https://doi.org/10.1038/s41586-020-2404-8 Accelerated Article Preview The effect of large-scale anti-contagion policies on the COVID-19 pandemic EW Received: 22 March 2020 Solomon Hsiang, Daniel Allen, S?bastien Annan-Phan, Kendon Bell, Ian Bolliger, I Accepted: 26 May 2020 Trinetta Chong, Hannah Druckenmiller, Luna Yue Huang, Andrew Hultgren, Emma Krasovich, Peiley Lau, Jaecheol Lee, Esther Rolf, Jeanette Tseng & TiffanyV Wu Accelerated Article Preview Published online 8 June 2020 E Cite this article as: Hsiang, S. et al. The effect This is a PDF file of a peer-reviewed paper that has been accepted for publication. of large-scale anti-contagion policies on Although unedited, the content has been subjected to prelimRinary formatting. Nature the COVID-19 pandemic. Nature https://doi. is providing this early version of the typeset paper as a service to our authors and org/10.1038/s41586-020-2404-8 (2020). readers. The text and figures will undergo copyediting aPnd a proof review before the paper is published in its final form. Please note that during the production process errors may be discovered which could affecLt theE content, an d all legal disclaimers apply. IC AR T ED T ER A CE L AC Nature | www.nature.com Article The effect of large-scale anti-contagion policies on the COVID-19 pandemic https://doi.org/10.1038/s41586-020-2404-8 Solomon Hsiang1,2??, Daniel Allen1, S?bastien Annan-Phan1,3, Kendon Bell1,4, Ian Bolliger1,5, Received: 22 March 2020 Trinetta Chong 1, Hannah Druckenmiller1,3, Luna Yue Huang1,3, Andrew Hultgren1,3, Emma Krasovich1, Peiley Lau1,3, Jaecheol Lee1,3, Esther Rolf1,6, Jeanette Tseng1 & Tiffany WEu1 W Accepted: 26 May 2020 Published online: 8 June 2020 Governments around the world are responding to the novel coronavirus (COVID-19) pandemic1 with unprecedented policies designed to slow the growth rateV of infections. Many actions, such as closing schools and restricting populations to their homes, impose large and visible costs on society, but their benefits Ecannot be directly observed and are currently understood only through processR-based simulations2?4. Here, we compile new data on 1,717 local, regional, and nPational non-pharmaceutical interventions deployed in the ongoing pandemic across localities in China, South Korea, Italy, Iran, France, and the United States (US). We then apply reduced-form econometric methods, commonly used to measure the effect of policies on economic growth5,6, to empirically evaluate the effect thatE these anti-contagion policies have had on the growth rate of infections. In theL absence of polic y actions, we estimate that early infections of COVID-19 exhibIit eCxponential growth rates of roughly 38% per day. We find that anti-contagion policies have significantly and substantially slowed this growth. Some policies have different impacts on different populations, but we obtain consistent evidence that the policy packages now deployed are achieving large, beneficial, and measurable hTealth outcomes. We estimate that across these six countries, interventionRs prevented or delayed on the order of 62 million confirmed cases, corresponAding to averting roughly 530 million total infections. These findings may help inform whether or when these policies should be deployed, intensified, or lifted, anDd they can support decision-making in the other 180+ countries where COVID-19 has been re ported7. The COVID-19 pandemic is forcing societies worldwEide to make con- increase unemployment and school closures impact educational out- sequential policy decisions with limiteAd infoTrmation. After contain- comes. It is therefore not surprising that some populations have hesi-ment of the initial outbreak failed, attention turned to implementing tated before implementing such dramatic policies, especially when non-pharmaceutical interventions designed to slow contagion of the their costs are visible while their health benefits ? infections and deaths virus. In general, these policies Raim to decrease virus transmission that would have occurred but instead were avoided or delayed ? are by reducing contact among individuals within or between popula- unseen. Our objective is to measure the direct health benefits of these tions, such as by closing restaurants or restricting travel, thereby slow- policies; specifically, how much these policies slowed the growth rate of ing the spread of COVID-19 to a manageable rate. These large-scale infections. To do this, we compare the growth rate of infections within anti-contagion policLies aEre informed by epidemiological simula- hundreds of sub-national regions before and after each of these policies tions2,4,8,9 and a small number of natural experiments in past epidem- is implemented locally. Intuitively, each administrative unit observed ics10. However, tEhe actual effects of these policies on infection rates in just prior to a policy deployment serves as the ?control? for the same the ongoing pandemic are unknown. Because the modern world has unit in the days after it receives a policy ?treatment? (see?Supplemen-never coCnfronted this pathogen, nor deployed anti-contagion poli- tary Information for accounts of these deployments). Our hope is to cies of such scale and scope, it is crucial that direct measurements of learn from the recent experience of six countries where early spread poClicy impacts be used alongside numerical simulations in current of the virus triggered large-scale policy actions, in part so that socie-decision-making. ties and decision-makers in the remaining 180+ countries can access ASocieties around the world are weighing whether the health benefits this information.of anti-contagion policies are worth their social and economic costs. Here we directly estimate the effects of 1,717 local, regional, and Many of these costs are plainly seen; for example, business restrictions national policies on the growth rate of infections across localities within 1Global Policy Laboratory, Goldman School of Public Policy, UC Berkeley, Berkeley, USA. 2National Bureau of Economic Research & Centre for Economic Policy Research, Cambridge, Massachusetts, United States. 3Agricultural & Resource Economics, UC Berkeley, Berkeley, USA. 4Manaaki Whenua ? Landcare Research, Lincoln, New Zealand. 5Energy & Resources Group, UC Berkeley, Berkeley, USA. 6Electrical Engineering & Computer Science Department, UC Berkeley, Berkeley, USA. ?e-mail: shsiang@berkeley.edu Nature | www.nature.com | 1 Article China, France, Iran, Italy, South Korea, and the US (see Figure?1 and Sup- the latter are confounded by the effects of policy. These growth rates plementary Table?1). We compile subnational data on daily infection are not driven by the expansion of testing or increasing rates of case rates, changes in case definitions, and the timing of policy deployments, detection (see?Methods and Extended Data Fig.?2) nor by data from including (1) travel restrictions, (2) social distancing through cancella- individual regions (Extended Data Fig.?3). tions of events and suspensions of educational/commercial/religious Some prior analyses of pre-intervention infections in Wuhan suggest activities, (3) quarantines and lockdowns, and (4) additional policies slower growth rates (doubling every 5?7 days)17,18 using data collected such as emergency declarations and expansions of paid sick leave, from before national standards for diagnosis and case definitions were first the earliest available dates to April 6, 2020 (see?Supplementary Notes, issued by the Chinese government on January 15, 202019. However, case also Extended Data Fig.?1). During this period, populations remained data in Wuhan from before this date contain multiple irregularities: almost entirely susceptible to COVID-19, causing the natural spread of the cumulative case count decreased on January 9; no new cases were infections to exhibit almost perfect exponential growth11,12. The rate reported during January 9-15; and there were concerns that informa- of this exponential growth could change daily, determined by epide- tion about the outbreak was suppressed20 (see?Supplementary Table 2). W W miological factors, such as disease infectivity, as well as policies that When we remove these problematic data, utilizing a shorter but more alter behavior9,11,13. Because policies were deployed while the epidemic reliable pre-intervention time series from Wuhan ( January 16?2E1), we E unfolded, we can estimate their effects empirically. We examine how recover a growth rate of 43% per day (SE = 3%), doubling everIy 2 days) I the daily growth rate of infections in each locality changes in response consistent with results from all other countries except Iran (Figure?2a, to the collection of ongoing policies applied to that locality on that day. Supplementary Table 3).During the early stages of an epVidemic, a large V proportion of the population remains susceptible to the virus, and if the spread of the virus is left uninhibited by policy oEr behavioral change, E Methods Summary exponential growth continues until the fRraction of the susceptible We employ well-established ?reduced-form? econometric techniques5,14 population declines meaningfully11,13,21,22. After correcting for estimated R commonly used to measure the effects of events6,15 on economic growth rates of case-detection23, we compuPte that the minimum susceptible rates. Similar to early COVID-19 infections, economic output generally fraction across administrative units in our sample is 72% of the total P increases exponentially with a variable rate that can be affected by population (Cremona, Italy) and 87% of units would likely be in a regime policies and other