Study on the decoupling relationship between CO2 emissions and economic development based on two-dimensional decoupling theory: A case between China and the United States

Ecological Indicators 102 (2019) 230–236

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Original Articles

Study on the decoupling relationship between CO2 emissions and economic development based on two-dimensional decoupling theory: A case between China and the United States

T

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Yong Songa,b, Ming Zhanga,b, , Min Zhoua,b a b

School of Management, China University of Mining and Technology, Xuzhou 221116, China Jiangsu Energy Economy and Management Research Base, China University of Mining and Technology, Xuzhou 221116, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Decoupling theory EKC hypothesis CO2 emissions Economic development

The current decoupling theory cannot distinguish the decoupling state of a region with different economic development level. To overcome this problem, this paper first studies the internal relationship between decoupling theory and EKC hypothesis. Furthermore, we establish a two-dimensional decoupling theory of economic development and CO2 emissions. Finally, taking China and US as a case, this theory is used to explore the decoupling relationship between economic development and CO2 emissions over the period 1965–2016. If the EKC curve satisfies the inverted U type characteristic, the critical point between strong decoupling and weak decoupling can be approximately obtained at the extreme point of EKC curve. Based on the Tapio decoupling theory and extreme point of EKC curve, the two-dimensional decoupling model with 16 kinds of decoupling sates is established. For China and the United States, the EKC curve of carbon emissions and per capita GDP satisfies the inverted U type characteristic. The threshold value of per capita GDP for China and the United States are $7999.5 and $50980.52, respectively. At present, China's economy is experiencing a low level of economic development. The development of the United States in 2014–2015 and 2015–2016 presented strong decoupling with high level of economic development.

1. Introduction Energy plays a vital role in driving economic development (Guo et al., 2018; Zhang et al., 2018). With the continuous development of the economy, fossil fuel-based energy consumption has led to large amounts of CO2 emissions (Zhang and Da, 2015; Zhang et al., 2018; Zhang and Zhang, 2018). However, the rate of change in economic development is not necessarily proportional to the rate of change in CO2 emissions. As the largest emitters of CO2 in the world, China and the United States are facing big pressure of reducing CO2 emissions to realize its duty as a big country. To eliminate the pressure of CO2 reduction, it is necessary to further analyze the decoupling relationship between CO2 emissions and economic development, which is of great significance for achieving high quality development. At present, the decoupling theory and EKC (Environmental Kuznets Curve) hypothesis are widely used to depict the relationship between economic development and CO2 emissions. The correlation of synchronous changes between economic development and industrial pollution emissions is firstly described by OECD (2010) as “decoupling”.

⁎

OECD defined the decoupling index as the ratio of pollution discharge divided by GDP in the target year t to that in the base year 0 . Since then, OECD has released the decoupling index of different countries every year. However, the decoupling index defined by OECD changes with the choice of the base period (OECD decoupling method), which cannot accurately depict the decoupling status between economic development and pollution discharge. To solve the problem of uncertainty in the selection of base period, Tapio (2005) defined the decoupling index based on the idea of elastic coefficient. The Taipo decoupling index is defined as the ratio of change rate of carbon dioxide to that of traffic volume. To better distinguish the decoupling degree, Tapio (2005) defined 8 decoupling states. Since then, the Tapio decoupling theory has been applied by many scholars, such as Climent and Pardo (2007) and Ren and Hu (2012). Based on the result of the refined Laspeyres decomposition model, an IDA-CL decoupling index was defined by Diakoulaki and Mandaraka (2007), which was utilized to assess the real efforts undertaken in each country and their effectiveness in dissociating the economic and environmental dimensions of development. Based on the influence factors decomposed by LMDI method, an IDA-

Corresponding author at: School of Management, China University of Mining and Technology, Xuzhou 221116, China. E-mail address: [email protected] (M. Zhang).

https://doi.org/10.1016/j.ecolind.2019.02.044 Received 24 January 2019; Received in revised form 18 February 2019; Accepted 20 February 2019 1470-160X/ © 2019 Elsevier Ltd. All rights reserved.

