## Main

There exist substantial concerns in the United States about the pervasive harms of racism, which modern scholarship conceptualizes as either active or passive normalization of racial or ethnic inequities1. (In this Article, we use ‘racism’ in the modern descriptive sense that does not hinge on the intent of the perpetrator(s); that is, actions and policies that promote race-based inequities are racist, whether or not such an outcome is intended.) Particularly worrisome is the potential for institutionalized (or systemic) racism—in the form of policies, regulations and norms that favour certain racial or ethnic groups2—to perpetuate such harm via democratic processes. Rigorous quantitative evidence of institutional racism can be difficult to come by because the effects of various social and institutional processes that may embed bias (for example, urban planning and environmental regulation) often overlap in space and time and thus stymie attempts at more specific attribution (for example, ref. 3). This in turn makes policy proposals that address racism head-on more difficult to justify. This has long been the case with environmental injustice, or the manifestation of systemic racism in environmental policymaking and enforcement4. (The term ‘environmental injustice’ is often used more broadly to describe disparities across multiple demographic dimensions, including, but not limited to, race and ethnicity. In this Article, for clarity, we use this more specific definition with a primary focus on racial and ethnic bias in environmental policy.)

Disparities in air pollution concentrations provide a clear example of this attribution problem5,6. Air pollution is linked to a wide range of negative health consequences7 and is estimated to cause nearly 9 million premature deaths globally per year8. On average, these health effects are not distributed evenly among different demographic groups9,10,11, running counter to the notion that society’s environmental burdens should be equally shared5,6,12. However, despite observable exposure gradients across racial and ethnic groups, causally ascribing such inequities to bias in environmental policy has proved difficult. (In this Article, we consider ‘environmental policy’ to be the full landscape of policies, laws, statutes, regulations and enforcement mechanisms governing environmental quality. This definition includes gaps; that is, existing loopholes, lack of regulation and non-enforcement of rules are also forms of policy.) Economic and other social policymaking (for example, housing, transportation, education) over generations has created the modern geography of who lives where. Over time, myriad physical and social confounds—including variable atmospheric transport processes13, economic inequalities10,14 and neighbourhood demographics9,15—have become correlated with present-day pollution exposures. As such, moving beyond simple observations of disparate but confounded exposures in contemporary cross sections to causal attribution of environmental injustice requires additional evidence. This can be achieved by a random perturbation to the status quo16; such a shock to the policy regime was provided by the initial COVID-19 economic shutdown in California17.

In early 2020, governments implemented unprecedented policies to limit the public health impacts of the COVID-19 pandemic, including stay-at-home orders and travel limitations, with California instituting some of the most aggressive lock-down measures in the United States18. The well-known side effect of these policies was widespread economic shutdown: businesses closed, factories shuttered and employees temporarily discontinued their daily commutes19. (In California, 60.51% of businesses reported a decline in demand, 22.27% reported closure due to government mandate and only 13.9% indicated that the pandemic had no impact on their business20; the transport sector accounted for an estimated 97.5% of the decline in CO2 emissions in spring 2020 over the same period in 201921.) Because pollutants such as particulate matter with diameter smaller than 2.5 μm (PM2.5) and nitrogen dioxide (NO2) are produced by transportation, industrial processes, energy production and agriculture22, pollutant concentrations tend to track aggregate economic activity23,24. The lock-down corresponded to reductions in both satellite and ground-based observations of NO2 and PM2.5 concentrations, particularly in transportation-heavy metropolitan regions25,26. We leverage this period (March–April 2020) as a natural experiment that partially disentangles the confounding underlying legacy of historical social and economic policy from average air pollution exposures by providing a comparison between shutdown and non-shutdown (status quo) pollution distributions.

We employ established generalized difference-in-differences methods to quantify declines in ambient concentrations of two criteria pollutants, ground-level PM2.5 and tropospheric column number density NO2, during March–April 2020 and test for the existence of heterogeneous effects associated with the racial and ethnic composition of neighbourhoods. We utilize data from a relatively new network of low-cost particulate matter monitors that are predominantly privately owned and deployed outside homes, along with data from state-run air-quality sensors, satellite measurements, demographic and socioeconomic information, geographic data and cell-phone-based location data. By combining these datasets, we disentangle the contribution of local conditions (income, mobility, urban geography, weather) to local air pollution exposures. Data on mobility—defined as the extent to which individuals spend time away from their homes—are particularly important: they characterize variability in the shutdown’s effect on the local activity of different communities, as essential worker status and economic insecurity are associated with less time spent at home27,28.

