uniform unit of heat. The CO₂ emission factors for coal, oil, and natural gas are 0.7476 tC/tonne of standard coal, 0.5825 tC/tonne of standard coal, and 0.4435 tC/tonne of standard coal, respectively. CO₂ emissions are recorded as CC.

Fig. 1.

Research framework diagram.

CO₂ emission intensity: CO₂ emission intensity is the ratio of carbon emissions to total energy consumption (tC/tonne), which is referred to as CI.

Energy intensity: Energy intensity is the ratio of total energy consumption (tC/tonne) to total GDP (CNY billion) in Hubei Province, which is referred to as EI.

Population: Population size is based on the Hubei Statistical Yearbook and is expressed as the total population (per ten thousand people) at the end of each year in Hubei Province, which is referred to as P.

Economic development level: Economic development level is expressed as per capita GDP in Hubei Province, which is referred to as PGDP.

We take natural logarithms to eliminate heteroscedasticity and multicollinearity. All variables of CO₂ emissions, per capita GDP, population size, energy intensity, and carbon intensity of energy were taken as lnCC, lnPGDP, lnP, lnEI, lnCI.

The data frequency is annual and the sample interval is 1985–2020. The raw data are from Hubei Provincial Statistical Yearbook and Statistical website.

Table 1 shows the main variables conform to the stable data structure. After logarithmic treatment, the statistical properties of the variables themselves differ less. where the mean values of lnCC, lnEI and lnCI are 8.6456, -0.4317, and 0.5504, respectively, and the medians are 8.3762, -0.4772, and 0.4877, respectively. The standard deviations of the three variables are 0.7835, 0.1142, and 0.8210, and these data show good results. The variables of lnP and lnPGDP also do not have large deviations. Statistical results surface data can enable the next step of empirical modeling analysis.

TVP-VAR Model

The VAR model was introduced by Sims [28] and it relies on the statistical nature of the data and constructs the model by taking each endogenous variable in the system as a function of the lagged values of all the endogenous variables. The VAR model has been widely used for predicting interrelated time-series systems and analyzing the stochastic perturbations of the system dynamic shocks.

Traditional VAR is difficult to apply for estimating non-linear time series, and cannot adequately explain the time-varying dynamic characteristics between variables. Primiceri [29] improved and developed the TVP-VAR model by introducing parameters that fluctuate over time. These time-varying parameters capture the model’s dynamic and nonlinear features, enabling a more nuanced analysis of the time-varying and nonlinear impacts on CO₂ emissions.

A traditional VAR model can be expressed as:

Where y_t is a k × 1 dimensional observable variable, A, F₁, ..., F_s are k × k dimensional coefficient matrices, and u_t is a k × 1 dimensional structural shock. Assume that u_t ~ N(0,∑∑)

Model (3) is simplified to:

Where B_i = A^-1F_i, i = 1, …, s . The elements of B_i are superimposed in columns to form the k² × 1 dimensional vector β. Define x_t = I_s ⨂ (y_t–1, …, y_t–s), ⨂ as the Kronecker product. Then the model can be further simplified as:

Changing model (5) to a time-varying parametric model yields the TVP-VAR model:

The elements in A_T can be further simplified:

where hit=lnσit2,i=1,⋯,k;t=s+1,⋯,n

The time-varying parameters are assumed to obey a random wandering process:

Where βs+1~N(μβ0,Σβ0), αs+1~N(μα0,Σα0), hs+1~N(μh0,Σh0).

Referring to Nakajima [30], after the model is constructed, this paper will apply Markov Monte Carlo simulation (MCMC algorithm) in a Bayesian framework for estimation, so assume that β, α, and h obey the a priori normal distribution. Mean of μ_β0 = μ_α0 = μ_h0 = 0, covariance matrix ∑_β0 = ∑_α0 = ∑_h0 = 10 × I. Also, assume that the ith diagonal element of the covariance matrix obeys the following gamma distribution:

The model was estimated using prior distribution ω = (∑_β, ∑_α, ∑_h) for model estimation. First, initialize β, α, h, ω; then, sample the data from the high-dimensional posterior distribution of the parameters, and iterate the loop until MCMC reaches convergence.