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verified by many scholars, such as Lindmark (2002), Jalil and Mahmud (2009), Acararci and Ozturk (2010). Some scholars have found there existed heterogeneity in environmental pollution caused by economic growth in different countries or regions. In addition, different sample areas and econometric models can lead to different curve results (Lee et al., 2009; Jaunky, 2011). The decoupling theory is mainly used to explain the correlation of synchronous changes between economic development and CO2 emissions. However, the EKC hypothesis is mainly used to describe the nonlinear relationship between economic development and CO2 emissions. The EKC hypothesis confirms that the threshold of pollutant emission exists at the extreme point of the inverted U curve (Grossman and Krueger, 1995). Combining EKC hypothesis with decoupling theory, Xia and Zhong (2016) explored the relationship between economic development and environmental pollution. Based on the complex assumptions, they deduced the relationship between EKC hypothesis and decoupling theory. They roughly proved that the Per capita GDP corresponding to the extreme point corresponds to the critical point between relative decoupling and absolute decoupling. Based on the critical point and Tapio decoupling criteria, Xia and Zhong (2016) further established a two-dimensional decoupling model with economic growth greater than zero. And six kinds of decoupling status are presented in that model. However, the relationship between the EKC hypothesis and the decoupling theory, presented by Xia and Zhong (2016), is difficult to understand and not accurate enough. Firstly, this paper gives a concise and precise derivation of the relationship between the EKC hypothesis and the decoupling theory. Then, based on the critical point and Tapio decoupling criteria, we establish a two-dimensional decoupling theory between economic development and CO2 emissions with 16 kinds of decoupling sates. Finally, the two-dimensional decoupling model is used to study the decoupling relationship between economic development and CO2 emissions over the period 1965–2016 in China and the United States. The remaining structure of this paper is as follows. The derivation of the relationship between EKC hypothesis and decoupling theory is presented in Section 2. Section 3 establishes the two-dimensional decoupling theory. The case study of decoupling model is given in Section 4. Section 5 summarizes the conclusions.

LMDI decoupling indicator was developed by Zhang et al. (2013), which was utilized to explore the decoupling status between China’s electricity consumption and economic growth over 1991–2009. Zhang and Da (2015) also introduced the IDA-LMDI decoupling indicator to explore the decoupling relationship between CO2 emissions and GDP in China. The Taipio decoupling index only describes which decoupling state occurs, but it cannot find the cause why the decoupling state occurs. Combining with index decomposition model, Zhang et al. (2015) constructed the decoupling index decomposition model, which provided a method to analyze the causes of decoupling state. Referring to the theory of index decomposition model, Wang et al. (2017) developed a decoupling index change decomposition model, which can be used to explore why the decoupling index changes every year. Based on the results of complete decomposition analysis, De Freitas and Kaneko (2011) defined a decoupling indicator, which was used to study the decoupling state of CO2 emissions and Brazil’s economic growth during 1980–1994 and 2004–2009. Ang (2004) pointed that the Logarithmic Mean Divisia Index (LMDI) method was the most perfect decomposition technology. A new ZM-decoupling index was developed by Song and Zhang (2017) based on the influencing factors received by LMDI method, which can reflect the contribution of different influence factors to decoupling. Nowadays, the decoupling theory has been widely applied in different fields, such as greenhouse gas emissions (Mazzanti and Marin, 2009), NOx discharges (Gupta, 2015), haze pollution (Wang and Xu, 2015), and resource consumption (Wang et al., 2017). Most studies showed that countries with weaker economic base were more difficult to decouple than those with better economic base (Enevoldsen et al., 2007). Some studies have found that some countries or regions had presented the alternating characteristics of “decoupling” and “coupling” between economic growth and carbon emissions in the long run (Wang and Li, 2015). Some scholars found that economic agglomeration, population agglomeration, environmental regulation and other measures were also the causes of different decoupling states (Xia and Hu, 2017). The existing decoupling theories cannot distinguish the same decoupling state in regions with different economic development levels. The determinant factor of economic development was added to the Taipo decoupling standard by Xia and Zhong (2016), which can overcome the problem of possible decoupling of regions with different levels of economic development. Nowadays, a growing number of studies have been focused on the decoupling relationship between energy consumption or CO2 emissions and economic development across the world, as listed in Table 1. The EKC hypothesis, first put forward by Grossman and Krueger (1995), is used to study the inverted U curve relationship between environmental pollution and per capita GDP. The EKC hypothesis has been widely to explore various indicators of environmental degradation, such as water quality indicators (heavy metals, pathogens, water oxygen regime), air quality indicators (CO2, SO2, NOX, CO, VOC and SPM), and various other environmental indicators (municipal solid wastes, access to safe drinking water, deforestation) (Dinda, 2004). The panel data or time series cross sectional data are used to estimate the model in most empirical studies (Suri and Chapman, 1998; Richmond and Kauffmann, 2006). The EKC hypothesis of inverted U type has been

