Spatioethnic Household Carbon Footprints in China and the Equity Implications of Climate Mitigation Policy: A Machine Learning Approach

This article relies on the first and only representative survey data to estimate household carbon footprints (CFs) of China’s large yet vastly understudied ethnic minority population, documenting for the first time significant ethnic disparities in CFs driven by ethnic minorities’ relatively worse-off living standards: From 2010 to 2020, China’s ethnic minority population contributed less than 6 percent of residential emissions, about 50 percent less than expected based on population share alone. Next, results from a counterfactual policy analysis find that the distributive effects of a carbon tax are regressive in urban areas but not in rural areas, increasing within and between ethnic group inequality in urban China. A carbon tax with revenue-neutral schemes, by contrast, helps to mitigate existing inequalities in society, reducing income- and ethnic-based forms of inequality. Results are robust to machine learning techniques employed to simulate potential heterogeneous household abatement scenarios. The findings emphasize the potential benefits of a carbon tax, contributing to a more comprehensive understanding of climate justice and informing policy decisions that promote equitable outcomes for vulnerable segments of society.

T he rapid and unprecedented increase in anthropogenic greenhouse gas emissions, and ensuing intensification of climate hazards, represents one of the most imminent threats facing the global community (Mora et al. 2018).A carbon tax policy is considered to be one of the quickest and most efficient carbon pricing instruments to help curb emissions from fossil fuels, supported empirically in developed and developing country contexts (Pradhan et al. 2017). 1 Yet, concerns about harming the poor and exacerbating existing inequalities hinder policy implementation around the world (Beiser-McGrath and Bernauer 2019;Povitkina et al. 2021;Soergel et al. 2021). 2 This highlights the important need to investigate the social equity implications of carbon pricing initiatives and better understand potential trade-offs between climate mitigation efforts and development goals.
Coinciding with the increasing recognition about the adverse effects of climate change on inequality and the urgent need for climate mitigation (Burke, Hsiang, and Miguel 2015), important debates in geography and other social sciences have emerged around the role of climate equity and climate justice (Bailey 2017;Chen 2022;Luke 2023).The distinct yet overlapping concepts refer to the fair and just distribution of the costs and benefits associated with climate mitigation efforts, including carbon tax and other carbon pricing policies.Climate equity, in particular, entails designing and implementing climate mitigation initiatives in a way that considers the specific needs of vulnerable groups in society, including ethnic minorities and indigenous populations, aiming to reduce disparities, promote social justice, and address historical injustices (Newell and Mulvaney 2013).
In the related empirical literature, a growing number of studies mainly in economics and public policy estimate the distributive effects of a carbon tax on income inequality by comparing the effective tax burden on poorer versus richer household groupings. 3 Existing studies tend to observe regressive impacts of a carbon tax in higher income countries, but the results are more mixed in lower income countries. 4 Notions of climate equity and justice are largely excluded from the empirical economics literature, however.
The potential distributive effects of carbon pricing initiatives on ethnic minorities and ethnic-based dimensions of inequality remain critical but overlooked equity dimensions.This is because ethnic minorities in large, ethnically diverse countries like China (and the United States and Brazil) tend to be overrepresented in lower ends of the income distribution and might be disproportionately affected by climate change (Akee, Jones, and Porter 2019;Howell 2020).The main concern is that a carbon tax might also disproportionately burden vulnerable ethnic minority groups in society, increasing income and ethnic-based forms of inequality due to the policy's regressive nature, capable of potentially undermining social stability. 5 China offers an interesting case study.As the world's largest carbon emitter, China must reduce its carbon emissions by 90 percent to meet the goal established by the 2015 Paris Agreement to keep global temperature rise this century to 1.5 C (Duan et al. 2021).China's residential sector is one of the leading contributors to carbon emissions in the country, accounting for two-thirds of black carbon emissions (Kanaya et al. 2021), yet no carbon tax scheme exists in the country. 6An International Monetary Fund report estimates that a carbon tax that increases annually by $5 between 2017 and 2030 could reduce CO 2 emissions by 30 percent and save nearly 4 million lives due mainly to coal use deterrence (Parry et al. 2016), although the potential equity implications have yet to be considered.
Taking the aforementioned literature into account, this article estimates the distributional effects of competing carbon tax policies in both rural and urban parts of China, and their implications for income-and ethnic-based forms of inequality.To do so, it is necessary to first estimate carbon footprints (CFs).Estimates of CF are obtained by combining an environmentally extended multiregional inputoutput (MRIO) model with household expenditure information from the China household ethnic survey (CHES).
The CHES is unique in that it offers the only available source of representative microdata from China's large yet understudied ethnic minority areas located in the country's lagging western region (Gustafsson, Hasmath, and Ding 2020).Included in the CHES is detailed socioeconomic information on more than 10,000 rural-urban households, 55 percent of which belong to an ethnic minority group (e.g., Tibetan and Uighur, among others).Sample weights are used to offset the oversampling of ethnic minorities to provide a representative sample.
The CHES data are combined with an MRIO model to estimate household CF per capita.The initial set of findings document for the first time the existence of significant ethnic-based disparities in emissions: Han emit 1.5 times more carbon on average compared to the average ethnic minority.The ethnic CF disparity reflects similar Han-minority gaps in consumption, irrespective of rural or urban location.Due to their relatively worse-off living standards, it is estimated that China's ethnic minority population (114 million) contributed less than 6 percent of the country's residential emissions during the 2010 to 2020 time period, roughly half the amount expected based on their population share alone.
Next, I estimate the distributive effects of a tax on fossil fuel products levied on coal, petroleum products, and natural gas based on the tons of CO 2 (tCO 2 ) produced per unit of fuel.It is important to note that CHES households studied in this context contribute minimally to China's overall emissions, particularly poorer households from economically lagging inland regions.The climate implications of reducing, in absolute terms, their carbon emissions are in some sense trivial given CHES households' relatively small CF to begin with.For this reason, this article focuses on investigating the potential equity implications of a carbon tax with and without redistributive measures.
The empirical results reveal that a 200 yuan/tCO 2 carbon tax without revenue recycling leads to an increase in income inequality but only in urban areas via a 4.63 percent increase in the Theil-L index.Subsequent decomposition analysis shows that the carbon tax increases urban inequality between and within ethnic groups via respective increases of 3.88 percent in the between-ethnic group component and 4.96 percent (4.85 percent) in the within-Han (within-minority) group component.In rural areas, by contrast, the carbon tax has the opposite effect, leading to decreases in income and ethnic dimensions of inequality.The contrasting ruralurban outcomes are driven by location-as well as ethnic-specific differences in the scale and pattern in the consumption of high carbon goods that turn the policy regressive in urban areas but progressive in rural areas.