Augmented Dickey-Fuller Stable Test of Variables

In order to prevent spurious regressions and ensure the stability of variables, the Augmented Dickey-Fuller (ADF) unit root test is typically used. The final result is that ADF statistics for lnCI, lnCC, lnPGDP, lnEI, are all greater than their critical values, indicating that they are unstable, with the exception of lnP. When differenced at first order, lnCC, lnCI, pass the test of smoothness at the 10% level of significance. When differenced at the second order, all series pass the smoothness test at the 1%, 5%, and 10% significance levels. Therefore, lnCI, lnCC, lnPGDP, lnEI, and lnP are all smooth series as shown in Table 2.

Johansen Cointegration Test Results

The Johansen test is a better method of conducting multivariate cointegration tests. The Johansen cointegration test was conducted on lnCI, lnPGDP, lnP, lnEI, and lnCC (Table 3).

The model assumptions are no constant and time trend terms. Trace Statistic and Prob both reject the original hypotheses of R = 0, R ≤ 1 and R ≤ 2 at the 5% significance level and accept the original hypotheses of R ≤ 3 and R ≤ 4. The Johansen test indicates that lnCC, lnPGDP, lnP, lnEI, and lnCI are co-integrated, a long-term equilibrium relationship between CO₂ emissions and economic development level, population size, energy intensity, and CO₂ emission intensity in Hubei Province.

Model Estimation under the MCMC Algorithm

The model is estimated by Markov chain Monte Carlo simulation (MCMC algorithm) based on the Bayesian framework, and the optimal lag order of the model is determined to be 2 according to the optimal lag determination criterion of the VAR model. In addition, the number of MCMC samples is set to 10,000, and the first 1,000 samples are discarded to ensure the accuracy and reliability of the sampling results.

Table 4 shows that the values of the Geweke statistic are all smaller than the 95% critical value of 1.96 for the normal distribution, so the parameters cannot reject the original hypothesis of the test, which implies that the parameters estimated b y the simulation cannot be rejected to converge to the posterior normal distribution. The Inefficiency Factors serve to identify the number of irrelevant samples generated by the simulation, the smaller the value of the factor, the greater the number of irrelevant samples. The Inefficiency Factors in the table are less than 100, indicating that the samples obtained are valid.

Fig. 2.

Sample autocorrelation coefficient, sample path, posterior distribution density.

Meanwhile, Fig. 2 gives the sample autocorrelation coefficient, sample path, and density function plot of the posterior distribution. From Fig. 2, the autocorrelation coefficient of the samples is significantly reduced to the vicinity of 0, indicating that there is basically no autocorrelation in the samples sampled by Gibbs. The sample paths show strong smoothness, indicating that the simulated samples of the 10,000 times of the MCMC samples are valid correlation samples. The posterior distribution density functions of the parameters are approximately normal, which meets the requirements of constructing the TVP-VAR model. Taken together, the model appears to be adept at estimating, and we further established that the model system built by CI, CC, EI, PGDP, and P is robust and can reasonably analyze and identify the time-dependent interrelationships among the CO₂ emission influencing factors in Hubei. This is particularly relevant in the context of the current global low-carbon perspective and China’s high-quality transformational development. The robustness of the system developed by the TVP-VAR model also objectively shows the superiority of using the expanded VAR model in this paper, which can be better used to study the time variability of the dynamic transmission mechanism among the carbon emission impact factors.

Equally Spaced Impulse Response Function

An equally spaced impulse response is the impulse response function of a variable induced by shocks of different time horizons (lags). Unlike the two-dimensional impulse response under the VAR model, the TVP-VAR model can use variable parameters to calculate the impulse response plots of each variable at all time points with different lags [31–33]. For the selection of time intervals, lag 4, lag 8 and lag 12 are chosen to measure the impacts of the factors affecting CO₂ emissions in Hubei Province over the short, medium, and long terms, respectively.

Firstly, as shown in Fig. 3, the impact of the level of economic development on CO₂ emissions is positive in the long term, while the short-term impact effect is significantly higher than the long-term effect, indicating that economic development will have a sustained impact on the changes in CO₂ emissions. Yet, the trend of impact is slowing down as the level of the economy continues to rise. This observation is consistent with the findings of previous studies on the relationship between the level of economic development and CO₂ emissions, including in India, Pakistan, and other developing countries [34, 35]. What’s more noteworthy is that CO₂ emission intensity and energy intensity both have negative impacts on CO₂ emissions, but energy intensity has a short-term negative impact that is smaller than the long-term impact, while CO₂ emission intensity has a short-term negative impact that is larger than the long-term impact. With advancements in energy utilization technology and the gradual increase in the proportion of clean energy, the CO₂ emissions per unit of energy will be reduced year by year, and the decrease in CO₂ emission intensity will be larger than the decrease in energy intensity, which provides substantial evidence that the higher the efficiency of energy utilization in Hubei Province, the better the low-carbon development mode. Simultaneously, CO₂ emission intensity partially reflects the control over the energy consumption structure, not only regarding total energy consumption but also the structure of energy consumption itself.

