The air pollution tradeoff in India: saving more lives versus reducing the inequality of exposure

Chronic exposure to ambient fine particulate matter (PM2.5) represents one of the largest global public health risks, leading to millions of premature deaths annually. For a country facing high and spatially variable exposures, prioritizing where to reduce PM2.5 concentrations leads to an inherent tradeoff between saving the most lives and reducing inequality of exposure. This tradeoff results from the shape of the concentration–response (C-R) function between exposure to PM2.5 and mortality, which indicates that the additional lives saved per unit reduction in PM2.5 declines as concentrations increase, suggesting that more lives can be saved by reducing exposures in clean locations than in dirty locations. We estimated this C-R function for urban areas of India, finding that a 10 µgm−3 reduction in PM2.5 in already-clean locations will reduce the mortality rate substantially (4.2% for a reduction from 30 to 20 µgm−3), while a 10 µgm−3 reduction in the dirtiest locations will reduce mortality only modestly (1.2% for a reduction from 90 to 80 µgm−3). Policymakers face a troubling tradeoff between maximizing lives saved and reducing the inequality of exposure. Many air pollution policies impose an upper limit on exposure, thereby cleaning the dirtiest locations and reducing exposure inequality. We explore the implications of this PM2.5/mortality relationship by considering a thought experiment. If India had a fixed amount of resources to devote to PM2.5 concentration reductions across urban areas, what is the lives saved/inequality of exposure tradeoff from three different methods of deploying those resources? Across our three scenarios: (1) which reduces exposures for the dirtiest districts, (2) which reduces exposures everywhere equally, and (3) which reduces exposures to save the most lives—scenario 1 saves 18 000 lives per year while reducing the inequality of exposure by 65%, while scenario 3 saves 126 000 lives per year, but increases inequality by 19%.