conditions. Here, this technique aims to measure of uninhibited exponential growth (> 95% susceptible) if policies were the total magnitude of the effect of changes in policy, without requir- removed on the last date ofE our sample. E ing explicit prior information about fundamental epidemiological Consistent with preLdictions from epi demiological models2,10,24, we parameters or mechanisms, many of which remain uncertain in the find that the combined effect of policies within each country reduces L current pandemic. Rather, the collective influence of these factors is the growth raIte of infections by a substantial and statistically significant empirically recovered from the data without modeling their individual amount (FigureC?2b, Supplementary Table 3). For example, a locality in Ceffects explicitly (see?Methods). Prior work on influenza16, for example, FranceT with a baseline growth rate of 0.33 (national average) that fully Ihas shown that such statistical approaches can provide important deployed all policy actions used in France would be expected to lower complementary information to process-based models. its daily growth rate by ?0.17 to a growth rate of 0.16. In general, the T To construct the dependent variable, we transform location-specific, eRstimated total effects of policy packages are large enough that they subnational time-series data on infections into first-differencesA of can in principle offset a large fraction of, or even eliminate, the baseline Rtheir natural logarithm, which is the per-day growth rate of infections growth rate of infections?although in several countries, many locali-(see?Methods). We use data from first- or second-level administra- ties have not deployed the full set of policies. Overall, the estimated tive units and data on active or cumulative cases, dependDing on avail- effects of all policies combined are generally insensitive to withholding A ability (see?Supplementary Information). We employ widely-used regional (i.e. state- or province-level) blocks of data from the sample panel regression models5,14 to estimate how the daEily growth rate of (Extended Data Fig.?3).infections changes over time within a location when different combi- In China, only three policies were enacted across 116 cities early in Dnations of large-scale policies are enacted (seTe?Methods). Our econo- a seven week period, providing us with sufficient data to empirically metric approach accounts for differences in the baseline growth rate estimate how the effects of these policies evolved over time without E of infections across subnational locatioAns, which may be affected by making assumptions about the timing of these effects (see?Methods time-invariant characteristics, such as demographics, socio-economic and Fig.?2b). We estimate that the combined effect of these policies Tstatus, culture, and health systems; it accounts for systematic patterns reduced the growth rate of infections by ? 0.026 (SE = 0.046) in the in growth rates within countries unrelated to policy, such as the effect first week following their deployment, increasing substantially in the A of the work-week; it is robust to syRstematic under-surveillance specific second week to ? 0.20 (SE = 0.049), and essentially stabilizing in the to each subnational unit; and it accounts for changes in procedures to third week near ? 0.28 (SE = 0.047). In other countries, we lack sufficient R diagnose positive cases (seeE?Methods and Supplementary Information). data to estimate these temporal dynamics explicitly and only report L the average pooled effect of policies across all days following their Edeployment (see?Methods). If other countries have transient responses Results E similar to China, we would expect effects in the first week following LWe estimate that in the absence of policy, early infection rates of deployment to be smaller in magnitude than the average effect we COVID-19 grow 43% per day on average across these six countries report. In Extended Data Fig.?5a and Supplementary Methods Sec- E (Standard Error [SE] = 5%), implying a doubling time of approximately tion 3, we explore how our estimates would change if we impose the 2 dCays. Country-specific estimates range from 34% per day in the US assumption that policies cannot affect infection growth rates until C(SE = 7%) to 68% per day in Iran (SE = 9%). We cannot determine if the after a fixed number of days; however, we do not find evidence this Ahigh estimate for Iran results from true epidemiological differences, improves model fit.data quality issues (see?Methods), the concurrence of the initial out- The estimates above (Figure?2b) capture the superposition of all poli- Cbreak with a major religious holiday and pilgrimage (see?Supplementary cies deployed in each country, i.e., they represent the average effect of Notes), or sampling variability. Excluding Iran, the average growth rate policies that we would expect to observe if all policies enacted anywhere A is 38% per day (SE = 5%). Growth rates in all five other countries are in each country were implemented simultaneously in a single region independently estimated to be very near this value (Figure?2a). These of that country. We also estimate the effects of individual policies or estimated values differ from observed average growth rates because clusters of policies (Figure?2c) that are grouped based on either their 2 | Nature | www.nature.com similarity in goal (e.g., library and museum closures) or timing (e.g., and the duration for which they have been applied. Several of these policies deployed simultaneously). Our estimates for these individual estimates are subject to large statistical uncertainties (see intervals in effects tend to be statistically noisier than the estimates for all poli- Figure?4). Sensitivity tests (Extended Data Fig.?7) that assume a range cies combined. Some estimates for the same policy differ between of plausible alternative parameter values relating to disease dynam- countries, perhaps because policies are not implemented identically ics, such as incorporating a Susceptible-Exposed-Infected-Removed or because populations behave differently. Nonetheless, 22 out of 29 (SEIR) model, suggest that interventions may have reduced the sever- point estimates indicate that individual policies are likely contributing ity of the outbreak by a total of 55?66 million confirmed cases over to reducing the growth rate of infections. Seven policies (one in South the dates in our sample (central estimates). Sensitivity tests varying W Korea, two in Italy, and four in the US) have point estimates that are the assumed infection-fatality ratio (Supplementary Table 6) suggest positive, six of which are small in magnitude (< 0.1) and not statisti- a corresponding range of 46?77 million confirmed cases (490?580 E cally different from zero (5% level). Consistent with greater overall million total infections).I uncertainty in these dis-aggregated estimates, some in China, South W Korea, Italy, and France are somewhat more sensitive to withholding V regional blocks of data (Extended Data Fig.?4), but remain broadly Discussion E robust to assuming a constant delayed effect of all policies (Extended Our empirical results indicate that large-scale anti-contagionI policies E Data Fig.?5b). are slowing the COVID-19 pandemic. Because infection rates in the Based on these results, we find that the deployment of anti-contagion countries we study would have initially followed rapiVd exponential policies in all six countries significantly and substantially slowed the growth had no policies been applied, our results suggest that these R pandemic. We combine the estimates above with our data on the timing policies have provided large health benefits. For eExample, we estimate of the 1,717 policy deployments to estimate the total effect of all poli- that there would be roughly 465 ? the observed number of confirmed P cies across the dates in our sample. To do this, we use our estimates to cases in China, 17 ? in Italy, and 14 ? in the URS by the end of our sample predict the growth rate of infections in each locality on each day, given if large-scale anti-contagion policies had not been deployed. Consist-the actual policies in effect at that location on that date (Figure?3, blue ent with process-based simulationPs of COVID-19 infections2,4,8,9,22,26, E markers). We then use the same model to predict what counterfactual our analysis of existing policies indicates that seemingly small delays growth rates would be on that date if the effects of all policies were in policy deployment likely produced dramatically different health L removed (Figure?3, red markers), which we call the ?no-policy scenario.? outcomes. EThe difference between these two predictions is our estimated effect While the limitations of available data pose challenges to our analysis, C that all deployed policies had on the growth rate of infections. During our aim is to use what Ldata exist to estimate the first-order impacts of I our sample, we estimate that all policies combined slowed the average unprecedented policy actions in an ongoing global crisis. As more data growth rate of infections by ?0.252 per day (SE = 0.045, p < 0.001) in become availabCle, related findings will become more precise and may T China, ? 