Kovacs, Roxanne; Dunaiski, Maurice; Tukiainen, Janne
Working Paper
Compulsory face mask policies do not affect community
mobility in Germany
Suggested Citation: Kovacs, Roxanne; Dunaiski, Maurice; Tukiainen, Janne (2020) : Compulsory face
mask policies do not affect community mobility in Germany, ZBW – Leibniz Information Centre for
Economics, Kiel, Hamburg
This Version is available at:
https://hdl.handle.net/10419/218945
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Compulsory face mask policies do not affect community
mobility in Germany
Roxanne Kovacs
∗
Maurice Dunaiski
†
Janne Tukiainen
‡
June 5, 2020
Abstract
There is currently a heated debate about whether to introduce policies requiring
the general public to wear protective face masks to contain COVID-19. A key con-
cern is that compulsory face mask policies will make the public feel safer (due to risk
compensation), and may consequently undermine the most important public-health
advice to contain COVID-19 – which is to reduce mobility and maintain social distanc-
ing. This study provides first evidence on the impact of compulsory face mask policies
on community mobility. We use a difference-in-differences design, which exploits the
staggered implementation of compulsory face mask policies by German states. We
use anonymised GPS data from Google’s Location History feature to measure daily
mobility in public spaces (groceries and pharmacies, transport hubs and workplaces).
We find no evidence that compulsory face mask policies affect community mobility in
public spaces in Germany. The evidence provided in this paper makes a crucial contri-
bution to ongoing debates about how to best manage the COVID-19 pandemic.
Keywords: COVID-19, face masks, social distancing, community mobility
JEL Codes: D9, H12, I12, I18
∗
London School of Hygiene & Tropical Medicine, Department of Global Health and Development, Keppel
St, Bloomsbury, London WC1E 7HT, United Kingdom. email: roxanne.kov[email protected]
†
London School of Economics & Political Science, Department of Government, Houghton St, Holborn,
London WC2A 2AE, United Kingdom. email: [email protected]
‡
Department of Economics, Turku School of Economics, Rehtorinpellonkatu 3, FI-20014 Univer-
sity of Turku; VATT Institute for Economic Research, Arkadiankatu 7, Helsinki FI-00101. email:
janne.tukiainen@utu.fi
1 Introduction
The ongoing coronavirus disease (COVID-19) pandemic has, as of June 2020, led to the
death of over 380,000 people [WHO, 2020] and is expected to trigger a severe economic
crisis, with global GDP growth predicted to fall to -3% [IMF, 2020]. One of the main
ways in which governments have attempted to contain the spread of COVID-19 is through
non-pharmaceutical interventions targeting citizens’ behaviour. Policies that aim to curtail
the spread of COVID-19 centre around reducing citizens’ mobility and social contacts in
order to disrupt the chain of transmission. Examples include closing schools, banning public
gatherings, social distancing rules or lock-downs forbidding individuals to leave their homes
[Mellan et al., 2020].
There is currently a heated debate about whether the general public should be required
to wear protective face masks to further reduce the spread of COVID-19. For instance,
the World Health Organization
1
advocates against the use of face masks by the general
public, whilst the US Centres for Disease Control
2
advise the opposite. Nonetheless, over
50 countries already require the wearing of face masks in public spaces.
3
Those arguing
against introducing compulsory face mask policies frequently point to limited evidence on
effectiveness, concerns about individuals wearing masks incorrectly, as well as high demand
on masks reducing availability for healthcare workers [Feng et al., 2020, Greenhalgh et al.,
2020]. Another key argument against making face masks compulsory, which motivates this
paper, is the concern that individuals will feel safer and might therefore disregard the most
important public-health advice to contain the spread of COVID-19 – which is to reduce
mobility and maintain social distancing [Greenhalgh et al., 2020].
