Energy mix, financial development, and carbon emissions in China: a directed technical change perspective

Based on a two-sector (clean energy and dirty energy) model of directed technical change, we examine the relationship between carbon emissions, clean energy consumption, and financial development in China using the ARDL method. The results show that clean energy consumption reduces carbon emissions effectively but the effect of financial development is opposite, suggesting that financial development increases carbon emissions, contradicting the findings of many existing studies. Then, we decompose financial development on carbon emissions into two different effects: substitution and income effects. The substitution effect reflects more dirty energy consumption as a result of directed technological change promoted by financial development, leading to more carbon emissions. The income effect results in a decline in carbon emissions because financial development enables firms to use more clean energy. The empirical results indicate that the net effect of financial development has caused more carbon emissions and a 1% increase in financial development results in a 0.45–0.79% increase in carbon emissions. The policy implication is also discussed.


Introduction
After the reform and opening-up policy implemented in 1978, China has witnessed a staggering rate of economic growth over the last 40 years, accompanied by severe environmental degradation. As the largest carbon emitter in the world, China is facing tremendous pressure to reduce carbon emissions. The ability and willingness of China to reduce carbon emissions would have a critical influence on the global low carbon transition. It aims to reduce its carbon emissions per unit of GDP by 65% from the 2005 level and promote non-fossil energy accounting for about 25% of the country's primary energy consumption by 2030. 1 Moreover, the Chinese government has set a carbon reduction target, named the "3060" goal. 2 The low carbon economy means energy transition from traditional fossil fuels to clean energy, and requires huge investment. The financial sector plays a critical role in credit allocation and its development will inevitably have a significant impact on energy transition and low carbon transition.
More and more studies have paid attention to China's carbon emissions, energy consumption, and financial development. Ma et al. (2019) indicate that the main carbon emissions in China come from energy consumption of the industrial sector. Dong et al. (2018) investigate the dynamic causal impact of renewable energy and nuclear energy consumption on carbon emissions in China, showing that clean energy plays an important role in reducing carbon emissions in both the short and long terms. Rong et al. (2020) study the residential energy consumption in Kaifeng (China) and find that more than 75% of carbon emissions are from electricity consumption. Wu et al. (2020) discuss the nonlinear relationship between energy consumption and carbon emissions, indicating that environmental regulation could reduce carbon emissions in eastern and central China. Similarly, Ahmed et al. (2021) find that a 1% increase in clean energy consumption reduces per capita CO 2 emissions by 5.50% in Australia. Moreover, Tamazian et al. (2009) point out that higher development levels of economy and financial depth could reduce carbon emissions in the BRIC countries. Jalil and Feridun (2011) examine the long-run equilibrium relationship between financial development and carbon emissions, suggesting that financial development leads to a reduction in carbon emissions. Xie et al. (2021) investigate the impact of financial market in the energy transition, finding that financial markets in China and South Africa play a more significant role in low-carbon electricity transition than the other BRICS countries. At the G20 Summit in 2016, the heads of states reach an important consensus on "green finance" and set a series of actions to achieve this goal. Zhang et al. (2020) find that credit availability of manufacturing results in lower energy efficiency in China. These findings suggest that financial development is a key determinant in environmental protection .
While many researchers have focused on the impact of various factors, such as renewable energy, nuclear energy, or financial development on carbon emissions, few have comprehensively considered the impact of energy mix, financial development, technological change, and foreign trade in the development process. We examine the impacts of financial development and clean energy consumption on carbon emissions from a directed technical change perspective following Acemoglu (2002). Using a large dataset spanning a long period in China during 1965-2017, it is found that the effect of clean energy consumption on carbon emissions is significantly negative but the effect of financial development is opposite, suggesting that financial development increases carbon emissions other than reducing it, contradicting the findings of many existing studies. This implies that China's energy transition is endogenous to the industrial structure and financial sector reform, suggesting that financial sector reform in the future should consider its impact on energy mix as well as carbon emissions.
To explain the effect of financial development on carbon emissions further, we decompose it into two parts: the substitution effect and the income effect. On the one hand, financial development may direct firms to consume relatively more fossil fuels because it changes the relative prices between fossil fuels and clean energy, leading to the so-called substitution effect in favor of fossil fuels. On the other hand, financial development may also lead to faster economic growth and increased capital intensity, which would enable consumers to use more clean energy, leading to a reduction in carbon emission intensity. This is the so-called income effect, which is found to be smaller than the so-called substitution effect in our data, resulting in a net increase in carbon emissions in China over the sample period. We will carefully discuss the substitution effect and income effect later in this paper.
