IntroductionHuman health impacts from ambient fine particulate matter air pollution (PM2.5) are large enough that the corresponding economic externalities often represent a substantial fraction of national gross domestic product (GDP)1,2. Poor air quality can present a challenge to political stability3, in part because air pollution burdens are often not equitably distributed among the populace4,5,6 and policies that promote inequality are often unsustainable7,8,9. Therefore, understanding the extent and causes of exposure to PM2.5 is important for effective political-economic management.International trade has been shown to substantially impact PM2.5 pollution10,11,12,13,14,15,16. For example, Zhang et al.10 found that 22% of the 3.45 million mortalities caused by PM2.5 in the year 2007 resulted from trade among the 13 global regions they studied. Wang et al.17 reported that over half of China’s emissions are linked to goods and services consumed outside the region of production. Similar results have been reported in studies of individual or groups of countries15,18.Modeling the transport, transformation, and removal of air pollution after its emission is necessary for obtaining useful estimates of the health impacts of those emissions, as impacts can vary widely by location, source, and emission type19. However, comprehensive modeling of these phenomena is computationally expensive owing to the necessity of representing disparate spatial and temporal scales across many state variables20,21. In this context, previous analyses of the air pollution impacts of trade have either consolidated countries into 13 global regions for analysis10,16, have only studied trade within a single country13,17, or have only reported emission amounts rather than pollution concentrations or health impacts13,18. There does not exist a comprehensive analysis of air-pollution-related health impacts of trade among individual nations, even though trade policy is often enacted at the national rather than the regional level. Here, we conduct such an analysis, with a particular focus on health impacts of trade between countries across a gap in economic production (GDP; per-capita Gross Domestic Product) and explore how the related transfers of health burdens interact with methods for their economic valuation.We represent economic transactions within and among countries using Multi-Regional Input-Output (MRIO) modeling22,23, a method used widely to assess energy use and CO2 emissions24,25—and also water26 and air quality10,17,18 impacts—related to trade. We connect the MRIO models to an inventory of air pollutant emissions27 and to a reduced-complexity model of air pollution transport, transformation, and removal28,29. The use of a reduced-complexity air quality model differentiates our analysis from the previous studies of global air pollution health impacts and trade10,15, allowing to us to perform the analysis at the granularity of approximately 200 countries rather than 13 regions. This fine-grained analysis reveals country-level patterns masked in region-aggregated studies, including differences among individual countries in Central and South America, Africa, and Europe. Finally, we use the results of previous epidemiological analysis30 to estimate the human mortalities caused by our modeled PM2.5 concentrations and the corresponding economic externality values31, including an exploration of the relationship between valuation methodologies and resulting incentives.ResultsWe present results for the year 2017. To partially quantify uncertainty, we use two separate MRIO models, GTAP version 1032 and EORA33 (see Methods). We provide most numerical results as ranges from the lower to the higher result of the two models. Presented rankings are based on GTAP results, with EORA rankings only discussed if they substantially differ from GTAP. Figures here are derived from GTAP results; equivalent figures based on EORA are available in the Supplementary Materials.Consumption- vs. production-based accountingAttribution of pollution impacts to emission sources is most commonly conceived in a “production-based” manner: responsibility is assigned to the physical source of the emissions, or to a geographical entity containing the emissions source.Here, we perform production-based accounting of PM2.5 health impacts based on MRIO economic sectors and regions, which usually coincide with national political boundaries. (We use the terms “region”, “nation”, and “country” interchangeably when referring to MRIO regions.) Countries causing the largest number of production-based mortalities include China (950–959 k mortalities), India (436–453 k), Indonesia (112–120 k), Japan (84.4–89.1 k), and Brazil (74.7–81.6 k). Air pollution can travel long distances, affecting neighboring countries and even regions far away from the source. Countries whose emissions cause the largest number of these transboundary-pollution-related mortalities include India (90.0–94.3 k), Pakistan (38.5–40.3 k), China (37.9–40.5 k), Turkey (35.7–37.4 k), and Saudi Arabia (33.8–36.8 k).Alternatively, responsibility for pollution health burdens can be assigned to the entity at the end of a series of economic transactions that ultimately result in the pollution emissions. Assigning emissions responsibility of this “final demand” activity is referred to as “consumption-based” accounting, which we perform here by assigning PM2.5 health impacts to the MRIO regions where final demand occurs. Countries causing the largest number of consumption-based mortalities