Effects of thermal inversion induced air pollution on COVID-19
EEffects of thermal inversioninduced air pollution on COVID-19 ∗ Klauber, H. † , Koch, N. , and Kraus, S. Mercator Research Center on Global Commons and Climate Change (MCC) Potsdam Institute for Climate Impact Research (PIK) Technical University of Berlin (TU)
November 24, 2020
Abstract
Air pollution is a threat to human health, in particular since it aggravates respiratory dis-eases. Early COVID-19 outbreaks in Wuhan, China and Lombardy, Italy coincided withhigh levels of air pollution drawing attention to a potential role of particulate matter andother pollutants in infections and more severe outcomes of the new lung disease. Bothair pollution and COVID-19 outcomes are driven by human mobility and economic ac-tivity leading to spurious correlations in regression estimates. We use district-level paneldata from Belgium, Brazil, Germany, Italy, the UK, and the US to estimate the impact ofdaily variation in air pollution levels on COVID-19 infections and deaths. Using randomvariation in air pollution generated by thermal inversions, we rule out that changes inmobility and economic activity are driving the results. We find that a 1%-increase in airpollution levels over the three preceding weeks leads to a 1.5% increase in weekly cases.A 1%-increase in air pollution over four weeks leads to 5.1% more COVID-19 deaths.These results indicate that short-term measures to reduce air pollution can help mitigatethe health damages of the virus.
The detrimental effects of air pollutants on human health are well documented and somereductions in human exposure to them can be achieved fast and at low-cost. Since COVID-19 is a respiratory disease, policy-makers are considering short-term measures against airpollution as a means to mitigate infections and severe outcomes from the disease. A UKHouse of Commons working group, the
All Party Parliamentary Group Air Pollution , has forinstance launched a strategy to reduce COVID-19 risks associated with air pollution. InFrance, local politicians have called on the national government to take "emergency mea-sures", for instance to create low emissions zones, limit the use of liquid manure, and re-place old wood stoves. ∗ We thank Jeffrey Wooldridge for advice on our two-stage procedure. We thank Yujie Wang for advice withthe air pollution data. † Corresponding author, [email protected] a r X i v : . [ phy s i c s . s o c - ph ] A ug arly research has shown an association between COVID-19 outcomes and long-term and short-term air pollution exposure for specific individual regions or countries.Air pollution is not randomly assigned to places, but results from different dimensions ofhuman behaviour, some of which cannot be measured. Therefore, any correlation betweenair pollution and COVID-19 outcomes is likely to be biased. Air pollution levels have fallenas a result of COVID-19 outbreaks and lockdowns. This pollution reduction can be dueto direct behaviour changes as a reaction to the health threat, such as less car use (reversecausality) or due to a third, omitted variable that is driving both air pollution and COVID-19 outcomes, such as policy changes that occur independent from local infection clusters.We expect these reductions in air pollution to lead to substantial improvements in generalhuman health Cicala et al. [13], but a robust cross-country estimate of the effects of air pol-lution reductions on COVID-19 outcomes is still lacking.Here, we use thermal inversions that trap air pollution as a natural experiment to esti-mate the links between short-term increases in air pollution and COVID-19 infections anddeaths. Satellite imagery and climate models let us measure thermal inversions and air pol-lution at high spatial resolution. We compile data from all countries that publish COVID-19infections or deaths at the district-level to match the scale of our local weather-driven nat-ural experiments. Our baseline sample comprises a geographically diverse set of countries– Belgium, Brazil, Germany, Great Britain, Italy and the US. Therefore, we expect our anal-ysis to have higher external validity than individual-country studies.