The new contributions of this paper mainly consist of the following three aspects. First, it builds a simple two-sector model embedded with directed technical change and examines the relationships between carbon emissions and financial development as well as clean energy consumption using a unified theoretical mechanism. Second, it decomposes financial development into two parts following the principle of Slutsky decomposition-the substitution effect and the income effect-because financial development can lead to an increase in both technical innovation and capital intensity. The former results in a reduction in the relative price of dirty energy compared to clean energy in response to technical change, encouraging enterprises or households to consume more fossil fuels. The latter enables consumers to shift energy consumption away from dirty energy toward clean energy sources, and hence reduce carbon emissions. The empirical results in our data period suggest that the former effect outweighs the latter one, leading to a net effect of financial development as more carbon emissions. The policy implication is that financial development should take into account its potential impact on energy consumption behavior and carbon emissions as far as environmental protection is concerned. Third, both the shares of manufacturing and foreign trade as a proportion of GDP have a positive impact on carbon emissions. In particular, the rapid expansion of carbon emissions after China's accession to WTO supports the so-called "pollution haven" hypothesis, i.e., more developed countries tend to relocate their polluting industries to the less developed economies such as China.
The rest of this paper is organized as follows. The "Literature review and propositions" section reviews the related literature on carbon emissions concerning financial development and clean energy consumption respectively and makes two theoretical propositions. The "Data, model, and methodology" section discusses data, model, and research methodology. The "Empirical results and discussion" section presents the empirical results and explanations. The last section concludes with some policy recommendations.

Literature review
Climate change caused by greenhouse gases, especially carbon dioxide emissions, has long attracted attention from theoretical and empirical economists since Nordhaus (1977Nordhaus ( , 1982Nordhaus ( , 1991 introduced it to economic analysis. More and more studies have paid attention to the relationship between clean energy consumption and carbon emissions (Bilgili et al. 2016;Yao et al. 2019;Ahmed et al. 2021). For example, Dong et al. (2018) indicate that nuclear energy and renewable energy in China play an important role in carbon emissions reduction both in the short and long terms, while Baek (2016) finds that renewable energy does so only in the short term. Yang et al. (2021) stress on the importance of energy mix on carbon emissions in Shandong, China. While almost all the existing studies based on econometric analysis confirm the emissions reduction effect of clean energy employing different datasets, they do not discuss the mechanisms affecting clean energy consumption and thus could not provide a unified framework of economic theory. Therefore, it is imperative to build a unified economic framework for carbon emissions reduction and clean energy promotion.
Another type of literature on carbon emission reduction focuses on the effect of financial development. Financial intermediary development may boost the rate of technological innovation in a well-functioning financial institution, thus reducing environmental pollution. Some recent empirical studies (Dasgupta et al. 2004;Wang and Jin 2007;Tamazian et al. 2009;Jalil and Feridun 2011;Acheampong 2019) reveal that financial development improves environmental performance, such as reducing carbon emissions. Tamazian and Rao (2010) argue that financial development plays a positive role in reducing carbon emissions with a strong institutional framework considering 24 transition economies during 1993-2004. Abid (2017) studies the relationship between institutional quality and carbon emissions, indicating that financial development could improve environmental quality. Moreover, Zhao et al. (2021b) find that financial development measured by different indicatorsfinancial depth and financial efficiency-on environmental pollution is opposite. Wang et al. (2019) conclude that China's energy mix change is driven by capital deepening and biased technical change toward capital-intensive modern energy in the long run from the new structural economics (NSE) perspective. Adams and Kwame (2018) point out that financial development is still a significant determinant of environmental degradation after accounting for the political effect. However, Chen et al. (2019) reveal that the effect of financial development is limited to energy reduction for OECD countries because their financial systems are mature. Using Turkey's data in 1974-2014, Pata (2018 shows that financial development aggravates the environmental condition by increasing carbon emissions. In addition, Zhang et al. (2020) find that credit availability of manufactures leads to lower energy efficiency. Assi et al. (2021) suggest that financial development does not significantly promote renewable energy consumption in ASEAN+3 countries. Therefore, specific financial reform is required to provide adequate incentives to reduce carbon emissions (Abid 2016). Some earlier literature (Tamazian and Rao 2010;Jalil and Feridun 2011) reveal that financial development can reduce carbon emissions without considering the energy mix, while other recent studies (Dong et al. 2018;Yao et al. 2019) argue that promoting the proportion of clean energy can reach the target of carbon emissions reduction ignoring the effects of other factors such as financial development. Although some latest studies (Acheampong 2019;Acheampong et al. 2020) find that carbon emission intensity increased with total energy consumption when discussing the impact of financial development, the existing studies have not paid attention to the combined effect of financial development and energy mix on carbon emissions. To focus on this research point, we develop a theoretical mechanism to explain the relationship between financial development, the proportion of clean energy consumption, and carbon emissions from a directed technical change perspective. On the one hand, financial development would encourage firms to expand production as financial resources become more easily available, resulting in more carbon emissions. On the other hand, it may also increase firm's capital ability to substitute fossil fuels with clean energy. Therefore, the net effect of financial development on carbon emissions would depend on the two counteractive forces. To fully understand the exact mechanism, we follow the Slutsky decomposition approach to decompose financial development into two parts, the substitution effect and the income effect, and suggest that financial development may not necessarily lead to carbon emission reduction because the substitution effect may outweigh the income effect on carbon emissions during China's rapid industrialization/urbanization process.