Introduction
India faces some of the worst air pollution levels in the world from a growing number of coal-fired power plants [1], household air pollution [2], and numerous other sources such as open burning of agricultural residue [3]. Fifteen of the 20 most polluted cities in the world are in India, leading to significant numbers of premature deaths each year [4][5][6][7][8].
Reducing air pollution, specifically, fine particulate matter (PM 2.5 ), would reap benefits for India in terms of improved health [9,10].
An important question is how and where air pollution mitigation efforts should be focused. In other words, what are the benefits, in terms of lives saved, of improving air quality in dirty or clean areas of India? A strategy that appeals to our sense of environmental justice, and is perhaps the most intuitive, involves reducing air pollution in those places facing the highest concentrations. Indeed, that is exactly the directive of the Indian National Ambient Air Quality Standard (NAAQS), with a goal of reducing PM 2.5 concentrations below 40 µgm −3 in all locations [3,11], a level exceeded by half of the population in India [12].
Here we scrutinize this recommendation by illustrating an inherent tradeoff for PM 2.5 pollution policy for high-concentration countries: more lives can be saved by reducing PM 2.5 in locations with already low concentrations than in locations with high concentrations. The concept itself is somewhat paradoxical to conventional notions of environmental improvements (i.e. that the greatest incremental benefit of eliminating pollution ought to be to those facing the worst pollution), and it is antithetical to most people's moral imperative to reduce inequality (be it pollution exposure, income, access to healthcare, etc.). We explore these ideas to make explicit the tradeoffs that are often not included in discussions of air pollution policy.
First, why are more lives saved by reducing PM 2.5 from low-than from high-concentration locations? The answer is found in the shape of the concentration-response (C-R) function between PM 2.5 concentration exposure and premature adult mortality. Growing evidence suggests that the C-R function is supralinear, which means that the incremental (or marginal) increase in the risk of mortality declines as PM 2.5 concentrations rise [6,[13][14][15][16][17]. To be sure, this marginal risk is always positive (i.e. higher concentrations always pose a greater risk of death), but the incremental risk becomes smaller as concentrations rise. The consequence of this shape is that as we improve air quality, each additional unit of reduction in PM 2.5 at already-low concentrations reduces mortality risk by more than each additional unit of reduction at high concentrations.
The evidence for a supralinear shape is abundant and increasingly accepted as likely for relatively lowconcentration locations (in particular in the United States and Europe) [6,13,17]. The implication of this shape in relatively clean countries is that there are large benefits to reducing PM 2.5 concentrations to very low levels [18][19][20].
For countries that experience much higher concentrations, the evidence is less clear, and so are the implications. For these countries, if the C-R is supralinear then substantial reductions in PM 2.5 concentrations would be required before there are large reductions in mortality risk. Two C-R functions, the integrated exposure response [16] and the global exposure mortality model (GEMM) [15] were estimated to understand the potential improvements in global health from reductions in PM 2.5 concentrations, but these functions rely primarily on studies from relatively low-concentration countries.
Here we provide an estimate of the C-R function for the Indian urban districts (henceforth referred to as districts), and assess the implications for the Indian air quality improvement efforts. We find clear evidence of the supralinear shape of the C-R function and note a pronounced flattening of the curve at high concentrations. Our estimate displays a similar general shape to GEMM, though it shows substantially lower mortality risk at middle and high concentrations than does GEMM. We acknowledge that our estimate, comparing the mortality rates across Indian districts by PM 2.5 concentrations from 1998 to 2015, is not a state-of-the-science approach using a long-term cohort survival study. Even so, our analysis serves as an initial estimate of this relationship at high concentrations, and also allows us to explore the difficult and counterintuitive policy options that accompany India's efforts to improve air quality.
We pose the question: given a set amount of resources to reduce PM 2.5 in India, how many lives can be saved by directing those resources to different locations? Specifically, we introduce the concept of a person-PM 2.5 unit, defined as a reduction in PM 2.5 exposure of 1 µgm −3 to a single individual. Reducing exposure by 10 µgm −3 for the residents of an urban district with population of 100 000, for example, would reduce one million person-PM 2.5 units.
It is important to note that this concept of person-PM 2.5 units, does not include the actual cost of pollution abatement, and assumes that a given resource usage in clean and dirty locations achieves the same pollution reduction.
Using our dataset of Indian districts, and our estimate of the C-R function, we propose a thought experiment in which we imagine having a certain budget of person-PM 2.5 units to 'spend' to improve air quality in India. And then we compare the outcomes of three possible scenarios regarding how best to spend this budget. Importantly, in each scenario, the same total number of person-PM 2.5 units are used.
• Equal reduction (hereafter 'Equal'): all districts receive the same reduction in exposure to PM 2.5 (in our main results all districts improve their air quality by 10 µgm −3 -equivalent to a roughly 20% reduction in PM 2.5 , on average). We chose a 10 µgm −3 reduction in pollution as it aligns with the National Clean Air Programme, a national-level strategy in India that aims to reduce PM 2.5 by 20%-30% by 2024. • Uniform standard (hereafter 'Standard'): no district is permitted to be exposed to PM 2.5 above some limit (i.e. set some limit, reduce exposure in all districts above the limit, and then lower the limit incrementally until the budget is exhausted). • Optimized lives saved (hereafter 'Optimized'): prioritize exposure reductions to those locations in which each person-PM 2.5 unit has the largest reduction in the mortality rate (in our preferred log-log model estimates, these are the locations with the lowest initial concentration and the highest initial mortality rate).
With these three scenarios (each of which produces the same population-weighted average exposure across the districts under study) we compare the number of lives saved, and the inequality in pollution exposure across districts. Inequality in exposure is measured by the Gini coefficient (generally used as a measure of wealth or income inequality), which captures the degree to which exposure to pollution varies across locations. To illustrate the importance of the shape of the C-R function, we produce our results using three estimates of the mortality/PM 2.5 relationship-two from our dataset, referred to as log-log and log-linear, and one from the existing literature: GEMM.

Data sources
Annual mortality and PM 2.5 data was collected for 110 Indian urban districts for the years 1998-2015.
Our dataset is at the urban district level, which is an administrative division within a state that is a conglomeration of towns and cities. The data for mortality as collected by the civil registration system (CRS) is known to have substantial differences between the actual number of deaths and registered deaths, with actual deaths being much higher than what is registered. To account for this discrepancy, India's vital statistical system uses the sample registration survey to estimate the state level registration rate, which indicates the completeness of the data. We use this state-level registration and the district-level crude death rate obtained from the CRS to calculate the estimated district-level mortality rate, which we call adjusted mortality rate (AMR). The AMR is used as the primary outcome in our econometric analysis. We obtained PM 2.5 data from the Atmospheric Composition Analysis Group [21] using satellite data, measured at the 0.1 • × 0.1 • scale using the global geographically weighted regression method. To convert the PM 2.5 measurements at the grid level to our district-level data, we average all data points within a district. Monitor data for PM 2.5 in India was not collected until 2014, and hence the satellite data in our data set cannot be validated against monitor data for PM 2.5 . Studies show that there is a higher likelihood that the satellite based measurements are biased downwards at higher PM 2.5 concentrations [22]. This bias could affect the model coefficients, and is a limitation of the data. A more detailed data section is described in S.1 in the supplemental information.