1
https://www.who.int/emergencies/diseases/novel-coronavirus-2019/advice-for-public/when-and-how-
to-use-masks
2
https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/diy-cloth-face-coverings.html
3
https://www.aljazeera.com/news/2020/04/countries-wearing-face-masks-compulsory-
200423094510867.html
1
The effect of compulsory face mask policies on citizen’s mobility is a priori ambiguous. In
line with concerns of policymakers,
4
face masks could increase mobility due to risk compen-
sation. A large economics literature examines behavioural responses to changes in perceived
or actual risk [Peltzman, 1976]. Whilst the findings are mixed overall [Godlonton et al.,
2016], a number of studies find evidence for risk-compensating behaviour, for instance, more
risky sexual behaviour among recipient of the HPV vaccine [Kapoor, 2008], car accidents as
a result of seat belt laws [Miller and Blomquist, 1989] and bicycle helmets triggering dan-
gerous driving by cars [Walker, 2007]. Risk compensating behaviour is therefore a plausible
mechanism through which protective technologies such as face masks, that reduce personal
risk (whether actual or perceived), could lead to an increase in mobility.
In contrast, salience and what we refer to as the “hassle factor” provide reasons to expect that
compulsory face mask policies reduce mobility. Face masks differ from previously studied
risk-reducing technologies as they need to be worn constantly (unlike one-off treatments
such as vaccines). Face masks might therefore serve as a constant reminder to citizens that
the COVID-19 pandemic is ongoing and serious. It is therefore possible that compulsory
face masks increase the salience of the COVID-19 pandemic in individuals’ decision making
about their mobility [Van Der Pligt and De Vries, 1998]. Availability bias (where individuals
judge events that come to mind more easily to be more likely) potentially exacerbates such
an effect. For instance, studies have found that frequent exposure to drug advertisement
influences individuals’ perceptions about disease prevalence [An, 2008]. Face masks might
similarly inflate perceptions about the true prevalence of COVID-19 – which could affect
mobility decisions about whether to visit any public space (i.e. not only locations where
face masks are required by law). Another way in which face masks differ from previously
studied risk-reducing technologies is that that they are bothersome to use (much more so
than, for instance, seat belts). Wearing a face mask creates disutility, as wearers suggest
4
see e.g. https://www.theguardian.com/uk-news/2020/jun/04/do-face-coverings-reduce-risk-and-
spread-of-coronavirus? and https://www.theguardian.com/commentisfree/2020/apr/24/face-masks-
mandatory-spread-coronavirus-government
2
that masks can be hot, uncomfortable, humid, itchy and odorous [Li et al., 2005]. This
disutility, which we refer to as the “hassle factor”, can spoil the fun of non-essential outings
and could incentivise individuals to minimise the frequency of essential outings – which could
reduce mobility. Due to the extensively studied process of adaptation, through which one
quickly adjusts to new or changed circumstances, we expect that any such effects should be
short-lived [Dolan and Kahneman, 2008]. In addition, as the hassle factor only comes into
play when masks are worn, it should primarily affect mobility in locations where face masks
are required by law.
5
This study provides first evidence on the effect of compulsory face mask policies on commu-
nity mobility. To isolate the causal effect of such policies, we use a difference-in-differences
design, which exploits the staggered introduction of policies requiring the wearing of face
masks in shops and public transport by German states (Bundesl¨ander). Saxony was the
first state to introduce compulsory face masks on the 20
th
of April 2020, Schleswig-Holstein
was the last to do so on the 29
th
of April 2020.
6
To measure community mobility, we rely
on the Google COVID-19 Community Mobility Reports, which use GPS data from Google’s
Location History users to provide anonymised and aggregated (state-level) measures of the
number of hours spent at home as well as the number of times public spaces are visited
each day. Community mobility has been previously measured in this way in epidemiological
studies [Mellan et al., 2020] to estimate the basic reproduction number R
0
, which is a key
parameter of transmission intensity and therefore highly relevant for containing the spread
of COVID-19.
We measure community mobility within each German state between March 23
rd
and May 21
st
2020. Our main outcome is an aggregate measure of mobility in public spaces, which captures
5
In a setting where face masks are voluntary, an additional reason why masks could reduce mobility is
that individuals perceive masks as a signal for a larger preferred social distance by the wearer, as found by
Seres et al. [2020]
6
All states except Berlin introduced compulsory face masks in shops and public transport on the same
date. In Berlin, masks became compulsory in public transport on April 27
th
and in shops on April 29
th
.
3
visits to grocery and pharmacy shops, workplaces and transport hubs. We also measure the
number of hours spent in places of residence as well as mobility patterns in specific locations.