Different from the recent literature (Tamazian et al. 2009;Jalil and Feridun 2011;Wang et al. 2019;Acheampong et al. 2020), our paper shows that financial development could not reduce carbon emissions without upgrading the industrial structure and shifting the energy mix in China. That is, the main impact of the current financial development has encouraged manufacturers to expand production scale instead of upgrading production technology or shifting the energy mix. Our finding is in line with the theories of directed technical change proposed by Acemoglu (2002) and Acemoglu et al. (2012Acemoglu et al. ( , 2016 and the new structural economics by Lin (2011).

The effects of financial development with directed technical change
In the initial analysis of this paper, firms are regarded as producers of a unique final good and consumers of energy, constrained by profit maximization or cost minimization. Our discussion begins with an economy possessing two types of energy, clean energy (renewable energy and nuclear power) and dirty energy (fossil fuels). According to Acemoglu et al. (2012), a unique final good is produced using a combination of two different energy sources (clean energy and dirty energy). 3 Clean energy is a "normal good," whose demand increases with income. The demand for a clean environment grows as a result of economic growth and life quality improvement (Grossman and Krueger 1995;Bilgili et al. 2016), so the consumption of fossil fuels declines correspondingly. Therefore, fossil fuels are treated as "inferior" goods as far as environmental protection is concerned.
The effect of financial development on carbon emissions may be different from what has been found in the existing literature once directed technical change is taken into account. Technological change is not neutral in some specific situations and it may favor some production factors more than others. This phenomenon is called directed technical change according to Acemoglu (2002). Based on a framework of directed technical change, Acemoglu et al. (2012Acemoglu et al. ( , 2016) make a distinction between dirty innovation and clean innovation and hold that the market size effect encourages innovation toward the larger input sector. For instance, fossil fuels still dominate the energy market in China, accounting for about 80% of total energy consumption. The storage and transport technology are important deterrents to promoting electricity generated by renewable energy (Blazquez et al. 2018). Yang et al. (2018) suggest that the production technology of China's industrial sector is biased toward fossil fuels instead of clean energy. Yao et al. (2019) indicate that the energy mix among countries is subject to their different technological conditions and economic development levels so that fossil fuels dominated energy consumption in many developing and newly industrializing economies, including China. This would correspond to a low degree of substitution between the two types of energy because more consumption of non-energy commodities using less effective transport technologies would increase energy demand. According to Acemoglu et al. (2012), dirty energy/ fossil fuels in our discussion are relatively abundant and not exhaustible in the foreseeable future.
Financial development brings capital accumulation in both the research and production sectors of the economy. More research funding through R&D activities enables the country to improve technologies for energy development and utilization. Lin (2011) suggests that firm performance and the country's comparative advantage are closely related. In a developing economy where relatively more advanced technologies in the exploitation and utilization of fossil fuels are more easily available than those in the development of renewable energy during the initial stage of economic development, thus only research activities focusing on fossil fuels could maintain or increase the country's competitiveness in the short and medium terms. Acemoglu et al. (2012) argue that this will lead to a relative reduction in fossil fuel prices as compared to the prices of renewable energy, implying that technical change is more directed to fossil fuels, called the market size effect and initial productivity advantage. This phenomenon is even more sharp in China. For clean energy, such as nuclear power, hydropower, solar power, and wind power, its utilization is mainly in the form of electricity. Zhao et al. (2021a) find that carbon intensity growth in northwest and northeast China is caused by the coal-dominated energy mix. Meanwhile, the provinces located in Northwest China are endowed with abundant renewable energy, such as wind and solar power, but about 30% of wind electricity has been abandoned. 4 It is the inefficient storage and transmission technologies that are hampering the utilization of renewable energy (Apergis et al. 2010). While the fossil fuel market is international, the clean energy market is still largely isolated. China is the largest oil importer, but it is difficult to import clean energy. Electricity prices vary from region to region and from energy source to energy source across the country. Gridconnected tariffs for wind power are higher than those for coal power. Therefore, the relative price of fossil fuel is lower than clean energy, which is determined by the so-called market size effect.
