Abstract
We use the synthetic control method to analyze the effect of face masks on the spread of COVID-19 in Germany. Our identification approach exploits regional variation in the point in time when wearing of face masks became mandatory in public transport and shops. Depending on the region we consider, we find that face masks reduced the number of newly registered severe acute respiratory syndrome coronavirus 2 infections between 15% and 75% over a period of 20 days after their mandatory introduction. Assessing the credibility of the various estimates, we conclude that face masks reduce the daily growth rate of reported infections by around 47%.
Many countries have experimented with several public health measures to mitigate the spread of COVID-19. One particular measure that has been introduced are face masks. It is of obvious interest to understand the contribution made by such a measure in reducing infections.
The effect of face masks on the spread of infections has been studied for a long time. The usefulness of facial protection for clinical personnel is beyond dispute, even though there are many questions left open (1). There is also evidence that face masks helped in mitigating the spread of earlier epidemics such as SARS 2003 (severe acute respiratory syndrome 2003) or influenza (see SI Appendix, section E for a brief literature survey). The impact of face masks worn in public on the spread of COVID-19 has yet to be systematically analyzed. This is the objective of this paper.
There is a general perception in Germany that the mandatory use of face masks in public reduces COVID-19 incidences considerably. This perception stems mainly from the city of Jena. After face masks became mandatory between 1 April and 10 April 2020 the number of new infections fell almost to zero. Jena is not the only region in Germany, however, that introduced face masks. Six further regions made masks compulsory before the introduction at the federal state level. Eventually, face masks became mandatory in all federal states between 20 April and 29 April 2020 (see SI Appendix, section A for background).
We quantify the effectiveness of face masks by employing the synthetic control method (SCM; refs. 25). Our identification approach exploits this regional variation in the point in time when face masks became mandatory. We use data for 401 regions in Germany (municipal districts) to estimate the effect of this particular policy intervention on the development of registered infections with COVID-19. We consider the timing of mandatory face covering as an exogenous event to the local population: Masks were imposed by local authorities and were not the outcome of some process in which the population was involved. We compare the COVID-19 development in various regions to their synthetic counterparts. The latter are constructed as weighted averages of control regions that are structurally similar to treated regions. Structural dimensions considered include prior COVID-19 cases, the demographic composition, and the local health care system.
A detailed analysis of the timing of all public health measures in the regions we study guarantees that we correctly attribute our findings to face masks (and not erroneously to other public health measures). We also employ a standard SIR (susceptibleinfectedremoved) model and undertake an analysis of the distribution of the lag between infection and reporting date. This allows us to provide a precise interpretation of our empirical effectiveness measure and to pin down the point in time when the effects of face masks should be visible in the data.
We find statistically significant and sizeable support for the general perception that the public wearing of face masks in Jena strongly reduced the number of incidences. We obtain a synthetic control group that closely follows the COVID-19 trend before the introduction of mandatory masks in Jena. The difference between Jena and this group becomes significant thereafter. Our findings indicate that the early introduction of face masks in Jena has resulted in a drop in newly registered COVID-19 cases of around 75% after 20 d. Put simply, if the control region observes 100 new infections over a period of 20 d, the mask region observes only 25 cases. This drop is greatest, by more than 90%, for the age group 60 y and above. Our results are robust to different sensitivity checks, among which are placebo-in-space and placebo-in-time analyses.
As a means to verify the generalizability of our findings for Jena, we move from a single- to a multiple-treatment approach and estimate average treatment effects of introducing face masks on the spread of COVID-19 for all regions that introduced masks by 22 April (8% of all German regions). Although the estimated average treatment effect is smaller compared to the one found for Jena, it is still statistically significant and sufficiently large to support our point that wearing face masks is an effective and cost-efficient measure for fighting COVID-19. When we summarize all of our findings in one single measure (SI Appendix, section D.2), we conclude that the daily growth rate of COVID-19 cases in the treatment group falls by around 47% due to mandatory mask-wearing relative to the synthetic control group.*
Our findings can be aligned with earlier evidence on face masks, public health measures, and the epidemic spread of COVID-19, although consolidated scientific knowledge is limited (SI Appendix, section E). While there is a growing consensus from clinical studies that face masks significantly reduce the transmission risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and COVID-19 (7, 10), nonclinical evidence on the effectiveness of face masks is still largely missing. Ref. 11 surveys evidence on the population impacts of a widespread community mask use and stresses that no randomized control trials on the use of masks has been published. The study which is the most relevant paper for ref. 11 is one that analyzed exhaled breath and coughs of children and adults with acute respiratory illness (ref. 12, p. 676), that is, used a clinical setting. Concerning the effect of masks on community transmissions, the survey needs to rely on preCOVID-19 studies.
