The long-term relationship between emissions and economic growth for SO₂, CO₂, and BC

The main analysis in our study utilizes the global emission inventory developed at Peking University (hereafter referred to as PKU). The PKU dataset includes the three pollutants examined here (Su et al 2011, Wang et al 2012, 2013, 2014) and has been applied in a number of studies that estimate human exposure to air pollution (e.g. van der Werf et al 2010, Liu et al 2015, Tao et al 2018). The PKU inventory spans 1960–2014. It is composed of 64 individual emission sources, with all sources except for 8 representing biomass burning and international shipping included here. In total, our analysis includes sectoral emissions of SO₂, CO_2, and BC from 199 countries (see table S1 is available online at stacks.iop.org/ERL/13/124021/mmedia). The few, small countries not included lack the information to calculate source-specific emissions. The analysis spans 1980–2014, which was selected for two reasons. First, it is an era of dramatic changes in global emissions of atmospheric pollutants. Second, it features significant temporal overlap with many other studies exploring the relationship between economic growth and emissions (e.g. Stern and van Dijk 2017, Stern et al 2017). We aggregate all 56 applicable sources into four sectors: power, industry, residential, and transportation (see table S2). It should be noted that end-use emissions, rather than life-cycle emissions, are used in sectoral classification, following common practice.

In addition, three other widely used global emission inventories are analyzed to test the robustness of historical income-emission trajectories and avoid potential bias due to inventory-dependent assumptions. These inventories include the Emission Database for Global Atmospheric Research (EDGAR; Crippa et al 2018), the evaluating the climate and air quality impacts of short-lived pollutants (ECLIPSE) dataset (Stohl et al 2015, Klimont et al 2017), and the community emissions data system (CEDS) dataset (Hoesly et al 2018). Due to data limitations, only the PKU and CEDS datasets are used for analyses of CO₂. In addition, data limitations required use of slightly different time ranges for each of the inventories (1980–2014 in CEDS and PKU, 1990–2010 in ECLIPSE, and 1980–2010 in EDGAR). As long-term trajectories and their growth rates were used in this analysis, the influence of these differences should be quite limited.

We adopt a recently developed methodology using long-term growth rates to model the income-emission relationship (Stern et al 2017). This method reconciles several previous concerns in the EKC literature by integrating the three major approaches, the beta convergence model (Criado et al 2011), the IPAT-type green Solow model (Brock and Taylor 2010), and the basic EKC model, into one general modeling framework. We apply this general model in our study on a sectoral and pollutant-by-pollutant basis. The model is summarized by the following equation:

$$\begin{eqnarray*}&&\begin{array}{l}\widehat{{E}_{i}}={\alpha }_{0}+{\alpha }_{1}\widehat{{G}_{i}}+{\beta }_{1}\widehat{{G}_{i}}{G}_{i0}+{\beta }_{2}{E}_{i0}\\ \,\,+\,{\beta }_{3}{G}_{i0}+\displaystyle \sum _{j}^{k}{\beta }_{i}{X}_{ji}+{\varepsilon }_{i},\end{array}\end{eqnarray*}$$