include China (670–844 k mortalities), India (344–356 k), the United States (239–246 k), Japan (99.3–114 k), and Indonesia (84.7–99.6 k).Consumption- and production-related mortalities for all GTAP and EORA regions are available as Supplementary Data 1–434.Imports and exports of air quality-related mortalitiesIn input-output economic analysis, a nation’s imports are defined as economic production in other countries resulting from its final demand, and its exports are defined as its economic production resulting from final demand in other countries. Concordantly, we define a nation’s exports of PM2.5-related mortalities as the mortalities occurring in other nations but caused by its final demand. And its imports of mortalities are the mortalities it suffers that are caused by final demand in other nations. In this notation, imports of goods and services tend to result in exports of mortalities. Of the 2.82–2.91 million mortalities caused by exposure to PM2.5 from economic activity in 2017 (out of 5.1 million total PM2.5 mortalities), economic demand for exports was responsible for 40–48%. For ~ 80% of countries, the majority of mortalities caused by their consumption of goods and services occur outside of their borders. The largest exceptions are China, Indonesia, Brazil, Colombia, Peru, India, and the Philippines, which each domestically bear more than 2/3 of the global mortalities caused by their consumption.The largest net exporters of mortalities include the United States (166–175 k mortalities exported), the United Kingdom (27–42 k), France (27–35 k) and Germany (17–33 k), while the largest net importers are China (206–372 k mortalities imported), India (89–120 k), Indonesia (12–35 k), and Bangladesh (27–30 k) (Fig. 1A–H). Net exports of mortalities can also be conceived as the sum of bidirectional trade relationships among nations (Fig. 1I), with some nations acting as net exporters in the majority of their relationships—for example Norway (96.3–97.1% of relationships), Ireland (94.7–95.0%), and Finland (92.0–92.1%)—and some nations typically acting as net importers—for example China (92.5–97.9% of relationships), Bangladesh (93.6–96.8%), and Cambodia (93.5–93.6%). (Detailed bidirectional relationship data is available in Supplementary Figs. S4, S5 and Supplementary Data S9, S10 $10,000, and a total of $0.35–0.36 trillion in decreased externalities in countries with GDP < $10,000 (Fig. 5D). (Detailed externality data is available in Supplementary Data 11, 1234 include additional discussion and quantification of uncertainty.)Our United-States-centric perspective on policy and valuation practices is an additional limitation. Although the U.S. is the largest exporter of air pollution mortalities (Fig. 2A), this perspective does not reflect the diversity of international decision-making processes. Finally, our analysis only illuminates causal mechanisms in a limited sense: trade causes air pollution only in the sense that economic demand causes supply. We do not provide information on how changes in trade might induce changes in air pollution; this information cannot be reliably derived from an MRIO framework such as we use here owing its linearized representation of inherently non-linear phenomena.The link between air pollution externality valuation and the actions of nations or firms is indirect and tenuous—it is mainly relevant in the context of environmental cost-benefit analysis, the actual application of which is rare among all relevant decisions and actors. However, environmental cost-benefit analysis is an influential tool nonetheless52, and as such it is useful to explore the relationship between methodological choices in its application and the incentive structure it provides, even though the incentives may not bear directly on the vast majority of relevant decisions.The widespread exportation of PM2.5-related mortalities from higher-GDP to lower-GDP countries (Fig. 3) is intertwined with standard methods for assigning economic value to those mortalities. This interrelationship appears in the “Business as Usual” accounting scheme (Fig. 5A): mortalities in external countries are given a value of zero, providing an incentive for firms to conduct highly-polluting activities abroad. (This is independent from the “pollution haven” hypothesis53, which stipulates that polluting activities are drawn to weakly-regulated locations; we do not seek here to infer a cause for the pollution exports we quantify. Instead, we simply point out the existence of an incentive embedded in common environmental accounting methods, with the hypothesis that changing the accounting methods could neutralize the incentive.)The “Global Community” accounting method (Fig. 5B), which is facially more comprehensive and has been the basis for U.S. climate policy39, would incentivize the location of polluting activities in lower-income rather than higher-income countries, as mortalities in lower-income countries result in a lower externality value than an equivalent number of mortalities in a higher-income country. For example, because many of the United States’ exports of mortalities are to much lower-income countries, changing from “Business as Usual” to “Global Community” accounting increases U.S. externalities from 3.1% to 5.2% of GDP, which is a ~ 5 × smaller change than the 14.2% increase from “Global Community” to the “Fair Trade in Pollution” valuation method. As above, the existence of an incentive is not proof of an outcome; we only seek to demonstrate that although the “Global Community” method