Ref. 13 is among the first to estimate the population impact of face masks on SARS-CoV-2 infections. The authors track the development of COVID-19 in three pandemic epicenters, Wuhan, Italy, and New York City, between 23 January and 9 May 2020 and find sizable mitigating effects of face masks on epidemic spread. While their study offers important insights into the population effects of face masks, a methodical limitation is that estimates are only carried out in a beforeafter manner with no use of a strict control group approach. This may limit the causal interpretation of results. We therefore follow the spirit of ref. 4 and provide causal evidence identifying the population impact of mandatory face masks on the spread of COVID-19.
Results: The Effects of Face Masks on the Spread of COVID-19
All results are obtained by applying the synthetic control method. It is described briefly in Method and Data and in more detail in SI Appendix, section B.
Discussion
We set out by analyzing the effect of face masks on the spread of COVID-19 for a comparative case study of the city of Jena. Our quasi-experimental control group approach using SCM shows that the introduction of face masks on 6 April reduced the number of newly registered COVID-19 cases over the next 20 d by 75% relative to the synthetic control group. Comparing the daily growth rate in the synthetic control group with the observed daily growth rate in Jena, the latter shrinks by around 70% due to the introduction of face masks. This is a sizeable effect. The introduction of mandatory face masks and the associated signal to the local population to take the risk of person-to-person transmissions seriously apparently helped considerably in reducing the spread of COVID-19. Looking at average treatment effects for all other regions puts this result in some perspective. The reduction in the daily growth rate of infections amounts to 14% only. By contrast, when we focus on larger cities, we find a reduction in the daily growth rate of infections by roughly 47%.
What would we reply if we were asked what the effect of introducing face masks would have been if they had been made mandatory all over Germany? The answer depends, first, on which of the percentage measures we found above is the most convincing and, second, on the point in time when face masks are made compulsory. The second aspect is definitely not only of academic interest but would play a major role in the case of a second wave.##
We believe that the reduction in the daily growth rates of infections between 47% and 70% is our best estimate of the effects of face masks. Arguments in favor of the high 70% stress that Jena introduced face masks before any other region did so. It announced face masks as the first region in Germany while in our posttreatment period hardly any other public health measures were introduced or eased. Hence, it provides the most clear-cut quasi-experimental setting for studying its effects. Second, as described in Method and Data, Jena is a fairly representative region of Germany in terms of COVID-19 cases. Third, the smaller treatment effects observed in the multiple-treatment analysis may also result from the fact thatby the time that other regions followed the example of Jenabehavioral adjustments in Germanys population had already taken place. Wearing face masks gradually became more common and more and more people started to adopt their usage even when it was not yet required. The results for the subsample of larger cities are, however, quantitatively similar to Jena.
Arguments for the lower 47% state that the stronger impact of face masks on the infectious in Jena may thereby partly be driven by a Hawthorn effect. The population in this pioneer region might have reacted very strongly to the mandatory introduction of face masks by taking the other imposed public health measures and hygiene rules (washing hands, limiting interactions, staying at home more, etc.) more seriously.
Concerning the point in time (or better, the point in the epidemic cycle) when face masks become mandatory, all of our estimates might actually be modest. The daily growth rates in the number of infections when face masks were introduced in Jena was around 2 to 3%. These are low growth rates compared to the early days of the epidemic in Germany, where daily growth rates lay above 50% (20). One might therefore conjecture that the effects might have been even greater if masks had been introduced earlier.
This timing effect might also explain the difference between Jena estimates and lower estimates for other regions. By the time Jena introduced face masks on 6 April, the general trend in development of COVID-19 cases was still relatively dynamic across German regions. In mid-April, when other regions followed the example of Jena and introduced face masks before the general introduction at the federal state level, overall daily growth rates were already lower.
We simultaneously stress the need for further complementary analyses. First, Germany is only one specific country. Different regulations, norms (which relate to compliance), or climatic conditions might change the empirical picture for other countries. Second, we ignored the impact of the number of tests on reported infections. While we do not believe that this matters for Germany as rules for testing are homogenous across regions, this might play a bigger role for international comparisons. Third, we have ignored spatial dependencies in the epidemic diffusion of COVID-19. This might also matter. Fourth, there are various types of face masks. We cannot identify differential effects since mask regulations in German regions do not require a certain type. Finally, economic costs should be taken into account. When we compare masks with other common measures,*** the implied economic costs for community masks seem comparatively low. This applies to disposable masks and reusable nonmedical masks. Yet, the cost of information campaigns should be taken into account. While a detailed costbenefit analysis is needed, we would expect that a comparison with other policy actions would speak in favor of face masks. [See SI Appendix, section E.3 for a brief introduction to the literature. We estimate that costs (of households only) for face masks amount to 1.4 to 2.5% of disposable income.]