Because the reduction of pollution when shutting down most of the in-person economy corresponds to the pollution burden created by that portion of the economy, pre-pandemic, we interpret statistically larger reductions in air pollution exposures for minority racial and ethnic groups—conditional on other confounding factors—as evidence of embedded bias in the generation and control of pollution from the in-person economy in the status quo. (We use the term ‘in-person economy’ to refer to economic activity from businesses, including transportation to and from those businesses, that closed during the COVID-19 economic shutdown. As outlined in Executive order N-33-20 of the State of California, closures affected all businesses except those in 16 critical infrastructure sectors: chemical; commercial facilities; communications; critical manufacturing; dams; defence industrial base; emergency service; energy; financial service; food and agriculture; government facility; healthcare and public health; information and technology; nuclear reactors, materials, and waste; transportation systems; and water and wastewater systems sectors. We note that while these sectors had the option to stay open, many did not, or continued operations in a reduced manner.) Our approach also demonstrates complementary inequities in the monitoring of pollution, shedding light on a path towards pro-actively addressing the identified inequities through air pollution monitoring policy that is itself environmentally just.

## Results

Using daily and weekly pollution observations, along with demographic, geographic and mobility data, we estimate how much race and ethnicity alone explain the changes in air pollution exposures experienced during the COVID-19 shutdown in California. We account for time-varying factors (local mobility, weather, seasonality) and relatively static factors (population density, income, proximity to roads) known to contribute to heterogeneous pollution exposures. Our approach is described in detail in Methods as well as schematically in Fig. 1g and Extended Data Fig. 1.

Our study area and data are summarized in Fig. 1. Daily aerosol PM2.5 measurements are drawn from a network of 830 monitors (106 public monitors from the California Air Resources Board (CARB) and 724 privately owned PurpleAir monitors; Extended Data Fig. 2a) and cover the period from 1 January to 30 April for both 2019 and 2020 to facilitate comparison across economic conditions at the same time of year. The low-cost PurpleAir sensors have been shown to correlate well with research-grade mass-based sensors, although they tend to have a high bias, which we have corrected before analysis (Methods and Supplementary Information). The PM2.5 monitors are located in 733 unique census block groups (CBGs) across California. Satellite-derived tropospheric NO2 (Fig. 1b) measurements from the TROPOMI instrument cover close to all 23,212 CBGs of California (22,503) but at an ~weekly timescale due to the overpass frequency of the Sentinel-5 precursor satellite. Local social, demographic and geographic characteristics (Fig. 1c–f; Methods), including income and population shares for race and Hispanic ethnicity, are heterogeneously distributed across the state; for example, income tends to be higher in coastal communities and cities, and the southeast and Central Valley regions have higher Hispanic population shares. Asian population share is highest in Los Angeles and the San Francisco Bay Area; Asian persons represent over 50% of the population in more than 1,400 CBGs. By contrast, fewer than 300 CBGs have majority Black populations, and these are spread more evenly throughout the state. (We use terminology derived from the census (Methods); Hispanic ethnicity is tallied independently of other race information in the United States and is therefore not mutually exclusive from race (Supplementary Fig. 1)). This complex human geography demonstrates the importance of rich measurement networks in addressing questions of environmental justice. The PurpleAir monitors provide a sevenfold increase in the number of sampled CBGs, although this increase still represents only 3.2% of all California block groups (Supplementary Information).

In 2019 (the year before the pandemic), without controlling for other sources of heterogeneity, areas with lower income and larger Black and Hispanic population shares were exposed to higher-than-average concentrations of both PM2.5 and NO2 compared with wealthier and White, non-Hispanic communities (Extended Data Fig. 3). Such descriptive air-quality differences have long been noted by environmental justice scholars and advocates29,30,31,32,33, but these relationships are confounded by other drivers of pollution exposures (Extended Data Fig. 1). It is thus difficult to isolate any potential racial or ethnic bias in environmental policy from economic forces or other policies that contributed to the distributions of different populations around the state (for example, redlining)34.