2. Theoretical derivation 2.1. EKC hypothesis The EKC hypothesis describes the inverted U relationship of carbon emissions with the increase of per capita GDP. The EKC curve is a function of linear and quadric entries of per capita GDP, which can be estimated by the following formula:

C t = α 0 + α1 g t + α2 (g t )2

(1)

where C t denotes the CO2 emissions in year t ; g t represents the per capita GDP in year t ; α 0 is the constant term, which represents a collection of other factors affecting carbon emissions except per capita GDP; α1 is the first-order coefficients of per capita GDP; α2 is the secondorder coefficient of per capita GDP. If α1 > 0 and α2 < 0 , the EKC curve

Table 1 Representative literature for decoupling method. Author

Method

Time interval

Research object

OECD (2010) Taipio (2005) Diakoulaki and Mandaraka (2007) Zhang et al. (2013) Xia and Zhong (2016) Song and Zhang (2017)

OECD decoupling method Taipio decoupling method IDA-CL decoupling index IDA-LMDI decoupling indicator Two-dimensional decoupling model ZM-decoupling index

1980–1998 1970–2001 1990–2003 1991–2009 2004–2013 1991–2012

OECD’s countries Road traffic in EU EU manufacturing sector China’s electricity sector 271 prefectural cities in China China

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According to the decoupling criteria listed in Table 1, the conditions between strong decoupling and weak decoupling are D = 0 and ΔG > 0 . α Thus r > 0 . Let D = 0 . We can obtain g t = − 2α1 + r and g t = r . Because 2 2 r represents the change of per capita GDP in adjacent two years. Then, t g = r has no economic significance. Therefore, the critical point beα tween strong decoupling and weak decoupling is g t = − 2α1 + r . 2 2 If the EKC curve satisfies the inverted U type characteristic, the extreme point of Eq. (1) can be expressed as:

Table 2 The decoupling criteria for eight logical possibilities.

1 2 3 4 5 6 7 8

ΔC

ΔG

D

Decoupling state

>0 >0 >0 >0 <0 <0 <0 <0

<0 >0 >0 >0 >0 <0 <0 <0

D≤0 0.8 ≥ D > 0 1.2 ≥ D > 0.8 D > 1.2 D≤0 0.8 ≥ D > 0 1.2 ≥ D > 0.8 D > 1.2

strong negative decoupling (SND) weak decoupling (WD) expansive coupling (EC) expansive negative decoupling (END) strong decoupling (SD) weak negative decoupling (WND) recessive coupling (RC) recessive decoupling (RD)

α1 + 2α2 g t = 0 α

Thus, the threshold of carbon dioxide emissions is g t = − 2α1 . Due to 2 r > 0 , the critical point between strong decoupling and weak decoupling can be obtained at the right side of the extreme point of EKC curve.

is inverted U-shaped. This paper assumes that the EKC curve satisfies the inverted U type characteristic.