Household Carbon Footprints in China and Climate Mitigation Policy
Two alternative revenue-neutral policy scenarios are also considered that devote carbon tax revenues to either fund: (1) a carbon dividend, 7 or (2) to increase the size of social welfare transfers under the Dibao program. 8With revenue recycling, both alternative scenarios turn the policy progressive in urban areas and even more so in rural areas.The carbon dividend is funded primarily by urban individuals and mainly redistributed to rural individuals, however, leading to significant decreases in rural but not urban inequality.The targeted Dibao redistribution scheme, by contrast, helps to significantly decrease ethnic (within-and between-group) inequality in both rural and urban locations.
A key assumption of the MRIO model is that households reduce emissions uniformly regardless of initial income.To relax this unrealistic assumption, machine learning techniques are relied on to predict heterogeneous behavioral changes in emissions reduction between rich and poor households.The main results remain robust even under scenarios where a relatively high degree of heterogeneous abatement behavior exists.This article's findings contribute to the literature in the following ways.The first set of findings contribute to the growing number of studies that estimate carbon emissions in China (Wiedenhofer et al. 2017;Li, Zhang, and Su 2019;Mi et al. 2020;Zheng et al. 2020).These existing studies reveal important insights into the spatial and sectoral variations, underlying drivers, and socioeconomic implications of emissions in the country.Yet, a comparison of ethnic CF disparities is nonexistent in the literature, until now. 9This is the first study to document the extent of ethnic-based CF disparities and quantify China's ethnic minority contribution to residential emissions in the country. 10 The second set of findings from this article contribute to the rapidly growing carbon tax literature (Dennig et al. 2015;Pradhan et al. 2017;Fremstad and Paul 2019;Goulder et al. 2019;Hu, Dong, and Zhou 2021;Moz-Christofoletti and Pereda 2021), providing the first evaluation of competing carbon tax schemes on ethnic inequality in China, and perhaps elsewhere.Specifically, the findings reveal the adverse equity implications of a carbon tax without redistribution but that appear to be mitigated with an appropriate policy design mechanism like revenue recycling.These findings relate to broader concerns about policy design and the potential trade-off between climate mitigation initiatives and development goals (Marron and Toder 2014;Klenert et al. 2018;Budolfson et al. 2021), underscoring the key point that a revenue-neutral carbon tax policy can be designed to help ameliorate rather than amplify existing socioeconomic inequalities within society.

Data
Implemented through multiple single-round site visits, the 2012 CHES survey is the only large-scale survey to study the socioeconomic conditions of ethnically diverse households in China.The CHES data include detailed socioeconomic and demographic information on more than 7,000 rural households and 3,000 urban households from nearly 700 villages and thirty city prefectures spread out across seven provinces and regions: Hunan, Guizhou, Guangxi, Inner Mongolia, Ningxia, Qinghai, and Xinjiang.
The survey locations are sampled across rural and urban areas with a substantial share of China's ethnic minority population based on the 2010 census, drawing from China's poor, lagging inland regions.Rural and urban locations are randomly selected from a subset of the official Rural and Urban Household Surveys collected by the National Bureau of Statistics (NBS).Within each sampled location, households are selected by random sampling based on their agricultural or nonagricultural census address codes. 11 Minority households comprise 55 percent of the sample.Information is included for the following main large ethnic minority groups: Mongolian, Hui, Tibetan, Uighur, Miao, Dong, Zhuang, and an Other category that includes twenty-seven smaller ethnic minority groups.Sample weights based on the 2010 census are used to offset the oversampling of ethnic minorities to provide a representative sample of Han-minority households.
CHES provides information on eight essential household consumption spending categories: food, clothing, residence, household facilities, transport and telecommunications, education and culture, health care, and other miscellaneous.The residence expenditure category includes spending on household electricity, heating, fuel, and water utilities.The household facilities category includes housing rent, 960 Howell maintenance, management, and mortgage.Transport expenditures include local transport, oil, and vehicle loans.