The COVID-19 pandemic temporarily removed a large portion of this confounding economic geography by ‘turning off’ most local in-person economic activity in the state. Figure 2 shows the depth and dimensions of this natural experiment across the state. The unique response to the spread of COVID-19, including stay-at-home orders, precipitated a steep decline in the average fraction of the day that people spent away from their homes (hereafter, mobility), which took a little under two weeks after the statewide emergency declaration (4 March 2020) to fully emerge (Fig. 2a). Importantly, reductions in time away from home did not occur equally for all state residents. CBGs with relatively high Hispanic population shares had both higher baseline mobility and much smaller mobility reductions during the shutdown than those with relatively low Hispanic population shares (Fig. 2b and Supplementary Table 1). This is probably due to the greater designation of essential jobs and economic vulnerability among Hispanic populations, relative to non-Hispanic populations, that preclude working from home35. This disparity is present, although much less pronounced, for CBGs with high and low Black population shares, and the pre- and post-shutdown differences are reversed for CBGs with high and low Asian population shares. We account for these different local responses in the statistical framework described below.

Using a series of generalized difference-in-differences models (Methods), we estimate the relative magnitudes of the reductions in PM2.5 and NO2 concentrations before and after the shutdown (adjusting for 2019 concentrations) across different demographic gradients (we show and discuss PM2.5 results in the main text, with NO2 results in the Supplementary Information, for brevity). The best-fit coefficients for these models (Supplementary Tables 2, 3, 6 and 7, Fig. 3 and Extended Data Fig. 4) correspond to the statistically identifiable expected changes in air pollution, across the COVID-19 shutdown window, for a 0% versus 100% share of a given demographic group at the CBG level, or roughly a doubling of non-share variables (for example, income, road density, population density). (We note that estimating the population average change would require a stronger statistical assumption than we make about the similarity of other conditions between 2019 and 2020 (for example, seasonality; see Methods).) These coefficients show that lower-income neighbourhoods in California experienced greater reductions in PM2.5 concentration (Fig. 3a); the positive and statistically significant coefficient for income indicates that lower incomes were strongly associated with a greater reduction of pollutant levels during shutdown. For example, our estimates indicate that a block group with an average income that is half that of a wealthier block group would have experienced a 1.0 μg m–3 greater reduction in PM2.5 exposures. Changes in mobility, road density and population density at the level of a CBG are only weakly associated with changes in PM2.5 concentrations (Fig. 3a).

We consider mobility to be a proxy for local pollution-causing economic activity and assume that decreased mobility directly corresponded to reduced vehicle emissions along with a suite of local business-related emissions (for example, restaurant closures). Therefore, the relationship between the relative decline in local mobility and the relative decline in local air pollution gives insight into the pollution impacts of a block group’s own economic activity. Figure 3b and Supplementary Table 4 show that residents in lower-income neighbourhoods reduced their mobility less than those in richer neighbourhoods during the shutdown period. Combined with the fact that lower-income areas experienced a larger drop in PM2.5 concentrations, this finding suggests that local activity is not the primary driver of disparate exposures across the income gradient in California.

To further probe potential heterogeneity in the magnitude of shutdown impacts, we examine exposure changes across neighbourhood demographic gradients, with and without accounting for various local characteristics (Fig. 3c,e and Supplementary Tables 2 and 3). We identify substantial racial and ethnic disparities in air-quality improvements, even when accounting for income, road and population density and very fine-grained differences in weather patterns over space and time that strongly affect surface pollutant concentrations (Methods and Supplementary Information). We first examine the gradient for all non-White populations (that may also be Hispanic) and then decompose this group into the three largest racial and ethnic subgroups in the state. A ten-percentage-point increase in the non-White population share of a census block is associated with a 0.26 μg m–3 reduction in PM2.5 concentration after the shutdown. This falls to about 0.23 μg m–3 once we include local mobility and allow for heterogeneous effects of the shutdown in terms of income, road density and population density (mobility impacts are shown directly in Fig. 3d and Supplementary Table 4). The decomposition reveals similar estimates for Hispanic and Asian populations, where we find reductions in PM2.5 concentrations of 0.29 and 0.23 μg m–3 per 0.1 increase in population share, respectively. We interpret this as evidence that in-person economic activity places a disproportionate pollution burden on non-White (and specifically Hispanic and Asian communities), only about a seventh of which is explained by differences in incomes and other location characteristics.

