A. Data and Methodology

The raw data used in this section include the gross CO2 emissions from the Global Carbon Project, PPP GDP per capita from the World Bank, and coal and oil consumption from BP’s Statistical Review of World Energy (2020) compiled by Our World in Data.

Note that the CO2 emissions we use are highly correlated with the greenhouse gas (GHG) emissions. As CO2 data are available for more countries, particularly for emerging markets, we choose to focus on CO2. In addition, we use gross emissions instead of net emissions due to the lack of accurate estimation of the latter. Moreover, as noted in the introduction, neither natural nor artificial carbon sinks are able to remove carbon from the atmosphere on the necessary scale to fight global warming, and the carbon stored in natural sinks is released into the atmosphere again through forest fires, etc., highlighting the importance of reducing gross carbon emissions (European Parliament, June 24, 2021).

For all variables in levels, we use their logarithm in the analysis. Specifically, we take the annual data from 1965 to 2019 for countries that have ranked among the top 20 in terms of the cumulative carbon emissions as of 2019. These 20 countries are (from high to low emissions): USA, CHN, RUS, DEU, GBR, JPN, IND, FRA, CAN, UKR, POL, ITA, ZAF, MEX, IRN, AUS, KOR, BRA, SAU, and ESP.⁶ In total, their cumulative emissions account for 80 percent of the world’s total cumulative emissions as of 2019.

Note that this section does not use the climate policy data because this section takes a data-driven approach to identify structural breaks in the carbon emissions (without considering climate policies per se) rather than a policy-evaluation approach. The climate policy data will be discussed in a subsequent section.

In terms of the methodology, we conduct a machine learning-based approach of indicator saturation to detect structural changes in carbon emissions. An important feature of this approach is that it allows us to remain agonistic ex ante about the dates of structural changes while letting the data speak about the shifts in the trends of carbon emissions. This then allows us to compare the identified periods of structural changes with major economic and policy events to determine the necessary conditions that lead to long-term carbon emission reductions. The same approach is used by, for example, Hendry (2020) to identify the structural breaks and their driving forces in the United Kingdom’s CO2 emissions.

We consider a standard regression with a constant and a linear trend:

y_t = α + βz_t+ ε_t,

where y_t is carbon emissions of a country at time t; z_t is k-dimensional vector containing exogenous regressors as well as lagged values of y_t. Following the dummy saturation approach, originally proposed in Hendry, Johansen, and Santos (2008), Johansen and Nielsen (2009), and Castle, Doornik, and Hendry (2012), the regression can be saturated with dummies in the following general form:

where D_{i,t}^I=I_{t=i} is an impulse indicator, D_{i,t}^S=I_{t\ge i} is a step indicator, and D_{i,t}^T=(t-i)I_{t\ge i} is a trend indicator.

The impulse indicators capture outliers in carbon emissions, while the step and trend indicators capture structural changes. As the indicator dummies are colinear—for example, an impulse indicator is the same as the difference of two step indicators— and our primary interest is in structural changes, we drop impulse indicators and focus only on step and trend indicators. Because there are more explanatory variables than there are observations, we employ a machine learning-based block search algorithm to eliminate statistically insignificant indicators through a general-to-specific (GETS) approach.⁷ The statistically significant indicators that are selected will then indicate periods when structural breaks occur, which is what we are after. Castle, Doornik, and Hendry (2012) show that under the null of no outliers or breaks, αT impulse indicators are retained on average at a level of significance α. More generally, the proportion of spuriously retained variables, also referred to as gauge in the GETS literature, is close to α (Pretis, Reade, and Sucarrat, 2018). Throughout, we choose α to be 0.05.⁸ We conduct both unconditional analysis and conditional analysis. The unconditional analysis examines the pattern of carbon emissions without controlling for any contributing factors, whereas the conditional analysis controls for the major (non-policy) contributing factors, particularly GDP growth. This is to account for the extensive evidence that the economic development affects a country’s carbon emissions, while allowing maximum flexibility for the model to identify other drivers of emissions.