where $\widehat{{E}_{i}}$ is the natural log of the long-term growth rate of emissions per capita for country $i$ (i.e. the linear change over a specified period, $\widehat{{E}_{i}}=({E}_{iT}-{E}_{i0})/{T},$ where T is the number of years in the studied time range), ${E}_{i0}$ is the natural log of emission per capita in the initial year. The same notation applies to $\widehat{{G}_{i}},$ which is the natural log of the long-term growth rate of GDP per capita for country i. ${\alpha }_{0}$ is an estimate of the mean $\widehat{{E}_{i}}$ for countries with no economic growth and all dummy control variables held at the default values and all continuous variables at the mean levels. ${\alpha }_{1}$ is an estimate of the emission-income elasticity. ${\beta }_{1}$ is the coefficient for the 'EKC interaction term', which is significantly less than zero when the trajectory is said to have a 'turning point.' This 'turning point' can be calculated as $\exp \left(-\displaystyle \frac{{\alpha }_{1}}{{\beta }_{1}}+{\mu }_{G}\right),$ where ${\mu }_{G}$ is the mean of the initial natural log of GDP per capita across all countries. ${\beta }_{2}$ and ${\beta }_{3}$ are the coefficients of the initial levels of income and emissions per capita. These terms are included to test convergence-type theories. ${X}_{ji}$ is a vector of ${j}$ control variables for each country $i.$ These control variables are included to capture unobserved effects at individual country levels. Additional details regarding this model can be found in Stern et al (2017). We report results on the coefficients of the non-control variables (i.e. ${\alpha }_{0},$ ${\alpha }_{1},{\beta }_{1},{\beta }_{2},{\beta }_{3}$) in tables within the text and coefficients of control-variables in the SI. As a guide to the reader: ${\alpha }_{1}$ describes the linear relationship between emissions and income (when an EKC is not found); a negative ${\beta }_{1}$ indicates the existence of an EKC pattern; a negative ${\beta }_{2}$ indicates emissions convergence across countries; and a negative ${\beta }_{3}$ indicates emissions intensity convergence across countries.

GDP and population data are retrieved from the Penn world table version 9.0 (Feenstra et al 2015), which provides a time series of country-level GDP values adjusted for purchasing power parity. Our set of control variables follow the setup described in Stern et al (2017). They include: (1) a binary variable indicating if a country has a centrally planned economy; (2) a binary variable for English (default) and non-English (German, French, and Scandinavian, individually) legal origins (La Porta et al 2008); (3) average summer and winter temperatures by country, adjusted by hemisphere (Mitchell et al 2002); (4) fossil-fuel endowments based on Norman (2009); and (5) average population density for 1980–2014 from the World Bank. Regression results for control variables are reported in the SI (table S3). Continuous variables are standardized by subtracting the sample mean and countries with incomplete data are omitted.

We compare the historical income-emission trajectories derived from the PKU inventory with future trajectories from several IAMs to assess similarities and differences in the evolution of emissions. IAMs are widely used tools that make long-term projections of emissions, with inputs including, but not limited to, projections of economic development and population change. Our analysis includes output from the Global Change Assessment Model (GCAM), Asia-Pacific Integrated Model (AIM) (Nejat et al), and Model for Energy Supply Strategy Alternatives and their General Environmental Impact (MESSAGE). These IAMs were used to develop several of the Representative Concentration Pathways (RCPs) and the SSPs. The three scenarios considered here were a baseline scenario from GCAM with a radiative forcing of ∼6.5 W m⁻², RCP 6.0 from AIM, and RCP 8.5 from MESSAGE. All three of these scenarios assume fairly weak, if any, application of climate policy during the century. The projections from these IAMs include 2000 through 2100. Thus, the comparisons of the income-emission relationships from the PKU inventory and the IAMs are not direct, but the historical empirical trajectories can provide insight into the future projections. In addition, data from the IAMs do not include every country, but are classified into several regions: 33 in GCAM and 24 in AIM/MESSAGE. Both the AIM and MESSAGE projections were obtained from the International Institute for Applied Systems Analysis's RCP database. GDP per capita data were obtained from the GEA Public Scenario Pathway Database and AIM's website. Emissions and GDP per capita data for GCAM were obtained from the output of a baseline simulation.

SO₂ emissions exhibit a long-term EKC pattern in both the power and industry sectors (see ${\beta }_{1}$ in tables 1–2), with turnover incomes of $19 000 and $50 000 USD, respectively. However, it should be noted that the turnover in the industry sector exhibits large uncertainty and is less significant. For CO₂, visualization of the emission trajectories suggests that a slowing-down of CO₂ emission growth rates among wealthier countries is occurring in both sectors (figure 1(a)), but the model finds no evidence of a significant turnover (tables 1–2). While the model reports a turnover for CO₂ in the industrial sector, the turnover income is very high ($190 000 USD per capita) and is not significant. There is significant beta-convergence (β₂ in table 2) in the industrial sector, however, implying that less wealthy countries tend to have faster growth rates in emissions and high-income countries tend to have lower growth rates. The model reports no EKC pattern for BC in either sector. However, the model again suggests beta-convergence, and also shows a linear increase that is correlated with economic growth in both sectors (see β₂ and ${{\boldsymbol{\alpha }}}_{1}$ values in tables 1–2).