Method and Data
Acknowledgments
We are grateful for an almost uncountable number of worldwide comments on the earlier version of this paper, from colleagues from many disciplines, public administration, and the general public. They considerably helped in improving this analysis. We would especially like to thank Enikö Bán, Soeren Enkelmann, Jan Franke, Manfred Hempfling, Christof Kuhbandner, Falk Laser, and Philip Savage and two reviewers for their constructive comments. Carolin Kleyer and David Osten provided excellent research assistance. K.W. thanks IZA Institute of Labor Economics. This paper would have never taken this shape without a visiting research position at IZA.
Footnotes
- Author contributions: T.M., R.K., J.R., and K.W. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.
- The authors declare no competing interest.
- This article is a PNAS Direct Submission.
- *The main channel through which masks reduce transmission of SARS-CoV-2 is the limiting effect for the spread of exhaled air, as argued by ref. 6. Refs. 6 and 7 argue that aerosols (as opposed to larger droplets) are filtered only by high-quality masks. Droplets are also filtered by home-made masks. Earlier work includes ref. 8 that was recently extended by ref. 9. Ref. 9 finds that all face covers (without an outlet valve) reduce the front flow through jet by more than 90%. As surgical and hand-made masks generally do not tightly fit, they generate backward and downward jets.
- Ref. 10 conducts a systematic review and meta-analysis. They do not report a study (see their table 1) that analyzes the entire population of a country.
- As a measure for the quality of the fit between the treated region and its synthetic control group, the pretreatment root-mean-square prediction error (RMSPE) can be calculated and compared to a reference case. For Jena the pretreatment RMSPE is 3.145. This is considerably lower than an average RMSPE of 6.669 for all other 400 regions and their synthetic controls in the pretreatment period until 6 April. This points to the relatively good fit of the synthetic control group for Jena in this period.
- §For a German-wide news report see, for example, ref. 14.
- #See local newspaper reports, for instance ref. 15.
- Further requirements, that are less central to our application, are listed in Method and Data and are discussed in SI Appendix, section B.
- **We follow the method proposed in ref. 16 to calculate confidence intervals from P values. As pointed out in ref. 17, the interpretation of confidence intervals and P values is restricted to the question of whether or not the estimated effect of the actual treatment is large relative to the distribution of placebo effects.
- We analyze a measure that is introduced for the first time in this region. One might conjecture that our estimation measures both the true effect of a face mask but also any other change in behavior (washing hands, limiting interactions, staying at home more, etc.) that was triggered by this policy. This change in behavior is known as the Hawthorn effect. Individuals in this pioneer region might take the crisis more seriously than in the other areas. Although German health authorities had been strongly recommending such behavioral changes in daily life since mid-March, we cannot fully rule out this mixing of effects. Mobility data for federal states in SI Appendix, section C.6.2 show that federal states moved in a relatively coordinated way in this respect. Unfortunately, mobility data for Jena are not easily available.
- Alternatively, we have also tested for pseudo-treatment effects in Jena over a period of 20 d before the introduction of face masks. This period is equally split into a pre- and pseudo posttreatment period. As SI Appendix, Fig. S11B shows, there is no strong deviation from the path of the synthetic control group.
- §§This is perfectly in line with ref. 7 given the reduction in aerosols and droplets via using masks.
- ##We implicitly assume that compliance to rules in Germany is sufficiently homogenous. Some field observations in this respect would be very useful, especially across federal states in Germany and worldwide. Ref. 19 reports that compliance for distancing rules rises when masks are worn. As a first guess and assuming a compliance of 100% in our treated regions, one would expect that a reduction in compliance by x% of the population leads to a reduction of the effects of masks by x%.
- ***Common measures can be grouped inter alia into closures (of, e.g., restaurants or hotels, educational institutions or clubs, and leisure facilities), contact bans (for individuals, faith groups, or visits to hospitals or retirement homes), and contact rules (social distancing or quarantines after traveling).
- We chose T = 29.5 as this yields a date when masks show an effect in the data on T + Dm = 40 where the epidemic is already beyond its peak in our simple model. This is consistent with Jena, where the incidence had already been declining when face masks became mandatory. Numerical solutions are computed in MATLAB. The code is available in SI Appendix.
- This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2015954117/-/DCSupplemental.
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