We focus on an aggregate measure of mobility in public spaces, as policymakers are likely
most interested in changes in overall mobility patterns, rather than changes in mobility for
specific locations (for instance, only grocery shops).
We do not find evidence to suggest that compulsory face mask policies affect community
mobility in public spaces in Germany. Effect sizes are precisely estimated and we can rule
out even small increases in mobility that are larger than 0.03 SD. We only find a small
reduction in average community mobility on the day of the policy change (-0.14 SD), but find
no longer-term effects thereafter. We also find no evidence suggesting that, beyond a short-
term increase during the first four days, compulsory face mask policies affect the number
of hours spent at home, which is another “catch-all” measure of community mobility. We
take this to suggest that these policies are complementary to interventions aimed at reducing
mobility and disrupting the chain of transmission of COVID-19. When we examine mobility
in specific locations, we find that mobility patterns are lower in grocery shops and pharmacies
for five days following the introduction of compulsory face masks, but that the magnitude of
the reduction is modest. We find no effects on mobility patterns in workplaces or transport
hubs (subways, buses or train stations).
This paper makes three main contributions. First, it provides new evidence that is crucial to
ongoing policy debates on how to best manage the COVID-19 pandemic. Policymakers and
researchers have expressed concerns that making face masks compulsory could lead people
to disregard measures that are key for containing COVID-19. We are unable to provide
evidence on important individual-level behaviours such as hand-washing or social distancing.
However, community mobility plays a key role in reducing the spread of COVID-19 [Mellan
et al., 2020] and we find no evidence to suggest that, in Germany, compulsory face mask
policies led to an increase in mobility. If anything, we observe a temporary decrease in
4
mobility in grocery shops and pharmacies. This is important information for policy-makers
considering the costs and benefits of compulsory face mask policies, as such analysis likely
do not have to account for spillovers on mobility.
Second, we contribute to the small but rapidly growing literature using aggregate GPS data
to study the effect of policies trying to contain the spread of COVID-19 on mobility patterns
[Allcott et al., 2020, Wellenius et al., 2020, Dasgupta et al., 2020]. Using GPS data is one of
the main alternatives to using surveys [Briscese et al., 2020, Jørgensen et al., 2020], which
likely do not provide reliable data on mobility due to social desirability bias [Daoust et al.,
2020].
Finally, our findings speak to the behavioural economics literature on risk compensation
[Godlonton et al., 2016, Peltzman, 1976, Kapoor, 2008, Miller and Blomquist, 1989, Walker,
2007]. To our knowledge, only one previous study has examined the effect of face masks on
risk compensating behaviour, finding that physical distancing increases by on average 9cm
when individuals wear masks - supposedly because others interpret face masks as a signal
for a larger preferred distance [Seres et al., 2020]. This paper complements the study by
Seres et al. [2020] by providing evidence from a large sample. This study is also the first
to investigate the general equilibrium effect of introducing compulsory face masks - where
signalling is unlikely to play a role. We show that even though compulsory face mask policies
may reduce personal risk and risk imposed on others, there is no evidence of an undesirable
aggregate effect on community mobility.
5
2 Background
Germany is frequently put forward as a positive example for how to manage the COVID-19
pandemic.
7
As of June 5
th
2020, there have been 183.271 confirmed cases of COVID-19 in
Germany and 8,613 deaths [RKI, 2020]. There are arguably two main reasons for Germany’s
relative success in handling the COVID-19 pandemic. First, Germany started testing early
and it tested a broad sample of the population. This stands in contrast to some other
European countries, which focused on testing elderly populations or those in critical care
[Stafford, 2020]. Due to its federal healthcare system, Germany also does not face testing
constraints created by having only a few central laboratories, as is the case in many other
countries [Stafford, 2020]. Second, containment measures to reduce the population’s mobility
(e.g. closing schools, retail businesses and banning public gatherings), and to thereby break
the chain of transmission, began comparatively earlier than in other countries [Stafford,
2020].
Germany’s 16 states introduced compulsory face mask policies at different times in late April
2020.