Financial development could affect energy consumption through three channels: households effect, wealth effect, and business effect (Acheampong 2019). It stimulates energy consumption, including fossil fuels and clean energy (Sadorsky 2010;Acheampong 2019). However, as more advanced technologies becoming available with lower fossil fuel prices, consumers tend to use relatively more fossil fuels than clean energy to maximize their utilities. Consequently, financial development leads to more energy consumption, particularly more consumption of fossil fuels due to cost minimization or profit maximization consideration. For example, the price of electricity in China is made up of two components: cost and profit plus. As a result, it is difficult for the more expensive wind power to be used on the grid, which results in a waste of renewable energy.
To examine exactly the effect of financial development on carbon emissions, we firstly decompose the financial development effect into two components following Slutsky's decomposition principle (Nechyba 2016): (1) the substitution effect directed by technical change due to the price decline of dirty energy relative to clean energy price; and (2) the income effect due to increased demand for clean environment corresponding with rich capital intensity and rising per capita income. Both of these two effects resulting from financial development are illustrated in Fig. 1.
In Fig. 1, C 1 , C 2 , and C 3 represent respectively the original budget, the compensated budget, and the final budget lines, corresponding with the indifference curves U 1 , U 2 , and U 3 as well as the equilibrium points E 1 , E 2 , and E 3 . With technological progress in the dirty energy sector, the relative price of fossil fuels declines; hence, the budget line changes to C 3 from C 1 , and the corresponding equilibrium point of energy consumption changes from E 1 to E 3 . Following Slutsky's decomposition principle (Nechyba 2016), we decompose the changes in the energy mix into two parts, i.e., the substitution effect and the income effect. As previously discussed, financial development leads to technological progress, reducing the relative price of fossil fuels and raising the capability of firms to consume relatively more clean energy. Yang et al. (2018) and Yao et al. (2019) argue that the developing economies had more available technologies in fossil fuels at the early stage of economic development so that the technical change was directed to dirty energy, which is called the directed technical change in this paper. The price reduction of fossil fuels directed by technical change promotes the demand for dirty energy to accelerate economic growth. That is, the substitution effect is a result of financial development. On the other hand, financial development enables firms to use more clean energy instead of fossil fuels as higher incomes raise the awareness of environmental protection. This is the so-called income effect of financial sector development in this paper. The income effect is expected to reduce carbon emissions because the increase of capital intensity and income level is a prerequisite for firms to use more clean energy and reduce the consumption of fossil fuels.
Specifically, E 1 E 2 in the vertical axis represents the magnitude of the substitution effect, which measures the increase of demand for fossil fuels due to the relative price change between the two types of energy. E 2 E 3 is the income effect, measuring the reduced demand for fossil fuels under the new budget constraint. These two consumption changes in the opposite directions lead to the net effect on the demand for fossil fuels as a result of financial development, represented by E 1 E 3 in Fig. 2 . The net effect satisfies the equation |E 1 E 3 |=|E 1 E 2 |-|E 2 E 3 |. That is, the impact of financial development on carbon emissions depends on the absolute value of the sum of these two effects. If the value of E 1 E 3 is positive, the financial sector development leads to more fossil fuel consumption and more carbon emissions. Based on the above theoretical discussion, we put forward the following two propositions below.
Proposition 1: Promoting clean energy consumption can lead to carbon emissions reduction controlling other factors such as financial development. Proposition 2: Financial development results in more carbon emissions if the substitution effect is larger than the income effect. Financial development enables firms to expand production through consuming more fossil fuels and promote energy structural change toward using more clean energy, but the former may dominate the process. Therefore, financial development may lead to more pollution especially in the early stage of economic development in a developing economy, such as China.

Data, model, and methodology
Model and data Following Tamazian et al. (2009), Jalil and Feridun (2011), and Dong et al. (2018, we use the gross domestic product (GDP) and its quadratic and cubic terms, the share of clean energy consumption as a proportion of total energy consumption, the level of financial sector development, foreign trade, industrial structure, and CO 2 emissions in a single multivariate regression framework. Using cross-sectional data, Sebri (2016) shows no evidence in favor of an inverted U-shaped environmental Kuznets curve, but in most cases, an evolution into an N-shaped relationship. Yao et al. (2019) and Zhao et al. (2021b) suggest that there is an N-shaped relationship instead of the usual inverted U-shaped curve between CO 2 emissions and GDP in China. Based on the previous studies, we specify a log nonlinear model with a cubic term as follows: or, where co 2 is per capita CO 2 emissions and gdp denotes per capita real GDP. cler and fd are the main explanatory variables, which represent energy structure and financial sector development respectively. In addition, the model also includes other variables, sind and stra, controlling industrial structure and economic structure. ε is a random error term. The related variables in Eq.