would incentivize the reduction of overall exports of mortalities by assigning value to mortalities that occur abroad, there would also be an incentive for the remaining exported mortalities to occur in lower-income nations.As it is designed to not incentivize exporting mortalities across an income gap, the “Fair Trade in Pollution” valuation method proposed here could be used as a tool in lower-GDP nations to negotiate with potential investors or trading partners for arrangements that are beneficial for both economic prosperity and public health. For example, cost-benefit analysis for a proposed industrial site could be conducted with the expected air pollution damages evaluated using the VSL of the country of the owners of the proposed facility, rather than the country where the facility would be located. It could also be used as a part of a cost-benefit analysis to help decision-makers in higher-income nations to direct partnerships and investments in a manner that does not incentivize exporting pollution to lower-income nations, which could be part of a larger effort to reduce the likelihood of the negative spillover effects discussed above39.The results presented herein do not negate the extensive evidence of the likely causal relationship between trade openness and economic growth54. Instead, we build on the well-recognized existence of non-market motivations for55 and outcomes of trade, which can include shifting air pollution burdens10. We have quantified these impacts at the national level (where trade policy is often set) and provided a framing through which pollution-related trade equity can be considered; these are two potential ingredients for broadly realized joint economic and health prosperity.MethodsOur analysis is based on datasets describing air pollutant emissions, baseline human mortality rates, and the structure of the global economy, coupled with models describing 1) air pollution transport, transformation, and removal, and 2) the human health impacts of air pollution. In particular, we used the Community Emissions Data System (CEDS) inventory27 to obtain gridded annual average emissions of PM2.5 and its precursors (primary PM2.5, SO2, NH3, NO3, and volatile organic compounds (VOCs)) from 11 anthropogenic sectors (Supplementary Table S3) and four fuel categories. We used these emissions as inputs to the Intervention Model for Air Pollution (InMAP)28 to determine ambient PM2.5 concentrations attributable to each emissions source sector. Subsequently, we coupled estimated concentrations with the Multi-Region Input-Output (MRIO) model for each economic sector to derive concentration factors. These factors represent the amount and spatial distribution of ambient PM2.5 due to economic activity, i.e., the ground-level PM2.5 concentration per unit of USD economic output in a given sector in a given country. We then applied the concentration factors to the economic output resulting from economic demand (or “consumption”) from different sectors, resulting in the attribution of PM2.5 concentrations to the consumption activities in different economic sectors in different countries. Upon attaining the concentration distributions across different sectors and countries, we estimated excess mortality rates attributable to global PM2.5 concentrations utilizing the Global Exposure Mortality Model (GEMM)30, alongside with baseline incidence rates sourced from the Global Burden of Disease (GBD)56,57. Finally, the number of mortalities was multiplied by the Value of Statistical Life (VSL)31,40 to assess economic externalities across various countries and quantify disparities therein. The year 2017 was chosen for analysis to ensure consistent data availability across all datasets used in this study. Our overall workflow is outlined in Supplementary Fig. S14, and the individual components are described in detail below.MRIO AnalysisMRIO analysis is used in economic and environmental studies to understand how regions and sectors within an economy are interconnected. It is useful for studying the structure of the economy, but because MRIO tables aggregate activity of all firms or subsectors within a country an sector, and because they assume linear relationships between inputs and outputs, they are best suited for aggregate, descriptive analysis, rather than analysis of causal relationships or relationships among individual firms or subsectors. In this study, we utilized two MRIO tables: the EORA dataset33,58 and the Global Trade Analysis Project (GTAP) version 10 dataset32, allowing us to use the difference between the two models as an estimate of uncertainty in the structure of the economy. The EORA26 year-2017 dataset includes 26 sectors across 190 regions for the year 2017. We have excluded the EORA regions representing the former USSR and the Netherlands Antilles from our analysis due to their division into multiple countries (regions), which are also all represented in the dataset. The GTAP-MRIO dataset we use comprises 65 sectors and 141 regions for the year 2017.We selected GTAP due to its wide adoption, global coverage, consistent structure, and granular regional aggregation—for example, Africa is represented by multiple regions rather than a single aggregate. EORA was used as a complementary dataset to strengthen our findings. Although EORA is less widely used than GTAP, it includes additional countries not individually represented in GTAP, such as Macao and the Democratic People’s Republic of Korea, and gives us an estimate of the structure of the economy that is