We use quasi-experimental methods from panel data econometrics to estimate the effect ofair pollution on the number of infections and deaths from COVID-19. Rather than buildinga statistical model that fits the evolution of the pandemic well, we aim at recovering a singleparameter. To this end, we use a Poisson model with case and death counts as the outcomesand air pollution predicted by the strength of thermal inversions as the treatment. Similar"reduced-form" approaches have for instance been applied to study the effect of weatheron influenza and the effect of anti-contagion policies and weather on COVID-19.Since it is difficult to find an empirical context, where individuals are plausibly randomlytreated by air pollution, our parameter of interest can be best recovered in an ecologicalstudy. We use thermal inversions that generate random temporal and spatial variation inair pollution as a natural experiment. These episodes of lower temperatures at the groundlevel than in higher pressure levels trap air pollution. Our estimates are exclusively basedon shifts in air pollution that are caused by these inversion events. This directly addressesconcerns about reverse causality. For this instrumental variable approach to also restricttreatment variation to plausibly random variation, we need to argue that after removingvariation with additional variables and fixed effects there is no other causal channel fromthermal inversions to COVID-19 outcomes. This is called the "exclusion restriction". In-versions do not impact human health directly, but there could be a number of threats to ourresearch design, which we address as follows.2istrict-level data on cases and deaths allows us to control for time-invariant features, suchas topography, institutional strength or social capital at a high geographical resolution. Wedo this with a vector of dummy variables ("fixed effects") for each district in the sampleleaving out one. This means we are only using changes within the same district over timeto estimate our effect. Thereby we rule out that differences between districts in baselineconditions that are due to a history of inversions and human sorting behaviour as a reac-tion to pollution are driving the effect. We also absorb time-varying factors at the country-month and week levels.If, after removing fixed effects, there remained causal channels between thermal inversionsand COVID-19 outcomes that do not run through air pollution changes exclusively, the ex-clusion restriction would be violated. This could be the case if people are more prone tousing their cars on days with inversions or if people spend more time with others indoorsas a result of the temperature changes that create thermal inversions. We use thermal in-versions at night, since day-time inversions can sometimes be seen and, thus, may createa systematic link between inversions and outcomes that violates the exclusion restriction.We also control for weather variables, such as precipitation, ground temperature, wind andUV radiation that vary daily at the district-level.Our measure of thermal inversions is based on data from the ERA5 climate model and asour air pollution variable we use fine particulate matter smaller than 2.5 µ m in diameter( PM ) measured by Aerosol Optical Depth on MODIS satellite images. Since COVID-19outcomes are affected with time-lags, we estimate the effect of thermal inversion inducedair pollution changes during the current and two preceding weeks on weekly cases andcurrent and three preceding weeks on weekly deaths. We also investigate the daily evolu-tion of cases and deaths. This allows us to show that our results are robust to estimatingour effect only based on variations within districts in the same month and removing allfactors that vary in the same state on a weekly level and in the same country on a dailylevel. These could be changes in policies, economic activity, medical system performance,and testing regimes that introduce trends in our model that bias the comparisons betweentreated and control units at any given day and in any given intensity and that fixed ef-fect regressions implicitly control (see Methods Section 5.5 for a discussion of the commontrends assumption). The effect of thermal inversions on ambient air pollution
First, we present evidence that the relationship between thermal inversions and ambientair pollution is strong. Table 1 shows the estimated effect of an additional degree in inver-sion strength on the logged mean PM concentration. Because we assume that infectionsand deaths may be impacted by pollution with varying time lags, we estimate two differ-ent First Stage specifications. The left panel of Table 1 presents the effect of inversions onaverage PM concentrations in a three-week time window, while the right panel uses afour-week time window. 