Estimating Household Carbon Footprints
To understand how different household types would be affected, microsimulations are performed on the basis of representative CHES data and MRIO data.A key advantage of this approach is that microlevel household consumption data contained in CHES can be connected to macrolevel economic models capable of tracking carbon emissions originating from domestic and global supply chains.The environmentally extended MRIO approach is relied on to estimate CF separately across rural and urban sampled regions, expressed as where CF i is the per-capita CF of household i, h is a vector of industrial carbon emission intensities, and ðI − AÞ −1 is the Leontief inverse.I is the identity matrix and A ¼ ½a sj is the technical coefficient where a sj ¼ x sj =X j is the monetary flows from sector s to sector j and X j is the total output of sector j. y k i is the per-capita household consumption for category k, differentiating between domestic (self-production and domestic inflow) and international imported goods.The CF estimated by the MRIO model is aggregated into eight major categories of consumption: food, clothing, residence, household facilities, transport, education, health care, and others.Directed energy-related emissions from direct household energy use of coal, natural gas, and electricity are allocated to the residence category, whereas oil emissions are allocated to the transport category.

General Entropy Measure of Inequality
The general entropy measure with parameter value 0, also known as the Theil-L measure, is used to decompose the inequality measure. 12The general entropy class provides the most common decomposition-based measures, which takes the following form, where f i is the population share of household i, y i is per-capita household income, l is the average percapita household income, and c is a parameter to be selected.Following the existing literature (Shorrocks 1980(Shorrocks , 1984)), this article decomposes the Theil-L measure into within-and between-components by rewriting the expression as follows, where j refers to the subgroup, g j refers to the population share of subgroup j, and GE j refers to inequality in subgroup j.The first term captures the between-group component of inequality and the second term gives the within-group component.

Data Sources and Availability
Information used to estimate CF comes from the following sources.The 2012 MRIO tables, which describe the economic linkages among thirty sectors in thirty Chinese regions, and carbon emission inventories are made available through the China Emission Accounts and Data Sets (http://www.ceads.net/; Liu et al. 2015;Mi et al. 2018).The global MRIO tables for 140 regions and fifty-seven economic sectors are constructed based on the GTAP database (Version 9).The pricing data for China's input-output (IO) tables come from the China Statistics Yearbook.The pricing data for China's imports and global MRIO tables come from the National Accounts Main Aggregates Database.The CHES was purchased from China's NBS and made available to the author by the Institute on Ethnology and Anthropology at the Institute of Ethnology and Anthropology, Chinese Academy of Social Sciences (IEA-CASS) under a data use agreement that prohibits any public sharing of the data.The CHES data are available from the author on reasonable request and permission of IEA-CASS.The code for all analyses in this study is available on request.

Unequal Han-Minority Carbon Footprint
The average per-capita CF for Han (1.95 tCO 2 ) is 1.5 times larger compared to a typical ethnic minority (1.30 tCO 2 ) (Figure 1A).The Hedges g summary statistic reveals that the average CF for Han is 0.40 standard deviations (95 percent CI [0.36,0.43])larger than the CF for the typical ethnic minority, indicating a moderately large effect size.Despite representing 8.51 percent (114 million) of the population in 2010, the CHES data imply that ethnic minorities account for only 5.67 percent of China's CF, 50 percent less than expected based on their population share.Due to their relatively higher population growth rates, a typical ethnic minority would contribute 51 percent less than expected by 2020 given CF remain unchanged but CO 2 emissions continue to increase with population.
One explanation for the observed Han-minority CF disparity could conceivably be related to location-specific rather than ethnic-specific factors-ethnic minorities tend to be overrepresented in poorer rural areas compared to Han, who tend to reside in comparatively richer urban areas.Indeed, large spatial variations are clearly visible both between regions (northwest-southwest) and locations (ruralurban; Figure 1B).The CF ranges from 0.734 tCO 2 in Guizhou to 2.91 tCO 2 in Inner Mongolia.When taking into account rural-urban locations, the largest urban CF in Inner Mongolia is 5.1 tCO 2 , roughly fifteen times larger than the lowest rural CF of 0.35 tCO 2 in Guizhou.
Yet, location-specific factors do not appear to explain the observed Han-minority CF disparity.Looking across urban (rural) locations, the CF for Han is 3.14 tCO 2 (1.20 tCO 2 ) compared to 2.66 tCO 2 (0.98 tCO 2 ) for minorities, leading to similar Han-minority gaps of 1.18 (1.21), irrespective of location.At the regional level, mapped CF become visibly smaller across most sampled locationsexcept for Mongolian-dominated areas in Inner Mongolia-after excluding Han households from spatial aggregation.
Besides the large Han-minority gap observed in Figure 1A, considerable heterogeneity is also observed across the ethnic minority groups.CFs for specific ethnic minorities range from 0.816 tCO 2 for Miao to 2.89 tCO 2 for Mongolian.Except for Mongolians in Inner Mongolia, Han tend to exhibit the largest CF within each sampled region, however, with the largest ethnic gap for both rural and urban households emerging between Han and Uighur in Xinjiang (Supplemental Material,Figure S.1).
Turning to the CF sources, residence tends to be the highest consumption-based emissions category, followed by food and transportation.The residence category includes relatively high energy-consuming indirect sectoral emissions and direct household emissions, such as electricity and fossil fuels used for day-to-day purposes like cooking and heating.In northwest China, the residence category tends to constitute more than 50 percent of total emissions due to the expensive and high energy demand during the cold winter months.
Although this analysis provides new and important insights on spatio-ethnic disparities in CF, it is important to note that the CHES data set does not offer detailed breakdowns within household consumption categories.This limitation prevents further exploration into the underlying location-specific sources (e.g., cooking, heating, fuel, electricity use) that contribute to the observed CF disparity between Han and ethnic minority households.Future research could benefit from more detailed information on household energy use to provide a more nuanced understanding of these disparities.