We further integrate the current developmental context of Hubei to dissect the reasons behind the short-term impact of energy intensity is smaller than the long-term impact, which can be elucidated through three key perspectives: first, the policy orientation, Hubei Province has implemented a series of long-term energy saving and emission reduction policies, such as optimizing the industrial structure, and the effects of these policies may not be immediately visible in the short term, but they can be visible in the long term. Second, Hubei Province is gradually reducing its reliance on coal within its energy structure and transitioning to clean energy sources, such as water, wind, and hydrogen. The province’s abundant wind energy resources, mainly relying on the jurisdiction of mountains and plains, along with its rich water energy resources that rely on the Yangtze River Basin, indicate significant potential for energy development. In terms of hydrogen energy, the “Several Measures to Support the Development of Hydrogen Energy Industry” has been issued, which explicitly proposes to take Wuhan, the capital city of Hubei Province, to establish a national hydrogen energy industry demonstration core area to support the rapid development of the hydrogen energy industry. The effect of many of the above structural changes on the reduction of energy intensity may not be obvious in these short term. Furthermore, in the long term, the carbon emissions trading market will lead to adjustments in market mechanisms and corporate behavior [36], thus gradually guiding enterprises to reduce energy consumption. Whereas CO₂ emissions intensity with a short-term negative impact having a more significant effect than a long-term impact may often be due to the government’s introduction of stricter environmental regulatory policies, the immediate impact of such policies may lead to a significant short-term decline in CO₂ emissions intensity. As one of the first pilot provinces for national carbon emissions trading, carbon trading implementation may cause enterprises to take quick measures to reduce CO₂ emissions in the short term in order to adapt to the new market rules and minimize costs. From this, the combined analysis and comparison of the aforementioned reasons reveal that equally spaced impulse response results of the CO₂ emission influencing factors in Hubei Province demonstrate the impact of the establishment of the carbon emissions trading market. We will continue to verify the above conclusions through experiments using the variable time point impulse response.

Variable Time Point Impulse Response Function

Variable time-point impulse response refers to the impulse response function at various specific time points, thus it can further examine the time-varying pattern of the impact of key time-point policies on CO₂ emissions. Furthermore, it can also characterize the dynamic transmission mechanism between CO₂ emissions but also its factors. To simplify the analysis process, we choose three typical time points to calculate the impulse response function, namely 1992, 2001, and 2014, which represent the rough development stage of the industrial economy, the beginning stage of industrial economic transformation and upgrading, and the low-carbon transformation stage of the industrial economy. Especially focusing on the key time points in 2014, this paper differs from previous literature that uses difference-in-differences carbon trading policy for assessment. Instead, this paper utilizes a complex system of carbon emission impact factors, as established by the TVP-VAR model. It examines the dynamic effect of the carbon emission trading market on CO₂ emissions and the dynamic transmission mechanism generated by CO₂ emissions with the impact factor shocks at variable time points.

The impact of specific variable-time point shocks is specifically analyzed in conjunction with Fig. 4. Firstly, the upgrading of economic development has a continuous positive impact on CO₂ emissions, with the establishment of the market economy in 1992 and China’s accession to the WTO in 2001, the level of China’s economy continues to develop. The rising economic level and the continuous development of the industrial economy will inevitably lead to a continuous increase in CO₂ emissions, and this point with the passage of time, the effect of this economic development induced by an increase in CO₂ emissions will still be sustained. The effect of population-induced CO₂ emissions is relatively more complex. On the one hand, population growth tends to cause environmental congestion and an increase in CO₂ emissions, but it may also reduce carbon emissions due to the development of the economy, the improvement of people’s quality of life, and the implementation of environmental protection policies. In Hubei, the population factor has a weak positive impact on CO₂ emissions, but subsequently becomes a weak negative impact, before rising to a positive impact, which also indicates that as the population continues to grow, it will continue to increase CO₂ emissions in the long term.