0.248 (SE = 0.089, p < 0.01) in South Korea, ?0.24 (SE = 0.068, capture morIe complex interactions. Furthermore, this analysis does p < 0.001) in Italy, ?0.355 (SE = 0.063, p < 0.001) in Iran, ?0.123 (SE = 0.019, not account for interactions between populations in nearby localities13, R p < 0.001) in France and ?0.084 (SE = 0.03, p < 0.01) in the US. These nor moTbility networks3,4,8,9. Nonetheless, we hope these results can sup-results are robust to modeling the effects of policies without grouping port critical decision-making, both in the countries we study and in the A them (Extended Data Fig.?6a and Supplementary Table 4) or assuming oRther 180 + countries where COVID-19 infections have been reported7.a delayed effect of policy on infection growth rates (Supplementary A key advantage of our reduced-form ?top down? statistical approach Table 5). is that it captures the real-world behavior of affected populations D The number of COVID-19 infections on a date depends on the grow Ath without requiring that we explicitly model underlying mechanisms rate of infections on all prior days. Thus, persistent reductions in growth and processes. This is useful in the current pandemic where many E rates have a compounding effect on infections, until growDth is slowed process-related parameters remain uncertain. However, our results by a shrinking susceptible population. To provide a sense of scale for cannot and should not be interpreted as a substitute for ?bottom up? T our results, we integrate the growth rate of infectiEons in each local- process-based epidemiological models specifically designed to provide ity from Figure?3 to estimate cumulative infections, both with actual guidance in public health crises. Rather, our results complement exist- A anti-contagion policies and in the no-policy couaccount for the declining susceptible populatioTnterfactual scenario. To ing models, for example, by helping to calibrate key model parameters. n in each administrative We believe both forward-looking simulations and backward-looking unit, we couple our econometric estimAates of the effects of policies empirical evaluations should be used to inform decision-making.R with a Susceptible-Infected-Removed (SIR) model11,13 that adjusts the Our analysis measures changes in local infection growth rates asso-susceptible population in each administrative unit based on estimated ciated with changes in anti-contagion policies. A necessary condition E case-detection rates23,25 (see?MeRthods). This allows us to extend our for this association to be interpreted as the plausibly causal effect of projections beyond the initEial exponential growth phase of infections, these policies is that the timing of policy deployment is independent L a threshold that many localities cross in our no-policy scenario. of infection growth rates14. This assumption is supported by estab-Our results suggest Lthat ongoing anti-contagion policies have already lished epidemiological theory11,13,27 and evidence28,29, which indicate E substantially reEduced the number of COVID-19 infections observed that infections in the absence of policy will grow exponentially early in in the world today (Figure?4). Our central estimates suggest that the epidemic, implying that pre-policy infection growth rates should be C there wo(correspCuld be roughly 37 million more cumulative confirmed cases constant over time and therefore uncorrelated with the timing of policy onding to 285 million more total infections, including the deployment. Further, scientific guidance to decision-makers early in C coCnfirmed cases) in China, 11.5 million more confirmed cases in South Korea the current epidemic explicitly projected constant growth rates in the (38 million total infections), 2.1 million more confirmed cases in Italy absence of anti-contagion measures, limiting the possibility that antici-A A(49 million total infections), 5 million more confirmed cases in Iran pated changes in natural growth rates affected decision-making 2,22,30,31. (54 million total infections), 1.4 million more confirmed cases in France In practice, policies tended to be deployed in response to high total (45 million total infections), and 4.8 million more confirmed cases numbers of cases (e.g. in France)32, in response to outbreaks in other (60 million total infections) in the US had these countries never enacted regions (e.g. in China, South Korea, and Iran)33, after delays due to any anti-contagion policies since the start of the pandemic. The magni- political constraints (e.g. in the US and Italy), and often with timing tudes of these impacts partially reflect the timing, intensity, and extent that coincided with arbitrary events, like weekends or holidays (see?Sup- of policy deployment (e.g., how many localities deployed policies), plementary Notes for detailed chronologies). Nature | www.nature.com | 3 Article Our analysis accounts for documented changes in COVID-19 testing 10. Hatchett, R. J., Mecher, C. E. & Lipsitch, M. Public health interventions and epidemic procedures and availability, as well as differences in case-detection intensity during the 1918 influenza pandemic. Proceedings of the National Academy of Sciences 104, 7582?7587 (2007). https://doi.org/10.1073/pnas.0610941104. across locations; however, unobserved trends in case-detection could 11. Ma, J. Estimating epidemic exponential growth rate and basic reproduction affect our results (see?Methods). We analyze estimated case-detection number. 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Accessed: abb6105. R 2020-04-13. 8. Li, R. et?al. Substantial unLdocumEented infection facilitates the rapid dissemination of Publisher?s note Springer Nature remains neutral with regard to jurisdictional claims in novel coronavirus (SARS-CoV2). Science (2020). https://doi.org/10.1126/science.abb3221. published maps and institutional affiliations. E9. Tang, B. et?al. Estimation of the transmission risk of the 2019-nCoV and its implication for public health inEterventions. Journal of Clinical Medicine 9, 462 (2020). ? The Author(s), under exclusive licence to Springer Nature Limited 2020 ELC AC AC C 4 | Nature | www.nature.com IE W WIE RE V V P PR E LE LE TIC IC AR AR T ED ED AT TR Fig. 1 | Data on COVID-19 infections and large-scale anti-contagion policies. Left: Daily cumulative confirmed cases of COAVID-19 (solid black line, left axis) and deaths (dashed black line) over timRe. Vertical lines are deployments of E anti-contagion policies, with height indicating the number of administrative units instituting a policy that dL policy types are shown per couE ay (right axis). For display purposes only, ? 5 ntry and missing case data are imputed unless all sub-national units areL missing. Right: Maps of cumulative confirmed cases E by administrativeE unit on the last date of each sample. CCA AC C Nature | www.nature.com | 5 Article IE W WIE RE V EV P PR LE LE TIC TIC AR AR ED ED T T Fig. 2 | Empirical estimates of unmitigated COVID-19 infection growth rates and the effect of anti-contagion policies. MAarkers are country-specific A estimates, whiskers are 95% CI. ColumRns report effect sizes as a change in the continuous-time growth rate (95% CI in parentheses) and the day-over-day percentage growth rate. (a) Estimates of daily COVID-19 infection growth rates R in the absence of policy (LdasheEd lines = averages with and without Iran, both excluding Wuhan-specific estimate). (b) Estimated combined effect of all Epolicies on infection growth rates. (c) Estimated effects of individual policies or policy groups oEn the daily growth rate of infections, jointly estimated and Lordered roughly chronologically within each country. *Reported effect of ?home isoClation? includes effects of other implied policies (see?Methods). EChina: N = 3669; South Korea: N = 595, Italy: N = 2898, Iran: N = 548, France: N = 270, US: N = 1238.C CCA A 6 | Nature | www.nature.com EWI IE W RE V V P PR E E E TIC L L TIC AR AR ED D T Fig. 3 | Estimated infection growth rates based on actualE anti-contagion policies and in a ?no policy? counterfactual scenaTrio. Predicted daily A growth rates of active (China, South Korea) or cumulative (all others) COVID-19 infections based on the observed timing of all policy deployments within each R country (blue) and in a scenario where no poliAcies were deployed (red). The difference between these two predictRions is our estimated effect of actual E anti-contagion policies on the growth rate of infections. Small markers are daily estimates for sub-nationaEl administrative units (vertical lines are 95% CI). L Large markers are nationLal averages. Black circles are observed daily changes in log(infections), averaged across administrative units. Sample sizes are the same E as Figure?2. E AC C AC C Nature | www.nature.com | 7 Article IE W W V VI E E E PR PR LE LE TIC ICR RT Fig. 4 | Estimated cumulative confirmed COVID-19 infections with and A A without anti-contagion policies. The predicted cumulative numDber of confirmed COVID-19 infections based on actual policy deployments (blue) and in the no-policy counterfactual scenario (red). Shaded areas show uncertainty D based on 1,000 simulations where empirically estimated parameters are resampled from their joint distribution (dark = inner 70% of predictions; light = inner 95%). Black dotted line is observed cumulativeE infections. E Infections are not projected for administrative units that never report infections in the sample, but which might havAe experTienced infections in a Tno-policy scenario. R A LE LE R CC E E A AC C 8 | Nature | www.nature.com Methods was previously updated daily through March 2542. We obtained data on France?s policy response to the COVID-19 pandemic from the French Data Collection and Processing government website, press releases from each regional public health We provide a brief summary of our data collection processes here (see site43, and Wikipedia44. the?Supplementary Notes for more details, including access dates). Epidemiological, case definition/testing regime, and