Econometric analysis
We run the following model, with the natural log of AMR in district i and year t as the dependent variable against the natural log of PM 2.5 (ln (PM 2.5 )) for each district-year, and control for district level fixed effects (δ i ), year fixed effects (τ t ), district-specific linear and quadratic trends (denoted by δ i × t and δ i × t 2 respectively), and urban literacy rates (X it ) (see S.2 in supplemental information for alternative estimated models) [9].
The mortality data for India includes many high and low outliers. To provide a more precise estimate of the mortality-PM 2.5 relationship, we use the Huber M-estimator [23], which corrects for outliers by using Cook's distance as the weight for the data, applying higher weight for those data points that are closer to the mean. In addition, we follow a rigorous identification strategy that addresses issues of reverse causality, unobserved heterogeneity, cumulative exposure, measurement error, violation of stable unit treatment value assumption, and omitted variable bias that may confound our main parameter of estimate of interest (see S.3 in supplemental information for the details of our identification strategy). We present our econometric results in terms of the relative risk of mortality, which shows the ratio of the risk of mortality for a given concentration to the risk of mortality at a reference concentration (see S.4 in supplemental information for details).

Pollution reduction scenarios
Unlike the estimated C-R functions, which utilize a panel of data over 18 years, we use a single data point for each district in our pollution-reduction scenarios. For each district, we take the average from 2011 to 2015 of the population (pop i ), PM 2.5 concentration (PM 0 i ), and the mortality rate. To construct our scenarios, we start with a budget (B) of person-PM 2.5 units required to reduce the pollution level of all districts by 10 µgm −3 -the budget is equal to the sum of the population of each district times 10 µgm −3 of reduc- The budget is the same for all three scenarios. These 10 µgm −3 reductions everywhere also represent our Equal scenario. For the Standard scenario, we start with a limit on PM 2.5 , max PM , and all districts with a baseline concentration (PM 0 i ) above this limit are reduced to this level and calculate the person-PM 2.5 units required for this reduction. We progressively set a lower max PM level until the budget is exhausted, which occurs at a limit of max PM = 53 µgm −3 . For the Optimized scenario we calculate the marginal change in the mortality rate for each district of reducing the PM 2.5 concentration by 1 µgm −3 , and then reduce the concentration by a small amount (ε = 0.1 µgm −3 ) in the district with the highest marginal change in the mortality rate. This process is repeated many times until the budget is exhausted (we set a minimum limit of 5 µgm −3 which no district can drop below). For each scenario we calculate the number of lives saved from the pollution reduction in each district (see S.4 and S.5 in supplemental information for the calculation of lives saved and additional details of the pollutionreduction scenarios).

Inequality of exposure metric
The Gini coefficient (G) for pollution exposure inequality is a value between 0 and 1, with 0 representing perfect equality, and 1 representing perfect inequality. It is calculated for the initial concentration and for the concentration in each pollution reduction scenario. We calculate the change in inequality as a percentage change from the initial concentration Gini coefficient (see details of the calculation in S.6 of the supplemental information).