Ethnic Distribution of CF by Decile
When individuals are sorted by per-capita household expenditures, the CF in rural (urban) areas ranges from 0.12 tCO 2 (0.96 tCO 2 ) for minorities in the bottom decile to 2.41 tCO 2 (5.51 tCO 2 ) for Han in the top decile (Figure 2A; Supplemental Material, Table S.2).Rural Han (minorities) in the top decile emit 12.7 (16.5) times more carbon emissions than their respective counterparts in the bottom decile.
Urban Han (minorities) in the top decile, by contrast, emit 3.90 (5.25) times more carbon emissions compared to their respective counterparts in the bottom decile.Comparing the ethnic gap within income groupings, rural (urban) Han in the bottom decile emit 1.58 (1.34) times more than their respective minority counterparts in the bottom decile.Moving along the income groupings, the ethnic gap decreases slightly down to 1.22 (1.10) in the top decile.962 Howell One explanation for the relatively larger ethnicbased gap between the poor and rich in rural areas is expected to arise in part due to variations in the consumption sources that contribute to the CFs.Existing research finds that 18 percent (23 percent) of rural Han (minorities) rely primarily on biomass for cooking and heating (Howell 2023).These differences in the use of modern energy sources in rural areas would result in the poor rural minorities spending relatively less as a share of total expenditures on electricity and other energy sources captured in the residence category, relative to their richer minority or poor Han counterparts.
This explanation is supported by comparing the share of consumption-based contributions to CF across and within deciles (Figure 2B).The residence category constitutes a smaller share of the rural CF in the bottom decile, especially for minorities (14 percent), compared to richer minorities in the top decile (33 percent) or poor Han counterparts (27 percent).In urban areas, by contrast, an opposite pattern emerges: The residence category constitutes a larger share of the CF in the bottom decile, especially for minorities (55 percent), compared to roughly 30 percent for minorities and Han in the top decile.
The observed variation in the CF and the underlying consumption-based sources reflect similar variations in the patterns and scale of consumption (Figure 3, Supplemental Material, Table S.3).Percapita expenditures in rural (urban) areas range from 1,047 yuan (2,453 yuan) for minorities in the bottom decile to 7,278 yuan (20,534 yuan) for Han in the top decile.The gap in expenditures between the top and bottom decile is 4.74 (5.74) for Han (minorities) in rural areas, a gap that increases to 5.65 (6.75) in urban areas.Rural (urban) Han in the bottom decile exhibit 1.47 (1.48) times higher expenditures compared to their respective minority counterparts in the bottom decile, a gap that decreases down to 1.21 (1.24) in the top decile.