policy data for United States. We used state-level epidemiological data from usafacts. each of the six countries in our sample were collected from a variety org45, which they compile from multiple sources. For policy responses, of in-country data sources, including government public health web- we relied on a number of sources, including the U.S. Centers for Disease W sites, regional newspaper articles, and crowd-sourced information on Control (CDC), the National Governors Association, as well as various Wikipedia. The availability of epidemiological and policy data varied executive orders from county- and city-level governments, and press E across the six countries, and preference was given to collecting data at releases from media outlets.I the most granular administrative unit level. The country-specific panel W datasets are at the region level in France, the state level in the US, the Policy Data. Policies in administrative units were coded as binary vari- V province level in South Korea, Italy and Iran, and the city level in China. ables, where the policy was coded as either 1 (after the dateI th Eat the Due to data availability, the sample dates differ across countries: in policy was implemented, and before it was removed) or 0 otherwise, E China we use data from January 16 - March 5, 2020; in South Korea from for the affected administrative units. When a policy only affected a February 17 - April 6, 2020; in Italy from February 26 - April 6, 2020; fraction of an administrative unit (e.g., half of the couVnties within a in Iran from February 27 - March 22, 2020; in France from February state), policy variables were weighted by the percentage of people R 29 - March 25, 2020; and in the US from March 3 - April 6, 2020. Below, within the administrative unit who were treated bEy the policy. We used we describe our data sources. the most recent population estimates wRe could find for countries? P administrative units (see the Population Data section in the Appendix). China. We acquired epidemiological data from an open source GitHub In order to standardize policy types across countries, we mapped each project34 that scrapes time series data from Ding Xiang Yuan. We country-specific policy to one of theP broader policy category variables E extended this dataset back in time to January 10, 2020 by manually in our analysis. In this exercise, we collected 168 policies for China, collecting official daily statistics from the central and provincial (Hubei, 59 for South Korea, 214 forE Italy, 23 for Iran, 59 for France, and 1,194 L Guangdong, and Zhejiang) Chinese government websites. We compiled for the United States (see?Supplementary Table 1). There are some policies by collecting data on the start dates of travel bans and lock- cases where we encode policies that are necessarily in effect whenever C downs at the city-level from the ?2020 Hubei lockdowns? Wikipedia another policy iCs in plaLce, due in particular to the far-reaching implica-I page35 and various other news reports. We suspect that most Chinese tions of home isolation policies. In China, wherever home isolation is cities have implemented at least one anti-contagion policy due to their documentedI, we assume a local travel ban is enacted on the same day if T reported trends in infections; as such, we dropped cities where we could we haveT not found an explicit local travel ban policy for a given locality. not identify a policy deployment date to avoid miscategorizing the In France, we assume home isolation is accompanied by event cancella-R policy status of these cities. Thus our results are only representative tRions, social distancing, and no-gathering policies; in Italy, we assume for the sample of 116 cities for which we obtained policy data. home isolation entails no-gathering, local travel ban, work from home, A Aand social distancing policies; in the US, we assume shelter-in-place South Korea. We manually collected and compiled the epidemiologi- orders indicate that non-essential business closures, work from home cal dataset in South Korea, based on provincial government reports, policies, and no-gathering policies are in effect. For policy types that D policy briefings, and news articles. We compiled policy aDctions from are enacted multiple times at increasing degrees of intensity within a news articles and press releases from the Korean Centers for Disease locality, we add weights to the variable by escalating the intensity from E Control and Prevention (KCDC), the Ministry of FoEreign Affairs, and 0 pre-policy in steps up to 1 for the final version of the policy (see the local governments? websites. Policy Data section in the Appendix).T Iran. We used epidemiological data from thTe table ?New COVID-19 Epidemiological Data. We collected information on cumulative con-A cases in Iran by province? 36 in the ?2020 cAoronavirus pandemic in Iran? firmed cases, cumulative recoveries, cumulative deaths, active cases, and Wikipedia article, which were compiled from data provided on the Ira- any changes to domestic COVID-19 testing regimes, such as case defini-nian Ministry of Health website (in Persian). We relied on news media tions or testing methodology. For our regression analysis (Figure?2), we R reporting and two timelines of pRandemic events in Iran36,37 to collate use active cases when they are available (for China and South Korea) and policy data. From March 2-3, Iran did not report subnational cases. cumulative confirmed cases otherwise. We document quality control E Around this period the couEntry implemented three national policies: a steps in the Appendix. Notably, for China and South Korea we acquired recommendation against local travel (3/1), work from home for govern- more granular data than the data hosted on the Johns Hopkins University L ment employees (3/3)L, and school closure (3/5). As the effects of these ( JHU) interactive dashboard48; we confirm that the number of confirmed policies cannot be distinguished from each other due to the data gap, cases closely match between the two data sources (see Extended Data E we group themE for the purpose of this analysis. Fig.?1). To conduct the econometric analysis, we merge the epidemiologi-cal and policy data to form a single data set for each country.C Italy. WeC used epidemiological data from the GitHub repository38 main-tained by the Italian Department of Civil Protection (Dipartimento Reduced-Form Approach. The reduced-form econometric approach C della Protezione Civile). For policies, we primarily relied on the Eng- that we apply here is a ?top down? approach that describes the behavior lish version of the COVID-19 dossier ?Chronology of main steps and of aggregate outcomes y in data (here, infection rates). This approach A Alegal acts taken by the Italian Government for the containment of the can identify plausibly causal effects 5,14 induced by exogenous changes in COVID-19 epidemiological emergency? written by the Dipartimento independent policy variables z (e.g., school closure) without explicitly della Protezione Civile39, and Wikipedia40. describing all underlying mechanisms that link z to y, without observ- ing intermediary variables x (e.g., behavior) that might link z to y, or France. We used the region-level epidemiological dataset provided without other determinants of y unrelated to z (e.g., demographics), by France?s government website41 and supplemented it with numbers denoted w. Let f(?) describe a complex and unobserved process that of confirmed cases by region on France?s public health website, which generates infection rates y: Article to the policy?s introduction, thereby encompassing any lagged effects y = f (x1(z1, ?, zK ), ?, xN (z1, ?, zK ), w1, ?, wM) (1) of policies. ?t is a mean-zero disturbance term that captures inter-period changes not described by policyt. Using this approach, infections each Process-based epidemiological models aim to capture elements day are treated as the initial conditions for integrating Equation?4 of f(?) explicitly, and then simulate how changes in z, x, or w affect y. through to the following day. This approach is particularly important and useful in forward-looking We compute the first differences log(It)?log(It?1) using active infec- simulations where future conditions are likely to be different than tions where they are available, otherwise we use cumulative infections, historical conditions. However, a challenge faced by this approach is noting that they are almost identical during this early period (except that we may not know the full structure of f(?), for example if a patho- in China, where we use active infections). We then match these data to gen is new and many key biological and societal parameters remain policy variables that we construct using the novel data sets we assemble uncertain. Crucially, we may not know the effect that large-scale policy and apply a reduced-form approach to estimate a version of Equation?6, (z) will have on behavior (x(z)) or how this behavior change will affect although the actual expression has additional terms detailed below.W W infection rates (f(?)). Alternatively, one can differentiate Equation?1 with respect to the Estimation. To estimate a multi-variable version of EVquation E?6, we E kth policy zk: estimate a separate regression for each country c. ObservationIs are for I subnational units indexed by i observed for each day t. Because not all ?y N? ?y ?xj = (2) localities began testing for COVID-19 on the same date, these samples V ?zk j=1 ?xj ?zk are unbalanced panels. To ensure data quality, we restrict our analysis to localities after they have reported at least ten cuEmulative infections. E