8
Saxony was the first state, on the April 20
th
2020, followed by Saxony-Anhalt on April
23
th
and Thuringia on April 24
th
. Twelve states adopted compulsory face mask policies on
April 27
th
, and Schleswig-Holstein followed suit on April 29
th
. All states except Berlin made
face masks compulsory in public transport as well as in shops at the same time. In Berlin,
face masks first became compulsory in public transport (April 27
th
) and in shops two days
later. As of June 5
th
, compulsory face mask policies remain in place in all German states,
although some state governments have expressed a desire to abolish the requirement.
9
In
7
e.g. https://www.theguardian.com/world/2020/may/21/covid-19-track-and-trace-what-can-uk-learn-
from-countries-got-it-right
8
In all states, the face mask requirement is fulfilled by wearing a non-surgical mask, bandana or scarf
that covers one’s mouth and nose (called Mund-Nasen-Bedeckung). Children under the age of six and people
with disabilities are usually excluded from the face mask requirement.
9
see https://www.theguardian.com/world/2020/may/25/german-state-causes-alarm-with-plans-to-ease-
lockdown-measures-thuringia-second-wave-coronavirus and https://www.zeit.de/politik/deutschland/2020-
05/thueringen-kontaktverbot-corona-verordnung-lockerung
6
Appendix A we provide a complete overview of the staggered introduction of compulsory
face mask policies in Germany. We also record when other policies related to COVID-19
(e.g. school or retail re-openings) were implemented, given that these policies may have also
affected community mobility in the study period.
10
Even though compulsory face mask policies make it illegal not to wear a mask in designated
spaces, only nine out of 16 states introduced fines for not wearing masks.
11
Overall, the
German approach “seems to be characterised more by appealing on compliance to rules
rather than on enforcing them by micromanagement law” [Stafford, 2020]. Although data on
compliance with compulsory face mask policies are, to our knowledge, currently not available,
these policies appear to be widely supported by the German public. Nationally representative
survey evidence suggests that, before the first state-wide introduction in late April 2020,
compulsory face mask policies were supported by more than 85% of the population
12
. More
than one month into the nation-wide face mask requirement, support remains high at around
80%.
13
Several factors could explain why some states implemented compulsory face mask policies
earlier than others. First, one could see the staggered introduction as being due to a process
of bottom-up policy diffusion. For example, Thuringia implemented a state-wide compulsory
face mask policy around two weeks after its second-largest city, Jena, became the first city in
Germany to require face masks in public spaces.
14
The federal government largely took a back
seat and continued to recommend voluntary face mask use, even as several states had already
10
In some instances, these additional policy changes coincided with the introduction of compulsory face
mask policies. We discuss the implications for our identification strategy in Section 3.
11
Fines of varying amounts are in place in Baden-Wuerttemberg, Bavaria, Berlin, Hamburg, Hesse, Lower
Saxony, Mecklenburg-West Pomerania, North Rhine-Westphalia and Rhineland-Palatinate. In some cases
(e.g. NRW), fines vary within the state and are enforced at the discretion of local councils.
12
BfR Corona Monitor, 26 May 2020: https://www.bfr.bund.de/cm/349/200526-bfr-corona-monitor-
en.pdf
13
BfR Corona Monitor, 26 May 2020: https://www.bfr.bund.de/cm/349/200526-bfr-corona-monitor-
en.pdf
14
In Jena, the local health authority had recommended compulsory face masks (see
https://www.spiegel.de/panorama/gesellschaft/die-stadt-der-schoenen-muster-a-7a65406c-6b4e-4e8f-8734-
483942e59d5d)
7
introduced compulsory measures.
15
A second interpretation is that variation in the supply
of face masks and concerns about compulsory face masks leading to panic-buying played a
role. For example, the governments of Bavaria, Lower Saxony and North Rhine-Westphalia
initially resisted moves to introduce compulsory face masks on these grounds.
16
Third,
geographic variation in transmission rates could have prompted some cities (and states) to
move earlier than others. For example, Jena was considered a COVID-19 “hotspot” before
it introduced compulsory face masks.
17
Even though some evidence from the USA suggests that party ideology is associated with
support for face masks,
18
this does not appear to be the case in Germany. For instance, Jena
is governed by the liberal FDP. The first state to implement compulsory face masks (Saxony)
is governed by the centre-right CDU, while another early mover (Thuringia) is governed by
the left-wing Die Linke.
3 Data and methods
3.1 Data
To measure community mobility, we use the publicly available Google’s COVID-19 Commu-
nity Mobility Reports for Germany.