Hispanic and Asian are the two largest racial and ethnic minority groups in the state, making up about 39% and 16% of the population, respectively. While they share some similarities in historical inequitable treatment, there are several major differences in the socioeconomic attributes of the two groups. Acknowledging that we necessarily aggregate diverse subpopulations within racial and ethnic groups36 (Supplementary Information), Asian Californians are predominately concentrated in urban areas and have on average higher incomes and education, whereas Hispanic populations are more skewed towards rural areas and have on average lower incomes and education.37 Moreover, as described, the two groups had different baseline exposures and opposite average mobility responses to the shutdown. Despite these large circumstantial differences, their disproportionate exposure to economy-scale pollution is substantially similar, providing strong, albeit indirect, evidence of the influence of systemic racism in the mechanisms and institutions responsible for pollution control.

We do not find statistically significant pollution reductions associated with increased Black population share. That is, while the shutdown economy became more equitable in its pollution distribution vis-a-vis Hispanic and Asian communities, the same was not true for Black neighbourhoods, where substantial baseline pollution gradients remained unchanged. This may be in part statistical—the overall Black population share is around 7% and there are relatively few majority Black CBGs in the state (Fig. 1f)—but it also suggests that the in-person economy is not the main driver of pollution disparities for Black communities in California.

The findings from surface air-quality data are largely consistent with results from an analogous set of models using weekly satellite-derived NO2 concentrations as the outcome, although some small differences between the two reflect both coverage discrepancies and the distributions of PM2.5 and NO2 sources in the state (Extended Data Fig. 4 and Supplementary Tables 6 and 7). The PM2.5 results are also robust to consideration of sub-regions of California, for example, excluding Los Angeles, the Central Valley or both (Extended Data Fig. 5), suggesting that the findings are not driven by the seasonality of pollution, different pollution sources, demographics or unique airshed dynamics of these key regions. For both pollutants, the importance of accounting for fine-grained weather patterns is evident from the difference (for example, in Fig. 3 and Extended Data Fig. 4) between estimates from our full model (All) and a model that includes all controls except weather (‘w/o weather’). Prevailing weather patterns (Methods) that potentially transport pollution do account for some of the exposure disparities observed, with some variation by region and pollutant, but do not fully explain the observed patterns.

## Discussion

In this Article, we provide new causal estimates of unequal air pollution exposure reductions experienced during California’s COVID-19 economic shutdown. Because these reduction disparities are associated with widespread economic curtailment, they point to systemic racial and ethnic bias in the status quo generation and control of air pollution from the state’s in-person economy. While this finding is robust to various specifications and data subsets, and is consistent across surface- and satellite-based data, our analysis nevertheless requires some contextualization and care in interpretation.

Importantly, while we note that exposure disparities are not explained by local mobility, the ability to fully distinguish local and non-local economic activity is limited, and representative spatial scales of local versus non-local may vary (for example, geographically, culturally or seasonally). We additionally note that while we focus on the non-local drivers of exposure disparities, local mobility-related pollution generation may nevertheless be caused by structurally unjust policy in other sectors (for example, housing or transportation). More broadly, it is important to recognize that contemporary and historical biases in other policy areas can lead to disparate average exposures, even if environmental policy surrounding the in-person economy were unbiased. This may be what explains our finding of higher average pollution exposures, but no disproportionate air-quality benefit from the COVID-19 shutdowns, for Black communities in California.

Our analysis consistently identified that lower-income communities in the state are disproportionately affected by pollution from the in-person economy. While we primarily employed income as a control, this income disparity represents an important concern in and of itself and presents policy challenges that are unique from those associated with combating institutional racism. California has one of the highest rankings for income inequality among US states37, and our findings provide additional evidence that wealthier communities both are able to buy environmental quality (for example, via higher housing prices that embed air quality) and can afford to stay at home more fully during a pandemic.

Our empirical results complement a growing body of literature that uses chemical transport models (or reduced complexity models) to estimate pollutant exposures and map them to local socioeconomic and demographic characteristics. Importantly, such studies have been instrumental in identifying that a vast array of pollution sources contribute to baseline exposure disparities15. While these tools have become ever more powerful and accurate, and have the benefit of full coverage (compared with sparse monitoring networks), they do require accurate emissions inventories as inputs. Such inventories have rapidly improved in temporal resolution for long-lived greenhouse gases (for example, ref. 21) but remain notoriously uncertain for air pollution, especially over short timescales and under abnormal economic conditions38. Our analysis strategy based on high-frequency observations of actual ground-level (or atmospheric column) pollution does not require emissions inventories and is thus well suited for understanding short-run changes in a way that modelling studies would be unable to capture.