Mathematically, the unconditional analysis attempts to detect any structural break in carbon emissions using a machine-learning model. The model only employs a combination of step indicator saturation (SIS) and trend indicator saturation (TIS), both of which are based on the raw carbon emission data instead of other controls. That is,

By contrast, the conditional analysis attempts to detect any structural break in carbon emissions by controlling for some other contributing factors to emissions. That is, it adds to equation (1) a vector of control variables:

where the vector z_t could consist of contributing factors such as the GDP. Consequently, the “indicator coefficient path”, {\Sigma }_{i=1}^T({\psi }_i{D}_{i,t}^S+{\omega }_i{D}_{i,t}^T), captures carbon emissions over and above those induced by the controlled factors. This term is essentially the residual term while regressing the carbon emissions y_t on a constant and the controls z_t (the real residual term in such a regression also includes the ε_t in the above equation). Therefore, for simplicity, we will refer to this “indicator coefficient path” as the “residual carbon emissions”. As discussed later, we will focus on the specification that controls for GDP only, i.e., the vector z_t we consider is a degenerate vector with one element, the GDP variable.

In both unconditional and conditional analysis, our focus is on the number, timing, and magnitude of trend indicators and step indicators. A negative trend indicator indicates a decreasing pace of carbon emissions or an accelerating pace of carbon reductions, while a negative step indicator signals a downward level shift in carbon emissions. Since the models are agnostic about what brings about structural breaks, we place the timing of those structural breaks in the context of major economic, political, and environmental changes.

B. Unconditional Analysis: Results and Interpretation

The unconditional analysis is useful in identifying the changes in the absolute level of emissions, which is ultimately what matters for climate change mitigation. To reach net zero emissions, the absolute level has to decrease markedly for most countries over a sufficiently long period of time.

Figure 1 presents the CO2 emissions data (the red dotted line) and the structural breaks detected by our unconditional machine-learning model (the blue solid line), for six selected countries among the top 20 emitters. The six countries include three emerging markets (EMs) and three advanced economies (AEs). Appendix Figure 5 presents the results for the other 14 countries, including seven EMs and seven AEs. These two figures also make it clear that our model fits the data well.

Structural Breaks for Six Countries: Unconditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; and Authors’ calculations.

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Structural Breaks for Six Countries: Unconditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; and Authors’ calculations.

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Structural Breaks for Six Countries: Unconditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; and Authors’ calculations.

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Table 1 reports the years of structural breaks for the same six countries, and Appendix Table 11 reports those for the remaining 14 countries among the top 20 emitters. In the table, tis and sis represent a structural break in the trend and in the level, respectively; “1” and “-1” represent positive and negative signs, respectively. For example, the table indicates that the latest structural break in China’s carbon emission trend occurred in 1972, where the trend experienced a notable downward shift.

A few remarks are in order on the findings of our unconditional analysis:

First, since the 1990s, downward trend shifts in carbon emissions have been rare-- only 16 downward trend shifts in total--for the top 20 emitters, a result consistent with that in the panel data analysis in Appendix 1. This pattern is clear for the three EMs in Figure 1—China, India, and South Africa, none of which has witnessed any structural breaks in trends, implying that the pace of emissions has remained relatively unchanged in the past decades. Meanwhile, all three EMs have experienced positive level shifts in emissions, indicating that their carbon emissions are permanently higher after those shifts.

For the three AEs—the United Kingdom, the United States, Germany—the rapid decline in their carbon emissions reflects downward shifts in levels, but the pace of the decline did not accelerate in the last two decades except right after the global financial crisis. As Table 1 makes it clear, since 2000, the only structural break in the trend took place in 2008 for both the United Kingdom and the United States, and in 2018 for Germany; all other structural breaks were in the level rather than in the trend. The other 14 countries display the same pattern, as shown in Appendix Table 11. Note that the emissions in some countries, especially in AEs, experienced downward trend shifts around 1980, likely reflecting the lower oil consumption amid the oil crisis during the late 1970s and early 1980s.