19
These data capture daily changes in mobility patterns
in each German state based on GPS data from Google Account users who have opted-in to
15
https://www.bundesregierung.de/breg-de/themen/coronavirus/empfehlung-schutzmasken-1745224
16
https://www.dw.com/de/streit-¨uber-maskenpflicht-gegen-die-corona-pandemie-entbrannt/a-52969231,
kurier.de/inhalt.corona-massnahmen-spd-ministerpraesident-erwartet-baldige-maskenpflicht.84385fb6-ca08-
4226-9601-0336a812919d.html, and https://www.aachener-zeitung.de/nrw-region/spahn-und-laschet-gegen-
maskenpflicht-in-deutschland-aid-49847769
17
https://www.mdr.de/thueringen/ost-thueringen/jena/corona-jena-seit-einer-woche-keine-neuinfektion-
100.html
18
https://tompepinsky.com/2020/05/13/yes-wearing-a-mask-is-partisan-now/
19
Data are updated regularly (roughly once a week) and available at:
https://www.google.com/covid19/mobility/
8
the Location History feature. We use mobility data from the period between March 23
rd
and May 21
st
. We exclude observations from before the national lock-down (i.e. before
March 23
rd
), as mobility reduced drastically in the preceding days, which could distort our
estimates (see Figure 1 below).
Google’s COVID-19 Community Mobility Reports are disaggregated by place categories.
The data capture the number of visits to groceries and pharmacies (grocery markets and
food shops, food warehouses, farmers markets, drug stores, and pharmacies), transit stations
(transportation hubs including subway, bus, and train stations), parks (local and national
parks, beaches, marinas, public gardens) and retail and recreation (restaurants, cafes, theme
parks, shopping centres, museums, libraries and cinemas) [Aktay et al., 2020]. The data also
capture mobility patterns for places of work and residence. For workplaces, Google uses the
relative frequency of visits, as well as time and duration to calculate how many individuals
spent more than one hour at their place of work [Aktay et al., 2020]. A similar process is
used to calculate the number of hours spent in places of residence [Aktay et al., 2020].
For each day, the data record the percentage change in the number of visits (or length of
stay) relative to a baseline value for that day of the week. This baseline is the median
value for the corresponding day of the week in the five-week period between January 3
rd
and
Feburary 6
th
2020.
20
This process is similar the one used to create“popular times” for places
in Google Maps. Observations that do not meet Google’s required privacy thresholds are
coded as missing by Google.
21
Importantly, these data are based on Google Account users
who opted-in to the Location History feature. This means that the data are not necessarily
representative of the German population.
20
This means there are 7 x 16 baseline values, one for each state and day of the week. Google does not
provide data on the baseline total count/number (visits, hours spent), but only percentage changes relative
to the (unknown) baseline. We address this issue by including state * day-of-the-week fixed effects in our
model specification (see Section 3.3)
21
In our study period, this only pertains to mobility data for groceries and pharmacies on three Sundays
in Berlin
9
We focus on mobility in public spaces, captured by the percentage change in the number
of visits to (or time spent in) groceries and pharmacies (GP ), workplaces (W ) and transit
stations (T ). The main outcome of interest is the percentage change in average commu-
nity mobility in public spaces, equal to
GP +W +T
3
, relative to the baseline. We also use the
percentage change in the number of hours spent at home relative to the baseline as an addi-
tional catch-all measure. For the sake of simplicity, we use the terms “mobility patterns” or
“mobility”, to refer to percentage change in the number of visits to (or time spent in) public
spaces or number of hours spent at home.
We would like to highlight that the Google data can be used to measure community mobility
patterns, but do not provide a good measure of social distancing, as implied in several
recent studies [Wellenius et al., 2020, Schrimpf et al., 2020, Ansell, 2020]. The term “social
distancing” refers to the physical (Euclidean) distance between two people,
22
which is not
directly captured by the Google mobility data. Even though it is plausible that once mobility
(i.e. number of visits to public spaces) reaches a certain level, social distancing will be harder
to maintain in some locations, it is unclear how this can be accurately inferred from the data.