3he positive and statistically significant coefficients as well as F-statistics well above 10 inTable 1, show that inversions increase ambient particulate matter pollution robustly acrossspecifications. For instance, the coefficient in column (3), indicates that a 1-degree increasein inversion strength increases the average three-week PM concentration by about 0.58%.On average, the strength of an inversion on a single day equals 2.27. Our effect estimatetherefore implies that an additional weekday with an inversion leads to a 3.95% increasein the weekly PM level (0.0058 · · · · PM and PM range from 2 to4% when converted to the week-level. Sager [18] shows that the effect of a 1-degreechange in inversion strength increases the daily PM .5 concentration by about 10.47%. Thiscorresponds to a 0.50%-increase in the three-week and a 0.37%-increase in the four-weekpollution concentration, which is close to the effects estimated in Table 1. logged PM three-week window four-week window(1) (2) (3) (4) (5) (6) inversion strength ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ( 0.0006) ( 0.0006) ( 0.0006) ( 0.0006) ( 0.0007) ( 0.0007)F-statistic 93.51 163.95 104.39 17.08 23.08 25.61Observations 101,046 101,046 101,046 65,569 65,569 65,569Countries BEL, BRA, DEU, GBR, ITA, USA BEL, BRA, DEU, USA weather controls yes yes yes yes yes yescontainment controls yes yes yes yeshealth system controls yes yesIn each panel control variables are added sequentially from left to right. The first set of controls contains weather variables only, thesecond set adds controls for COVID-related containment and closure policies (e.g. school closings and stay at home requirements),and the third set adds COVID-related health system policies (e.g. testing policies and contact tracing). All regressions includedistrict, week and state-month fixed effects. Standard-errors clustered at the district level are in parentheses.Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 1: The effect of thermal inversions on ambient air pollution
The effect of ambient air pollution on COVID-19 outcomes
Next, we estimate how inversion-driven increases in air pollution affect COVID-19 infec-tions and deaths. The left panel of Table 2 presents coefficients from regressions of theaccumulated number of infections on the average predicted PM concentration over thepreceding three weeks. The right panel presents coefficients of the accumulated numberof deceased COVID-19 patients on the average predicted PM concentration over thepreceding four weeks. The reported coefficients represent elasticities, that is percentagechanges in the dependent variable linked to a 1%-increase in the PM mean. For instance,column (3) indicates that with every 1%-increase in PM in the preceding three weeks, thecase numbers grow by 1.478%. Given that we control for the accumulated case numbersof the preceding week, this 1.478%-change takes place over a 7-day period. Table 2 alsopoints to mortality effects. Column (6) shows, that a 1%-higher pollution level in the pastfour weeks is linked to 5.120% higher death counts. Again, this relative change refers tothe death count level seven days ago. 4he effect on case numbers and deaths becomes evident only when including policy con-trols. Regulations that are to restrict the spreading of the virus as well as changes in testingregimes both likely have a strong effect on the number of COVID-19 infections and caseseventually registered. Moreover, the different magnitudes of the coefficients in the left andright panel, point to a change in the rate of survival in registered COVID-19 patients. Ifdeaths increased exclusively because the total number of patients increased, we would ex-pect the relative effects to be approximately equal in magnitude. The difference could beexplained if air pollution increases the severity of the disease or if it increases the share ofvulnerable people in the registered patients. To ensure that the differences across panels isnot simply caused by the differing samples used, we re-estimate the left panel regressionswith the sample including only Belgium, Brazil, Germany, and the USA. The estimated ef-fects are very similar in magnitude. COVID-19 cases COVID-19 deaths three-week window four-week window(1) (2) (3) (4) (5) (6) predicted logged PM − ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ( 0.317) ( 0.189) ( 0.276) ( 2.607) ( 1.741) ( 1.632)Observations 72,021 72,021 72,021 20,658 20,658 20,658Countries BEL, BRA, DEU, GBR, ITA, USA BEL, BRA, DEU, USA weather controls yes yes yes yes yes yescontainment controls yes yes yes yeshealth system controls yes yesIn each panel control variables are added sequentially from left to right. The first set of controls contains weather variables only, thesecond set adds controls for COVID-related containment and closure policies (e.g. school closings and stay at home requirements),and the third set additionally adds COVID-related health system policies (e.g. testing policies and contact tracing). In the left panelwe control for the accumulated case number of the preceding week, in the right panel we control for accumulated death number ofthe preceding week. All regressions include district, week and state-month fixed effects. Standard-errors clustered at the districtlevel are in parentheses. Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 2: The effect of ambient air pollution on COVID-19 outcomes
The timing of pollution effects on COVID-19 outcomes