Results
Our preferred estimate of the relationship between PM 2.5 exposure and the all-cause mortality rate in Indian urban areas, denoted 'log-log,' expresses the natural log of mortality as a function of the natural log of the PM 2.5 concentration (see equation (1)). This estimate produces the supralinear shape of the C-R at higher concentrations (see orange line on left panel of figure 1). The relative risk between exposure at the mean (49.7 µgm −3 ) and 10 µgm −3 below the mean is 1.024 (95% confidence interval (CI): 1.006-1.042, p < 0.01). The 95% CI is based on the standard error (from table S2, column [1]) of 1.009, in terms of relative risk. With log-log, a 1 µgm −3 reduction in PM 2.5 at an already low concentration location yields a much larger reduction in mortality compared with a similar reduction at a high-concentration locatione.g. the reduction in the relative risk is 4.3 times greater for a reduction from 20 to 19 µgm −3 than for a reduction from 100 to 99 µgm −3 (see orange line in right panel of figure 1).
Our alternative estimate for comparison, denoted 'log-linear,' expresses the natural log of mortality as a function of the PM 2.5 concentration. The log-linear form is common in the epidemiological literature of health effects from air pollution. The relative risk between exposure at the mean and 10 µgm −3 below the mean is 1.014 (95% CI: 1.0004 to 1.028, p < 0.05). With the log-linear C-R, every µgm −3 reduction in the PM 2.5 exposure has a similar change in the relative risk (see gray line in right panel of figure 1). Log-log is our preferred estimate over log-linear (and several other specifications) as it improves the goodness of fit of the model to the data according to the Akaike information criterion and Bayesian information criterion measures, which apply a penalty to the models for the number of parameters used (see S.2 in supplemental information for discussion of model selection and goodness of fit). As a comparison to our estimated C-R relationships, we also calculate the results using GEMM. The GEMM function is steeper than our estimates (i.e. more lives are saved for each µgm −3 of PM 2.5 reduced), but has less curvature than our log-log estimate (i.e. the difference in shape between low-and high-exposure locations is not as large) (see black dotted line on left panel of figure 1). Figure 2 illustrates the key tradeoff between lives saved and inequality in air pollution exposure that we explore across the three scenarios and for the three functional forms of the C-R relationship. The y-axis of figure 2 shows the percent reduction in the Gini coefficient compared with the status quo pollution exposures-where positive values represent greater equality in exposures across districts, and negative values a widening of inequality. For each functional form, the Standard scenario provides the greatest gains in pollution exposure equality, but the fewest lives saved; the Equal scenario delivers more lives saved than the Standard scenario and a small reduction in inequality; and the Optimized scenario increases inequality of exposure but saves the greatest number of lives. Our focus is on the steepness of the lives saved/inequality tradeoff between the scenarios.
Using our alternative log-linear model, the tradeoff is very steep, suggesting that a relatively small number of additional lives are saved (13 600 lives) in the Optimized scenario compared with the Standard scenario, but at a huge cost in inequality of exposure (65% reduction in inequality to 9% increase in inequality).
Using our preferred log-log model, the tradeoff is much flatter, which means that although exposure inequality declines sharply as we move from the Optimized scenario to Equal, and then to the Standard scenario, the number of lives saved declines by over 80%. The Standard scenario, which reduces inequality by 65%, saves 28 000 fewer lives than reducing pollution by 10 µgm −3 in all locations (Equal scenario), which reduces inequality by only 14%. Compared with the Equal scenario, the Optimized scenario saves an additional 79 400 lives, but comes with an increase in the inequality of exposure (19% increase compared with the initial situation).
Using GEMM, the tradeoff is similar to log-log but shifted to the right-more lives are saved in all scenarios compared with log-log. Figure 3 examines the number of lives saved in each scenario (by the height of the bars) and also shows the initial concentration of the districts where the lives are being saved (by the colors). Across the three scenarios, it is not just that the number of lives saved varies, but the lives are saved from very different locations. The Standard scenario protects those who are initially exposed to the highest concentrations, whereas the Optimized scenario generally saves lives for those with relatively low initial concentrations. If the relationship is log-linear, the gains in lives saved in the Optimized and Equal scenarios over the  Standard scenario are relatively small, but the composition of those saved lives is very different.
With log-log, large gains are achieved under the Optimized scenario over the Standard scenario, in total lives saved (18 300 versus 125 700). However, the Standard scenario saves 14 000 lives for those exposed to over 75 µgm −3 , whereas the Optimized scenario saves zero lives from these high-exposure districts. The vast majority of the lives saved in the Optimized scenario (91%), are those of people living in below average PM 2.5 concentration locations. Again, GEMM illustrates a similar tradeoff in terms of lives saved and inequality of exposure to log-log, with larger overall magnitudes of lives saved, but lesser ratios of lives saved between the Optimized and Standard scenarios.