(1) Greenhouse gas (CO 2 ). Carbon dioxide is the primary greenhouse gas, so we use per capita CO 2 emissions (co 2 ) as the explained variable to indicate environmental pollution according to the previous studies. co 2 is the aggregate CO 2 emissions divided by population.
(2) Income level (GDP). gdp (per capita real GDP) is used to present income level and economic development. In addition, the squared and cubic terms of gdp are also included to examine the N-shaped relationship between environmental pollution and income level according to Sebri (2016), Yao et al. (2019), and Zhao et al. (2021b).
(3) Energy mix (clean energy rate, cer). Compared with fossil fuels, clean energy (including nuclear power) has low or even zero carbon emissions. Using clean energy to replace fossil fuels is an effective way to reduce carbon emissions (Yao et al. 2019;EIA 2019). Therefore, we employ the share of clean energy as a proportion of total primary energy consumption (cer) to describe energy mix. Clean energy includes nuclear energy, hydropower, solar power, wind power, geothermal power, biomass, biofuels, and other renewable energy sources. (4) Financial development (fd). As discussed in the "Literature review and propositions" section, financial development influences carbon emission from two perspectives: substitution effect and income effect. Its net effect depends on the two counteractive forces. It is difficult to estimate the value size of substitution effect and income effect for the availability of data. To avoid this inconvenience, we just estimate its net effect instead of estimating the substitution effect and income effect, respectively. Therefore, the positive coefficient of fd means that financial development promotes carbon emission, but it actually implies that the substitution effect outweighs the incomer effect. Beck and Levine (2004) point out that there is not a perfect index of financial development. Due to the availability of data, we employ the most common proxies of banking sector development (scred and pcred) to indicate financial development (Chakroun 2020). scred is the share of domestic credit to the private sector as a proportion of GDP and pcred indicates per capita domestic credit. (5) Economic structure. Energy consumption is closely related to economic structure. The manufacturing industry consumes more energy than others. In addition, China as the "world factory," foreign trade accounts for a large proportion of GDP. Therefore, controlling industrial structure (sind) and foreign trade (stra) could make the estimation more precise. In the empirical model, sind is the share of the manufacturing industry value added as a proportion of GDP and stra is the share of foreign trade as a proportion of GDP, which presents the openness of an economy. Table 1 reports the definition and implication of variables in Eq. (2). The data of CO 2 emissions, primary energy consumption, and clean energy consumption are obtained from BP (2018); nominal GDP and population are obtained from the China Statistical Yearbook and China Compendium of Statistics (1949Statistics ( -2008; GDP deflator, the share of foreign trade, and domestic credit to the private sector are obtained from the World Bank Database (2019). Real GDP is obtained by dividing the nominal GDP by the GDP deflator (2015=100). We employ EViews 10 for the regressions after taking natural logarithms of the relevant data series. Table 2 reports the descriptive statistics of the variables over the sample period. As shown in Fig. 2, the relationship between lngdp and lnco 2 looks like an N-shaped curve, consistent with Yao et al. (2019) and Zhao et al. (2021b). Therefore, the cubic term of lngdp used in the model is suitable.

Methodology
We use the autoregressive distributed lag (ARDL) approach and cointegration methods (including fully modified OLS/ FMOLS and dynamic OLS/DOLS) to identify the relationship among the variables. The empirical methodologies in the later section of the paper include the following stages: first, employing the unit root tests to examine the stationarity of the time series; second, testing the cointegration relationship among the variables using the ARDL approach; third, estimating the long-run coefficients using FMOLS and DOLS estimators; fourth, using the Granger causality test to examine the short-run and long-run causalities. The advantages of ARDL method and empirical results are presented in the "Empirical results and discussion" section.

Unit root tests
In cointegration analyses, it is important to first make sure that all the time series are stationary and integrated of the same order. The unit root test is the most common approach to test the stationarity and integrated order of data (Hu et al. 2018;Yao et al. 2019;Ahmed et al. 2021). This method starts with the time series in level term. If the data are nonstationary in level terms and a unit root exists, we can then derive the first differences of the data and retest them until the results are stationary.