Table 1.  Model results for the power sector.

Variable	Sulfur dioxide	Carbon dioxide	Black carbon
${{\boldsymbol{\alpha }}}_{0}$	−0.015	−0.035***	−0.071***
Constant	(0.013)	(0.010)	(0.021)
α1	0.65***	0.54***	0.44***
Coefficient of income growth rate $\widehat{{{\boldsymbol{G}}}_{{\boldsymbol{i}}}}$	(0.19)	(0.11)	(0.15)
${{\boldsymbol{\beta }}}_{1}$	−0.33***	−0.065	−0.087
Coefficient of product of income growth rate and initial income $\widehat{{{\boldsymbol{G}}}_{{\boldsymbol{i}}}}{{\boldsymbol{G}}}_{{\boldsymbol{i}}0}$	(0.10)	(0.059)	(0.076)
${{\boldsymbol{\beta }}}_{2}$	0.0013**	−0.0015	−0.0047**
Coefficient of initial emissions ${{\boldsymbol{E}}}_{{\boldsymbol{i}}0}$	(0.0006)	(0.0012)	(0.0019)
${{\boldsymbol{\beta }}}_{3}$	0.0093**	0.0063**	0.0047
Coefficient of initial income ${{\boldsymbol{G}}}_{{\boldsymbol{i}}0}$	(0.0045)	(0.0028)	(0.0038)
EKC income per capita turning point	19	NA	NA
(1000s of US dollars)	(15)
Sample size	89	102	107
R-squared	0.33	0.30	0.29

Note. Values in parentheses are standard errors for each coefficient from the regressions and the EKC turning points. Standard error of EKC income per capita turning point are calculated using a delta method. Significance levels of the regression coefficients are indicated as: *10%, **5%, ***1%. In the regressions, the sample mean has been subtracted from each non-dummy variable. EKC turning point is reported as an income per capita value, in 1000s of US dollars.

Table 2.  Model results for the industry sector.

Variable	Sulfur dioxide	Carbon dioxide	Black carbon
${{\boldsymbol{\alpha }}}_{0}$	−0.029***	−0.084***	−0.052***
	(0.007)	(0.017)	(0.019)
${{\boldsymbol{\alpha }}}_{1}$	0.50***	0.55***	0.46***
	(0.14)	(0.12)	(0.13)
${\boldsymbol{\beta }}{{\boldsymbol{\beta }}}_{1}$	−0.17**	−0.13**	−0.070
	(0.07)	(0.06)	(0.069)
${{\boldsymbol{\beta }}}_{2}$	0.0017**	−0.0084***	−0.0038**
	(0.0007)	(0.0021)	(0.0017)
${{\boldsymbol{\beta }}}_{3}$	−0.0045	0.012***	−0.0013
	(0.0034)	(0.004)	(0.0038)
EKC turning point	50	190	NA
	(70)	(410)
Sample size	80	111	113
R-squared	0.52	0.46	0.48

Note. As in table 1.

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For these two sectors, historical trajectories vary among the global datasets, indicating that the results are inventory dependent. In the power sector, only the PKU inventory reports an EKC turnover for SO₂, no inventory reports an EKC turnover for CO₂, and only EDGAR reports an EKC turnover for BC (tables S4–S5). The industry sector features more consistency, with the PKU inventory and CEDS reporting an EKC turnover for SO₂, PKU reporting an EKC turnover for CO₂, and only EDGAR reporting an EKC turnover for BC (tables S4–S5). It should be noted that the level of significance for each of these turnovers varies among the inventories, with some results featuring unrealistically high turnover values (e.g. PKU CO₂ emissions in the industry sector). However, there was high consistency among the inventories regarding the existence of beta-convergence (see β₂ in tables S4–S5). Therefore, the magnitude of future emissions will depend greatly on the patterns of emissions growth in less wealthy, developing countries.