Nevertheless, statistical studies like ours require accurate and unbiased characterization of the system under study and have their own shortcomings. For example, we cannot illuminate some of the more specific mechanisms of shutdown-induced variation in air pollution, such as whether being near to and downwind from a major road is more likely for ethnic/racial minorities39,40. A key point of contrast to modelling studies is that we do not explicitly account for individual point source emissions or wind, but instead use areal road density summaries (Methods), and detailed temperature, precipitation and relative humidity controls (see Extended Data Fig. 6), to capture much of this variation. Because our analysis focuses on differences within census blocks over time, the average influences of these and other unobserved factors are taken into account. Still, we cannot rule out that some of our measured effects may be driven by either variations in emissions or meteorological conditions that are correlated with both the demographic characteristics of a neighbourhood and the COVID-related shutdown. Future studies could focus on more thoroughly accounting for natural seasonal swings in air pollution and the full range of its spatial and temporal variability through the inclusion of more years of data17. This was not possible here due to the short timescale of PurpleAir and Sentinel data availability; however, our use of 2019 as a comparison for 2020, and the similarity of estimates made with pre- and post-shutdown 2020 data alone (Supplementary Table 8), underscore that the exposure disparities we estimate are not likely to be systematically changed by inclusion of more years of observations.

Beyond revealing disparities in pollution exposure generated by the in-person economy, our analysis also highlights inequality in local air pollution information. As we show, monitor placement matters for detection of exposure gradients. CARB recently re-focused air-quality monitoring in designated environmental justice communities41, which has resulted in a more accurate sample of the state’s Hispanic population distribution than (for example) PurpleAir. The PurpleAir monitoring network, established through the individual purchase and placement of (relatively) low-cost sensors, shows that citizen-science networks can be exceedingly useful for increasing the amount of public data but that those networks are unlikely to be optimally placed for addressing environmental justice questions (for which sensors are needed that accurately reflect the spatial distribution of all subpopulations). PurpleAir sensors also require care in correcting biases compared with monitoring-grade instruments42. On the public monitoring side, local governments that are responsible for choosing locations of sensors mandated by the Clean Air Act (that is, CARB) may also strategically place sensors to improve their chances of being in attainment43,44. This strategic placement reduces the ability of those sensor networks to detect environmental injustice45 and makes adjustments for sampling bias, such as those proposed here, relevant for the larger literature (Supplementary Information). In addition, while we show that satellite-based observations can be helpful in understanding the spatial distribution of pollutants that underlies ground-based monitoring network samples, satellite data are spatially coarse compared with the average CBG and are more limited temporally (Supplementary Information). As such, satellites may not be able to replace ground-based monitoring when high spatial and temporal resolution are required. While a more spatially dense ground measurement network would vastly improve the ability to detect and address environmental injustice, reliability, cost, distribution and data curation would need to be considered in choosing a scale-up strategy46,47.

Finally, while our analysis documents that the generation and control of pollution from California’s in-person economy disproportionately and negatively affects the state’s largest racial and ethnic minority communities, it also has potential applications in environmental policymaking. The United States has a multidecadal history of justifying environmental regulation through the use of an efficiency-based net benefit criterion (the simple objective that regulatory benefits exceed costs)48,49. Many state and federal entities additionally mandate that regulatory impact analysis include assessment of impacts to disadvantaged and vulnerable groups (for example, refs. 49,50), and recently this has been identified as a major environmental policy priority51. It is difficult, however, for equity considerations to obtain equal footing with efficiency criteria when best practices for benefit–cost analysis are strictly codified52, but there is no standard assessment criterion for justifying interventions that mitigate inequities53. For race- and ethnicity-based equity considerations, our methodology suggests that a net equalization criterion for environmental regulation could be constructed as follows and utilized in conjunction with benefit–cost analysis:

$$\begin{array}{lll}{\mathrm{Net}}\ {\mathrm{Equalization}}&=&{{\Delta }}{\mathrm{Exposur{e}}}_{{\mathrm{non}}{\mbox{-}}{\mathrm{White}}| {\mathrm{Income}}}\\&&-{{\Delta }}{\mathrm{Exposure}}_{{\mathrm{White}},{\mathrm{non}}{\mbox{-}}{\mathrm{Hispanic}}| {\mathrm{Income}}}\end {array}$$
(1)