Our prior results suggest that a higher pollution exposure is linked to increases in COVID-19 infections and deaths. However, from the findings at the weekly level, we cannot in-fer how quickly these effects occur after pollution increases and whether this timing isplausible given existing knowledge about the disease. PM exposure is linked to cardio-vascular and respiratory comorbidities that are in turn associated with worse COVID-19outcomes. Studies also show, that air pollution can hamper the immune response to infec-tions and propagate their transmission. While we cannot provide insightinto potential mechanisms that apply with regards to COVID-19, we can derive that, if thedevelopment of symptoms or even the probability of transmission was affected, changesin the case numbers are unlikely to occur in the first days immediately after the pollutionincident. This is because the average incubation time equals five days and becausetesting and reporting introduce an additional time lag. Moreover, we would expect pos-itive effects roughly in a time frame of two weeks after the pollution incident, as the vastmajority of infected people develops symptoms within 12 days. To test these theoreticalconsiderations and to robustify our prior results, we now turn to an analysis at the dailylevel. 5
OVID-19 cases (1) (2) (3) week t = − week t = − week t = − inversion strength day t = ∗∗∗ ( 0.0004) ( 0.0004) ( 0.0004)inversion strength day t = ∗ ∗ ( 0.0005) ( 0.0005) ( 0.0003)inversion strength day t = − ∗∗ ( 0.0005) ( 0.0007) ( 0.0003)inversion strength day t = ∗ − ∗ ( 0.0005) ( 0.0007) ( 0.0003)inversion strength day t = ∗ day t = day t = − BEL, BRA, DEU, GBR, ITA, USA
The regression includes district-month, state-week and country-day fixed effects. We control forweather covariates as well as accumulated case numbers of the preceding day. Standard-errorsclustered at the district level are in parentheses. The sample size is 236,074.Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 3: Pollution effects on COVID-19 case numbers by daysTable 3 shows how the total number of COVID-19 cases is affected by the presence of a ther-mal inversion on the past 21 days. For instance, the first coefficient in column (1) representshow a 1-degree increase in inversion strength on the current day changes registered casescompared to those registered yesterday. The last coefficient in column (3) represents the re-spective effect of the same change in inversion strength 20 days ago. In turning to the dailylevel, we adopt more restrictive fixed effects that control for district-month, state-week andcountry-day specific changes in the virus development. Because our policy controls vary atthe country-day level they are redundant in this specification and we include weather co-variates only. Overall, the table indicates statistically significant increases in the registeredCOVID-19 cases with a delay of 5 to 16 days, which is consistent with theoretical consid-erations. The effect estimated most precisely occurs at the 14th lag. Note that we do notintend to actually pin down effects to specific days. Rather, we view our daily analysis asindicative of a time range when pollution effects occur.To compare the effects estimated in Table 3 with those in Table 2, we conduct a back-of-the envelope calculation. Dividing the sum of all 21 coefficients in Table 3 by the effectof a 1-degree increase in inversion strength on the daily PM average (0.006/0.0315 = = Given that these diseases are comorbidities increasingthe death risks of COVID-19, contemporaneous shifts in air pollution could have short-term effects on deaths among COVID-19 patients. Again, given delays in reporting, wewould expect such effects to show only after a few days. If, as the results in Table 3 sug-gest, the number of symptomatic cases increases as a result of air pollution episodes, we6 OVID-19 deaths (1) (2) (3) (4) week t = − week t = − week t = − week t = − inversion strength day t = ∗∗∗ ( 0.0019) ( 0.0014) ( 0.0012) ( 0.0010)inversion strength day t = ∗∗ ∗∗ ( 0.0024) ( 0.0015) ( 0.0012) ( 0.0009)inversion strength day t = − ∗ ( 0.0025) ( 0.0014) ( 0.0011) ( 0.0008)inversion strength day t = − − day t = ∗∗∗ ( 0.0018) ( 0.0016) ( 0.0011) ( 0.0009)inversion strength day t = day t = − BEL, BRA, DEU, USA
The regression includes district-month, state-week and country-day fixed effects. We control for weathercovariates as well as accumulated death numbers of the preceding day. Standard-errors clustered at thedistrict level are in parentheses. The sample size is 82,423. Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 4: Pollution effects on COVID-19 deaths by dayswould expect death numbers to rise with a longer delay. The median number of days be-tween first symptoms and death is 18. Therefore, if air pollution on the current day leadsalready infected people to develop symptoms and newly infected to develop symptomsafter the incubation time of about five days, we would expect to see effects mainly aroundthe 18th and the 23nd lag or somewhat later due to additional administrative delays.Column (4) in Table 4 shows statistically significant coefficients for the 22nd to 26th lag.While the observed effects concentrate on the fourth week after pollution exposure, we doobserve an earlier increase at the 16th lag as well. These findings support the hypothesisthat air pollution increases the number of symptomatic cases. However, we do not observestatistically significant coefficients in the first weeks which would have been indicative ofcontemporaneous pollution effects on COVID-19 deaths. To compare the magnitude of theestimated effects with those in Table 2, we again derive the approximate elasticity. Divid-ing the sum of all 28 coefficients by the daily pollution effect (0.0249/0.0315 = = We find that air pollution episodes created by thermal inversion increase COVID-19 in-fections and deaths. A 1%-increase in PM levels over the three preceding weeks leadsto 1.5% more weekly cases. A 1%-increase in PM levels over the four preceding weeksleads to a 5.1% increase in COVID-19 deaths. Thermal inversions also drive daily increasesin cases and deaths that are consistent with common priors on time lags of the disease andits measurements. 