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

Simplified assumptions regarding the relationship between per capita income and emissions are oftentimes utilized to generate future emission scenarios in integrated assessment models (IAMs). One such relationship is an environmental Kuznets curve (EKC), where emissions first increase, then decline with income growth. However, current knowledge about this relationship lacks the specificity needed for each sector and pollutant pairing, which is important for future emission scenarios. To fill this knowledge gap, we analyze the historical relationship between per capita income and emissions of SO2, CO2, and black carbon (BC) utilizing widely-used global, country-level emission inventories for the following four sectors: power, industry, residential, and transportation. Based on a modeling setup using long-term growth rates, emissions of SO2 from the power and industrial sectors, as well as CO2 from the industrial and the residential sectors, largely follow an EKC pattern. Income-emission trajectories for SO2 and CO2 from other sectors, and those for BC from all sectors, do not show an EKC, however. Results across different global inventories were variable, indicating that uncertainties within historical emission trajectories persist. Nonetheless, these results demonstrate that long-term income-emission trajectories of air pollutants are both sector and pollutant specific. Future reference trajectories of SO2 and BC from three IAMs show earlier estimates of turnover incomes and faster rates of emission declines when compared to historical data. Users of future emission scenarios derived using EKC assumptions should consider the underlying uncertainties in such projections in light of this historical analysis.


Introduction
Society faces steep challenges regarding climate change and atmospheric pollution with several pollutants contributing to both issues. Sulfur dioxide (SO 2 ) is an air pollutant that oxidizes in the atmosphere to form climate-influencing aerosols; CO 2 is a greenhouse gas and has contributed most to modern climate change; and black carbon (BC) is an aerosol with global impacts on climate and human health. While a large portion of the atmospheric release of these pollutants is related to fuel combustion, there is wide variability in the sectoral processes that drive the emissions of each pollutant. For example, CO 2 emissions are closely related to the energy content of fuels, SO 2 is dependent on the sulfur content of fuels, and BC is mainly generated through incomplete combustion processes. Given the different sources, processes, and economic drivers at work, each pollutant develops distinct emission trajectories. Understanding the long-term income-emission relationship is one useful way to study the trend of emissions associated with social and economic development (Heil and Selden 2001, Aldy 2006, Chakravartya et al 2009, Nordhaus 2010, Stern and van Dijk 2017. The spatial scale of emission impacts traditionally determines the incentives and barriers to emission reductions. Local pollutants, such as SO 2 , carbon monoxide (CO), nitrogen oxides (NO x ), and particulate matter (PM) are conventionally thought to have more environmental Kuznets curve (EKC)-like patterns, where emissions first increase then decline with income growth (Holtz-Eakin and Selden 1995). Indeed, economists have used EKCs to empirically study SO 2 , CO, NO x , and PM trajectories since the early 1990s (Grossman andKrueger 1991, Selden andSong 1994). SO 2 is the most well studied, with a common view that an EKC pattern exists at the country and state or provincial level in many parts of the world (Carson 2009). However, a consensus has not been reached on the turnover income level for peak emissions, with estimations ranging from $3000 to $20 000 USD (Selden and Song 1994, Stern et al 1996, Roca et al 2001, Stern and Common 2001, Millimet et al 2003, Stern 2004, Perkins and Neumayer 2008. Studies have started to consider the income-emission relationship of CO 2 , but conclusions on the existence of an EKC pattern are divided (Lantz and Feng 2006). No studies to date have analyzed whether historical BC trajectories feature EKC patterns, even though it is an important factor in public health and climate scenarios. Despite differences in pollutant-by-pollutant trajectories, two findings are common. First, the rate of emissions are largely driven by income and energy consumption, but can be reduced by technological and structural changes. Second, low-income countries often have higher rates of growth in emissions than middle-and high-income countries.
With the prevalence of future scenarios that integrate socioeconomic developments and emission trajectories (e.g. the shared socioeconomic pathways (SSPs) (O'Neill et al 2014, Riahi et al 2017 increasing, there is a need for a comprehensive examination of the sector-specific long-term income-emission relationships (i.e. EKC patterns) for different pollutants. Without an empirically determined existence of such relationships, the reliability of widespread EKC-like patterns in future long-term emission trajectories may be undermined. This paper analyzes the relationship between per capita income and emissions of SO 2 , CO 2 , and BC for the power, industry, residential, and transportation sectors. This is in contrast to most previous studies, which exclusively focus on economy-wide results, and allows us to systematically examine how sectoral emissions have evolved with socioeconomic trends.

Emission inventories
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, 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 SO 2 , 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 andvan 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 CO 2 . In addition, data limitations required use of slightly different time ranges for each of the inventories (1980-2014in CEDS and PKU, 1990-2010in ECLIPSE, and 1980-2010. As long-term trajectories and their growth rates were used in this analysis, the influence of these differences should be quite limited. Econometric modeling using long-term growth rates We adopt a recently developed methodology using long-term growth rates to model the income-emission relationship . 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: = + + + + + + dummy control variables held at the default values and all continuous variables at the mean levels. a 1 is an estimate of the emission-income elasticity. b 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 where m G is the mean of the initial natural log of GDP per capita across all countries. b 2 and b 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 .
We report results on the coefficients of the noncontrol variables (i.e. a , 0 a b b b , , , 3 ) in tables within the text and coefficients of control-variables in the SI. As a guide to the reader: a 1 describes the linear relationship between emissions and income (when an EKC is not found); a negative b 1 indicates the existence of an EKC pattern; a negative b 2 indicates emissions convergence across countries; and a negative b 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 . 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  (table S3). Continuous variables are standardized by subtracting the sample mean and countries with incomplete data are omitted.
Linking to integrated assessment model (IAM) projections 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.