Second, for all the top emitters that do display some downward patterns, the reduction in the CO2 emission level has not been fast enough. For example, Germany has been making steady progress in reducing its CO2 emission level since 1980. However, over almost 40 years, its gross CO2 emission level has reduced from around 1.1 Gt (20.8 log tons) in 1980 to 0.7 Gt (20.4 log tons) in 2019, or a 33 percent reduction. While such a reduction is an impressive feat against the background of Germany’s strong economic growth, the challenges of further reduction are non-trivial, particularly from a low base. Even maintaining the current rate of CO2 reduction, Germany would be able to reduce the gross CO2 emission to half of its 2019 level only by 2053⁹ and to zero only by 2088. Although reaching the net-zero goal does not require the gross emission level to be zero due to, e.g., the absorption by natural sinks¹⁰, these simple calculations still highlight the challenges for reaching the goal with the current rate of CO2 reduction, let alone it is harder to cut the emissions from a lower base.

Third, downward trend shifts do not seem to occur following major climate initiatives. For example, the Kyoto Protocol, which was adopted in December 1997 and entered into force in February 2005, was not followed by statistically significant downward trend shifts in carbon emissions.¹¹ Neither was the Paris Agreement, which was adopted in December 2015 and entered into force in November 2016. Of course, this is a simplifying observation because it takes time for countries to enact specific policy measures and for these measures to take effect. However, it is still noteworthy that these global major initiatives did not seem to have significantly arrested the trends of carbon emissions for the top emitters. The result is also consistent with IMF (2021, GFSR Chapter 3) that the major climate events such as the Paris Agreement are not associated with significant changes in the returns and flows of investment funds.

Fourth, as suggested by Figure 1 and Table 1, economic development significantly affects carbon emissions, and structural breaks in carbon emissions typically occurred around major economic crises. The same crisis, however, may have opposite impacts on different countries. For instance, Figure 1 and Table 1 show that while the 2008 global financial crisis was not associated with either level or trend shifts of carbon emissions for major EM emitters, it induced top AE emitters to fall on a declining emission path. One interpretation is that the dramatic economic developments and policy responses during major economic crises may have affected demand for energy and with the arrival of cheaper shale oil and gas, more expensive and higher carbon-generating inputs such as coal saw strong declines (see further below). In the case of EMs, economic rescue measures following the 2008 crisis, such as large infrastructure projects, may have led to more carbon emissions and offset the reduction of emissions associated with the crisis-era economic contractions. In the case of AEs, the rise in coal/oil prices and the decline in gas/solar energy prices after 2008 might have contributed to trend shifts in carbon emissions. However, many other factors are at play for structural breaks in carbon emissions. To examine factors beyond economic development, we will need to conduct conditional analysis controlling for GDP, as discussed in the subsequent section.

Finally, the effect of carbon taxes has yet to show up as major structural breaks in large emitters. Of the six emitters considered in Figure 1, only the United Kingdom implemented nationwide carbon taxes during the sample period, with an introduction of carbon price support in 2013. Table 1 identifies two level shifts for the United Kingdom in 2014 and 2016, respectively, providing some evidence that the United Kingdom carbon price support might be associated with structural breaks. Of the 14 other breaks among the top 20 emitters in the Appendix Table 11, only Ukraine displayed a level shift in 2014 after it introduced carbon tax in 2011. This is not to say that carbon taxes might not be useful; to the contrary, country case studies have shown that they are quite effective (Lin and Li, 2011; Rivers and Schaufele, 2015; Haites, 2018; Best, Burke, and Jotzo, 2020, among others). One reasons why effects are not detectable via large shifts in carbon emissions, is that higher taxes and wider implementation may be needed (Nordhaus , 2015; Gillingham and Stock, 2018; and Pahle et al, 2018).