Distributive Effects of a Carbon Tax Model Setup
Household CFs are examined to study the distributional impact of implementing a hypothetical carbon tax.The amount of the carbon tax is set to 200 yuan/tCO 2 , approximating the lower bound amount ($40/tCO 2 ) necessary to achieve the targets of the Paris Agreement.Existing findings based on general equilibrium modeling estimate that a 200 yuan/tCO 2 tax would decrease total emissions by 11.96 percent in the short run (Lu, Tong, and Liu 2010).
Based on the CHES data, Han-minority household consumption generated 2.16 gigatons of CO 2 in 2011.If average per-capita CF remains unchanged but CO 2 emissions continue to increase with the population, Han-minority household consumption generated 2.28 gigatons of CO 2 in 2020.Relying on this 2020 projection as a starting point, a carbon tax of 200 yuan/tCO 2 reduces total emissions to 2.01 gigatons and imposes 201 billion yuan in taxes after deducting an estimated 13.5 billion yuan in abatement costs under a linear marginal abatement cost curve.
Potential concerns might arise from the decision to somewhat arbitrarily set carbon emissions based on the projected 2020 levels and the carbon tax at 200 yuan/tCO 2 .To address this, additional sensitivity tests are employed to evaluate the carbon tax implications under alternative tax amounts set at 100 yuan/tCO 2 and 300 yuan/tCO 2 .It is important to note that modifying the tax amount has a similar impact to changing the carbon emissions base.Reducing (increasing) the carbon tax amount affects the incentive structures for emissions and operates on the results in the same direction as reducing (increasing) carbon emissions. 13 It is also worth mentioning several limitations of IO models.First, the effect of carbon tax schemes on wages and interest rates is ignored and it is assumed that consumers bear the full cost of the carbon tax.Second, the analysis focuses on the immediate impacts of carbon tax schemes rather than effects over the individuals' lifetimes.
Third, the IO model does not predict the extent to which households respond to the price increase of carbon-intensive goods.Rather, the model assumes uniform emissions reduction among individuals across the income distribution.To relax this assumption, machine learning techniques are relied on as a robustness check to simulate potential heterogeneous behavioral responses across poor and rich income groups.
In the two considered revenue-neutral carbon tax scenarios, I quantify the magnitude of carbon dividends or increase in Dibao cash transfers that could The benefit of the carbon dividend or increasing targeted Dibao subsidies is the respective payout minus the per-capita incidence charge associated with the initial carbon tax prior to redistribution.Prior to the redistribution of revenues, the initial tax incidence is progressive in rural areas: The average Han (minority) in the lowest decile pays 2.46 percent (1.87 percent) of expenditures compared to 5.90 percent (5.69 percent) for the highest decile (Figure 4; Supplemental Material, Table S.1).In urban areas, by contrast, the initial tax incidence is regressive: The average Han (minority) in the lowest decile pays 6.01 percent (6.80 percent) of   ) of competing carbon tax policies by decile and ethnic status.CIs obtained from bootstrapped standard errors with 1,000 repititions.A positive value indicates a contributor to the carbon tax fund: the per-capita payment amount (yuan, as percentage of expenditure) that must be paid by the average person within a particular decile due to the carbon tax.A negative value indicates a net beneficiary of the carbon tax fund due to alternative revenue recycling schemes: the per-capita payment amount (yuan, as percentage of expenditure) received by the average person within a particular decile.Corresponding results are reported in table format in Supplementary Material, Table S.1, along with payment amounts.Note: MLSA ¼ Minimum Living Security Allowance.
expenditures compared to 4.84 percent (5.35 percent) in the top decile.Within the bottom decile, the typical ethnic minority in rural (urban) areas faces a 31.6 percent lower (13.1 percent higher) tax incidence compared to a poor Han counterpart.
Variations in the consumption-based sources of CF help to explain the underlying factors that drive the contrasting rural-urban outcomes (recall earlier results).The relatively high-carbon-consumption residence category, for instance, constitutes a larger share of CF for the poor versus the rich: 41 percent (57 percent) for a typical Han (minority) in the bottom decile compared to around 34 percent (34 percent) in the top decile (Supplemental Material, Figure S.2, Table S.2).In rural areas, by contrast, the residence category constitutes a smaller share of CF for the poor versus the rich: 27 percent (14 percent) for a typical Han (minority) in the bottom decile compared to 46 percent (33 percent) in the top decile.The regressive (progressive) incidence in urban (rural) areas arises because the mix of products consumed by the poor is more (less) carbon intensive than what is consumed by the rich.

Carbon Tax after Redistribution
With revenue recycling, a carbon dividend that redistributes tax revenues via an equal lump-sum payment leads to (1) a 17 percent (26 percent) income gain for a typical Han (minority) in the bottom decile of rural areas compared to a 1.62 percent (0.74 percent) loss in the top decile; and (2) a 2.16 percent (5.46 percent) income gain for a typical Han (minority) in the bottom decile of urban areas compared to a 3.22 percent (3.48 percent) loss in the top decile.In the targeted Dibao redistribution scheme, by contrast, increasing Dibao transfers to existing program beneficiaries with carbon tax revenues generates income gains for the typical Han (minority) in the bottom decile of 26 percent (45 percent) in urban areas and of 9 percent (31 percent) in rural areas.In the top income deciles, Han (minority) are ineligible to receive Dibao transfers, contributing the same amount as they would in the initial carbon tax scheme without redistribution.
The results reveal that the carbon dividend scenario effectively redistributes resources from higher income people to lower income people, but with a strong rural bias.The main reason for this spatial bias relates to the existing rural-urban income gap, resulting in the carbon dividend being funded primarily by richer urban individuals.Because the carbon dividend is designed as an equal lump-sum payment for all rural and urban individuals, the cross-regional transfer of assistance is redistributed in a way that mainly benefits rural individuals up to around the eighth income decile.
Targeted Dibao redistribution, by contrast, leads to significant welfare improvements for the poor in both rural and urban areas, especially among ethnic minorities.Because the Dibao program is administered at the county level, local governments set local income thresholds separately for rural and urban areas to better target the poor relative to local living conditions.This decentralized decision-making mechanism helps to ensure that both the rural and urban poor benefit from carbon tax revenue redistribution via larger Dibao transfers.By design of the means-tested program, ethnic minorities are initially targeted by Dibao to a greater extent, both in terms of coverage and transfer amount, explaining their significantly higher observed income gains from redistribution.