Results
Trajectories in the power and industry sectors SO 2 emissions exhibit a long-term EKC pattern in both the power and industry sectors (see b 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 CO 2 , visualization of the emission trajectories suggests that a slowing-down of CO 2 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 CO 2 in the industrial sector, the turnover income is very high ($190 000 USD per capita) and is not significant. There is significant beta-convergence (β 2 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 β 2 and a 1 values in tables 1-2).
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 SO 2 , no inventory reports an EKC turnover for CO 2 , 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 SO 2 , PKU reporting an EKC turnover for CO 2 , 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 CO 2 emissions in the industry sector). However, there was high consistency among the inventories regarding the existence of beta-convergence (see β 2 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, SO 2 trajectories are driven by increasingly strict endof-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 SO 2 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, Bagayev and Lochard, 2017, Zhao et al 2017. For CO 2 , some countries in the high-income end are rich in resources that produce minimal CO 2 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 CO 2 ). 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.

Trajectories in the residential sector
The income-emission trajectories in the residential sector show different results for each pollutant (figure 2). The relationship is unclear for SO 2 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.   1980-1989, 1990-1999, 2000-2009, and 2010-2014 (i.e. four observations for each country). Colors indicate the five income groups: HOECD: high-income OECD countries; HIC: high-income non-OECD countries; UMC: upper middle-income countries; LMC: lower-middle income countries; LIC: low-income countries. Size of circles represent the relative size of average total emissions (not on per capita basis) over each specific period for the specific country.
feature an EKC turnover for CO 2 (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. Several factors contribute to these distinct trajectories. First, residential energy use has a lower income elasticity relative to other sectors (Joyeux andRipple 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 CO 2 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-lowincome countries, with household cooking in upper income countries equipped with electricity or natural gas burners that produce minimal BC (BP 2018).

Trajectories in the transportation sector
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 SO 2 or CO 2 (see tables S4-S5). Only the ECLIPSE inventory featured an EKC pattern for BC in the transportation sector. 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    SO 2 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 CO 2 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. SO 2 and BC emissions decrease significantly in all three IAM projections through the end of the century, whereas CO 2 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 nonexistent climate policy (MESSAGE; RCP 8.5), and reductions are likely faster in scenarios that include substantial climate policy.

Conclusion
Empirically derived trajectories of long-term incomeemission relationships have been extensively studied and, to date, generated ambiguous conclusions. One reason may be that most results are at economy-wide scales, lacking sectoral analyses. We analyzed the historical, sectoral income-emission trajectories of SO 2 , CO 2 , and BC using data from four widely used global emission inventory and a statistical model that assesses the relationship between long-term emissions and income rates of change. Our results show that income-emission trajectories for various sector and pollutant combinations differ substantially. SO 2 emissions in the power and industry sectors exhibit EKC patterns, with turnover incomes of $19 000 and $50 000 USD, respectively. CO 2 emissions featured an EKC pattern in the industrial and residential sectors. However, the turnover income calculated in the residential sector is far below a majority of the income levels globally and is likely driven by strong emissionsconvergence. Emissions from the transportation sector show linear increases with income without any signs of turnover for SO 2 and CO 2 . For BC, we find that emissions do not exhibit an EKC pattern in any sector. Rather, BC emissions from the residential sector, which contributes the most to economy-wide BC emissions, shows a negative relationship between per capita BC emissions and income. Results were sensitive to the global inventory used, due to uncertainties in historical emissions. However, there was consistency for several sectoral and pollutant pairings. A majority of the inventories considered here did not report an EKC turnover for SO 2 in the power and transportation sectors, neither of the two inventories used to analyze CO 2 reported an EKC turnover for CO 2 in the power or transportation sectors, and a majority of the inventories considered here did not report an EKC turnover for BC in any sector. Rather, emissions-convergence, where less wealthy countries tend to have faster growth rates in emissions and highincome countries tend to have slower growth rates, was found in most sectoral and pollutant pairings.
We also compared the income-emission trajectories from the PKU historical emission inventory with projected trajectories from three IAMs. The comparison revealed several differences, especially in the transportation sector. IAMs tend to project a massive decline in emissions from the transportation sector paired with economic growth, whereas historical emissions suggest a more linear positive correlation between emissions and income. The trajectories presented by these widely used scenarios are thus optimistic when compared to historical patterns, even though they are largely baseline scenarios without explicit climate policy (i.e. they appear to assume that very successful air quality policies, or perhaps fuel switching, always accompany income increases).
The results presented here demonstrate that the historical income-emission relationships for many pollutants vary by sector over time and a broad EKC relationship is largely absent from historical data. It thus appears important to carefully consider the sector and pollutant-specific mechanisms at work when generating emission projections based on socioeconomic development.