Various factors are driving the trends for each sector and pollutant combination. In the power sector, SO₂ trajectories are driven by increasingly strict end-of-pipe regulations originating in high-income countries (Srivastava et al 2001, Taylor et al 2003, Crippa et al 2016, Kharol et al 2017). In contrast, the industrial sector SO₂ EKC trajectory is likely driven by the shift to cleaner and more service-based economies, which normally transfers heavily polluting factories to less developed countries (Davis et al 2011, Peters et al 2011, Bagayev and Lochard, 2017, Zhao et al 2017). For CO₂, some countries in the high-income end are rich in resources that produce minimal CO₂ emissions, such as hydropower or nuclear power plants (BP 2018). These include Switzerland, Norway, Iceland, and France (the lower HOECD points in figure 1(a) for CO₂). The shift to a serviced-based economy in developed countries and the globalization of manufacturing could have also contributed to the observed turnover and convergence (Davis and Caldeira 2010, Su et al 2010, Feng et al 2013). In power plants, BC emissions are small but those that do exist are mainly a product of incomplete combustion and, as discussed previously, generally feature a linear relationship with economic growth. As such, the higher BC emission levels among middle-and-high-income-countries are likely due to their higher per capita demand for electricity.

The income-emission trajectories in the residential sector show different results for each pollutant (figure 2). The relationship is unclear for SO₂ emissions. CO₂ emissions feature an EKC turnover (β₁ in table 3) and there is an emission convergence pattern for BC (β₂ in table 3). However, the turnover income for CO₂ ($1900) is far below a majority of the income levels globally and is likely driven by strong beta-convergence. Two other emission inventories did feature EKC patterns for SO₂ in the residential sector (EDGAR and CEDS; see table S5) and CEDS did not feature an EKC turnover for CO₂ (see table S4). This indicates that the trajectory of these emissions in the residential sector is uncertain. In contrast, all inventories did not feature an EKC turnover for BC.

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Table 3.  Model results for the residential sector.

Variable	Sulfur dioxide	Carbon dioxide	Black carbon
${{\boldsymbol{\alpha }}}_{0}$	−0.0043	−0.018	−0.021*
	(0.0098)	(0.011)	(0.011)
${{\boldsymbol{\alpha }}}_{1}$	−0.083	−0.028	−0.059
	(0.14)	(0.058)	(0.059)
${{\boldsymbol{\beta }}}_{1}$	0.022	−0.093***	0.0014
	(0.090)	(0.031)	(0.030)
${{\boldsymbol{\beta }}}_{2}$	−0.00018	−0.0026**	−0.0031**
	(0.00040)	(0.0013)	(0.0013)
${{\boldsymbol{\beta }}}_{3}$	−0.0056	0.0032*	−0.0032**
	(0.0044)	(0.0016)	(0.0015)
EKC turning point	NA	1.9	NA
		(1.1)
Sample size	100	101	99
R-squared	0.28	0.29	0.23

Note. As in table 1.

Several factors contribute to these distinct trajectories. First, residential energy use has a lower income elasticity relative to other sectors (Joyeux and Ripple 2011, Fouquet 2014). In other words, residential emission intensities generally start high, and as economies grow, the relative increase in residential energy demand is mild, when compared to other sectors. Second, energy changes in the residential sector are primarily the result of primary fuel replacements, rather than end-of-pipe controls (Pachauri and Jiang 2008, Ruiz-Mercado et al 2011, Nejat et al 2015). As such, the improvement in efficiency and reduction of emissions is very sharp once cleaner fuels are adopted. Third, economies of scale impact residential emissions, where households with more members have lower emissions per capita (Ru et al 2015, Tao et al 2018). Lastly, household electrification has led to a re-categorization of an increasing fraction of residential emissions to the power sector. This electrification contributes to the EKC pattern shown for CO₂ emissions. All inventories show a negative relationship between per capita BC emissions and income. This is likely due to the widespread use of inefficient biofuel cook stoves in middle-and-low-income countries, with household cooking in upper income countries equipped with electricity or natural gas burners that produce minimal BC (BP 2018).