Fig. 3.

Result of equally spaced impulse response function.

However, energy intensity continues to have a negative shock effect on CO₂ emissions, and the negative shock effect represents a good carbon abatement effect, a dynamic abatement effect that was weak in 1992, strengthened in 2001, and still strengthened in 2014. The CO₂ emission intensity is also the strongest policy shock effect in 2014, although the shock effect of energy intensity in 1992, 2001, and 2014 all reached the peak point of -0.0901 after a lag of 5 periods, and then the shock effect weakened, but the weakening effect in 2014 is relatively more gentle, and the sustained effect of the negative shock is the most obvious. The results further prove that the carbon trading market in Hubei Province has created a continuous emission reduction effect. Next, we try to further analyze and explain the dynamic emission reduction effect of the Hubei carbon emissions trading market. Carbon Trading System (CTS) is a market-based environmental policy instrument that incentivizes companies to reduce greenhouse gas emissions by creating a market for carbon credits. Structural emission reduction, technical emission reduction, and engineering emission reduction are the three main ways to achieve carbon emission reductions, and CTS is the fundamental incentive to drive enterprises to adopt structural emission reduction, technical emission reduction, and engineering emission reduction instruments in a market-based manner. By setting emission caps for enterprises, allocating emission allowances, trading allowances in the market, and providing economic incentives through various means, enterprises in Hubei Province under the carbon emissions trading market are encouraged to realize the adjustment of energy structure. They are guided to reduce reliance on traditional fossil energy sources and shift to the development and use of clean energy sources such as wind, water, and hydrogen. Additionally, the promotion of energy-efficient technologies and equipment, along with the research, development, and investment in high and new technologies, aims to reduce the demand for enterprises to purchase carbon emission allowances. The Hubei government has also endeavored to diversify its carbon emission allowances by using a broad spectrum of financial instruments. Hubei also strives to offer financial support to large-scale engineering emission reduction projects and related enterprises with diversified carbon financial innovation products such as carbon asset trusteeships and carbon pledge loans. As one of the first pilot provinces, Hubei’s carbon market leads China in both liquidity and the cumulative turnover of carbon allowances [37], which demonstrates the high degree of activity and maturity of Hubei’s carbon market. Consequently, the policy-driven dynamic emission reduction effects are prominently evident. This also further confirms that the feedback effect of positive interaction has been formed between the CO₂ emission factors in Hubei Province, which realizes the effective dynamic transmission mechanism to promote the carbon emission reduction target [38–40]. Although compared with the more robust market mechanisms for auctioning allowances formed in mature carbon trading markets such as in Europe and the United States, China’s carbon emissions trading market is in the exploration and improvement stage of the initial allocation of allowances. However, by integrating the mature experiences from Europe and the United States, China is forging a differentiated carbon market emission reduction path that is tailored to its own national conditions. This paper takes Hubei, a typical pilot province, as a case study, and its experimental results have proved the dynamic emission reduction effect of China’s active carbon emissions trading policy, and provide effective experiences for the improvement of the national carbon emissions trading market.

Fig. 4.

Result of dynamic shock effects on CO₂ emission impact factors.

Analyzing the effects of CO₂ emissions themselves as shown in Fig. 5, an increase in CO₂ emissions will have a positive impact on economic development and population growth in Hubei. CO₂ emissions are often accompanied by an increase in energy consumption, which implies a phase of rapid industrialization and urbanization, and signifies continued economic growth. The results of the positive impact of carbon emissions on the economy aptly reflect the transition phase in Hubei Province’s industrial economy, from extensive growth to industrial structure optimization and upgrading, and then to the search for low-carbon transformation development. The increase in carbon emissions brought about by extensive growth may have a positive impact on the economy in the short term, but in the long term, this growth model is unsustainable and the impact is bound to weaken. Instead, the upgrading of industrial structure and the technological progress and innovation of enterprises forced by the increase in carbon emissions will become a sustained driving force for economic growth. Also of interest is the fact that the positive effect of CO₂ emissions on population growth will be stronger in 2001 than in 2014. Our explanation for this is the specificity of Hubei as a populous province in central China and its rich resources for university education. 2001 was a period of rapid development of higher education in China, and the establishment and development of universities in Hubei province attracted an influx of people. On the other hand, at this time, Hubei Province has steadily attracted a significant influx of migrant rural laborers by adopting the guiding principle of promoting employment and increasing income to develop job opportunities for rural labor. After the establishment of the carbon emissions trading market in 2014, the transition of high-emission industries to low-carbon or clean-energy industries will further increase the demand for low-carbon transformation and upgrading of enterprises, which may lead to a reduction of employment opportunities in certain industries. Simultaneously, the carbon market motivates enterprises to invest in high-tech research and development, leading to the inflow of high-quality talent from the surrounding area and the outflow of labor force from Hubei engaged in crude-type industries [41].