In this framework, the pollution reduction effect we identify as associated with the COVID-19 shutdowns had a net equalizing effect (although absent inclusion of public health benefits, uniform reduction of regional economic activity would be unlikely to satisfy the net benefit criterion). (As in our analysis, controlling for income would be critical for any equalization criterion, not just because income can be a confounding factor in identifying environmental racism, but also because the policy mechanisms by which societies might address income-dependent environmental injustice are different from those for addressing environmental racism.) When systemic bias is driving adverse outcomes, public policy intervention focused narrowly on addressing market failures may eventually result in reversion to inequality54. Revising regulatory impact analysis protocols to include a clear, quantitative equalization standard would instigate a shift in focus of environmental regulation beyond efficient reduction of externalities.

## Methods

### PM2.5 data

Surface station measurements of PM2.5 were downloaded from publicly available PurpleAir and CARB databases (Extended Data Fig. 7). We downloaded all outdoor PurpleAir data available (1,891 individual stations) for January–April 2019 and 2020. PurpleAir sensors are relatively inexpensive and are usually privately owned, but much of the data is publicly available. The quality of these data are lower than that of data from regulatory monitors, but PurpleAir sensors provide unprecedented spatial coverage. Most PurpleAir sensors contain two Particulate Matter Sensor 5003 sensors (Plantower), which measure particle counts in six size bins. Counts are converted to PM2.5 using two proprietary conversions, one intended for indoor use and the other for outdoor use; we use the outdoor conversion as recommended and tested by ref. 55. We also average the two sensors (when available) and exclude days when daily PM2.5 measurements within the same unit differ by at least 5 μm m−3 and at least 16% (ref. 42). In limited field evaluations, PurpleAir sensors have been shown to have strong correlations with high-quality sensors55,56,57,58. Ref. 55 also proposed a correction for effects of relative humidity, which we do not apply in part because we consider daily data rather than sub-daily. We do, however, apply a correction developed by the US Environmental Protection Agency, which tends to slightly over-correct the high bias of the PurpleAir instruments, meaning the presented results from these sensors are conservative (Supplementary Figure 2)42.

We retrieved (1 May 2020) all hourly CARB PM2.5 data in California available for January–April 2019 and 2020 using CARB’s Air Quality and Meteorological Information System (150 individual stations). Professional instruments and oversight, particularly for calibration, provide higher confidence in the data quality of the CARB sites. However, there are an order of magnitude fewer CARB stations than PurpleAir sensors in California, which means studies using the government data are statistically limited by a relatively small sample size. Unlike PurpleAir sensors, CARB sites often offer a wide variety of air pollutant measurements, although we use only hourly PM2.5 aggregated to the daily mean. For both CARB and PurpleAir data, days with mean PM2.5 equal to zero or greater than 500 μg m−3 are removed as outliers. Sites for which we remove more than 10% of data are excluded from the entire analysis. Sites with less than 80% data coverage during our study period are also excluded. For models that require 2019 and 2020 data, we apply these requirements to both years independently. This quality filtering removed 5.9% of daily CARB PM2.5 data and 11.4% of daily PurpleAir data, resulting in data from 1,664 individual stations (119 CARB and 1,545 PurpleAir). However, only 830 of those (106 CARB and 724 PurpleAir) include data for 2019 and 2020 for the pre-shutdown and shutdown period and were therefore used in our empirical statistical analysis.

### NO2 data

We used the Copernicus Sentinel-5 Precursor Tropospheric Monitoring Instrument (TROPOMI, version 1.03.02) offline tropospheric NO2 column number density59 for mean NO2 concentrations of the developed areas of each CBG. TROPOMI has a resolution of 0.01 arc degrees. Data were collected for January–April 2019 and 2020 and only for developed areas according to the US Geological Survey National Land Cover Database 201660. For this study, all data were prepared using the Google Earth Engine Python API61 and formatted as weekly means for each CBG. Weekly means were chosen to counteract the high frequency of missing data, particularly in northern California (Extended Data Fig. 8).