All three pollutants show a combination of linear income effects and emissions convergence in the transportation sector, with no EKC patterns reported (table 4). BC emissions feature reductions among the highest income countries (figure 3(a)), but a turnover was not reported in the model. Results were consistent among the inventories considered here. All inventories reported beta-convergence for all three pollutants and no EKC patterns for SO₂ or CO₂ (see tables S4–S5). Only the ECLIPSE inventory featured an EKC pattern for BC in the transportation sector.

Table 4.  Model results for the transportation sector.

Variable	Sulfur dioxide	Carbon dioxide	Black carbon
${{\boldsymbol{\alpha }}}_{0}$	0.0079	−0.099***	−0.12***
	(0.0073)	(0.016)	(0.02)
${{\boldsymbol{\alpha }}}_{1}$	0.74***	0.60***	0.27**
	(0.14)	(0.09)	(0.11)
${{\boldsymbol{\beta }}}_{1}$	0.017 (0.090)	−0.017	−0.020
		(0.052)	(0.056)
${{\boldsymbol{\beta }}}_{2}$	−0.020***	−0.0092***	−0.013***
	(0.002)	(0.0020)	(0.001)
${{\boldsymbol{\beta }}}_{3}$	0.019***	0.011****	0.0001
	(0.005)	(0.003)	(0.0032)
EKC turning point	NA	NA	NA
Sample size	63	110	116
R-squared	0.72	0.45	0.70

Note. As in table 1.

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The linear increases in emissions with income are due to a high correlation between fuel consumption and income in countries at all income levels. Downward drivers exist in many countries, such as sulfur content limits of fuels and regulations on fuel efficiencies. Yet these drivers are mild and outweighed by the global demand increase (Lakshmanan and Han 1997, Huo et al 2007, Lu et al 2009). Technological methods of reducing CO₂ emissions from the transportation sector include electrification of vehicles and use of biofuels, both of which face challenges. Since the early 1960s, developed countries have reduced BC emissions through a variety of technologies and policies, despite continuously increasing diesel consumption (Ban-Weiss et al 2008, Kirchstetter et al 2008). Some developing countries have learned from these experiences to more quickly reduce emissions (Minjares et al 2014). In general, regulations to reduce BC emissions can be achieved via three basic methods: targeting of new vehicles, fuels, and the in-use fleet (Minjares et al 2014). Most developed economies utilize standards for new vehicle emissions and fuels (International Enegy Agency 2016), while many developing countries encourage the retrofitting and replacement of high-emission older vehicles (Zhou et al 2010, Kaygusuz 2012, Ong et al 2012).

Future emission projections retrieved from three IAM reference or minimal/no climate policy simulations show widespread declines in SO₂, CO₂, and BC emissions in all sectors. Historical values of emissions in the calibration years are consistent with historical emissions from the PKU inventory, but significant deviations occur thereafter, driven by the underlying assumptions in the IAMs. Among the more dramatic examples of these differences are the trajectories of SO₂ and BC emissions from the transportation sector (figure 4). Both AIM and MESSAGE show weak increases in emissions with income growth in the historical period, followed-by sharp declines in the future. In comparison, the PKU historical values largely exhibit a slight flattening trend. If such sharp declines were to occur, a significant adoption of electric vehicles and/or extremely strict regulations on sulfur content in fuel and use of particulate filters would need to occur. For CO₂ emissions in the transportation sector, results from GCAM do not diverge significantly from the historical trajectories. The power, industry, and residential sectors show similar patterns. SO₂ and BC emissions decrease significantly in all three IAM projections through the end of the century, whereas CO₂ does not necessarily decline (e.g. in the industrial sector emissions projected by GCAM (figure S1). As noted, the scenarios considered here have modest (AIM; RCP 6.0) to non-existent climate policy (MESSAGE; RCP 8.5), and reductions are likely faster in scenarios that include substantial climate policy.

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