Implications of a Carbon Tax on Inequality Expectations and Measuring Inequality
The prior set of results suggest that the competing carbon tax scenarios could have important implications on income and ethnic-based forms of inequality.In urban (rural) areas, poorer minorities tend to face a higher (lower) tax incidence relative to their Han counterparts under the initial carbon tax scenario, indicating an increase (reduction) in the Han-minority income gap.Under the revenue-neutral carbon tax schemes, by contrast, ethnic minorities tend to enjoy relatively higher income gains observed throughout most of the income distribution, indicating a reduction in the Han-minority income gap.
The popular general entropy measure, Theil-L and its decomposition, is relied on to better quantify the implications of the considered carbon tax schemes on income and ethnic-based forms of inequality.In the baseline no carbon tax scenario, the Theil-L index for household per-capita expenditures is 0.33 (0.302) in rural (urban) areas (Supplemental Material,Table S.4).The between-ethnic-group 968 Howell component in rural (urban) areas is 0.128 (0.103), contributing 39 percent (34 percent) to overall inequality.The within-Han-group component is 0.089 (0.121) in rural (urban) areas and 0.113 (0.082) for ethnic minorities.
To study the implications of the carbon tax on inequality, the income losses or gains implied by the carbon tax are added to expenditures.In the initial carbon tax scenario, the tax payment is added to individual expenditures reflecting the amount of income that would be required for the individual to maintain the same level of consumption as in the observed no carbon tax scenarios.Similarly for individual contributors under the revenue-neutral carbon tax scenarios, the net carbon tax payment is added to expenditures.For individual beneficiaries, the net transfer amount is added to expenditures reflecting the welfare improvements induced by redistributing carbon tax revenues back to individuals.

Carbon Tax Prior to Redistribution
The introduction of a carbon tax without redistribution leads to an increase in income inequality in urban (but not rural) areas (Figure 5; Supplemental Material, Table S.4).In urban areas, the Theil-L index on income increases from 0.302 (95 percent CI [0.275, 0.33]) in the baseline no carbon tax scenario to 0.338 (95 percent CI [0.307, 0.368]) under the carbon tax scheme, an increase of 4.6 percent.The nonoverlapping 95 percent confidence intervals-calculated based on bootstrapped standard errors with 1,000 repetitions-imply that the increase in the Theil-L index induced by the carbon tax is statistically significant at the conventional 0.05 level.In rural areas, by contrast, the initial carbon tax decreases rural income inequality via a statistically significant reduction of 7.5 percent in the relative Theil-L index.
Subsequent decomposition analysis shows that the carbon tax prior to redistribution increases urban inequality within and between ethnic groups, but results in the opposite outcome in rural areas.The regressive policy in urban areas leads to a 3.88 percent increase in the between-ethnic-group component and a 5.00 percent (4.90 percent) increase in the within-Han (within-minority) group component.Whereas the progressive policy in rural areas leads to an 8.0 percent reduction in the between-ethnic-group component and a 6.7 percent (7.4 percent) reduction in the within-Han (within-minority) group component.

Carbon Tax after Redistribution
In the carbon dividend scenario, redistribution decreases rural income inequality relative to baseline inequality via a statistically significant reduction of 15.8 percent in the Theil-L index.Decomposition analysis further shows that the carbon dividend significantly decreases ethnic inequality via reducing the between-ethnic-groups, within-Han-group, and within-minority-group components, respectively, by 16.5 percent, 15.2 percent, and 15.5 percent.In urban areas, redistribution leads to some reduction in income and ethnic-based measures of inequality, although the size of the effects is quite trivial in both an economic and statistical sense.
In the targeted Dibao scenario, by contrast, redistribution significantly reduces income inequality in both rural and urban areas.Relative to baseline inequality, the Theil-L index in rural (urban) areas is reduced by 18 percent (12 percent).Decomposition analysis further shows that targeted Dibao redistribution decreases ethnic inequality in rural (urban) areas, reducing the between-ethnicgroup component by 19.6 percent (15.5 percent), the within-Han group component by 17.4 percent (10.0 percent), and the within-minority group component by 17.0 percent (10.3 percent).
A carbon tax with revenue recycling creates social equity benefits via reducing between-and within-ethnic inequality, although the size of the benefits depends critically on policy design and location.In the carbon dividend scenario, social equity benefits are limited mainly to rural areas because the cross-regional transfer of assistance is redistributed in a way that primarily benefits rural individuals.In the targeted Dibao redistribution scenario, by contrast, the decentralized eligibility setting mechanism and means-testing component of the program ensures that increasing Dibao transfers via redistributing carbon tax revenues benefits the poor in both rural and urban areas, especially ethnic minorities, creating large social equity benefits irrespective of rural or urban location.

Sensitivity Test: Alternative Carbon Tax Pricing
Alternative carbon tax pricing scenarios of 100 yuan=tCO 2 and 300 yuan=tCO 2 are considered.The pattern of results remains similar irrespective of the carbon tax pricing.The progressive (regressive) tax incidence in rural (urban) areas is preserved (Supplemental Material, Figure S.2).In general, Household Carbon Footprints in China and Climate Mitigation Policy redistributing a relatively smaller amount of carbon funds based on a 100 yuan=tCO 2 carbon tax leads to less meaningful reductions in the considered inequality dimensions in terms of economic and statistical significance, however.The change in income inequality as measured by the Theil-L index, for instance, fails to be statistically significant in the initial carbon tax without recycling (Supplemental Material, Figure S.3).A higher tax of 300 yuan=tCO 2 , however, generates a larger carbon fund that after redistribution leads to larger reductions in income and ethnic inequality. ) for Theil-L, and its decomposition into within-and between-group components, under competing carbon tax scenarios.CIs obtained from bootstrapped standard errors with 1,000 repetitions.Corresponding results are reported in table format in Supplemental Material, Table S.4).(B) Change (%) in index values induced by competing carbon tax policies relative to the baseline no tax scenario.970 Howell

Potential Heterogeneous Abatement Response: A Machine Learning Approach
Original IO Model Limitation The initial IO model does not take into account potential heterogeneous behavioral changes across the income distribution in response to price increases due to the carbon tax.Rather, the model assumes that households uniformly reduce emissions by 11.96 percent in response to a tax of 200 yuan/ tCO 2 based on published estimates from the literature.This assumption might not be reasonable, however.Higher income households tend to contribute the largest part of emissions reduction (Moz-Christofoletti and Pereda 2021).