C. Kaya Identity

To gain more insights into various forces behind carbon emissions, we resort to the Kaya Identity, a conceptual framework that analyzes the drivers of CO2 emissions (Kaya and Yokoburi, 1997; Wang, Tukker, and Rodrigues, 2019). It is an accounting identity expressing the total CO2 emission as the product of four factors: population, GDP per capita, energy intensity (per unit of GDP), and carbon intensity (per unit of energy consumed):

The energy intensity term, \frac{Energy}{GDP}, is closely related the structure of an economy: If a country relies more on heavy industries, then its energy intensity tends to be higher. For example, Peralta-Alva, Tavares, and Xi (2017) find that sectoral composition is an important factor behind cross-country differences in energy intensity. The carbon intensity term, \frac{CO2}{Energy}, reflects energy structure: If a country uses more “dirty” energy sources, then its carbon intensity tends to be higher. It is widely believed that the coal has the highest carbon footprint, followed by oil, gas, and renewables.

Despite its simplicity, the Kaya Identity is powerful in identifying the driving forces for the CO2 level. It has been widely used by scholars and policymakers alike. It plays a central role in the development of future emissions scenarios in the Special Report on Emissions Scenarios by the Intergovernmental Panel on Climate Change (IPCC, 2000). Moreover, many countrieshave expressed their climate policies based on the Kaya components: Under the Paris Agreement, treaty parties set their nationally determined contribution (NDCs) plans based on the Kaya Identity with respect to various CO2 emission scenarios (Aye and Edoja, 2017; Tavakoli, 2018), and the parties of the UNFCCC extend the Kaya components into different sectors for designing detailed NDC goals (UNFCCC, 2015).

Figure 2 plots the Kaya decomposition for the aforementioned six countries, with carbon emissions normalized to zero at the beginning year of the sample; see Appendix Figure 4 for the remaining 14 countries. The first notable observation is that the sudden drop of the CO2 (black) in 2008 for the US coincides with the contraction of its GDP per capita (grey) and the shift of its carbon intensity (red) that started around the same time. Following the enaction of the Energy Independence and Security Act in December 2007, there was a dramatic increase in natural gas production from shale and a sharp decrease in natural gas price from $16.75 per gallon in June 2008 to $3.12 in August 2009¹², leading to a switch from coal/oil to gas and a reduction in CO2 emissions. Note that, as the name suggests, the main goal of the Energy Independence and Security Act was to move the United States toward greater energy independence and security (i.e., lower dependence on energy imports), as opposed to curbing CO2 emissions per se (although some clauses of the Act did aim at achieving that goal).¹³

Kaya Decomposition for Six Countries

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; Our World in Data; and Authors’ calculations.

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Kaya Decomposition for Six Countries

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; Our World in Data; and Authors’ calculations.

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Kaya Decomposition for Six Countries

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; Our World in Data; and Authors’ calculations.

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The second notable observation is that, for three of the six countries (the UK, the US, and Germany), the contribution of their energy intensity (blue) to CO2 emissions has been increasingly negative over time since 1965. This likely reflects the shift of their economic structures away from energy-intensive industries to less intensive industries.¹⁴ China followed a similar pattern after the 1980s. For India and South Africa, however, the energy intensity contribution to CO2 emissions has remained broadly positive in the past decades (Figure 2). Such preliminary evidence points to the importance of changes in the economic structure.