The ARDL bounds testing procedure can be applied irrespective of whether the variables are I(0), I(1) or fractionally cointegrated. However, Ouattara (2006) argues that the computed F-statistics provided by Pesaran et al. (2001) become invalid in the presence of I(2) variables. That is, the bounds test is based on the assumption that the variables should be I(0) or I(1). It is, therefore, necessary to ensure that none of the variables is integrated at an order of I(2) or beyond in the ARDL procedure. For this purpose, we use the conventional augmented Dicky Fuller (ADF) tests and Phillips-Perron (PP) tests, which are the common unit root tests in related studies (Danish et al. 2017). As shown in Table 3, lnco 2 , lngdp, lnscred, lnpcred, lncler, lnsind, and lnstra are level and trend nonstationary, but their first differences are stationary, implying that they are all integrated of order 1, or I(1).

ARDL bounds test
After identifying the cointegration relationship among the relevant variables, we calculate the long-run and the short-run estimates based on Eq.
(2). The ARDL approach is adopted in this section for three reasons that make it superior to others: (1) it does not require the regressors to be integrated at the same order, no matter I(0) or I(1), when examining the longrun relationship among variables; (2) both short-run and longrun parameters of the variables are estimated simultaneously; and (3) the endogeneity problem can be avoided (Pesaran et al. 2001;Jebli and Youssef 2015;Belaïd and Youssef 2017). According to Jalil and Feridun (2011) and Dong et al. (2018), the complete procedure of the ARDL cointegration test includes three key steps. First is to check for the existence of a long-run relationship among the lagged variables using the ordinary least squares (OLS) method and an F-statistic to estimate Eq.
(2) as shown in the following: where Δ and θ 0 respectively represent the first different operator and the drift component. ε t is an error term. p denotes the maximum lag length. θ 1 -θ 8 depicts the error correction dynamics, and θ 9 -θ 16 represents the long-run relationships among the variables in the model. The null hypothesis for t h e n o n e x i s t e n c e o f a lo n g -r u n r e l a t i o n i s H 0 : θ 9 = θ 10 = θ 11 = θ 12 = θ 13 = θ 14 = θ 15 = θ 16 = 0, against the alternative hypothesis H 1 : θ 9 ≠ 0, θ 10 ≠ 0, θ 11 ≠ 0, θ 12 ≠ 0, θ 13 ≠ 0, θ 14 ≠ 0, θ 15 ≠ 0, θ 16 ≠ 0. Based on the Wald tests, this section calculates the F-statistic to test the presence of cointegration among the relevant variables. Pesaran et al. (2001) generated the upper and lower critical values for the F-statistic. In general, the null hypothesis of no cointegration will be rejected if the calculated F-statistic value is greater than the critical value of the upper bound, while the null hypothesis will not be rejected if the calculated F-statistic value is smaller than the critical value of the lower bound. Moreover, we cannot conclude when the F-statistic value is between the upper and lower bounds. In addition, several diagnostic tests, such as the serial correlation test, the normality test, and the heteroskedasticity test, are examined to ensure the model's goodness of fit and verify its reliability. Second, to estimate the long-run parameters employing the ARDL approach according to the R-square (R 2 ), F-statistic, Durban-Watson statistic (DW), and Akaike information criterion (AIC), we use the SIC criteria to choose the lag length, and a maximum of three lags is proper for our test.
Third, to detect the short-run dynamics of the variables, we estimate the error correction model (ECM) term as shown in Eq. (4).
where ECT t-1 is the lagged error correction term generated from Eq. (2) using OLS, which represents the speed at which Notes: the value is adjusted t-statistics for PP; lag length for ADF: 1 (Automatic, based on SIC, maxlag=10); bandwidth for PP: 2 (Newey-West automatic) using Bartlett kernel. In addition, I is intercept and I&T are intercept and trend the dependent variable converges to the long-run equilibrium after a shock of independent variables in the short run. Moreover, α is the speed of the adjustment coefficient. The sign of the coefficient of ECT t-1 must be statistically significant and its value between −1 and 0 (Jebli and Youssef 2015). We estimate Eq. (3) by the ARDL method for the long-run estimates during 1965-2017, including five separate models. The related literature employs the adjusted R 2 criterion, Hannan Quinn criterion, AIC, and SBC to find the coefficients of the level variables. Following Jalil and Feridun (2011), we present only the results of the model that are selected based on SBC because it is known to select the most parsimonious model, where the smallest possible lag length is selected and the loss of freedom degree is minimized. Table 4 presents the results of the ARDL method. It is clear that the results of the five models support the N-shaped relationship, showing that the econometric model with a cubic term is appropriate.