3. Framework of two-dimensional decoupling model

2.2. Tapio decoupling theory

The Tapio decoupling index cannot distinguish the influence of economic development level on decoupling status in different regions or periods of development. The phase with low economic development level can achieve the same decoupling state as the phase with higher economic development level. Regions with low level of economic development can also achieve the same decoupling state as those with relatively high economic development level. Therefore, the current decoupling index cannot distinguish the decoupling state with different economic development level. When constructing the decoupling theory, we should regard economic development level as a reference index. However, per capita GDP can well depict the level of economic development in different regions or stages. Based on the Tapio decoupling standards, this paper constructs a Cartesian coordinate system with the per capita GDP as the abscissa axis (g) and the decoupling index as the ordinate axis (D). According to the Tapio decoupling standard, 0, 0.8 and 1.2 are set as the critical points of the decoupling index of the longitudinal axis. Suppose there is a threshold value of per capita GDP ( g ∗) in the abscissa axis. The left side of g ∗ represents the regions or stages with low level of economic development (LE). However, the right side of g ∗ represents the regions or stages with high level of economic development (HE). According to the theoretical derivation of the relationship between EKC hypothesis and decoupling theory, r represents the change of per capita GDP for two years in succession. Therefore, r is relatively small. Hence, the critical point between strong decoupling and weak decoupling can be approximately obtained at the extreme point of EKC curve. The threshold value of per capita GDP in the abscissa axis is supposed as the α extreme point of EKC curve, i.e. g ∗ = − 2α1 . According to the plus sign 2 and the minus sign of ΔG , the specific decoupling standard is shown in the Fig. 1. If the change of economic development is more than 0, the divisions of decoupling state is shown in Fig. 1(a); otherwise, the decoupling

The Tapio decoupling index (Dt ) in the period [t − 1, t ] can be expressed as Eq. (2):

Dt =

Ct − Ct − 1 Ct − 1 Gt − Gt − 1 Gt − 1

(2)

ΔC t

Gt

Ct

Ct−1

= − where represents the GDP in year t ; represents the difference of CO2 emissions in the period [t − 1, t ]; ΔGt = Gt − Gt − 1 represents the difference of GDP in the period [t − 1, t ]. Thus, the decoupling criteria that presented by Tapio (2005) can be presented in Table 2 2.3. Theoretical derivation Let r = g t − g t − 1. The CO2 emissions in year t − 1, C t − 1, can be expressed as the following eq: C t − 1 = α 0 + α1 (g t − r ) + α2 (g t − r )2 . Here, Gt = g t × P t , P t denotes the total population in year t . This paper explores the decoupling in adjacent years. At the same time, taking into account the simplified model and the need for derivation, the paper assumes that the population change rate is 0. Thus, Gt = g t × P . Thus, Gt − 1 = g t − 1 × P = (g t − r ) × P . Thus, the Eq. (2) can be expressed as:

Dt

=

Ct − Ct − 1 Ct − 1 Gt − Gt − 1 Gt − 1

α 0 + α1 g t + α2 (g t )2 − α 0 − α1 (g t − r ) − α2 (g t − r )2

=

α 0 + α1 (g t − r ) + α2 (g t − r )2 g t × P − (g t − r ) × P (g t − r ) × P

α1 r + 2α2 g t r − α2 r 2 gt − r × t t 2 α 0 + α1 (g − r ) + α2 (g − r ) r (α1 + 2α2 g t − α2 r )(g t − r ) = α 0 + α1 (g t − r ) + α2 (g t − r )2 =

Fig. 1. The divisions of decoupling state of two-dimensional decoupling model. 232

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division is shown in the Fig. 1(b). The decoupling state in Fig. 1(b) will happen only when society goes backward, such as such as wars, major natural disasters, severe financial crisis. SND represents a region or stage with economic backwardness and a rise in carbon emissions. RD represents a region or stage with economic backwardness and a rapid decrease in carbon emissions. However, most countries or regions have adopted various ways to promote social progress. Therefore, most countries or regions experience decoupling states shown in Fig. 1(a). SD-HE represents a region or stage with high per capita GDP and strong decoupling, which not only avoids increasing environmental load simply by pursuing economic growth, but also avoids the simple pursuit of environmental protection by reducing the quality of economic development. END-LE represents a region or stage with slower economic growth and a sharp rise in carbon emissions, which also reflects the inefficient expansion of economic development. According to the experience of developed countries, a country or region, which pursues economic development and environmental protection, will experience a low level of economic development and low pollution emissions, to a high level of economic development and high pollution emissions, and then to a high level of economic development and low pollution emissions process. Therefore, the 16 decoupling states in Fig. 1 can characterize the developmental stages of different countries or regions.