which describes how changes in the policy affects infections through A necessary condition for unbiased estimates is that the timing of all N potential pathways mediated by x1,...,xN. Usefully, for a fixed pop- policy deployment is independent ofP naturRal infection growth rates14, a Rulation observed over time, empirically estimating an average value mathematical condition that should be true in the context of a new epi-of the local derivative on the left-hand-side in Equation?2 does not demic. In established epidemiological models, including the standard depend on explicit knowledge of w. If we can observe y and z directly PSIR model above, early rates of infection within a susceptible population and estimate changes over time ?y with data, then intermediate vari- ?z are characterized by constant exponential growth. This phenomenon is k ables x also need not be observed nor modeled. The reduced-form well understood theoreticalEly13,27,46, has been repeatedly documented in E econometric approach5,14 thus attempts to measure ?y directly, exploit- past epidemics28,29,47 aLs well as the curren t COVID-19 pandemic11,12, and ?z ing exogenous variation in policies z. k implies constant infection growth rates in the absence of policy inter- L vention. ThuIs, wCe treat changes in infection growth rates as condition-Model. Active infections grow exponentially during the initial phase of ally independent of policy deployments since the correlation between Can epidemic, when the proportion of immune individuals in a popula- a constTant variable and any other variable is zero in expectation. Ition is near zero. Assuming a simple Susceptible-Infected-Recovered We estimate a multiple regression version of Equation?6 using (SIR) disease model (e.g., ref. [11]), the growth in infections during the oRrdinary least squares. We include a vector of subnational unit-fixed Tearly period is effects ?0 (i.e., varying intercepts captured as coefficients to dummy variables) to account for all time-invariant factors that affect the dI Rt = (S ? ? ?)I = (? ? ?)I , (3) local growth rate of infections, such as differences in demographics, dt t t S tt ?1 socio-economic status, culture, and health systems5. We include a vec- where It is the number of infected individuals at time t, ? is the tran As- tor of day-of-week-fixed effects ? to account for weekly patterns in the A mission rate (new infections per day per infected individDual), ? is the growth rate of infections that are common across locations within a removal rate (proportion of infected individuals recovering or dying country, however, in China, we omit day-of-week effects because we each day) and S is the fraction of the population suscEeptible to the dis- find no evidence they are present in the data ? perhaps due to the fact Dease. The second equality holds in the limit S ? 1, which describes the that the outbreak of COVID-19 began during a national holiday and current conditions during the beginning of the COVID-19 pandemic. workers never returned to work. We also include a separate single-day E The solution to this ordinary differentiAal equTation is the exponential dummy variable each time there is an abrupt change in the availability function of COVID-19 testing or a change in the procedure to diagnose posi- Ttive cases. Such changes generally manifest as a discontinuous jump It 2 = e gR?(t2?t1), (4) in infections and a re-scaling of subsequent infection rates (e.g., See AIt 1 China in Figure?1), effects that are flexibly absorbed by a single-day E dummy variable because the dependent variable is the first-difference Rwhere It1 is the initial condition. Taking the natural logarithm and rear- of the logarithm of infections. We denote the vector of these testing ranging, we have L dummies ?. ELastly, we include a vector of Pc country-specific policy variables for Elog(It ) ? log(It ) = g ? (t2 ? t1).2 1 (5) each location and day. These policy variables take on values between Lzero and one (inclusive) where zero indicates no policy action and Anti-cContagion policies are designed to alter g, through changes to one indicates a policy is fully enacted. In cases where a policy variable E?, by reducing contact between susceptible and infected individuals. captures the effects of collections of policies (e.g., museum closures HoClding the time-step between observations fixed at one day (t2?t1 = 1), and library closures), a policy variable is computed for each, then they Cwe thus model g as a time-varying outcome that is a linear function of are averaged, so the coefficient on this type of variable is interpreted Aa time-varying policy as the effect if all policies in the collection are fully enacted. There are also instances where multiple policies are deployed on the same date in Cgt = log(It) ? log(It ?1) = ?0 + ? ? policyt + ?t, (6) numerous locations, in which case we group policies that have similar objectives (e.g., suspension of transit and travel ban, or cancelling of A where ?0 is the average growth rate absent policy, policyt is a binary events and no gathering) and keep other policies separate (i.e., busi- variable describing whether a policy is deployed at time t, and ? is the ness closure, school closure). The grouping of policies is useful for average effect of the policy on growth rate g over all periods subsequent reducing the number of estimated parameters in our limited sample of data, allowing us to examine the impact of subsets of policies (e.g. associated with non-systematic under-reporting resulting from docu- Fig.?2c). However, policy grouping does not have a material impact mented changes in testing regimes over space and time are absorbed on the estimated effect of all policies combined nor on the effect of by region-day specific dummies ?. actual policies, which we demonstrate by estimating a regression However, if the rate of under-reporting within a locality is changing model where no policies are grouped and these values are recalculated day-to-day, this could bias infection growth rates. We estimate the (Supplementary Table 4, Extended Data Fig.?6). magnitude of this bias (see Extended Data Fig.?2), and verify that it is In some cases (for Italy and the US), policy data is available at a quantitatively small. Specifically, if ?Iit = ?itIit where ?it changes more spatially granular level than infection data (e.g., city policies day-to-day, then W and state-level infections in the US). In these cases, we code binary ? ?policy variables at the more granular level and use population-weights log(Iit) ? log(Ii,t ?1) = log(?it) ? log(?i,t ?1) + gt (8)E to aggregate them to the level of the infection data. Thus, policy vari-I ables may take on continuous values between zero and one, with a where log(?it)?log(? W i,t?1) is the day-over-day growth rate of the value of one indicating that the policy is fully enacted for the entire case-detection probability. Disease surveillance has evolved slowly in V population. Given the limited quantity of data currently available, we some locations as governments gradually expand testing, which w Eould use a parsimonious model that assumes the effects of policies on infec- cause ?it to change over time, but these changes in testing capIacity do E tion growth rates are approximately linear and additively separable. not appear to significantly alter our estimates of infection growth rates. However, future work that possesses more data may be able to identify In Extended Data Fig.?2, we show one set of epidemiologiVcal estimates23 important nonlinearities or interactions between policies. for log(?it)?log(?i, t?1). Despite random day-to-dEay variations, which R For each country, our general multiple regression model is thus do not cause systematic biases in our point estimates, the mean of log(?it)?log(?i,t?1) is consistently small acrRoss the different countries: P g = log(I ) ? log(I ) 0.05 in China, 0.064 in Iran, 0.019 in South Korea, ? 0.058 in France, cit cit ci,t ?1 (7) 0.031 in Italy, and 0.049 in the US. The average of these estimates is Pc= ? + ? + ? + ? (? ? policy ) + ? 0.026, potentially accounting for 7.3%P of our global average estimate for E 0,ci ct cit cp pcit citp=1 the no-policy infection growth rate (0.36). These estimates of log(?it)? log(?L i, t?1 ) also do not display strong temporal trends, alleviating con- where observations are indexed by country c, subnational unit i, and cerns that time-varying unEder-reporting generates sizable biases in day t. The parameters of interest are the country-by-policy specific our estimated effects Lof anti-contagion policies.C coefficients ?cp. We display the estimated residuals ?cit in?Extended Data I Fig. 10, which are mean zero but not strictly normal (normality is not Transient dyInaCmics. In China, we are able to examine the transient re-a requirement of our modeling and inference strategy), and we estimate sponse of infection growth rates following policy deployment because T uncertainty over all parameters by calculating our standard errors only three policies were deployed early in a seven-week sample period robust to error clustering at the day level14. This approach allows the duringT which we observe many cities simultaneously. This provides us R covariance in ?cit across different locations within a country, observed wRith sufficient data to estimate the temporal structure of policy effects on the same day, to be nonzero. Such clustering is important in this without imposing assumptions regarding this structure. To do this, we A context because idiosyncratic events within a country, such as a holidAay estimate a distributed-lag model that encodes policy parameters using or a