### Climate data

For temperature, precipitation and relative humidity, we relied on the Gridded Surface Meteorological dataset62. This dataset provides daily information at 4 km resolution across the continental United States. For this study, data were aggregated in Google Earth Engine61 in its original daily frequency (for PM2.5 analysis) and as a weekly mean (for NO2 analysis) for each CBG. The weekly mean data were aggregated only for developed areas according to the US Geological Survey National Land Cover Database 201660.

### Mobility data

We use SafeGraph’s Social Distancing Metrics63, which were made available for research as part of the company’s COVID-19 response and have been validated elsewhere (for example, ref. 64). SafeGraph collects and cleans GPS pings from about 45 million mobile devices. The data are available daily at CBG resolution and are close to a random sample of the population. Our primary measure of mobility is not social distancing but rather the percentage of time spent away from home. We calculate this measure on the basis of the median time (in minutes) that a device was observed at its geohash-7 (about 153 m × 153 m) home location, which SafeGraph determines as the night-time residence of the device in the six weeks before. The data cover the entire period of observation from 1 January 2019 until the end of April 2020.

### Demographic data

We downloaded CBG-level demographic information from the US Census Bureau 2018 5 yr ACS for all CBGs in California using the tidycensus package65 for the R programming environment66 (29 June 2020). Demographic features included ACS sample-based CBG-level estimates of population count; White race count (alone or in combination with one or more other races), or ‘White’; Black or African American race count (alone or in combination with one or more other races), or ‘Black’; Asian race count (alone or in combination with one or more other races), or ‘Asian’; Hispanic or Latino origin (of any race) count, or ‘Hispanic’; and median income. The other census race designations (American Indian or Alaska Native; Native Hawaiian or Other Pacific Islander) represent a substantially lower share of the California population and were therefore excluded from our analysis due to small sample sizes. The CBG-level ‘share’ of these groups was calculated by dividing the CBG count by the CBG population. Population density was calculated as the CBG population divided by the area of the CBG. For the aggregate comparison, we compute the share of the non-White population that may be Hispanic as one minus the share of Whites that do not also identify as Hispanic. Because Hispanic is a separate designation from race in the ACS (that is, those categorized as Hispanic may also be of any race), we evaluated how distinct Hispanic was from race variables of interest (Supplementary Fig. 1). On average, less than 1% of those identified at the CBG level as Hispanic were also identified as Black or Asian; 61% of Hispanic were White. Thus, Hispanic is effectively distinct from Asian and Black categorizations, and we consider Hispanic, Asian and Black designations to be unique demographic indicators in our model. The baseline reference group in the more detailed comparison contains all other races and ethnicities and therefore consists almost entirely of people who identify as non-Hispanic White.

### Study period and design

We consider three periods between 1 January and 30 April in 2019 and 2020. The first period is ‘pre-shutdown,’ followed by a ‘transition’ and then ‘shutdown.’ The transition is defined as the period between the statewide emergency declaration (4 March 2020) and the statewide stay-at-home order (19 March 2020). The mobility data demonstrate that activity declined throughout this period (Fig. 2). This is consistent with recent literature that shows that fear was a potent driver of the decline in mobility and often pre-empted county-wide legal restrictions69. The shutdown period begins with the stay-at-home order and ends at the end of our study period. We exclude the transition from the analyses described below. This precludes the use of variation in treatment timing to assist with causal identification. Instead, we proceed by using the interaction between the shutdown and racial or ethnic composition of CBGs as the treatment, allowing us to directly estimate the additional pollution burden of economic activities that were halted during the shutdown on block groups with certain demographic compositions. This is standard practice, referred to as ‘generalized difference in differences’ (see Supplementary Information for details). In our case, there is no group that remains untreated and no variation in treatment timing but heterogeneity in treatment intensity.

### Empirical strategy

In our statistical analyses, our main dependent variable is an (average) measure of air quality (PM2.5 or NO2) in CBG i at day (or week) t. We focus on block groups to minimize the influence of aggregation bias or the ‘ecological fallacy’70 and study temporal variation in air quality across block groups using a difference-in-differences design. Difference-in-differences methods are commonly used to study causal effects in economics71. Our objective is to estimate the heterogeneity in the effect of the shutdown across different communities rather than the overall effect of the shutdown. We focus on the racial and ethnic composition of CBGs using population shares of California’s three biggest racial and ethnic minority groups (Hispanic, Asian and Black). We first establish the existence of air pollution exposure reduction inequities and then include a rich set of controls to assess the racial and ethnic inequities that remain after accounting for differences in mobility, income and location72,73,74.