semi-independent from GTAP.Other MRIO databases were excluded for the following reasons:World Input-Output Database (WIOD)59 was not used owing to its limited country coverage (44 countries), which excludes many smaller and lower-income nations, particularly across Africa.EXIOBASE60 also contains only 44 countries and a few Rest-of-World regions, which limits its suitability for our goal of nearly global coverage.OECD ICIO61 includes 76 countries, but still lacks many smaller and lower-income regions.EMERGING62 is a recently released MRIO dataset, with strong geographic detail and diverse service sector coverage (covering 135 sectors in 245 economies). Because it was released after the main stages of our analysis had been completed, and because the two MRIO tables we did include yielded largely consistent results, we did not use EMERGING in this study. We recognize its value and anticipate using it in future research.A simplified representation of an MRIO table is illustrated in Supplementary Fig. S15, where the blue segment denotes a square matrix of size NM × NM, with N representing the number of regions (190 for EORA and 141 for GTAP) and M denoting the number of economic sectors within each country (26 for EORA and 65 for GTAP). This matrix (which we will refer to as the Z matrix) quantifies inter-industry flows, where an entry \({{{\bf{Z}}}}_{(n-1)M+m,(\tilde{n}-1)M+\tilde{m}}\) signifies the monetary transaction from sector m of country n to sector \(\tilde{m}\) of country \(\tilde{n}\).The orange segment represents the final demand of each country from various sectors. Each entry \({{{\bf{D}}}}_{(n-1)M+m,\tilde{n}}\) is a vector holding to the multiple components of final demand, such as household and government final consumption expenditure. Therefore, the summation of the vector \(\sum {{{\bf{D}}}}_{(n-1)M+m,\tilde{n}}\) is the total demand of country \(\tilde{n}\) of goods and services from sector m of country n.The final demand FD of country \(\tilde{n}\) is computed using Equation (1). In addition, the total output of each sector (X) is determined as depicted in the gray segment for Supplementary Fig. S15 by summing up each row of Z and D:$${{{\bf{FD}}}}_{\tilde{n}}=\sum_{n=1}^{N}\sum_{m=1}^{M}\sum {{{\bf{D}}}}_{(n-1)M+m,\tilde{n}},\,\tilde{n}=1,\ldots,N.$$(1)The Z matrix above quantifies transactions between individual sectors in individual countries, but it does not give the total economic output resulting from demand for a given sector in a given country, which we refer to as the output matrix O. Supplementary Fig. S16 provides an overview of the calculation of O. Specifically, we first calculate the technology matrix by multiplying the inter-industry flows matrix Z with the inverted and diagonalized industry total output matrix \({\widehat{{{\bf{X}}}}}^{-1}\). Then, we obtain the Leontief inverse63 as shown in Step 2, where I is an identity matrix with the same size as the technology matrix. Finally, we can derive the output matrix from the multiplication of the Leontief inverse with the final demand matrix. Each element \({{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}\) represents the output from sector m of country n to satisfy the demand of country \(\tilde{n}\).Emissions and sectoral mappingAnthropogenic emission inputs were derived from the Community Emissions Data System (CEDS)27. CEDS incorporates national emissions inventories where available, providing estimates that are more consistent with official country-level data as compared to other options such as EDGAR64, while also offering sectoral disaggregation (RCOC, RCOR, RCOO) that aligns with MRIO sector categories. This facilitates a more direct mapping between emission sources and economic activities than is available in EDGAR. CEDS emissions are made available at 0. 5∘ × 0. 5∘ spatial resolution.In order to calculate concentration factors (the spatial pattern in ambient PM2.5 resulting from each unit of output from a given sector and region), we first constructed a concordance between the CEDS inventory anthropogenic emissions sectors and the MRIO economic sectors. Supplementary Tables S4, S5 provide descriptions of the GTAP and EORA economic sectors, respectively, along with the corresponding CEDS emissions sector each economic sector is mapped to (CEDS sectors are described in Supplementary Table S3).We then allocated emissions from each CEDS sector among the MRIO sectors it was mapped to in proportion to the amount of economic output from each sector of each country. In addition, all SLV (solvent) emissions were distributed among sectors associated with IND (industrial) or RCO (residential and other; including RCOC and RCOO) emissions, while WST (waste disposal and handling) emissions were distributed across all economic sectors in proportion to their economic output. We do not allocate emissions from the on-road transportation sector (ROAD) to any economic sector, as a substantial share of onroad transportation results from private activities rather than from economic transactions. We also exclude the RCOR (residential combustion) sector—corresponding to household fuel use and not linked to economic transactions—from the emission inventory when calculating consumption-based mortality impacts. (These exclusions result in conservative estimates of the impact of trade on air pollution.) Since certain business activities—including Financial Intermediation & Business Activities and Re-export & Re-import in GTAP and Insurance, Other Business Services, Other Financial Intermediation, and Real estate