Fig. 3. The trend of per capita GDP in China and the United States over 1965–2016.

roared to 16865.60 Trillion dollars in 2016 from 3926.42 Trillion dollars in 1965, with an average increase rate of 2.89%. The GDP gap between China and the US widened and then narrowed. However, the ratio of GDP between China and the United States has been getting smaller since 1977. In 2016, China’s GDP is only 56.35% the size of that of America. Meanwhile, China’s per capita GDP roared to 6894.46 dollars in 2016 from 187.27 dollars in 1965, as shown in Fig. 3. In the last fifty years, per capita GDP increases rapidly with an average annual growth rate of 7.32%. The trend of per capita GDP is similar to that of China's GDP curve. The curve of China's per capita GDP can also be divided into three phases: a slow growth phase between 1965 and 1990, a moderate increase phase from 1991 to 2002, and a rapid increase phase between 2003 and 2016. Furthermore, per capita GDP in the United States increased to 52194.88 dollars in 2016 from 20207.74 dollars in 1965. Fig. 3 also shows that the difference between the US and China in GDP per head is getting bigger. However, the ratio of per capita GDP in the United States to China decreased gradually. In 2016, China’s per capita GDP is less than one seventh of the United States’.

4. Case study China and the United States are the biggest carbon dioxide emitters in the world. Their carbon emission characteristics has typical representativeness. Thus, this paper selects China and the United States as a case to study the decoupling relationship between economic development and carbon dioxide emissions over the period 1965–2016 based on the two-dimensional decoupling model. The CO2 emissions, measured by Million tones (Mt), are collected from the BP Statistical Yearbook (BP (British Petroleum), 2017). The population is collected from the World Bank (WB (World Bank), 2017). The GDP measured by Million dollar (Md) in 2010 constant price is also collected from the World Bank (WB (World Bank), 2017). 4.1. Current situation of GDP and CO2 emissions in China and the United States

4.1.2. CO2 emissions With the sustained and rapid economic development in China, CO2 emissions shows a rapid growth trend, as shown in Fig. 4. CO2 emissions in China increased from 488.68 Mt (Million tons) in 1965 to 9123.04 Mt in 2016, with an average increase rate of 5.91%. The curve of CO2 emissions in China can also be divided into three phases: a slow growth phase between 1965 and 2000, a rapid increase phase from 2001 to 2014, and a slow decrease phase between 2015 and 2016. In the second stage, CO2 emissions increase rapidly with an average annual growth rate of 7.70%. Since 2015, the decline in CO2 emissions has

4.1.1. GDP As shown in Fig. 2, China’s GDP increased from 133.93 Trillion dollars in 1965 to 9505.15 Trillion dollars in 2016, with an average increase rate of 8.71%. The curve of China’s GDP, likes an exponent curve, can be divided into three phases: a slow growth phase between 1965 and 1980, a moderate increase phase from 1981 to 1990, and a rapid increase phase between 1991 and 2016. In the third phase, the average annual growth rate of China’s GDP reached 9.85%. However, the curve of the United States’ GDP likes linear function. And its GDP

Fig. 4. The trend of CO2 emissions in China and the United States over 1965–2016.

Fig. 2. The trend of GDP in China and the United States over 1965–2016. 233

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Table 4 The decoupling state of CO2 emissions in China over 1965–2016.