The coefficient of lncer is significantly negative, indicating that promoting clean energy consumption can improve environmental performance. This finding is consistent with the existing literature. More specifically, the value of the coefficient ranging between −0.233 and −0.283 implies that improving the share of clean energy to total energy consumption by 10% will lead to a reduction of per capita carbon emissions by up to 2.83% in the long run, supporting Proposition 1 proposed in the "Literature review and propositions" section.  Pesaran et al. (2001). The t-statistics are presented in square brackets and p values in parentheses. **Variable interpreted as Z = Z(−1) + D(Z). Bartlett kernel, Newey-West fixed bandwidth = 4.0.
As described in the "Model and data" section, we use two indicators measuring financial development-lnscred in model 1 to model 4 and lnpcred in model 5 for robustness test. All the coefficients of the variables measuring financial sector development are positive and significant (except the results in model 2), showing that financial sector development leads to more air pollution rather than reducing it. In other words, the substitution effect of financial development on carbon emissions is larger than the income effect, which supports the theoretical analysis in the "Literature review and propositions" section. The coefficient ranges between 0.45 and 0.69, implying that a 10% rise in financial sector development will lead to a 4.5-6.9% increase in per capita carbon emissions. This result is in sharp contrast to Tamazian et al. (2009) and Jalil and Feridun (2011), who suggested that financial sector development can lead to a reduction in air pollution. The empirical results in Table 4 support Proposition 2 presented in the last section.
The sign of lnsind is significant and positive in models 3-5, indicating a higher share of manufacturing in the national   Table 4 are statistically significant and positive, confirming that an increase in foreign trade also leads to more carbon emissions. These results are in line with the "pollution haven" hypothesis: a large amount of emissions in the developing countries is embodied in export commodities of the developing countries to be consumed by the developed economies. China's carbon emissions experienced rapid growth after joining the WTO in 2001. Similarly, the significant and positive coefficients of lnsind show that an increase in the manufacturing industry leads to environmental degradation. Therefore, we can conclude that manufacturing is the main resource of carbon emissions as well as the main resource of exports.
In Table 4, the coefficient of ECT t-1 shows the speed of the adjustment back to the long-run equilibrium after a short-run shock. The lagged error correction coefficients, ECT t-1 , are correct in sign and significant at the 1% level in all cases. This verifies the established cointegration relationship among the related variables. The values of the coefficients range between −0.395 and −0.652.
All the diagnostic tests show no evidence of serial correlation, normality, and heteroscedasticity. The last stage of ARDL estimation is to test the stability of the models. All the plots of the CUSUM and CUSUMSQ statistics shown in Fig. 3 are well within the critical bounds, confirming that all the coefficients in the ECM model are stable.
The results of VECM Granger causality tests Table 5 represents both the short-run and long-run Granger causality relationships among the variables and their causal directions thereof. The short-run causality tests state that there is a significant bidirectional relationship between clean energy consumption and carbon emissions. Similarly, clean energy consumption has a significant impact on economic growth, which in turn has a significant effect on the former. Financial sector development has a significant effect on carbon emissions through industrial structure change. The relationship between financial sector development and carbon emissions is unidirectional. Figure 4 summarizes the shortrun Granger causalities between the related variables.
From the long-run causality test results, the coefficients of the error correction terms (ECT) in all the models are statistically significant based on Eq. (4). The estimated coefficients are all within the range of (−1, 0), revealing a moderate speed of adjustment from the short-run to the long-run equilibrium. Looking into the short-run dynamics causality in Fig. 4 and the long-run dynamics causality in Table 5, we can highlight the main causal relationships.

Cointegration analysis
We further employ three different cointegration methods, such as the fully modified least squares (FMOLS), the dynamic least squares (DOLS), and the canonical cointegration regressions (CCR) to estimate Eq. (2) and test the validity and reliability of the results following Baek (2016) and Danish et al. (2017). The results of the four different models are reported in Table 6. The results of models I-IV all show that the coefficients of both lngdp and (lngdp) 3 are statistically significant and positive, while the coefficients of (lngdp) 2 are negative and significant. That is, the relationship between GDP and carbon emissions in China during 1965-2017 is N-shaped rather than inverted U-shaped, which is consistent with the results presented in Fig. 2 and the ARDL regressions.