backlog in testing laboratories, could generate nonuniform weekly lags based on the date that each policy is first implemented in country-wide changes in infection growth for individual days not explic- locality i. This means the effect of a policy implemented one week ago D itly captured in our model. Thus, this approach non-parametrically is allowed to differ arbitrarily from the effect of that same policy in accounts for both arbitrary forms of spatial auto-correlation or sys- the following week, etc. These effects are then estimated simultane-E tematic misreporting in regions of a country on any gthat it generates larger estimates for uncertainty thEiven dDay (we note ously and are displayed in Fig.?2 (also?Supplementary Table 3). Such an clustering by i). a distributed lag approach did not provide statistically meaningful T When we report the effect of all policies combined (e.g., Figure?2b) we insight in other countries using currently available data because there are reporting the sum of coefficient estimates for all policies ?Pcp=1 ?cp, were fewer administrative units and shorter periods of observation (i.e. A accounting for the covariance of errors in these estimates when com- smaller samples), and more policies (i.e. more parameters to estimate) puting the uncertainty of this sum. AT in all other countries. Future work may be able to successfully explore Note that our estimates of ? and ?0 in Equation?7 are robust to sys- these dynamics outside of China.R tematic under-reporting of infecRtions, a major concern in the ongo- As a robustness check, we examine whether excluding the transient ing pandemic, due to the construction of our dependent variable. response from the estimated effects of policy substantially alters our E This remains true even if dEifferent localities have different rates of results. We do this by estimating a ?fixed lag? model, where we assume under-reporting, so long as the rate of under-reporting is relatively that policies cannot influence infection growth rates for L days, recod-L constant. To see this,L note that if each locality i has a medical system ing a policy variable at time t as zero if a policy was implemented fewer that reports only a fraction ?i of infections such that we observe than L days before t. We re-estimate Equation?7 for each value of L and E ?Iit = ?iIit rather aEn actual infections Iit, then the left-hand-side of Equa- present results in Extended Data Fig.?5 and Supplementary Table 5.tion?7 will beC C ? ? Alternative disease models. Our main empirical specification is mo-log(Iit) ? log(Ii,t ?1) = log(?iIit) ? log(?iIi,t ?1) tivated with an SIR model of disease contagion, which assumes zero C C latent period between exposure to COVID-19 and infectiousness. If =log(? ) ? log(? ) + log(I ) ? log(I ) we relax this assumption to allow for a latent period of infection, as in i i it i,t ?1A A a Susceptible-Exposed-Infected-Recovered (SEIR) model, the growth of the outbreak is only asymptotically exponential11. Nonetheless, we =log(Iit) ? log(Ii,t ?1) = gt demonstrate that SEIR dynamics have only a minor potential impact on the coefficients recovered by using our empirical approach in this and is therefore unaffected by location-specific and time-invariant context. In Extended Data Figs.?8 and 9 we present results from a simula- under-reporting. Thus systematic under-reporting does not affect our tion exercise which uses Equations?9?11, along with a generalization to estimates for the effects of policy ?. As discussed above, potential biases the SEIR model11 to generate synthetic outbreaks (see?Supplementary Article Methods Section 2). We use these simulated data to test the ability of our slightly from the classical SIR interpretation of ? because in the public statistical model (Equation?7) to recover both the unimpeded growth data we are able to obtain, individuals are coded as ?recovered? when rate (Extended Data Fig.?8) as well as the impact of simulated policies on they no longer test positive for COVID-19, whereas in the classical SIR growth rates (Extended Data Fig.?9) when applied to data generated by model this occurs when they are no longer infectious. We adopt the SIR or SEIR dynamics over a wide range of epidemiological conditions. average of these two medians, setting ? =.08. We use medians rather than simple averages because low values for I induce a long right-tail Projections in daily estimates of ? and medians are less vulnerable to this distor- Daily growth rates of infections. To estimate the instantaneous daily tion. We then use our empirically-based reduced-form estimates of g? growth rate of infections if policies were removed, we obtain fitted (both with and without policy) combined with Equations?9?11 to pro- values from Equation?7 and compute a predicted value for the depend- ject total cumulative cases in all countries, shown in Figure?4. We ent variable when all Pc policy variables are set to zero. Thus, these simulate infections and cases for each administrative unit in our sam- estimated growth rates g? no policycit capture the effect of all locality-specific ple beginning on the first day for which we observe 10 or more cases W factors on the growth rate of infections (e.g., demographics), (for that unit) using a time-step of 4 hours. Because we observe con- day-of-week-effects, and adjustments based on the way in which infec- firmed cases rather than total infections, we seed each simulatiEon by EW tion cases are reported. This counterfactual does not account for adjusting observed It on the first day using country-speVcific eIstimates Ichanges in information that are triggered by policy deployment, since of case detection rates. We adjust existing estimates of case those should be considered a pathway through which policies affect under-reporting23 to further account for asymptomatic infections V outcomes, as discussed in the main text. Additionally, the ?no-policy? assuming an infection-fatality ratio of 0.075%25. We assume Rt = 0 on counterfactual does not model previously unobserved changes in the first day. To maintain consistency with the repEorted data, we report E behavior that might occur if fundamentally new behaviors emerge our output in confirmed cases by multiplying our simulated It + Rt even in the absence of government intervention. When we report an values by the aforementioned proportioRn of infections confirmed. R average no-policy growth rate of infections (Figure?2a), it is the average We estimate uncertainty by resampling from the estimated value of these predictions for all observations in the original sample. variance-covariance matrix of all regPression parameters. In Extended P Location-and-day specific counterfactual predictions (g? no policycit ), Data Fig.?7, we show sensitivity of this simulation to the estimated value accounting for the covariance of errors in estimated parameters, are of ? as well as to the use of a Susceptible-Exposed-Infected-Recovered shown as red markers in Figure?3. (SEIR) framework. In?SuppElementary T able 6, we show sensitivity of Ethis simulation to the assumed infection-fatality ratio (see?Supplemen- Cumulative infections. To provide a sense of scale for the estimated tary Methods SectionL 1). L cumulative benefits of effects shown in Figure? 3, we link our reduced-form empirical estimates to the key structures in a simple Reporting sIumCmary CSIR system and simulate this dynamical system over the course of our FurtheTr information on research design is available in the?Nature Isample. The system is defined as the following: Research Reporting Summary linked to this paper. T dSt = ? ? StIt (9)dt t ADRata availability RThe datasets generated during and/or analysed during the current dIt = (? S ? ?)I (10) study are available at https://github.com/bolliger32/gpl-covid. Future dt t t t D updates and/or extensions to data or code will be listed at http://www. A globalpolicy.science/covid19.dRt = ?It E (11)dt DCode availability where St is the susceptible population and Rt is the removed population. For easier replication, we have created a CodeOcean ?capsule? ? E Here ?t is a time-evolving parameter, dAetermined via our empirical which contains a pre-built computing environment in addition to estimates as described below. Accounting foTr changes in S becomes the source code and data. This is available at https://codeocean.com/ Tincreasingly important as the size of cumulative infections (It + Rt) capsule/1887579/tree/v1. Future updates and/or extensions to data or becomes a substantial fraction oRf the local subnational population, code will be listed at http://www.globalpolicy.science/covid19. Awhich occurs in some no-policy scenarios. Our reduced-form analysis provides estimates for the Egrowth rate of active infections (g?) for each 34. Lin, J. COVID-19/2019-nCoV Time Series Infection Data Warehouse. https://github.com/ Rlocality and day, in a regime where St ? 