Fig. 5. The trend of per capita CO2 emissions in China and the United States over 1965–2016.

been attributed to a series of stringent environmental measures taken by the state to control air pollution. And CO2 emissions in the United States roared to 5350.36 Mt in 2016 from 3631.20 Mt in 1965, with an increase of 47.34%. Since 2007, CO2 emissions in the United States have begun to decline along a wave-like curve. However, China has been the largest emitter of CO2 pollution since 2006 when it overtook the US. In 2016, China's CO2 emissions was 1.71 times that of the United States. Over the period 1965–2016, per capita CO2 emissions in China increased to 6.62t from 0.68t, with an average increase rate of 4.55%. As shown in Fig. 5, the curve of per capita CO2 emissions in China can also be divided into two phases: a slow growth phase between 1965 and 2002, and a rapid increase phase from 2003 to 2016. However, per capita CO2 emissions in the United States has a sudden rise and then drops slowly. In 2016, per capita CO2 emissions in the United States dropped to 16.55t. In 1965, China’s per capita carbon dioxide emissions were only 0.036 of that in the United States. But that value increased to 0.399 in 2016.

4.2. Decoupling analysis of China According to the EKC curve of Eq. (1) presented in Section 2, Table 3 lists the regression results of EKC estimation for China. The parameters in Table 3 show that the simulation fitness is high, and all variables are significant at 5% significant level. The EKC curve of China's CO2 emissions and per capita GDP satisfies the inverted U type characteristic. The threshold value of per capita GDP ( g ∗) equals $7999.5. According to the two-dimensional decoupling criteria presented in Section 3, the decoupling state of CO2 emissions in China over 1965–2016 is listed in Table 4. Because the threshold value of per capita GDP is bigger than China’s per capita GDP in 1965–2016. At present, China's economy is experiencing a low level of economic development (LE). Only 6 decoupling states occurred in the study period: ECLE, RD-LE, SND-LE, END-LE, WD-LE, and SD-LE. Weak decoupling with low level of economic development (WD-LE) only appeared in 28 years, i.e. 1972–1973, 1978–1979, 1979–1980, 1981–1982, 1982–1983, 1983–1984, 1984–1985, 1985–1986, 1986–1987, 1987–1988, 1989–1990, 1990–1991, 1991–1992, 1992–1993, 1993–1994, 1994–1995, 1995–1996, 1998–1999, 1999–2000, 2000–2001, 2005–2006, 2006–2007, 2007–2008,

g 2.3306 F 1803.67

p 0.0000001

ΔC

ΔG

D

g < g∗

State

1965–1966 1966–1967 1967–1968 1968–1969 1969–1970 1970–1971 1971–1972 1972–1973 1973–1974 1974–1975 1975–1976 1976–1977 1977–1978 1978–1979 1979–1980 1980–1981 1981–1982 1982–1983 1983–1984 1984–1985 1985–1986 1986–1987 1987–1988 1988–1989 1989–1990 1990–1991 1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015 2015–2016

>0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 <0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 <0 <0

>0 <0 <0 >0 >0 >0 >0 >0 >0 >0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0

0.80 1.78 −0.04 1.31 1.48 2.52 1.90 0.57 0.88 1.42 −2.93 1.23 0.83 0.37 0.11 −0.30 0.49 0.58 0.52 0.43 0.50 0.65 0.65 1.05 0.17 0.61 0.35 0.58 0.41 0.28 0.50 −0.04 −0.01 0.54 0.20 0.58 0.99 1.79 1.75 1.25 0.75 0.59 0.20 0.48 0.52 0.89 0.25 0.34 0.01 −0.09 −0.07

Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y

EC-LE RD-LE SND-LE END-LE END-LE END-LE END-LE WD-LE EC-LE END-LE SND-LE END-LE EC-LE WD-LE WD-LE SD-LE WD-LE WD-LE WD-LE WD-LE WD-LE WD-LE WD-LE EC-LE WD-LE WD-LE WD-LE WD-LE WD-LE WD-LE WD-LE SD-LE SD-LE WD-LE WD-LE WD-LE EC-LE END-LE END-LE END-LE WD-LE WD-LE WD-LE WD-LE WD-LE EC-LE WD-LE WD-LE WD-LE SD-LE SD-LE