7ur results indicate that even short-term reductions in air pollution can help mitigate thespread and severity of COVID-19. Since reductions in air pollution are known to gener-ate large net benefits, particularly in countries with high pollution levels, many short-termmeasures to curb air pollution are low regrets options, as long as they do not divert atten-tion from the core measures needed to mitigate COVID-19 directly.We only estimate the net short-term effect of air pollution on COVID-19 outcomes control-ling for baseline differences between populations in mid- and long-run exposure. There-fore, it can be considered a lower bound for the potential benefits from reducing air pol-lution over longer time periods. Estimates of the heterogeneity of COVID-19 outcomes interms of mid- and long-term exposure to air pollution are complementary to our approachand could help target policies at vulnerable populations, particularly if analyzed in inter-action with short-term air pollution shocks.Our reduced-form approach aims at getting as close as possible to a causal estimate of theeffect of air pollution on COVID-19 outcomes. Our empirical strategy builds on previousstudies in epidemiology and economics that have identified ther-mal inversions as natural experiments for episodes of increased air pollution. However, itdoes not speak to the biological mechanisms that create the effect. To learn more about theunderlying mechanisms, combining quasi-experimental variation in air pollution with in-dividual level health observations might be helpful. Differences in air filtration in the workplace or in schools created by regulations or renovation cycles could be a suitable settingfor an analysis. 8 eferences [1] Philip J. Landrigan et al. “The Lancet Commission on Pollution and Health”. In: The Lancet
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We compile daily data on COVID-19 cases and deaths at the district level. At the time ofdata collection in May/June 2020, we were able to find information at this fine spatial andtemporal resolution for six countries: Belgium, Brazil, Germany, Italy, United Kingdomand United States. All data are openly available online and provided by official sources.The following table provides an overview of the data by country. All data were scraped on9th June.We collect the number of accumulated COVID-19 cases and deaths. While we observe casenumbers for all six countries, death counts are available only for four of them. The report-ing of these numbers differs across and within countries. For instance, in some districtsthey include only lab-confirmed cases, while in others they also include probable cases.Moreover, the time of reporting may differ as well as the testing regimes within countriesand districts over time. While we are not able to observe these information in our data, ourempirical model addresses these differences with the inclusion of fixed effects.
Country Cases Deaths Original Source Reference
Belgium yes partly Sciensano Corona Data Scraper [1]Brazil yes yes Ministério da Saúde Cota [2]Germany yes yes Robert Koch-Institut Robert Koch Institut [3]Italy yes no Dept. of Civil Protection Krispin [4]United Kingdom yes no Dept. of Health and Social Care UK Government [5]United States yes yes local governments and health departments The New York Times [6]
We obtain data on atmospheric air temperature as well as weather conditions from ECMWF(The European Centre for Medium-Range Weather Forecasts). The product ERA5 providesinterpolated hourly data at 37 different pressure levels with a spatial resolution of 31km(0.28125 degrees).We define inversions as episodes when the difference in temperature between the 925 hPapressure level (ca. 600 m above sea level) and the 1000 hPa pressure level (ca. 30 m abovesea-level) is positive. We weight inversions by their strength, that is the continuous differ-ence between the two temperature layers. Following recent studies, we consider night-timeinversions using temperature measurings at 2 a.m. local time.
We aggregate the gridded data to the district level (GADM-GID2) by calculating the weightedmean, where the weights equal the fraction of the grid covered by the district. For our anal-ysis at the weekly level, we sum up all inversions within moving three-week and four weektime windows. Figure 1 shows that inversion episodes occur with great temporal and spa-tial variation across districts. Data for Belgium contain death counts only for Brussels. weekinversion strength U S U K I T D E B R B E The figure illustrates the frequency of inversion episodes. The vertical axis refers to the districts. Countries and capital cities arelabeled. The horizontal axis refers to the weeks. The color scale on the right indicates the strength of inversions. Weeks withoutinversion episodes are in white.