Machine Learning for Heterogeneous Treatment Effects
To test the sensitivity of the results, I assume that the economy still reduces emissions by 11.96 percent on average, but allow for abatement to be heterogeneous across the income distribution.A linear regression model could be set up to estimate heterogeneous treatment effects (HTEs) on abatement by regressing the initial carbon tax payment amount on interaction terms between treatment and covariates of interest such as income grouping and location, controlling for income, location, ethnicity, and other demographic controls.In this case, treatment is a simulated variable ranging from 0 to 1 with the mean set to equal 0.1196, representing the average treatment effect of the carbon tax on abatement.
As an alternative, machine learning techniques help to avoid overfitting and allow more flexible functional forms between variables compared to a linear regression model.Existing studies use machine learning to estimate the effects of an ex-post carbon tax and predict heterogeneous abatement in response to price increases (Abrell, Kosch, and Rausch 2022).To this end, I employ generalized random forest to estimate HTEs (Athey, Tibshirani, and Wager 2019), and obtain predicted values of abatement for a typical person across the income distribution.To impose some desired structure of heterogeneity, I multiply the predicted HTEs obtained for individuals in the bottom decile by g to obtain abatement for individuals in the top decile.
When g is set to 1.5, for instance, lower income deciles abate less than higher income deciles, with the richest decile abating at a rate that is 1.5 times more than the poorest decile.For each value of g, I run simulations to obtain 1,000 abatement scenarios predicted by machine learning.For each scenario, I calculate the implied carbon tax payment after taking into account heterogeneous abatement across income groups, add that payment to the original per-capita expenditures, and finally calculate the counterfactual Theil-L index.To consider all possible scenarios, a similar procedure is followed to allow individuals in lower income deciles to abate more than individuals in higher income deciles.

Results
To refute the original results based on a uniform emissions reduction assumption, the carbon tax with heterogeneous abatement would need to increase (decrease) baseline inequality in rural (urban) areas.The results from machine learning confirm this expectation, showing that the rich need to curb emissions to a greater (lesser) extent than the poor in rural (urban) areas to refute the main results.As g increases (decreases) in rural (urban) areas, an increasing share of the simulated Theil-L indexes obtained under the heterogeneous abatement scenarios (denoted as Theil-L g ) is larger (smaller) than the observed Theil-L in the baseline no carbon tax scenario (Figure 6A).
In rural areas, the first instance of a sign flip on the relative Theil-L g index is detected when g equals 4 (Figure 6B), although the change does not become statistically significant until g equals 6.The results imply that the original results based on uniform abatement are refuted starting at the point when the richest decile abates at six times the rate of the poorest decile (see Supplemental Material, Figure S.4), leading the carbon tax under heterogeneous abatement to increase rather than decrease rural inequality.In urban areas, the results based on uniform abatement are refuted starting at the point when the poorest decile abates at five times the rate of the richest decile, in which case the carbon tax under heterogeneous abatement would decrease rather than increase urban inequality.
The sensitivity analysis helps to quantify uncertainty by simulating the extent to which the rich must vary their emissions reductions relative to the Household Carbon Footprints in China and Climate Mitigation Policy  Howell poor before the original results based on uniform abatement are upended.The results based on machine learning indicate that even a reasonable amount of heterogeneity in abatement between the rich and poor fails to overturn the main findings observed under a uniform emissions reduction assumption.Due to the nature of redistribution under the alternative revenue-neutral tax schemes, the rich (poor) would have to abate to an even larger extent relative to their poor (rich) counterparts in rural (urban) areas to overturn their respective findings.

Conclusion Summary of Findings
A MRIO model with microlevel household expenditure data is first relied on to estimate and analyze Han-minority CFs.The first set of results reveals for the first time significant Han-minority CF disparities and quantifies the contribution of China's 114 million ethnic minority population to the country's residential emissions.Due to their relatively worse-off living standards, Han emit 1.5 times more carbon on average relative to a typical ethnic minority.Between 2010 and 2020, the CHES data imply that ethnic minorities emit 50 percent to 51 percent less than expected based on their population share alone.
The counterfactual tax policy results reveal that a carbon tax without revenue recycling is regressive in urban areas, increasing both income and ethnic dimensions of urban inequality.The same carbon tax has the opposite outcomes in rural areas.The contrasting rural-urban outcomes likely arise due to location-and ethnic-specific variations in the consumption share of high-carbon goods.
The carbon dividend and targeted Dibao redistribution schemes both redistribute resources from higher income people to lower income people.Redistributing carbon tax revenues in a way that targets the poor by increasing social welfare transfers under the Dibao program leads to significantly less inequality in rural-urban locations than what would otherwise be observed in the absence of a carbon tax.The targeted Dibao redistribution scheme also leads to significant reductions in within-and between-ethnic-group inequality.This is because Dibao targets ethnic minorities to a greater extent than Han due to their worse-off standards of living.