D. Conditional Analysis: Results and Interpretation

In this section, we combine the machine-learning analysis of structural breaks and the Kaya Identity-based analysis of driving forces. While the Kaya identity provides a useful accounting decomposition, it does not take into account the interlinkages between GDP, energy intensity, and carbon intensity. For example, as a country moves up the income ladder, the service sector typically takes up a larger share of the economy, which lowers energy intensity; meanwhile, better environmental regulations may restrict the use of dirty energies, which reduces carbon intensity. To examine the drivers of carbon emissions beyond GDP, we focus on the following equation:

As a comparison, the Kaya Identity can be rewritten in logarithms as the following, after merging the population with the GDP per capita:

In equation (3), by allowing the coefficient β before Ln(GDP)_t to be different from 1, the structural break in carbon emissions we identify could capture the effect of climate polices on emissions independent of the impact of such policies on GDP. To see this, suppose a country is moving from an agriculture-based to manufacture-based economy. In this process, both the country’s GDP and energy/GDP (i.e., energy intensity) would increase because of an increasing share of industrial output in the economy. From its pure accounting perspective, the Kaya Identity assumes the CO2 contribution of GDP and that of energy/GDP are independent from each other. However, these two contributions are in fact tightly linked because the increase in industrial output would increase both GDP and energy/GDP. What the conditional analysis does is that by projecting CO2 onto GDP, it strips out those factors that affect both GDP and energy/GDP. What is left in the “residual” can be considered as the part of energy/GDP that is unrelated to GDP. If a climate policy such as carbon taxation affects both GDP and energy/GDP, its partial impact on energy/GDP on top of its impact on GDP should be reflected in the “residual”, especially the non-GDP components (i.e., the step and trend indicators) of the right-hand-side of Equation (3).

Figure 3 graphically presents the residual carbon emissions for the same six countries in Appendix Figure 1, and Figure 3 presents that for the remaining 14 countries among the top 20 emitters. Table 2 presents the years when the identified structural breaks occurred, and Appendix Table 12 reports those for the remaining 14 countries. Similar to the unconditional machine-learning analysis results, downward trend shifts have been rare for all the top 20 emitters, and they do not seem to occur following major climate initiatives such as the Kyoto Protocol. Besides these, we would like to highlight the following additional patterns revealed by our unconditional analysis.

Structural Breaks for Six Countries: Conditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

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Structural Breaks for Six Countries: Conditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

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Structural Breaks for Six Countries: Conditional Analysis

Citation: IMF Working Papers 2022, 009; 10.5089/9798400200267.001.A001

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

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^{Table 2.}

Timing of Structural Breaks for Six Countries: Conditional Analysis

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

^{Table 2.}

Timing of Structural Breaks for Six Countries: Conditional Analysis

	CHN		IND		ZAF		GBR		USA		DEU
	Year	Sign	Year	Sign	Year	Sign	Year	Sign	Year	Sign	Year	Sign
Trend Shift	tisl978	-1	tisl971	1	tisl975	1	tisl966	-1	tisl970	-1	tisl981	-1
	tisl992	-1	tisl985	1	tisl987	-1	tisl990	1	tisl980	-1	tisl991	-1
	tis2001	1	tisl995	-1			tisl992	-1	tisl987	1	tisl993	1
	tis2012	-1	tis2007	1					tisl992	-1
			tis2013	-1
Level Shift	sis 1970	1	sis 1972	1	sis 1971	1	sis2014	-1	sis 1970	1	sis 1975	-1
	sis 1975	1	sis 1979	1	sis 1982	1	sis2016	-1	sis 1992	1	sis 1976	1
			sis 1985	1	sis2012	-1			sis2015	-1	sis 1981	-1
											sis2019	-1

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

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^{Table 2.}

Timing of Structural Breaks for Six Countries: Conditional Analysis

	CHN		IND		ZAF		GBR		USA		DEU
	Year	Sign	Year	Sign	Year	Sign	Year	Sign	Year	Sign	Year	Sign
Trend Shift	tisl978	-1	tisl971	1	tisl975	1	tisl966	-1	tisl970	-1	tisl981	-1
	tisl992	-1	tisl985	1	tisl987	-1	tisl990	1	tisl980	-1	tisl991	-1
	tis2001	1	tisl995	-1			tisl992	-1	tisl987	1	tisl993	1
	tis2012	-1	tis2007	1					tisl992	-1
			tis2013	-1
Level Shift	sis 1970	1	sis 1972	1	sis 1971	1	sis2014	-1	sis 1970	1	sis 1975	-1
	sis 1975	1	sis 1979	1	sis 1982	1	sis2016	-1	sis 1992	1	sis 1976	1
			sis 1985	1	sis2012	-1			sis2015	-1	sis 1981	-1
											sis2019	-1

Sources: Global Carbon Project; World Bank; and Authors’ calculations.