We also compile data on total precipitation, downward UV radiation, specific humidity,air temperature 2 metres above the surface and U and V wind components from ERA5.Following He, Pan, and Tanaka [9], we construct an indicator for still air from the windcomponent data, which is equal to one for wind speed no greater than 1 m/s.
We use Aerosol Optical Depth (AOD) derived from MODIS satellite-images to proxy for PM concentration in the atmosphere. We use the MCD19A2 V6 data product providedby NASA. It measures AOD (blue band 0.47 µ m) over land at a 1 kilometer resolutionwith global coverage combining images from the Terra and Aqua satellites. The data setcan be used on Google Earth Engine. A link to the main script used to extract AOD val-ues for our study units can be accessed here: https://code.earthengine.google.com/ac966bffe655ba22379698d5709d9163 We extract daily mean values of AOD pixels whose centroid lies in one of the districts, forwhich we have COVID-19 data. Note that Google Earth Engine’s . reduceRegions functiondoes not extract values from pixels that do not have their centroid in the polygon of in-terest and therefore only works well with high resolution data, if study areas are small.For most longitudes both the Terra and the Aqua satellite pass over at around the sametime during the day with a difference of around ± L ogg e d P M . I n v e rs i o n str e n g t h The figure shows a local polynomial regression fitting of the daily logged PM observations determined by daily inversionstrength. We bootstrap the fitting with 1000 repetitions. The white line represents the median of the fitted regression lines. Figure 2 shows the link between daily inversion strength and PM concentration. For ourregression analysis we aggregate the daily observations to the week level and average overthree weeks for regressions explaining COVID-19 cases and over four weeks for deaths.The aggregation accounts for potentially lagged effects of inversions on air quality. In addition to the weather controls, we use data from the Oxford Covid-19 GovernmentResponse Tracker (OxCGRT). The OxCGRT systematically collects information on coun-tries’ policy responses to the pandemic. It provides 17 indicators reflecting the extent ofgovernment action on a daily level. For our analysis we compose two control sets of thesevariables. The first one comprises containment and closure policies, namely, closings ofschools and universities, closings of workplaces, cancellings of public events, closing ofpublic transport, orders to "shelter-in-place" and otherwise confine to the home, and re-strictions on internal movement between cities or regions. The second one comprises healthsystem policies, namely, regulations on access to PCR testing and strategies for contact trac-ing after a positive diagnosis. To prevent high degrees of collinearity among the variables,we allow the sets to vary in size for the smaller sample in which we analyze COVID-19deaths.
The first-stage regression of the instrumental variable estimator is a generalized difference-in-differences regression model specified as: P iw = α I iw + α C iw − + W (cid:48) iw α + M (cid:48) iw α + T (cid:48) iw α + γ i + δ w + η cm + (cid:101) iw (1) where the dependent variable is the logged average PM concentration in district i andweek w over the past three or four weeks. The parameter of interest, α , represents the effect13f inversions that accumulated over the same three or four weeks and that are weightedby their intensity, I iw . We control for weather covariates W (cid:48) iw , COVID-related containmentand closure measures M (cid:48) iw , and testing policies T (cid:48) iw . The variable C iw − is the accumulatedCOVID-19 outcome, either cases or deaths, in the preceding week. The fixed effects γ i , δ w ,and η cm account for determinants of the dependent variable that are specific to each district i , each week w and each month m in state s .In the second stage, the predicted PM from equation 1 is used as an explanatory variablein C iw = β (cid:99) P iw + β C iw − + W (cid:48) iw β + M (cid:48) iw β + T (cid:48) iw β + γ i + δ w + η cm + µ iw (2) where C iw is the accumulated COVID-19 outcome of district i in week w . The coefficient β represents the percentage change in the dependent variable linked to a 1%-increase ininversion-driven air pollution (cid:99) P iw . We estimate the second stage using Poisson pseudo-maximum likelihood estimation. We bootstrap standard errors clustered at the districtlevel, where we assign treatment.We also estimate a model at the daily level C id = ∑ θ ρ θ I θ id + + ρ C id − + λ im + ζ sw + κ cd + ν id (3) where the COVID-19 outcomes, C id , and inversion variables, I id , are now given for district i and day d . We include θ lags of the inversion variable, where θ runs from -20 to 0 forregressions with cases as the dependent variable and from -27 to 0 for regressions withdeaths as the dependent variable. Fixed effects λ im , ζ sw , and κ cd absorb variation in C id thatis