activities in EORA—may have disproportionately large economic output but relatively low or no emissions compared to other sectors, we did not allocate any emissions to these sectors.Finally, natural sources including forest fires65, biogenic volatile organic compounds (BioVOCs), soil NOx, and mineral dust66 are considered in calculating baseline health outcomes as described in Section Excess Mortality Due to PM2.5, and are included in our estimate of total mortalities from PM2.5, but are excluded from the final calculation of trade-related mortalities.Air quality modelingWe use the Intervention Model for Air Pollution (InMAP28) configured for global simulations29,67 to model the relationship between emissions of PM2.5 and its precursors (including volatile organic compounds (VOCs), NOx, NH3, and SOx) and the resulting ambient PM2.5 concentrations. InMAP is a reduced-complexity model of air pollution transport, transformation, and removal, which contains simplified representations of chemistry and physics, allowing us to conduct a large number of simulations required for this analysis. However, as quantified in Section “Performance Evaluation against Measurements”, InMAP (and other simplified models) typically incur a reduction in accuracy as the price of computational speed.We use InMAP version 1.9.6 with a variable-resolution spatial grid, using a 2 × 2. 5∘ resolution for the largest cells, each of which are allowed to split into 4 smaller cells whenever a cell contains more than 100,000 people or when any part of the cells contains more than 55 million people per square degree. This splitting can occur up to 6 times recursively, resulting in a minimum grid cell size of 0.031 × 0.039∘ (or about 3 × 4 km2 at the equator). This configuration results in a total of ~ 270,000 grid cells at ground level. A similar configuration was previously used by Tessum et al.67.Our analysis includes 210 unique MRIO regions, with 141 in the GTAP dataset (described in Supplementary Tables S6, S7), and 188 regions in the EORA dataset (described in Supplementary Table S8), with 119 regions shared between the two. Each region intersects with 11 sectors in the CEDS dataset. For each region-sector combination, we conducted a simulation to estimate PM2.5 concentrations attributed to the emissions from that region and sector. (We used the “EmissionMaskGeoJSON” option in InMAP to exclude emissions located outside the region of interest.) In addition, we performed an aggregate simulation for each country, encompassing both anthropogenic and natural source emissions, to determine the total PM2.5 concentrations for comparison against observations and for calculating baseline health damages. This resulted in a total of 210 × 11 + 210 = 2520 InMAP simulations, with each simulation requiring approximately 800 CPU-hours29, resulting in approximately 2 million CPU-hours to conduct the entire set of simulations. Each simulation outputs annual-average concentrations in each of the ~ 270,000 grid cell locations. The outputs of all the simulations can be considered as a source-receptor matrix, where each source is a MRIO region and economic sector and each receptor is an InMAP grid cell location.Concentration FactorsTo prepare the results of our air quality simulations for use in MRIO analysis, we calculate “concentration factors”, representing the amount of ambient PM2.5 in each of the InMAP grid cell locations per unit of economic output from each sector in each country. The methodology for calculating these factors is outlined in Figure S17.First, we apply the sector mapping described in Section Emissions and Sectoral Mapping to the output matrix O to obtain a new output matrix \({{{\bf{O}}}}^{{\prime} }\) of size NMe × N, with Me representing the number of CEDS emission sectors within each country (Me = 11 in this case). Each element \({{{\bf{O}}}}_{(n-1){M}_{e}+{m}_{e},\tilde{n}}^{{\prime} }\) denotes the output from emission sector me in country n to satisfy the demand of country \(\tilde{n}\). Each element in O is derived from \({{{\bf{O}}}}^{{\prime} }\) as expressed in Equation (2), where S is the set containing all economic sector m that are classified under each emission sector me. The total output of each emission sector of country n is subsequently calculated according to Equation (3). We then construct a G × NMe production concentration matrix PC which holds the InMAP-calculated PM2.5 concentration resulting from emissions from each sector and country, where G represents the number of grid cells (273,738 in our analysis). Each entry \({{{\bf{PC}}}}_{g,(n-1){M}_{e}+{m}_{e}}\) in this matrix denotes the PM2.5 concentration in grid cell g resulting from the production processes of emission sector me in country n. Subsequently, we obtain the concentration factor matrix CF by dividing each concentration element in PC by the total economic output of the corresponding sector. Each element \({{{\bf{CF}}}}_{g,(n-1){M}_{e}+{m}_{e}}\) in matrix CF is calculated as shown in Equation (4). It represents the concentration per unit of output in grid cell g resulting from emission sector me of country n. Finally, the consumption concentration matrix CC is obtained by multiplying the concentration factor matrix CF by the emission sector output matrix \({{{\bf{O}}}}^{{\prime} }\). The dimensions of CC are G × N, with each element CCg,n representing the PM2.5 concentration in grid cell g attributed to the consumption activities of country n.