Contextualization of the results
In aggregate, the outcomes from our three scenarios show vast differences. Examining how the scenarios direct their budget of person-PM 2.5 units to different Indian districts, leading to these differences, is instructive for understanding how the scenarios are implemented. Figure 4 plots four outcomes (panels (A)-(D)) for each Indian district, across the three scenarios, using our preferred log-log estimate. The districts are organized across the x-axis according to the initial PM 2.5 concentration (each bubble represents a district, and the bubble size is proportional to the population). In panel (A), we see the concentration reduction for each district. In the Equal scenario (blue), all districts are reduced by 10 µgm −3 . The Standard scenario (red) takes the 27 districts with the highest concentrations and reduces them each down to 53 µgm −3 . With this standard, 82% of the person-PM 2.5 units are spent on reducing the eight districts with initial concentrations above 80 µgm −3 . The Optimized scenario utilizes its budget very differently, mostly reducing exposure for the cleanest districts. This scenario reduces pollution for 50 districts, 48 of which are in below average concentration locations. The pollution in each of these districts is reduced to a pristine level of 5 µgm −3 .
In panel (B), we see how the concentration reductions change the relative risk of mortality. This panel appears similar to (A), but here we see the effect of the supralinear shape of the C-R function. The Equal scenario reduces the risk of mortality substantially more for the initially low-concentration districts than the initially high-concentration districts, even though their concentration change is the same. This flattening is also seen in the other scenarios, most obviously for the Standard scenario such that despite very large reductions in concentrations, there are less substantial reductions in risks for the initially highconcentration districts.
Panel (C) is subtly different from panel (B), showing the reduction in the mortality rate, rather than the change in the relative risk. All else equal, 1 µgm −3 of reduction in pollution in a location with a high initial mortality rate will reduce the absolute mortality rate more than that same reduction in a location with a low initial mortality rate. The Optimized scenario directs its pollution reductions to those locations with relatively low initial concentrations-to take advantage of the steepest portion of the C-R function-and to those locations with the highest initial mortality rates. Panel (C) highlights the enormous improvements in conditions the Optimized scenario makes to the selected districts that are included.  all districts for the scenario, expending 42% of the exposure-reduction budget), and reduces the concentration from 106 to 53 µgm −3 . The Equal scenario saves 1070 lives in Delhi, representing 2.3% of the lives saved in the scenario but 8% of the person-PM 2.5 units in the budget. The Optimized scenario spends no resources on improving pollution from Delhi. In comparison, the Optimized scenario spends 9.4% of its budget of person-PM 2.5 units in the district of Bangalore (one-fourth as much of the budget as the Standard scenario spent on Delhi), reducing the concentration from 26.9 to 5 µgm −3 and saving 8200 lives.

Conclusion
In this paper we present an estimate of the relationship between all-cause premature mortality and PM 2.5 concentrations in India. For highconcentration countries, there is both a lack of empirical evidence on this relationship, and an underappreciation of the difficult tradeoffs that exist for air pollution policies. Those tradeoffs must strike a balance between saving the most lives and achieving goals of more equal pollution exposures across the population. The results of our thought experiment, comparing hypothetical policy scenarios, is designed to provide some clarity regarding both points.
Our empirical estimate of the C-R function shows clear evidence in support of the supralinear shape (see orange line in figure 1), which, for medium-low concentration locations, is largely consistent with the available literature. Below 40 µgm −3 , the curvature of our estimate is similar to GEMM, but the magnitude is slightly lower. For medium-high concentration locations we see a sharper bending down of the relationship than GEMM, and a substantially lower magnitude.
To compute the results of our scenarios (in particular the Optimized scenario), we found that it is necessary to reduce concentrations below the lowest observed concentrations in our sample, thereby taking our calculations outside the range of our observed data. As a sensitivity analysis, we reran our scenarios combining our log-log C-R function for concentrations in our sample (PM 2.5 ⩾ 17.1 µgm −3 ) with the GEMM C-R function for concentrations below 17.1 µgm −3 . The results are very similar, with modestly fewer lives saved in our Optimized scenario (see S.7 in supplemental information).
Our estimate indicates that in order to achieve large reductions in mortality, concentrations in the dirtiest locations require substantial reductions in PM 2.5 . This finding is consistent with a study in India showing that the avoided deaths from not building new coal power plants in India is lower in places with high pollution levels as compared to those places that are relatively cleaner [1]. Our panel (D) in figure 4 highlights this point, where the number of lives saved in Delhi approaches the number saved in Bangalore, which is much cleaner, only when a much greater level of cleanup is achieved.
The supralinear curvature is the essence of these difficult and perplexing tradeoffs. How should decision makers weigh the greater number of lives that could be saved by directing more resources to the already clean locations, against the unfairness of leaving behind those now suffering the effects of the worst pollution?
The current NAAQS policy in India aligns closely with the principles of environmental justice, focusing on the dirtiest places in India. Our analysis, however, suggests that the tradeoff of greater equality under a uniform standard is that fewer lives are saved. We recommend that policymakers acknowledge this tradeoff and wrestle with the implications of choosing one policy over another for their country based on its resources.
Our exercise is a substantial simplification of reality, and none of our three scenarios could be strictly implemented. First, our analysis assumes that the policy maker can focus on each location in isolation, but PM 2.5 pollution reductions are not confined to any one location, due to emissions dispersing up to thousands of kilometers from their source [24]. Second, the concept of person-PM 2.5 units is not directly analogous to any air pollution reduction policies, and probably overstates the resources required to reduce pollution in high-population locations. Still, we believe this is a useful concept for thinking about abatement resource allocation, and our results may offer a counsel of hope. The potential to improve human health through improvements in air quality, sizable even in the rich countries of the world, is especially large and striking in India. Further study of the health and policy implications of our findings might deliver real dividends for people.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.