Policy Implications
The findings reported here help to advance policy dialogue on climate mitigation by placing a particular emphasis on the intertwined nature of carbon reduction efforts and income-and ethnic-based dimensions of inequality.At its core, this study underscores a fundamental concern often viewed as an equity-efficiency trade-off: Although carbon mitigation policies are pivotal in the fight against climate change, they can inadvertently place a disproportionate burden on society's most vulnerable and often marginalized groups.
Whereas the broader discourse has often centered on absolute emission reductions, this research takes a different vantage point, emphasizing both efficiency and equity dimensions simultaneously.Specifically, focus is placed on understanding to what extent a carbon tax with and without appropriate safeguards affects poorer and more vulnerable groups in society.Through a detailed examination of Han-minority CF disparities and the subsequent implications of carbon taxation, this article offers insights into crafting policies that are both effective in reducing emissions and equitable in their impact.
The findings make a compelling case for the value of revenue-neutral policies that redistribute carbon taxes.Such approaches, rooted in principles of climate justice and equity, can be tailored to be progressive, ultimately helping to bridge income and ethnic-based inequalities.This not only enhances the comprehensiveness of our understanding of climate justice but also provides a roadmap for policymakers.It underscores the necessity of devising strategies that do not just combat climate change in isolation but do so while safeguarding the well-being of the marginalized and vulnerable.

Figure 1 .
Figure 1.Ethnic and spatial distribution of per-capita footprint.This figure displays the ethnic and spatial distribution of per-capita carbon footprints (CFs) across seven sampled China household ethnic survey locations: Inner Mongolia (IM), Xinjiang (XJ), Ningxia (NX), Qinghai (QH), Guangxi (GX), Hunan (HN), and Guizhou (GZ).(A) Distribution of household CF by Han-minority status and an overlaid violin plot for rural and urban (¼ All) locations as well as separately for rural and urban subsamples.The reported Hedges g summary statistic quantifies effect size, indicating how much Han differs on average from minority households.(B) Spatial distribution of average per-capita CF taking into account variations across regions, locations, and ethnic groupings and by consumption category source.

Figure 2 .
Figure 2. Consumption.(A) Rural versus urban per-capita carbon footprint (CF) by income decile and Han-minority status.(B) Corresponding share contribution by each consumption-based source category.Corresponding results are reported intable format in Supplemental Material, Table S.2.

Figure 3 .
Figure 3. Consumption.(A) Average per-capita consumption expenditures and (B) share by category by Han-minority status for each income decile based on equivalent household expenditures.Corresponding results are reported intable format in Supplemental Material, Table S.3.Note: CF ¼ carbon footprint.

Figure 4 .
Figure 4. Carbon tax incidence: Mean cost-benefit payment amount (along with 95 percent confidence intervals [CIs]) of competing carbon tax policies by decile and ethnic status.CIs obtained from bootstrapped standard errors with 1,000 repititions.A positive value indicates a contributor to the carbon tax fund: the per-capita payment amount (yuan, as percentage of expenditure) that must be paid by the average person within a particular decile due to the carbon tax.A negative value indicates a net beneficiary of the carbon tax fund due to alternative revenue recycling schemes: the per-capita payment amount (yuan, as percentage of expenditure) received by the average person within a particular decile.Corresponding results are reported in table format in Supplementary Material, TableS.1, along with payment amounts.Note: MLSA ¼ Minimum Living Security Allowance.

Figure 5 .
Figure 5. Change in inequality due to carbon tax.(A) Index values (along with 95 percent confidence intervals [CIs]) for Theil-L, and its decomposition into within-and between-group components, under competing carbon tax scenarios.CIs obtained from bootstrapped standard errors with 1,000 repetitions.Corresponding results are reported in table format in Supplemental Material, TableS.4).(B) Change (%) in index values induced by competing carbon tax policies relative to the baseline no tax scenario.

Figure 6 .
Figure 6.Heterogeneous behavioral response in abatement.Results based on machine learning techniques used to predict and simulate potential heterogeneous behavioral response in abatement induced by the initial carbon tax prior to redistribution.The simulation permits higher income deciles to abate more or less than lower income deciles with the richest decile abating at g 2 ð1=6, 1=5, :::, 5, 6Þ times the rate as the poorest decile.(A) Distribution of Theil-L g on the x-axis across heterogeneous abatement scenarios, g, plotted on the y-axis, color-coded with the percentage change in Theil-L g relative to the Theil-L observed in the baseline no carbon tax scenario.(B) The (blue) line represents the cross-model average change in Theil-L g with heterogeneity abatement induced by the initial carbon tax relative to the Theil-L observed in the baseline no carbon tax scenario.The rhombus symbol is the corresponding cross-model mean p value obtained from 95 percent confidence intervals.A density plot is overlaid showing the distribution of Theil-L g across the heterogeneous abatement scenarios.The shaded area in red corresponds to the value of g where the cross-model mean p value obtained for the percentage change in the Theil-L g relative to the baseline Theil-L is statistically different from the inequality results obtained under uniform abatement. 972 table format in Supplemental Material, Table S.2.
Household Carbon Footprints in China and Climate Mitigation Policy 965Carbon Tax Prior to Redistribution table format in Supplemental Material, Table S.3.Note: CF ¼ carbon footprint.