$${{{\bf{O}}}}_{(n-1){M}_{e}+{m}_{e},\tilde{n}}^{{\prime} }=\sum_{m\in S}{{{\bf{O}}}}_{(n-1)M+m,\tilde{n}},\,n=1,\ldots,N;\,{m}_{e}=1,\ldots,{M}_{e}$$(2)$${{{\bf{O}}}}_{(n-1){M}_{e}+{m}_{e}}^{{\prime} }=\sum_{\tilde{n}=1}^{N}{{{\bf{O}}}}_{(n-1){M}_{e}+{m}_{e},\tilde{n}}^{{\prime} },\,n=1,\ldots,N;\,{m}_{e}=1,\ldots,{M}_{e}$$(3)$${\!}{{{\bf{CF}}}}_{g,(n-1){M}_{e}+{m}_{e}} {\!}=\frac{{{{\bf{PC}}}}_{g,(n-1){M}_{e}+{m}_{e}}}{{{{\bf{O}}}}_{(n-1){M}_{e}+{m}_{e}}^{{\prime} }} {\!},\, {\!} n=1,\ldots,N;\,{\!}{m}_{e}=1,\ldots,{M}_{e};\,g=1,\ldots,G$$(4)Mapping Grid Cells to CountriesIn the previous step, we obtained the production and consumption concentration matrices (PC and CC, respectively), which indicate how production and consumption activities in each country contribute to global PM2.5 concentration levels. We next allocated each InMAP grid cell to the relevant countries. Algorithm S1 outlines the process of grid cell classification to achieve this task. We allocate grid cells to each nation based on the area-weighted fraction lying within national borders or Exclusive Economic Zones (EEZs), which extend 200 nautical miles (230 miles) beyond coastlines and are defined by the International Institute for Law of the Sea Studies68. Emissions within a country’s EEZ, including those from international shipping and aviation, are assigned to that country. This method for allocating international shipping and aviation emissions is consistent with a country’s authority to regulate transport emissions occurring within its EEZ69. Grid cells outside any EEZ are assigned to the Rest of World (ROW) region. Figure S18 illustrates this allocation process.Excess Mortality Due to PM2.5We employed the Global Exposure Mortality Model Non-Communicable Diseases Plus Lower Respiratory Infections (GEMM NCD+LRI) for individuals aged 25 years and older30 to estimate the excess mortality rate attributed to trade-related PM2.5. The model operates under the assumption of equal toxicity per total inhaled dose and relies solely on data from cohort studies of outdoor PM2.5 pollution. The GEMM NCD+LRI hazard ratio predictions are positively related to PM2.5 concentration, showing a supralinear association at lower exposure levels, transitioning to a nearly linear association as concentrations increase.To begin, reported incidence rates for NCD and LRI in each country, expressed per 100,000 population, were obtained from the Global Burden of Disease (GBD) Study56,57. Population data were used to calculate exposure by overlaying population counts onto the modeled PM2.5 concentration fields. Specifically, we used the 2017 gridded global population dataset from Liu et al.70, mapping it onto the InMAP grid to estimate population exposure at fine spatial resolution. Subsequently, the NCD-LRI cause-specific counterfactual baseline mortality rate for each country (i.e., the expected mortality rate in the absence of air pollution) was calculated following Algorithm S2. The hazard ratio is determined using the GEMM model described by Equation (9), where \({{\bf{Z}}}=\max \left(0,{{{\rm{PM}}}}_{2.5}-2.4\,\mu {{\rm{g}}}\,{{{\rm{m}}}}^{-3}\right)\), and (θ, α, μ, v) = (0.1430, 1.6, 15.5, 36.8).Next, we calculate the mortality rate attributable to PM2.5 per unit concentration for each country within a grid cell. To achieve this, we begin by identifying the countries that intersect each grid cell and calculating the proportion of each country’s population residing within that grid cell, as outlined in the previous step. Then, this proportion is multiplied by the country’s baseline mortality rate to estimate the base mortality for the grid cell. We then apply a hazard ratio based on the PM2.5 concentration to determine the excess mortality. Finally, we divide the total excess mortality by the PM2.5 concentration to obtain the mortality rate per unit concentration for each country intersecting the grid cell. This process is outlined in Algorithm S3.At this stage, we have a column of dictionaries, denoted as mort_per_con, with a length equal to the number of grid cells, G. These can be expanded into a matrix MUC of size N × G, where N represents the number of countries. Each element MUCg,n corresponds to the mortality rate attributable to per unit PM2.5 concentration for country n within grid cell g. If a country does not intersect with a particular grid cell, the corresponding matrix element is set to zero.Next, by multiplying the transpose of the production concentration matrix (TPC) and the consumption concentration matrix (TCC) by MUC, we obtain the production-based mortality rates matrix (PMR) and the consumption-based mortality rates matrix (CMR), respectively, as illustrated in Figure S19. The element \({{{\bf{PMR}}}}_{(n-1){M}_{e}+{m}_{e},\tilde{n}}\) represents the mortality rate attributable to emissions produced by sector me in country n, which results in mortalities in country \(\tilde{n}\). Similarly, \({{{\bf{CMR}}}}_{n,\tilde{n}}\) represents the mortality rate attributable to consumption in country n, which results in mortalities in country \(\tilde{n}\). The number of mortalities in each country is then calculated by multiplying these mortality rates (in units of mortalities per 100,000 population) by the total population (p) of the affected country, then dividing by 100,000.Finally, we can calculate the total number of mortalities caused by the production processes of country n but occurring worldwide (tol_pd_causedn) using Equation (5), and the total number of mortalities caused by the consumption activities of country n but occurring worldwide (tol_cd_causedn) using Equation (6). In addition, the total number of mortalities occurring in country n due to production from all other countries (tol_pd_inn) can be determined using Equation (7), which is equivalent to the total number of mortalities in country n caused by consumption from all other countries (tol_cd_inn), as described by Equation (8).