2008–2009, 2009–2010, 2011–2012, 2012–2013, and 2013–2014. Strong decoupling with low level of economic development (SD-LE) only occurred in 1980–1981, 1996–1997, 1997–1998, 2014–2015, and 2015–2016. The development in 1965–1966, 1973–1974, 1977–1978, 1988–1989, 2001–2002, and 2010–2011 presented expansive coupling with low level of economic development (EC-LE). However, the CO2 emissions presented expansive negative decoupling with low level of economic development (END-LE) with economic growth in 9 years: 1968–1969, 1969–1970, 1970–1971, 1971–1972, 1974–1975, 1976–1977, 2002–2003, 2003–2004, and 2004–2005. In 1966–1967, 1967–1968, and 1975–1976, the change of economic development was less than 0. Recessive decoupling with low level of economic development (RD-LE) only occurred in 1966–1967. The development in 1967–1968, and 1975–1976 presented strong negative decoupling with low level of economic development (SND-LE).

Table 3 The results of EKC estimation for China. China Coef R2 0.9865

Year

g2 −0.00001 g∗ $7999.5

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decoupling states occurred in the study period: EC-LE, END-LE, WD-LE, SD-LE, RD-LE, and SD-HE. Weak decoupling with low level of economic development (WD-LE) occurred in 20 years: 1970–1971, 1972–1973, 1976–1977, 1978–1979, 1983–1984, 1984–1985, 1985–1986, 1988–1989, 1991–1992, 1993–1994, 1994–1995, 1996–1997, 1997–1998, 1998–1999, 1999–2000, 2001–2002, 2002–2003, 2003–2004, 2004–2005, and 2013–2014. The development in 1977–1978, 1980–1981, 1982–1983, 1989–1990, 2000–2001, 2005–2006, 2010–2011, and 2011–2012 presented strong decoupling with low level of economic development (SD-LE). The CO2 emissions presented expansive coupling with low level of economic development (EC-LE) with economic growth in 10 years: 1965–1966, 1966–1967, 1969–1970, 1971–1972, 1975–1976, 1986–1987, 1987–1988, 1992–1993, 1995–1996, and 2006–2007. The expansive negative decoupling with low level of economic development (END-LE) only occurred in 4 years: 1967–1968, 1968–1969, 2009–2010, and 2012–2013. However, the development in 1973–1974, 1974–1975, 1979–1980, 1981–1982, 1990–1991, 2007–2008, and 2008–2009 presented recessive decoupling with low level of economic development (RD-LE). Since 2015, the US per capita GDP exceeds the threshold value. The development in 2014–2015 and 2015–2016 presented strong decoupling with high level of economic development (SD-HE).

Table 5 The results of EKC estimation for the United States. the United States Coef R2 0.8419

g 0.1916 F 130.471

p 0.0000001

g2 −0.00001 g∗ 50980.52

Table 6 The decoupling state of CO2 emissions in the United States over 1965–2016. Year

ΔC

ΔG

D

g < g∗

State

1965–1966 1966–1967 1967–1968 1968–1969 1969–1970 1970–1971 1971–1972 1972–1973 1973–1974 1974–1975 1975–1976 1976–1977 1977–1978 1978–1979 1979–1980 1980–1981 1981–1982 1982–1983 1983–1984 1984–1985 1985–1986 1986–1987 1987–1988 1988–1989 1989–1990 1990–1991 1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015 2015–2016

>0 >0 >0 >0 >0 >0 >0 >0 <0 <0 >0 >0 <0 >0 <0 <0 <0 <0 >0 >0 >0 >0 >0 >0 <0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 <0 >0 >0 >0 >0 <0 >0 <0 <0 >0 <0 <0 >0 >0 <0 <0

>0 >0 >0 >0 >0 >0 >0 >0 <0 <0 >0 >0 >0 >0 <0 >0 <0 >0 >0 >0 >0 >0 >0 >0 >0 <0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 >0 <0 <0 >0 >0 >0 >0 >0 >0 >0