A key concern is that differences in air quality are driven by interannual cycles in pollution and particle concentration that are unrelated to the shutdown75. We address this issue in several ways. First, we subtract observed air quality in 2019 from the 2020 value. All annual differences, after aligning the weekdays, are denoted by $${\tilde{y}}_{it}={y}_{it}-{y}_{i,t-364}$$. Second, we flexibly control for local weather conditions in 2020 and 2019 (see Extended Data Fig. 6 and Supplementary Information for details on selection of weather controls). Finally, we allow for a rich set of day or week fixed effects that capture the remaining differences in synoptic scale weather patterns. Putting all this together, we use Ordinary Least Squares to estimate the heterogeneous effect of the shutdown using variants of the following specification:

$$\begin {array}{l}{\tilde{y}}_{it}=\mathop{\sum }\limits_{k}{\gamma }_{k}\left({d}_{t}\times {x}_{i}^{k}\right)+\theta {\tilde{M}}_{it}+{f}^{2020}{\left(T,{\mathrm{RH}},P\right)}_{it}+{f}^{2019}{\left(T,{\mathrm{RH}},P\right)}_{it}\\\qquad+{\lambda }_{t}+{\mu }_{i}+{e}_{it}\end {array}$$
(2)

where dt is an indicator for the post-shutdown period, $${x}_{i}^{k}$$ are the population shares of the three minority groups studied here or other (relatively) time-invariant location characteristics k that vary at the CBG level, $${\tilde{M}}_{it}$$ is the annual difference in mobility on day t in CBG i (constructed analogously to $${\tilde{y}}_{it}$$), $${f}^{2020}{\left(\cdot \right)}_{it}$$ and $${f}^{2019}{\left(\cdot \right)}_{it}$$ approximate the nonlinear response of pollution and particle concentration to weather with interacted fixed effects for each decile of temperature (T), relative humidity (RH) and precipitation (P) in the corresponding year, λt are day (or week) fixed effects, μi are CBG fixed effects (capturing changes in the number of stations in a block group across years), and eit is an error term. We cluster all standard errors on the county level, as stay-at-home and local health ordinances are spatially and temporally correlated at this level.

We are interested in γk, which captures the heterogeneous impact of the shutdown across different demographic gradients (see Supplementary Information for a derivation). The baseline effect of the shutdown, dt, is not statistically identified without the assumption of constant seasonal emissions patterns, as that baseline effect occurs simultaneously for all block groups in California (Extended Data Fig. 9) and is therefore collinear with seasonal shifts in air quality that are unrelated to the COVID-19 shutdowns. Heterogeneous impacts are identified by variation among block groups experiencing a COVID-19 shutdown-related air pollution change only and can be interpreted as the effect of the shutdown relative to some baseline. This requires a weaker assumption: that the interannual differences in pollution are not simultaneously correlated with the timing of the shutdown and the spatial distribution of race and income. Our weather controls make this a plausible assumption by accounting for systematic differences in temperature, humidity and rainfall across different parts of the state. We interpret the coefficient on dt × %Hispanic as the difference in pollutant concentration for a block group that is 100% Hispanic relative to a block group that is 0% Hispanic. Differences in air pollution concentrations across the shutdown window are typically reductions in air pollution, which we consider to be equivalent to the expected increase after a return to ‘business-as-usual’ conditions. We address the representativity of monitor placement in both CARB and PurpleAir networks by comparing estimates based on each network alone, both networks combined, and both combined with weights derived to make the sampled locations (that is, CBGs with monitors) match state demographics (see Extended Data Figs. 2b and 10, and Supplementary Information for details).

### Software

All data processing and analysis other than acquisition and pre-processing of mobility information were done using the R programming environment66 and the Python API for Google Earth Engine61. ArcGIS was used to make the maps in Fig. 1 and Extended Data Figs. 2 and 8, and Adobe Illustrator was used for final assembly of composite figures.

### Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.