$${{{\bf{tol}}}\_{{\bf{pd}}}\_{{\bf{caused}}}}_{n}=\sum_{\tilde{n}=1}^{N}\sum_{{m}_{e}=1}^{{M}_{e}}{{{\bf{PMR}}}}_{(n-1){M}_{e}+{m}_{e},\tilde{n}}\times \frac{{{{\bf{p}}}}_{\tilde{n}}}{100,000},\,n=1,\ldots,N$$(5)$${{{\bf{tol}}}\_{{\bf{cd}}}\_{{\bf{caused}}}}_{n}=\sum_{\tilde{n}=1}^{N}{{{\bf{CMR}}}}_{n,\tilde{n}}\times \frac{{{{\bf{p}}}}_{\tilde{n}}}{100,000},\,n=1,\ldots,N$$(6)$${{{\bf{tol}}}\_{{\bf{pd}}}\_{{\bf{in}}}}_{n}=\frac{{{{\bf{p}}}}_{n}}{100,000}\times \sum_{\tilde{n}=1}^{N}\sum_{{m}_{e}=1}^{{M}_{e}}{{{\bf{PMR}}}}_{(\tilde{n}-1){M}_{e}+{m}_{e},n},\,n=1,\ldots,N$$(7)$${{{\bf{tol}}}\_{{\bf{cd}}}\_{{\bf{in}}}}_{n}=\frac{{{{\bf{p}}}}_{n}}{100,000}\times \sum_{\tilde{n}=1}^{N}{{{\bf{CMR}}}}_{\tilde{n},n},\,n=1,\ldots,N$$(8)$${{\rm{hr}}}(z)=\exp \left\{\frac{\theta \log \left(z/\alpha+1\right)}{1+\exp \left(-(z-\mu )/v\right)}\right\}$$(9)Economic externalitiesTo calculate economic externalities resulting from exposure to PM2.5, we multiply the number of mortalities as calculated above by the value of a Statistical Life (VSL). The VSL is a metric for assessing the monetary value individuals are willing to expend to mitigate the risk of mortality31,36. In the present investigation, we explored three separate methods, which are described in detail in the Main Text-to quantify the value of the VSL to use to estimate the economic externality resulting from ambient concentrations of PM2.5. For all three methods, we followed Viscusi and Masterman40 to quantify VSLs in different countries using adjustment factors based on income. (Our three valuation methods differ in how the VSL values are applied, rather than how they are calculated.) For countries not covered in the aforementioned study, we applied the methods used by Viscusi and Masterman to calculate VSLs for individual countries based on adjustments from the reported VSL value for the United States, which is $10 million. Under the assumption of constant and uniform income elasticity across the countries of interest, the transferred VSL for a given country c is calculated as depicted in Equation (10), where Yc denotes the World Bank Gross National Income (GNI) per capita for country c for the year 201571, and η signifies the income elasticity of the VSL, with a unit elasticity assumption (set to 1) employed in our computations. In addition, to improve consistency across data sources, adjustments were made to all VSLs to change the year from 2015 to 2017 using an inflation calculator. The lowest VSLs are $60,000, $75,000, and $84,000 in Malawi, Madagascar, and Guinea, respectively, whereas the highest VSLs are $16.7 million, $15.1 million, and $15 million in Norway, Switzerland, and Qatar, respectively.$${{{\bf{VSL}}}}_{c}={{{\bf{VSL}}}}_{{{\rm{US}}}}\times {\left(\frac{{{{\bf{Y}}}}_{c}}{{{{\bf{Y}}}}_{{{\rm{US}}}}}\right)}^{\eta }$$(10)Sectoral analysisIn addition to country-level estimates, our analysis incorporates sectoral information to explore the relationship between economic activity and PM2.5-related mortality. For production-based estimates, we can directly quantify the number of mortalities attributable to emissions from each economic sector in each country, using emissions sector mappings aligned with the MRIO structure.Overall, as shown in Supplementary Fig. S20, the IND sector accounts for the largest share (30.5–31.3%) of mortalities, followed by the ENE sector (24.8–25.5%) and the non-trade sectors, RCOR (12.9–13.2%) and ROAD (9.3–9.6%).For consumption-based mortality, although direct attribution of mortalities to final demand by sector is not feasible, we derive three sectoral fractions to characterize the role of different sectors in driving consumption-based impacts:1.Direct Final Demand Fraction (\({{{\bf{Frac}}}\_{{\bf{DFD}}}}_{\tilde{m}\tilde{n}}\)): This quantity represents the proportion of global final demand—including both household and government expenditures—directly allocated to each economic sector aggregated across all countries. It captures the immediate consumption of goods and services by consumers, firms, and governments from different economic sectors.Formally, the share of final demand assigned to aggregated global economic sector \(\tilde{m}\) for country \(\tilde{n}\), denoted as \({{{\bf{Frac}}}\_{{\bf{DFD}}}}_{\tilde{m}\tilde{n}}\), is defined as:$${{{\bf{Frac}}}\_{{\bf{DFD}}}}_{\tilde{m}\tilde{n}}= \frac{{{{\bf{FD}}}}_{\tilde{m}\tilde{n}}}{{{{\bf{FD}}}}_{\tilde{n}}} \\= \frac{{\sum }_{n=1}^{N}\sum {{{\bf{D}}}}_{(n-1)M+\tilde{m},\tilde{n}}}{{\sum }_{n=1}^{N}{\sum }_{m=1}^{M}\sum {{{\bf{D}}}}_{(n-1)M+m,\tilde{n}}}\,\tilde{m}=1,\ldots M;\tilde{n}=1,\ldots,N$$(11)where:N is the total number of countries,M is the total number of sectors in each country,\({{{\bf{FD}}}}_{\tilde{m}\tilde{n}}\) is the direct final demand of country \(\tilde{n}\) for goods and services from the aggregated economic sector \(\tilde{m}\),\({{{\bf{FD}}}}_{\tilde{n}}\) is the direct final demand of country \(\tilde{n}\) for goods and services from the all sectors and countries,\(\sum {{{\bf{D}}}}_{(n-1)M+m,\tilde{n}}\) is the direct final demand of country \(\tilde{n}\) of goods and services from sector m of country n.2.Total (Indirect-Adjusted) Final Demand Fraction (\({{{\bf{Frac}}}\_{{\bf{TFD}}}}_{\tilde{m}\tilde{n}}\)): This