Google also provides mobility data on parks as well as retail and recreation. However, these
locations are less relevant for our analysis. This is because some places that fall within the
park category are arguably not relevant for the spread of COVID-19 (for instance national
parks, where the risk of transmission is likely extremely low). We also do not consider retail
and recreation, given that for most of the study period, the places that fall into this category
(e.g. restaurants, cafes or cinemas) were required to close.
To create a timeline for when German states introduced compulsory face mask policies, we
consulted state-specific secondary legislation (Verordnungen), which are typically published
on states’ official websites. We also extracted information from the German Catalogue of
22
US Centres for Disease Control: https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-
sick/social-distancing.html
10
Fines (“Bußgeldkatalog”), which records penalties for not wearing face masks in different
states,
23
, as well as from official announcements made to national and local newspapers.
Through the same process, we identified when states implemented other important policies
related to the COVID-19 pandemic that could also affect community mobility patterns. We
systematically extracted information on the re-opening of schools and shops, as well as the
official start and end of state-specific stay-at-home orders (“Ausgangsbeschraenkungen”).
Finally, we obtain the daily number of new confirmed COVID-19 cases in each state from the
Robert Koch Institute (RKI), which is the German federal government agency responsible
for disease control and prevention.
24
We use RKI data for the period between March 23
rd
and May 21
st
.
3.2 Mobility trends
Figure 1 provides a descriptive overview of changes in average mobility in public spaces (gro-
ceries and pharmacies, workplaces and transit stations). It shows that mobility in public
spaces in Germany decreased substantially in the period leading up to the national-level
lock-down on March 23
rd
2020. As shown in Appendix B, similar patterns can be observed
for mobility trends in specific public spaces (separately for groceries and pharmacies, work-
places and transit station). The number of hours spent in places of residence increased over
the same time period, although changes appear less drastic, as individuals already spend a
large proportion of their time at home (see Appendix B).
23
https://www.bussgeldkatalog.org/corona/
24
https://npgeo-corona-npgeo-de.hub.arcgis.com/
11
Figure 1: Average mobility in public spaces in Germany
National lockdown
-80
-60
-40
-20
0
20
40
Change in average mobility (%)
15feb2020 04mar2020 22mar2020 09apr2020 27apr2020 15may2020
Note: This graph shows the percentage change in average mobility in public spaces
(groceries and pharmacies, workplaces, and transit stations) for each day between Feb
15
th
and May 21
st
2020 relative to the baseline. The baseline is the median value for
the corresponding day of the week in the five-week period between Jan 3
rd
and Feb 6
th
2020. Data: Google COVID-19 Community Mobility Reports.
3.3 Methods
To isolate the causal effect of compulsory face mask policies, we use a generalised difference-
in-differences (DD) design that exploits the staggered introduction of compulsory face mask
policies in German states. In this setup, all units are eventually “treated” (i.e. all states
implement a compulsory face mask policy), but at different times.
We first use a static DD model:
Y
st
= α
s
+ β
t
+ γD
st
+ X
0
st
+ η
0
+
st
(1)
where Y
st
is a measure of community mobility, D
st
is a treatment indicator equal to one for
12
states and dates where compulsory face mask policies are in place and zero otherwise,
25
α
s
denotes state-level fixed effects, β
t
denotes date fixed effects, and X
0
st
is a vector of time-
varying state-specific controls,
26
η
0
is a constant, and
st
is an error term. The coefficient of
interest is γ, which identifies the effect of compulsory mask policies on community mobility
under the parallel trends assumption.
27
Given that the static DD estimates can be biased when treatment effects vary over time
[Goodman-Bacon], we use an event study approach that allows us to examine the effect of the
policy for the days before and after implementation. In the main event study specification,
the data are trimmed so that the panel is balanced in time periods (days) relative to the
treatment, as recommended by Abraham and Sun [2018]. Our “trimmed” panel contains 22
days before and 22 days after the treatment date in each state.
28
To investigate pre-trends, we use a “fully dynamic” event study model, which is specified as
follows:
Y
st
= α
s
+ β
t
+
−2
X
`=−21
γ
`
D
`
st
+
22
X
`=0
γ
`
D
`
st
+ X
0
st
+
st
(2)
where D
`
st
= 1{t − E
s
= `} is a “switch-on switch-off” indicator for unit s being periods `
away from the initial treatment period E
s
at calendar time t. In the trimmed specification,
25
For Berlin, we code D
st
=1 following the introduction of compulsory face masks in public transport on
April 27
th
. The policy was extended to shops two days later.