1. Thus we knowL BlankerL/DXY-COVID-19-Data.35. COVID-19 pandemic lockdown in Hubei ? Wikipedia, The Free Encyclopedia. https://dIt en.wikipedia.org/w/index.php?title=COVID-19_pandemic_lockdown_in_Hubei EE /It|S?1 = g? = ? (12)dt t t ? ? oldid=955933271 (2020).36. COVID-19 pandemic in Iran ? Wikipedia, the free encyclopedia. https:// Len.wikipedia.org/w/index.php?title=COVID-19_pandemic_in_Iran oldid=956402285 but we doC not know the values of either of the two right-hand-side terms, (2020).37. Think Global Health. Timeline of the coronavirus. https://www.thinkglobalhealth.org/ Ewhich are required to simulate Equations?9?11. To estimate ?, we note article/updated-timeline-coronavirus.thCat the left-hand-side term of Equation?11 is 38. Presidenza del Consiglio dei Ministri. COVID-19. https://github.com/pcm-dpc/COVID-19.39. Civil Protection Department Website - Presidency of the Council of Ministers. Coronavirus CdR d emergency. http://www.protezionecivile.it/web/guest/home.A t ? (cumulative_recoveries + cumulative_deaths) 40. COVID-19 pandemic lockdown in Italy ? Wikipedia, The Free Encyclopedia. https://dt dt en.wikipedia.org/w/index.php?title=COVID-19_pandemic_lockdown_in_Italy Coldid=956053371 (2020).41. Roussel, O. Open platform for french public data - Fr-SARS-CoV-2. https://www.data.which we can observe in our data for China and South Korea. Comput- gouv.fr/en/datasets/fr-sars-cov-2 (2020). A ing first differences in these two variables (to differentiate with respect 42. Sante Publique France. Covid-19. https://www.santepubliquefrance.fr/. 43. Agence R?gionale de Sant?. Agir pour la sant? de tous. https://www.ars.sante.fr/. to time), summing them, and then dividing by active cases gives us 44. COVID-19 pandemic in France ? Wikipedia, The Free Encyclopedia. https://en.wikipedia. estimates of ? (medians: China = 0.11, Korea = 0.05). These values differ org/w/index.php?title=COVID-19_pandemic_in_France oldid=956505489 (2020). 45. USA Facts. Coronavirus locations: COVID-19 map by county and state. https://usafacts. collected policy data, DA cleaned data. France: SAP collected health data, SAP, JT, HD org/visualizations/coronavirus-covid-19-spread-map/. collected policy data, SAP cleaned data. Iran: AH collected health data and policy data, AH, 46. Kermack, W. O. & McKendrick, A. G. A contribution to the mathematical theory of DA cleaned data. USA: ER, KB collected health data, EK collected policy data, ER, DA, KB epidemics. Proceedings of the royal society of london. Series A, Containing papers of a cleaned data. IB collected geographic and population data for all countries. SH designed the mathematical and physical character 115, 700?721 (1927). econometric model. SH, SAP, JT conducted econometric analysis for all countries. KB, IB, AH, 47. Mills, C. E., Robins, J. M. & Lipsitch, M. Transmissibility of 1918 pandemic influenza. Nature ER, EK designed and implemented epidemiological models and projections. SAP, KB, IB, JT, 432, 904?906 (2004). https://doi.org/10.1038/nature03063. AH, EK designed and implemented robustness checks. HD created Fig. 1, TC created Fig. 2, JT 48. COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at created Fig. 3, ER created Fig. 4, DA created SI Table 1, LYH, JL created SI Table 2, JT created SI Johns Hopkins University. https://github.com/CSSEGISandData/COVID-19. Table 3, JT created SI Table 4, SAP, JT created SI Table 5, KB created SI Table 6, LYH created ED Figs. 1?2, SAP created ED Figs. 3?5, JT created ED Fig. 6, KB created ED Fig. 7, IB created ED Figs. 8?9, JT created ED Fig. 10. DA, IB, PL managed policy data collection and quality control. W Acknowledgements We thank Brenda Chen for her role initiating this work and Avi Feller for IB, TC managed the code repository. IB, PL ran project management. EK, TW, JT, PL managed his feedback. Funding: SAP, EK, PL, JT are supported by a gift from the Tuaropaki Trust. TC is literature review. LYH, EK, TW managed References. PL managed the Extended Data and supported by an AI for Earth grant from National Geographic and Microsoft. DA, AH, IB are Appendix.E supported through joint collaborations with the Climate Impact Lab. KB is supported by the I Royal Society Te Apa?rangi Rutherford Postdoctoral Fellowship. HD and ER are supported by Competing interests The authors declare no competing interests. W the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400 and 1752814, respectively. Opinions, findings, conclusions or recommendations expressed in Additional information E V this material are those of the authors and do not reflect the views of supporting organizations. Supplementary information is available for this paper at https://doi.org/10.1038/s41I586-020-2404-8.Author contributions SH conceived of and led the study. All authors designed analysis, Correspondence and requests for materials should be addressed to S.H. or S.H.E interpreted results, designed figures, and wrote the paper. China: LYH, TW collected health Peer review information Nature thanks Andrew Jones, Jeffery Shaman and Vthe other, data, LYH, TW, JT collected policy data, LYH cleaned data. South Korea: JL Collected health anonymous, reviewer(s) for their contribution to the peer review of this work.data, TC, JL collected policy data, TC cleaned data. Italy: DA collected health data, PL Reprints and permissions information is available at http://www.nEature.com/reprints. PR PR CL E LE TI TIC AR AR D D AT E TE R RA LE LE CC E E A AC C Article EW EW EV I EV I PR PR LE LE TICR RT IC A A ED ED Extended Data Fig. 1 | Validating disaggregAated epTidemiological data data we collect are from local administrative units that are more spatially Tagainst aggregated data from the Johns Hopkins Center for Systems granular than the data in the JHU CSSE database. a, In China, we aggregate our Science and Engineering. ComparisoRn of cumulative confirmed cases from a city-level data to the province level, and b, in Korea we aggregate province-level Asubset of regions in our collated epidemiological dataset to the same statistics data up to the country level. Small discrepancies, especially in later periods of from the 2019 Novel CoronavirEus COVID-19 (2019-nCoV) Data Repository by the outbreak, are generally due to imported cases (international or domestic) Rthe Johns Hopkins Center for Systems Science and Engineering (JHU CSSE)48. that are present in national statistics but which we do not assign to particular We conduct this comparLison for Chinese provinces and South Korea, where the cities (in China) or provinces (in Korea). LE CE CE AC AC EWI E W EV EV I PR PR LE LE RT IC TIC A AR ED ED RA T AT Extended Data Fig. 2 | Estimated treRnds in case detection over time within denoted in panel title) is the average growth rate of case detection, equal to E each country. Systematic trenEds in case detection may potentially bias the magnitude of the potential bias. For example, in the main text we estimate estimates of no-policy infection growth rates (see Equation?8). We estimate the that the infection growth rate in the United States is 0.29 (Figure?2a), of which L potential magnitude of this bias using data from the Centre for Mathematical growth in case detection might contribute 0.049 (this figure). Sample sizes Modelling of Infectious Diseases23 Markers indicate daily first-differences in are 75 in China, 41 in Iran, 40 in South Korea, 29 in France, 40 in Italy, and 32 in E the logarithm of the fraction of estimated symptomatic cases reported for the US.each country overE time. TLhe average value over time (solid line and value C C AC AC Article W W VI E VI E RE REP P CL E LE TI TIC AR AR D D Extended Data Fig. 3 | Robustness of the estimated infections and the combined effect of policies to w data from entire regions. For each country, we re-e data k times, each time withholding one of theA k first-T no-pEolicy growth rate of respectively. For each country panel, if a single region is influential, the ithholding blocks of estimated value when it is withheld from the sample will appear as an outlier. E stimated Eq.?7 using real Some regions that appear influential are highlighted with an open pink circle. level administrative As in Figure?2b of the main text, we estimate a distributed lag model for China T regions (?Adm1,? i.e. state or province) in that country. Each gray circle is either and display each of the estimated weekly lag effects (red circle is the same (a) the estimated no-policy growth ratRe or (b) the total effect of all policies ?without Hubei? sample for lags). The full sample includes 3,684 observations Acombined, from one of these k regressions. Red and blue circles show estimates in China, 595 in South Korea, 2,898 in Italy, 548 in Iran, 270 in France, and 1,238 from the full sample, identical Eto results presented in panels A and B of Figure?2, in the US. R EL EL E C AC AC C IE W IE W RE V RE V P P LE E TIC TIC L AR AR D D AT E TE ER ER A CE L EL C ExCtendedC Data Fig. 4 | Robustness of the estimated effects of individual highlighted with an open green circle. The full sample includes 3,669 policies to withholding blocks of data from entire regions. Same as observations in China, 595 in South Korea, 2,898 in Italy, 548 in Iran, 270 in Extended Data Figure?3, but for individual policies (analogous to Figure?2c in France, and 1,238 in the US.A Athe main text). In cases where two regions are influential, a second region is Article EW EW EV I EV I PR PR E E TIC L TIC L AR AR ED ED T T ER A RA EL E EL ExtendedC Data Fig. 5 | Evidence supporting models where policies affect a, R-squared values associated with fixed-lag lengths varying from zero to inCfection growth rates in the days following deployment. Existing evidence fifteen days. Center values represent the R squared value in our sample, Chas not demonstrated whether policies should affect infection growth rates in whiskers are 95% CI computed through resampling with replacement. Athe days immediately following deployment. It is therefore not clear ex ante In-sample fit generally declines or remains unchanged if policies are assumed Cwhether the policy variables in Eq.?7 should be encoded as ?on? immediately to have a delay longer than four days. b, Estimated effects for no lag (the model following a policy deployment. We estimate ?fixed-lag? models in which a reported in the main text) and for fixed-lags between one and five days. Center A fixed delay between a