accounts for both direct and indirect demand through upstream linkages. This is calculated using the output matrix, obtained by multiplying the Leontief inverse matrix (I−A)−1 by the final demand matrix. As illustrated in Supplementary Fig. S16, each element \({{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}\) of the output matrix represents the total output from sector m of country n required to satisfy the final demand of country \(\tilde{n}\). This value encompasses not only the direct consumption but also the indirect demand propagated through inter-sectoral supply chains. Therefore, \({{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}\) can be interpreted as the total final demand, including both direct and indirect contributions of country \(\tilde{n}\) for goods and services from sector m of country n.Formally:$${\!\!}{{{\bf{Frac}}}\_{{\bf{TFD}}}}_{\tilde{m}\tilde{n}}=\frac{\mathop{\sum }_{n=1}^{N}{{{\bf{O}}}}_{(n-1)M+\tilde{m},\tilde{n}}}{\mathop{\sum }_{n=1}^{N}\mathop{\sum }_{m=1}^{M}{{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}}\,\tilde{m}=1,\ldots,M;\,\tilde{n}=1,\ldots,N$$(12)where:\({{{\bf{O}}}}_{(n-1)M+\tilde{m},\tilde{n}}\) is the total (direct + indirect) output from sector \(\tilde{m}\) in country n needed to satisfy the final demand of country \(\tilde{n}\),\(\mathop{\sum }_{n=1}^{N}{{{\bf{O}}}}_{(n-1)M+\tilde{m},\tilde{n}}\) is the total (direct + indirect) output from sector \(\tilde{m}\) in all countries needed to satisfy the final demand of country \(\tilde{n}\),\(\mathop{\sum }_{n=1}^{N}\mathop{\sum }_{m=1}^{M}{{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}\) is the total (direct + indirect) demand of country \(\tilde{n}\) from all sectors and countries.3.Total Output Fraction ((\({{{\bf{Frac}}}\_{{\bf{TO}}}}_{\tilde{m}n}\))): The share of total national economic output generated by each sector. This provides a baseline indicator of a sector’s economic size within a country.Formally, the Total Output Fraction for sector m in country n, is defined as:$${{{\bf{Frac}}}\_{{\bf{TO}}}}_{\tilde{m}n}=\frac{\mathop{\sum }_{\tilde{n}=1}^{N}{{{\bf{O}}}}_{(n-1)M+\tilde{m},\tilde{n}}}{\mathop{\sum }_{m=1}^{M}\mathop{\sum }_{\tilde{n}=1}^{N}{{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}}\,\tilde{m}=1,\ldots,M;\,n=1,\ldots,N$$(13)where:\(\mathop{\sum }_{\tilde{n}=1}^{N}{{{\bf{O}}}}_{(n-1)M+\tilde{m},\tilde{n}}\) is the total (direct + indirect) output from sector \(\tilde{m}\) in country n needed to satisfy the final demand of all countries,\(\mathop{\sum }_{m=1}^{M}\mathop{\sum }_{\tilde{n}=1}^{N}{{{\bf{O}}}}_{(n-1)M+m,\tilde{n}}\) is the total (direct + indirect) output from all sectors in country n needed to satisfy the final demand of all countries.Overall, the Total Output Fraction reflects the supply side by measuring the share of a country’s total output contributed by each sector, indicating how much each sector produces relative to national output. In contrast, the Direct/Total Final Demand Fraction captures the demand side, representing the fraction of a country’s direct/total final demand satisfied by a given sector, showing how much the country relies on that sector.To assess how these sectoral structures relate to international mortality transfers, we compute correlations between the three sectoral fractions and the following two key metrics derived in the Main Text:G50foreign_world Fraction of mortalities caused by demand from countries with > 50% higher demand per capita.cause_L50foreign_world Fraction of mortalities caused by this country’s consumption that occurs in countries with > 50% lower demand per capita.To further investigate which sectors or major product categories contribute most to cross-border health burdens, we conducted a sector-resolved MRIO analysis using the GTAP dataset for the five countries with the highest consumption-based premature mortalities: the United States, China, India, Japan, and Indonesia. The analytical framework follows the same steps as outlined in Supplementary Fig. S16, with one modification in Step 3: Instead of multiplying the Leontief inverse, L, by the full global final demand matrix, FD, we multiply it by the diagonalized final demand matrix of an individual country, \({{\rm{diag}}}({{{\bf{FD}}}}_{\tilde{n}})\), where \(\tilde{n}\) denotes the consuming country. This isolates the global production activities required to satisfy the final demand originating solely from country \(\tilde{n}\).Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article.Data availabilityThe datasets supporting the findings of this study are publicly available from the following sources. Economic input-output data were obtained from the GTAP database (version 10, 2017)32 at https://www.gtap.agecon.purdue.edu/and the EORA MRIO database (version 26, 2017)33,58 at https://worldmrio.com/. Emissions data were obtained from the Community Emissions Data System (CEDS, version 2020)27 at https://doi.org/10.5194/essd-12-3413-2020. Population data were derived from the 2017 layer of a global gridded population dataset70https://doi.org/10.1038/s41597-022-01363-2. Baseline mortality and incidence rates were obtained from the Global Burden of Disease Study (2019)57 at https://vizhub.healthdata.org/gbd-results/. All maps were generated using Python (version 3.6) and matplotlib. Political boundary data were obtained from the Natural Earth public domain dataset at https://www.naturalearthdata.com/. Derived datasets generated during this study are publicly archived at the Illinois Data Bank