0.87 1.06 1.22 1.43 0.96 0.29 0.95 0.76 6.79 14.86 1.13 0.69 −0.20 0.68 13.56 −1.26 2.70 −0.09 0.64 0.07 0.02 0.93 1.11 0.51 −0.87 11.40 0.46 0.82 0.38 0.25 0.91 0.36 0.13 0.17 0.77 −1.93 0.32 0.43 0.45 0.18 −0.48 0.96 9.97 2.57 1.61 −1.49 −1.69 1.53 0.42 −1.07 −1.08

Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N N

EC-LE EC-LE END-LE END-LE EC-LE WD-LE EC-LE WD-LE RD-LE RD-LE EC-LE WD-LE SD-LE WD-LE RD-LE SD-LE RD-LE SD-LE WD-LE WD-LE WD-LE EC-LE EC-LE WD-LE SD-LE RD-LE WD-LE EC-LE WD-LE WD-LE EC-LE WD-LE WD-LE WD-LE WD-LE SD-LE WD-LE WD-LE WD-LE WD-LE SD-LE EC-LE RD-LE RD-LE END-LE SD-LE SD-LE END-LE WD-LE SD-HE SD-HE

5. Conclusions and discussion Comparing with the complicated deduction process presented by Xia and Zhong (2016), the deduction of the relationship between EKC hypothesis and decoupling theory in this paper is simple. If the EKC curve satisfies the inverted U type characteristic, the critical point between strong decoupling and weak decoupling can be approximately obtained at the extreme point of EKC curve. The current decoupling theory can better explain the correlation of synchronous changes between economic development and CO2 emissions. But it cannot distinguish the decoupling state of a region with different economic development level. To overcome this problem, Xia and Zhong (2016) developed a two-dimensional decoupling theory with economic growth greater than zero. But, only six kinds of decoupling status are presented in that model. If economic growth is less than zero, that index cannot distinguish the decoupling status. Then, the extreme point of EKC curve is supposed as the threshold value of per capita GDP ( g ∗), this paper established a two-dimensional decoupling theory of economic development and CO2 emissions with 16 kinds of decoupling sates. At last, the two-dimensional decoupling model was used to study the decoupling relationship between economic development and CO2 emissions over the period 1965–2016 in China and US. In 2016, China’s GDP is only 56.35% the size of that of the United States. However, China's CO2 emissions was 1.71 times that of the United States in 2016. In 2016, China's per capita GDP is less than one seventh of the United States'. However, China's per capita CO2 emissions were only 0.399 of that of the United States. For China and the United States, the EKC curve of CO2 emissions and per capita GDP satisfies the inverted U type characteristic. The threshold value of per capita GDP for China and the United States are $7999.5 and $50980.52, respectively. At present, China’s economy is experiencing a low level of economic development (LE). Only 6 decoupling states occurred in the study period: EC-LE, RD-LE, SND-LE, END-LE, WD-LE, and SD-LE. The United States has also experienced 6 decoupling states in the study period: ECLE, END-LE, WD-LE, SD-LE, RD-LE, and SD-HE. Furthermore, the US per capita GDP exceeds the threshold value since 2015. The development of the United States in 2014–2015 and 2015–2016 presented strong decoupling with high level of economic development (SD-HE). Compared with the United States, strong decoupling with high level of economic development (SD-HE) has not happened yet. Therefore, China needs to further optimize its industrial structure and energy structure.

4.3. Decoupling analysis of the United States According to the EKC curve of Eq. (1) presented in Section 2, the regression results of EKC estimation for the United States are listed in Table 5. The parameters in Table 5 show that the simulation fitness is high, and all variables are significant at 5% significant level. The EKC curve of the United States' CO2 emissions and per capita GDP satisfies the inverted U type characteristic. The threshold value of per capita GDP ( g ∗) equals $50980.52. The decoupling state of CO2 emissions in the United States over 1965–2016 is listed in Table 6. Only 6 235

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