The first notable pattern is that conditional emission patterns differ from unconditional emission patterns for several countries and time periods. For example, China and the United States both exhibited broadly increasing emissions before 2008 (Figure 1), while emissions conditional on GDP have been declining for both countries (Figure 2). This suggests that mitigating forces have been at work outside the channel of economic development.

Second, some structural breaks in the unconditional analysis disappear and new structural breaks appear in the conditional analysis. This reflects the role of economic development in inducing large changes in carbon emissions and helps identify policies and non-economic forces (such as political events) that significantly affect carbon emissions.

For example, the structural breaks in 2008 for emission trend of the United Kingdom and the United States are no longer present once conditioning on GDP (comparing Table 2 with Table 1). This suggests that the structural breaks in the unconditional emission trend are driven by the GDP contraction during the Global Financial Crisis (which reduced the oil consumption and emissions) rather than by other factors including climate policies that had been enacted up to then. In particular, it suggests that even the sharp gas price decrease (from $16.75 per gallon in June 2008 to $3.12 in August 2009) did not seem to have led to a structural break in the conditional emission trend of the United States.

By contrast, Germany’s conditional emission displays a downward trend shift in 1991 (even though the unconditional emission does not display a trend shift in the same year). This likely reflects the German reunification in October 1990 that brought about fundamental changes to its economic structure. Another example is the downward trend shift of China’s conditional emission in 1978, the year when the country started implementing its economic reforms and opening-up strategy that dramatically reshaped its economic structure away from heavy industries.¹⁵

The third notable pattern is that country-specific policy responses to pollution crises may have played a significant role in driving some downward shifts of the emission trends. Consider the example of China again, given that the country’s annual CO2 emission in 2019 accounted for 28 percent of the world’s total CO2 emission.¹⁶ After controlling for GDP, China’s emission trend had another downward shift in 2012. As documented by Finamore (2018), China went through a severe air pollution crisis in January 2013, which was widely regarded as a “turning point”. In response, in September 2013, the central government announced the Air Pollution Prevention and Control Action Plan, a four-year plan to significantly improve the air quality of the entire country by end-2017. And in December 2013, the central government announced that GDP growth would no longer be the most important factor when evaluating an official’s performance, a fundamental change to the long-standing GDP-oriented evaluation system that may have incentivized local officials to pursue high local GDPs at the cost of the environment.¹⁷

In sum, the major climate initiatives—such as Kyoto Protocol in 2005 and Paris Agreement in 2015–2016—and “traditional” climate policies do not seem to have reduced the trends of either unconditional or conditional carbon emissions. Instead, analysis of a few country cases shows that both the economic structural changes and policy changes in response to a pollution shock have played a significant role. Moreover, the comparison of structural breaks in the conditional analysis with those in the unconditional analysis helps us gain insights into what forces could induce changes in carbon emissions after accounting for the fact that carbon emissions may unavoidably increase as the economy expands (especially from a low level) and the country uses more energies.

These results (both unconditional and conditional) are obtained using a 5 percent significance level. The results under a 1 percent significance level are presented in Appendix Figure 6 for unconditional and Appendix Figure 7 for conditional. In both figures, the results for the ten EMs are presented first, followed by those for the ten AEs. These results are very similar to those under a 5 percent significance level. The major difference is that there are fewer structural breaks under the 1 percent significance level than under the 5 percent. This is intuitive because the criteria for determining structural breaks are more stringent under the 1 percent significance level.