While the coefficient of lnscred in models II and III is negative and significant, it is positive in model IV when we control the interaction term of lnscred*lnsind. Yang et al. (2021) suggest that industrial structure is the most important driving factor in reducing carbon emissions in Shandong province, so the term of lnscred*lnsind is employed to examine the moderating effect of industrial structure on carbon emission intensity. Financial development has a positive effect on carbon emissions in the results in the "ARDL bounds test" section. That is, financial sector development could affect environmental quality through changing the industrial structure. This is because the cost of capital becomes lower than before as a result of financial sector development, which allows firms to invest in research on new technologies and to develop renewable energy as well as nuclear power. Renewable energy and nuclear power belong to the so-called capital-intensive industries. Our research finding supports Grossman and Krueger (1995) who argued that more funding opportunities for private firms enable them to reduce their dependence on dirty energy.  The coefficients of lncer and lnstra in the models are negative and positive, respectively. They respectively indicate that increasing renewable energy consumption share in total energy consumption could reduce carbon emissions. In contrast, increasing foreign trade may lead to more carbon emissions. This finding also supports Grossman and Krueger (1995) who suggested that developing countries tend to develop dirty industries with a heavy share of pollutants due to their desire for fast industrialization despite knowing the significant cost of environmental pollution. As known, the growth rate of carbon emissions accelerated significantly since China's accession to WTO in 2001. However, the total amount of carbon emissions in America remains almost unchanged. This phenomenon is consistent with the "pollution haven" hypothesis as explained before.

Conclusions and policy implications
Based on a two-sector model from a directed technical change perspective, this paper examines the relationship between carbon emissions, clean energy, and financial sector development in China during 1965-2017 using the ARDL and the dynamic cointegration models. It tests the impacts of clean energy consumption, financial sector development, and economic growth on carbon emissions controlling the main related factors such as industrial structure and international trade. It is found that the effect of clean energy consumption on carbon emissions is significantly negative but the effect of financial development, measured by the proxies of banking sector development, is opposite. It suggests that financial development promotes carbon emissions instead of reducing them, contradicting the findings of many existing studies. To explain this puzzle, we build a theory by decomposing the effect of financial sector development on carbon emissions into two components: the substitution effect and the income effect following the Slutsky decomposition principle. Given dirty energy as an "inferior" good, the theory built in the "Literature review and propositions" section shows that the substitution effect outweighs the latter so that financial development in China leads to more carbon emissions. For the availability of data, it is difficult to estimate the substitution effect and income effect, respectively. For simplicity, we just estimate the net effect of financial sector development. The coefficient of financial development is positively significant in the empirical analysis. That is, the net effect of financial development raises carbon emissions, implying that the substitution effect is greater than the income effect. This finding has important policy implications as it implies that energy structural change should incorporate industrial structural transformation and finance sector reform to reduce carbon emissions more effectively.
The main findings of this paper include the following: (i) It proves the existence of the environmental Kuznets curve (EKC) hypothesis with a shape of N after controlling clean energy consumption, financial development, and other related factors. (ii) Clean energy has a significantly negative effect on carbon emissions in both the short and long runs. (iii) The effect of financial sector development on carbon emissions is positive, leading to more carbon emissions instead of reducing it. (iv) The manufacturing sector has a positive impact on carbon emissions, suggesting that it is the most important carbon emitter among all the industrial sectors in China. (v) The impact of foreign trade on carbon emissions is significantly positive, supporting the "pollution haven" hypothesis. (vi) Financial sector development affects environmental quality due to its impact on industrial structural change and firm revenue-generating capability.
Some latest studies such as Xu et al. (2020) quantified the progress toward the 17 United Nations Sustainable Development Goals (SDGs) at the national and regional levels in China. It was found that SDG 13 (climate action) showed the greatest decline, while SDG 17 (affordable and clean energy) presented the greatest improvement. It implies that shifting the energy consumption mix away from fossil fuels toward using more and more clean energy takes time although the process in China has long begun. The results of our paper suggest that the share of clean energy as a proportion of total energy consumption has gradually increased and clean energy consumption is shown to have had a significant impact on carbon emissions reduction although its impact has not been large enough to prevent total carbon emissions from rising. Therefore, promoting clean energy consumption through financial sector development is an important policy instrument helping China to achieve its ambitious goal of containing carbon emissions. In light of the two counteractive effects of financial sector development on carbon emissions discussed in the paper, energy structural change depends on a rising income effect and a declining substitution effect of financial sector development. In the case of China, the following policy recommendations can be made based on the theoretical and empirical analyses in this paper.
First, permanent policy intervention is required to prevent a climate disaster for the low substitution between the dirty and clean energy sectors. Second, promoting the efficiency of transportation and storage is an important way to increase the substitution between the two energy sectors. Third, using appropriate and differential tax policies to accelerate the energy structure shift away from fossil fuels to clean energy sources. Finally, research subsidies or profit taxes should be used to guide the direction of research in favor of the clean energy sector. Once the two energy sectors become highly substitutable, carbon taxes or research subsidies for a temporary period would be sufficient to induce technical change in favor of clean energy and to avoid climate disasters.