specific to a district-month, state-week, and country-day.Our instrumental variable approach can be conceptualized as a generalization of the difference-in-differences approach. Our regressions form comparisons between groups that switchtheir treatment intensity on a given day and those that do not. Similar to the standarddifference-in-differences context a crucial assumption here is that both treatment and con-trol group would have followed the same trend in the absence of treatment (common trendsassumption). Note that treatment and control groups can be different at the baseline, butshould be on the same trend. In our Poisson regressions we model the outcome as loga-rithmically distributed. Therefore, we assume that, after removing fixed effects and controlvariable variation, cases and deaths in districts hit by a shift in air pollution due to thermalinversion would have grown at the same rate as cases and deaths in districts that are notconcerned by this natural experiment in a given week.In the absence of random assignment into treatment, the main role of additional variables(controls and instruments) in our regression model is to eliminate reverse causality andomitted variable bias. For our estimate to capture a causal effect we have to rule out thata third confounding variable, such as mobility, economic activity or any other potentiallynon-measurable factor, is causally linked to both treatment (air pollution) and COVID-19outcomes (infections and deaths) in either of three ways: (1) outcomes cause reductions inhuman activity causing reductions in air pollution (reverse causality), (2) human activity is14riving both air pollution and outcomes (omitted variable bias), (3) air pollution and out-comes are both driving human activity (collider bias). In order to capture the net effect ofair pollution we avoid introducing control variables that can also potentially be mediatorsor bad controls that are for instance influenced by our outcome and remove wanted varia-tion if included in regressions. This approach is agnostic with regards to mechanisms anddoes not allow for an interpretation of variables beyond the treatment variable on whichwe focus our effort to restrict variation to quasi-experimental variation.
The main threat to our identification strategy are violations of the exclusion restriction.This central assumption for our instrumental variable strategy would be violated if ther-mal inversions affected COVID-19 outcomes through other channels than air pollution. Weconduct indirect tests to assess this hypothesis.First, if people are aware of thermal inversions they might change their behavior, for in-stance, spend less time outside. This, in turn, could affect how the virus spreads. To miti-gate this concern, we use nighttime-inversions. Nonetheless, we also analyze the effect ofinversions on relative changes in movement and the time spent at different types of loca-tions. We use movement data from the social media platform Facebook, which compilesinformation on people’s precise locations from their mobile devices. Data are availablestarting on 15th February 2020 at the district-level for Brazil and the United States and atthe state-level for the European countries in our sample. For every country we use dataat the highest resolution available and cluster standard errors respectively. The results inTable 5 do not point to causal effects of inversions on people’s activities.
Relative change Proportion staying withinin movement a single location(1) (2)inversion strength 0.0010 0.0000( 0.0007) ( 0.0003)Countries
BEL, BRA,DEU, GBR, ITA, USA
The regression includes district-month, state-week and country-day fixed effects. We control for weather co-variates. Standard-errors clustered at the district/state level are in parentheses. The sample size is 276,418.Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 5: The effect of thermal inversions on movementSecond, we provide reduced form estimates that represent the overall effect of thermalinversions on COVID-19 outcomes. If inversions have no effect on COVID-19 outcomesother than through air pollution, we would expect that the overall effect of inversions onCOVID-19 outcomes is approximately equal to the product of the effect of inversion-drivenair pollution on COVID-19 outcomes (Table 2) and the effect of inversions on air pollution(Table 1). The results in Table 6 confirm this hypothesis. For instance, when multiplyingthe coefficient in column (3) in Table 1 with the corresponding coefficient in Table 2, weobtain a value of 0.0086 which is close to the estimate in column (3) in Table 6.15