policy?s deployment and its effect is assumed values represent the point estimate, error bars are 95% CI. Estimates generally (see?Supplementary Methods Section 3). If a delay model is more consistent are unchanged or shrink towards zero (e.g. Home isolation in Iran), consistent with real world infection dynamics, these fixed lag models should recover with mis-coding of post-policy days as no-policy days. The sample size is 595 in larger estimates for the impact of policies and exhibit better model fit. South Korea, 2,898 in Italy, 548 in Iran, 270 in France, and 1,238 in the US. IE W IE W EV EV PR PR LE LE TIC TIC AR AR ED D T Extended Data Fig. 6 | Estimated infection or hospTitalizaEtion growth rates administrative unit, Wuhan, China. The sample size is 46 observations. c, Same with actual anti-contagion policies and in a ?no policy? counterfactual as Figure?3 in the main text, but using hospitalization data from France rather A scenario. a, The estimated daily growth ratesA of active (China, South Korea) or than cumulative cases (the French government stopped reporting cumulative cumulative (all others) infections based on the observed timing of all policy cases after March 25, 2020). The sample size is 424 observations. For all panels, deployments within each subnational unit (blue) and in a scenario where no the difference between the with- and no-policy predictions is our estimated R policies were deployed (red). IdenticaRl to Figure?3 in the main text, but using an effect of actual anti-contagion policies on the growth rate of infections alternative disaggregated encoding of policies that does not group any (or hospitalizations). The markers are daily estimates for each subnational E policies into policy packages. The sample size is 3,669 in China, 595 in South administrative unit (vertical lines are 95% confidence intervals). Black Korea, 2,898 in Italy, 548 in Iran, 270 in France, and 1,238 in the US. b, Same as circles are observed changes in log(infections) (or diamonds for L Figure?3 in the main text,L but Eq.?7 is implemented for a single example log(hospitalizations)), averaged across observed administrative units. CE E AC AC C Article EW EW EV I I EV PR PR LE LE TIC IC AR AR T Extended Data Fig. 7 | Sensitivity of estimated averted/delayed infections (a) and (b), which is the total number of averted/delayed infections. d, Same as to the choice of ? and ? in an SIR/SEIR framework. This figure displays the (c), but on a logarithmic scale similar to Figure?4 in the main text (a-c are on a sensitivity of total averted/delayed cases presented in FiguEre?4 of Dthe main text linear scale, trimmed to show details). Figure?4 in the main text uses ? = 0.079, Dto alternative modeling assumptions. We compute total cases across the which we calculate using empirical recovery/death rates in countries where we respective final days in our samples for the six countries presented in our observe them (China and South Korea, see?Methods). If we assume a 14-day E analysis. The figure displays how these totals vary wiTth eight values of ? delay between infected individuals becoming non-infectious and being (0.05-0.4) and four values of ? (0.2, 0.33, 0.5, ?), where the final value of ? (?) reported as ?recovered? in the data, we would calculate ? = 0.18. Figure?4 in the T corresponds to the SIR model. a, The simulated total number of infections main text assumes ? = ?. under no policy. b, Same, but using acRtual polAicies. c, The difference between RA EL E LE C CE AC AC IE W IE W RE V EV P PR LE LE TIC TIC AR AR ED D T Extended Data Fig. 8 | Simulating reduced-form esTtimatEes for the no-policy (??1) of the disease. ?? = ?? is equivalent to SIR disease dynamics. In each panel, growth rate of infections for different population regimes and disease Smin is the minimum susceptible fraction observed across all 1,000 45-day A dynamics. We examine the performance of reAduced form econometric simulations shown in each panel. In the real datasets used in the main text, after estimators through simulations in which different underlying disease correcting for country-specific under-reporting, Smin across all units analyzed R dynamics are assumed (see SI SectionR 3). Each histogram shows the is 0.72 and 95% of the analyzed units finish with Smin > 0.91. Bias refers to the distribution of econometrically estimated values across 1,000 simulated distance between the dashed grey and black line as a percentage of the true outbreaks. Estimates are for the no-policy infection growth rate (analogous to value. a, Simulations in near-ideal data conditions in which we observe active E Figure?2a) when three differentE policies are deployed at random moments in infections within a large population (such that the susceptible fraction of the L time. The black line showLs the correct value imposed on the simulation and the population remains high during the sample period, similar to those in our data red histogram shows the distribution of estimates using the regression in Eq.?7, for Chongqing, China). b, Simulations in a non-ideal data scenario where we are applied to data output from the simulation. The grey dashed line shows the only able to observe cumulative infections in a small population (similar to E mean of this distrEibution. The 12 subpanels describe the results when various those in our sample for Cremona, Italy).values are assigned to the mean infectious period (??1) and mean latency period CCA AC C Article EW EWI I RE V RE V P P E E TIC L IC L AR AR T ED D Extended Data Fig. 9 | Simulating reduced form estimates for are for the combined effect of three different policies (analogous to Figure?2b) E anti-contagion policy effects for different population regimes and that are deployed at random moments in time. assumed disease dynamics. Same as ExtendAed DataT Figure?8, but estimates ATR R EL E LE CC CC E A A EWI IE W EV EV PR PR LE LE IC Extended Data Fig. 10 | Regression residuals for the growth rates of (right) show quantiles of the cumulative density function (y-axis) plotted COVID-19 by country. These plots show the estimated residuals from against the same qCuantiles for a Normal Distribution. For additional details, see T Equation?7 for each country-specific econometric model. Histograms (left) Fig.?3 and the Econometric Analysis section of Methods.show the estimated unconditional probability density function. Quantile plots R RT I A A D D AT E AT E ER ER EL EL AC C AC C Corresponding author(s): Solomon Hsiang Last updated by author(s): May 13, 2020 Reporting Summary Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist. 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A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable. For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above. Software and code Policy information about availability of computer code Data collection Computer code was not used to collect data. Data analysis Python version 3.8, R version 3.5, Stata MP For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information. Data Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: - Accession codes, unique identifiers, or web links for publicly available datasets - A list of figures that have associated raw data - A description of any restrictions on data availability All data used in this analysis is from free, publicly available sources, and can be accessed at https://github.com/bolliger32/gpl-covid Field-specific reporting Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection. Life sciences Behavioural & social sciences Ecological, evolutionary & environmental sciences For a reference copy of the document with all sections, see nature.com/documents/nr-reporting-summary-flat.pdf 1 nature research | reporting summary October 2018 Behavioural & social sciences study design All studies must disclose on these points even when the disclosure is negative. Study description The study analyzes six different countries with varying policy implementations to estimate the impact of these anti-contagion policies on the growth rate of infections. Research sample The research sample consists of COVID-19 case counts from China, Korea, Italy, France, Iran, and the United States. Sampling strategy We chose countries to analyze among those that accounted for the majority of the global confirmed caseload at the beginning of our analysis (3/14/2020). We chose a selection of countries based on global interest and the languages spoken by the authors (for ease of data collection). Within each country, we collected all available data on active infections (where available) and cumulative infections, in addition to all available policy data. No sampling was required. Data collection Data collection is detailed in the appendix. Timing Data collection began on March 14, 2020 and ended on April 12, 2020. Data exclusions Case data were excluded from dates with < 10 confirmed cases because of concerns about statistical reliability. Non-participation No participants dropped out or declined participation because this study did not directly involve them. Randomization Randomization was not possible for this study because the paper investigates the growth rate of COVID-19 cases with policy interventions or in the absence thereof. Reporting for specific materials, systems and methods We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response. Materials & experimental systems Methods n/a Involved in the study n/a Involved in the study Antibodies ChIP-seq Eukaryotic cell lines Flow cytometry Palaeontology MRI-based neuroimaging Animals and other organisms Human research participants Clinical data 2 nature research | reporting summary October 2018