Fig. 5.

Result of CO₂ emission dynamics effects.

Fig. 6.

Variance decomposition analysis.

Variance Decomposition

The variance decomposition focuses on calculating the proportion of the sum of variances of structural shocks to the total variance of each endogenous variable at different horizons to measure the impact of structural shocks on endogenous variables, which can more specifically represent the importance of the interaction of endogenous variables. It can discriminate the relative importance of each stochastic disturbance affecting the endogenous variables and quantify the contribution of each shock to the change in the endogenous variables. Here, we focus on the contribution of shocks to lnPGDP, lnP, lnEI, and lnCI to lnCC of CO² emissions. The results are as Fig. 6 follows.

The contribution of CO₂ emissions to itself continues to decline, and after a short period of fluctuation, remains at 45% after period 11. Apart from CO₂ emissions themselves, CO₂ intensity and energy intensity make the largest contribution to the change in CO₂ emissions, with CO₂ intensity rising for a short period before declining and stabilizing at around 17% from period 9. The contribution rate of energy intensity reaches a maximum of 32.68% at a lag of 7 and remains at 31% for subsequent lags, indicating that it has a significant long-term impact. As a former industrial base in China, Hubei has a good industrialization base and a deep foundation, which is an important reason why carbon and energy intensity are the main CO₂ emissions contributors in Hubei. Although Hubei has attempted many measures for the transformation and development of industrial and economic structures, such as building a world-class new industry leader, “Optics Valley of China”, based on optoelectronic information technology, which has initially appeared to have an impact on the world. Furthermore, the Hubei government has introduced policy measures, including tax and fee reductions, project funding support, and technological innovation support, to encourage enterprises to increase technological innovation and facilitate the growth of low-carbon industries. There is also a carbon emissions trading market with Hubei characteristics that plays a role in driving corporate emission reductions and encouraging enterprises to adopt more energy-saving and emission-reduction measures. However, the current energy structure has not yet fully realized the transition, clean technology and more efficient production methods have not yet been fully promoted, and the inflection point of the Kuznets curve has not yet arrived. Once the issues hindering the implementation of the CO₂ intensity and energy intensity control degree have been resolved, the reduction in CO₂ emissions will become more obvious. It also requires more effective and targeted environmental regulatory policies and measures. The results also indicate the economic development level and population have a smaller contribution to CO₂ emissions, which differs from some of the conclusions reached in previous studies using typical countries and regions as samples. For example, factors of the innovation economy in developed countries, represented by the OECD, have become major contributors to CO₂ emissions [42]. While energy growth remains the primary driver of CO₂ emissions in the countries represented by the E7, there are also significant differences in the relationship between economic growth and carbon emissions within the E7 countries [43]. In eastern China, the relationship between economic growth, talent aggregation, and CO₂ emissions is more significant [44]. This paper analyzes that reason is closely related to the level of economic development and urbanization in the Hubei province. As an important province in central China, despite its strategic position, Hubei’s economic development still lags significantly behind that of the eastern seaboard. The current stage of Hubei’s economic growth implies that the impact of carbon emissions generated by the economy and population is relatively lower.

With the above variance decomposition analysis, the results that the relationship between energy consumption, economic progress, and CO₂ emissions varies across countries and regions has been reconfirmed [15], it also clarifies the meaning of studying the case of regional carbon emission impact factors. In the current era of global low-carbon transition and development, each country and region needs to differentiate emission reduction paths, taking into full account regional differences, but also giving full consideration to the flexible use of multiple emission reduction modes. Contributing “China power” to the development of global low-carbon transition, and contributing “Hubei power” to the realization of “dual-carbon” goals are the contributions that the findings of this paper hope to make.