OVID-19 cases COVID-19 deaths three-week window four-week window(1) (2) (3) (4) (5) (6) inversion strength ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ ( 0.0017) ( 0.0013) ( 0.0014) ( 0.0050) ( 0.0034) ( 0.0028)Observations 72,021 72,021 72,021 20,658 20,658 20,658Countries BEL, BRA, DEU, GBR, ITA, USA BEL, BRA, DEU, USA weather controls yes yes yes yes yes yescontainment controls yes yes yes yeshealth system controls yes yesIn each panel control variables are added sequentially from left to right. The first set of controls contains weather variablesonly, the second set adds controls for COVID19-related containment and closure policies (e.g. school closings and stay at homerequirements), and the third set additionally adds COVID19-related health system policies (e.g. testing policies and contacttracing). In the left panel we control for the accumulated case numbers of the preceding week, in the right panel we control foraccumulated death number of the preceding week. All regressions include district, week and state-month fixed effects. Standard-errors clustered at the district level are in parentheses. Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 6: The effect of thermal inversions on COVID-19 outcomesThird, we expand our control set of weather covariates. Inversion episodes are correlatedwith weather conditions. At the same time, local weather conditions strongly correlatewith how people spend their time and, thus, may affect infections. In our main analysis wecontrol for precipitation, humidity, temperature and still air. In Figure 3, we present esti-mates based on 14 alternative sets of controls that allow for more complex relations amongthe weather variables. The upper panels present the effect of inversions on logged PM levels, while the lower panels present their effect on COVID-19 cases and deaths. The es-timates highlighted in purple are our baseline results from Table 1 and Table 6. Given thatthe coefficients in all four panels are largely insensitive to the choice of weather controls,we believe that the exclusion restriction is likely to hold.16igure 3: Alternative weather controls three-week PM2.5 mean four-week PM2.5 meanCOVID-19 cases COVID-19 deathsWeather variablesFunctional formPrecipitationTemperatureHumidityStill AirWind componentsRadiation2 nd & 3 rd order polynomialsInteractions The four panels in the figure represent the effect of thermal inversions on the dependent variable stated above each panel. Ineach panel the coefficients are estimated using different weather control sets which are specified by the specification chart below.All regressions include containment and health system controls. Confidence intervals are plotted for the 5 and 10% level ofstatistical significance.
Spillovers
Another assumption of our identification strategy is that air pollution effects on COVID-19 outcomes do not spill across district borders. This is called the stable unit treatmentvalue assumption (SUTVA). However, this assumption may be violated given the natureof a pandemic outbreak. Infected people usually travel freely between districts and maythereby increase the infections in neighboring districts as well. With regards to our analysisthis means, that inversions may not only affect COVID-19 outcomes in the same district butalso in the surrounding ones. In this case, the estimated effects in Table 6 would be under-estimated. To assess the extent of a potential bias linked to cross-district spillover effects,we restrict our sample to districts and weeks that are subject to a restrictive lock-down. Weconsider only districts in which people are required to stay at home with exceptions fordaily exercise, grocery shopping, and essential trips. As these containment measures arespecifically targeted to prevent virus transmission beyond a small radius around an indi-vidual’s home, we assume that spillover effects are less of a concern in this sample. Table8 reproduces the regression coefficients of Table 6. We only control for weather covariates,because the districts remaining in this sub-sample are very similar in terms of containmentstrategies and control variables for political measures are therefore highly collinear. Com-pared to the inversion effect on COVID-19 case numbers in Table 6 (0.0088) the estimated17oefficient in Table 8 is slightly larger in magnitude. For COVID-19 deaths, however, coef-ficients are similar in magnitude. We conclude that if spillover effects exist, they are likelyto make our main results lower-bound estimates.
COVID-19 cases COVID-19 deaths three-week window four-week window(1) (2)inversion strength 0.0134 ∗∗∗ ∗∗∗ ( 0.0013) ( 0.0030)Observations 13,885 5,145Countries
BEL, DEU, GBR, ITA, USA BEL, DEU, USA
In the left panel we control for the accumulated case numbers of the preceding week, in theright panel we control for accumulated death number of the preceding week. All regressions in-clude district, week and state-month fixed effects as well as weather controls. Standard-errorsclustered at the district level are in parentheses. Signif. Codes: ***: 0.01, **: 0.05, *: 0.1
Table 7: The effect of thermal inversions on COVID-19 outcomes - lock-down sample.18 .7 Data and code availability
Data and code are available in the following github repository: https://github.com/hannahklauber/cov19_pollution
DOI: 10.5281/zenodo.3973516
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