26
The controls are an indicator for state-specific public holidays (Tag des Sieges in Berlin), an indicator
for when states relaxed their stay-at-home orders (Ausgangsbeschraenkungen), the daily new confirmed
COVID-19 cases in each state (lagged by one day), an indicator for when states re-opened secondary schools
for final year classes, an indicator for when states allowed retail shops < 800 m
2
to re-open, an indicator for
when states allowed retail shops to re-open without any size restrictions, and state*day-of-the-week fixed
effects.
27
The parallel trends assumption is that community mobility trends in treated and untreated states would
have developed in parallel in the absence of the compulsory face mask policies. We assess the plausibility of
this assumption by inspecting pre-treatment trends in a “fully dynamic” event study framework (see below)
28
Schleswig-Holstein is the last state to receive treatment on April 29
th
. A panel that is balanced in
periods relative to the treatment can contain at most 22 treatment leads and 22 treatment lags, given that
the Google mobility data available up until May 21
st
.
13
distant relative periods (where | ` |> 22) are excluded so that the panel is balanced in periods
relative to the treatment. Furthermore, the first and last treatment lead are set to zero to
address under-identification in the fully dynamic model [Borusyak and Jaravel, 2017].
To asses how treatment effects change over time, we instead use a ”semi-dynamic” event
study model, where all leads are set to zero. This specification is robust to event-time
treatment effect heterogeneity, so it is more likely to provide unbiased estimates of how the
face mask policy affects mobility patterns over time. The semi-dynamic model is specified
as follows:
Y
st
= α
s
+ β
t
+
22
X
`=0
γ
`
D
`
st
+ X
0
st
+
st
(3)
All models are estimated using OLS with robust standard errors clustered at the state
level. We also use a wild cluster bootstrap procedure to obtain more accurate p-values
[Roodman et al., 2019]. This is advisable given that in a setting with few clusters (16 states)
the standard cluster-robust variance estimator may lead to over-rejection of the null and
confidence intervals that are too narrow [Bertrand et al., 2004, Cameron et al., 2008]. We
report bootsrapped p-values in the main results table and refer to Appendix F.3 for more
details on the bootstrap procedure.
14
4 Results
4.1 Effect of compulsory face masks on mobility in public spaces
We first present results from our static DD specification (Equation 1) which investigates
the average effect of introducing compulsory face mask policies on community mobility. As
shown in Table 1, we do not find evidence to suggest that compulsory face mask policies
affect average mobility in public spaces. Overall, the estimated effects are not statistically
significant and relatively small in magnitude, lying between -0.8 percentage points (-0.05
SD) and -1.8 percentage points (-0.11 SD). Column 5 shows results for our preferred model
specification, which includes state and date fixed effects and a broad range of state-specific
controls: public holidays, the daily number of new COVID-19 cases in each state (lagged by
one day), and several policy changes that are likely to affect community mobility (lock-down
rules being relaxed, secondary schools and retail re-opening). The main treatment effect is
quite precisely estimates and we can rule out even small increases in mobility that are larger
than 0.03 SD.
Column 6 shows results for a more flexible model, which also includes an interaction between
day-of-the-week and state fixed effects. In contrast to all other models, the model suggests a
significant negative effect of -1.8. Our sense is that this is because this static model heavily
weighs changes occurring shortly after the treatment - an issue we examine further in the
next section.
15
Table 1: Effect of compulsory face mask policies on mobility in public spaces
(1) (2) (3) (4) (5) (6)
Face mask policy -0.759 -1.075 -1.074 -1.591 -1.500 -1.763**
(0.703) (0.692) (0.700) (0.946) (0.924) (0.605)
[0.333] [0.211] [0.214] [0.199] [0.210] [0.027]
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.965 0.973 0.973 0.973 0.973 0.985
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Wild cluster (state-level) bootstrap p-values in square brackets.
Outcome mean -30.19 and SD 16.94.
Appendix C shows results for specific public spaces. We find that the introduction of com-
pulsory face masks leads to a small but statistically significant reduction in mobility for
visits to grocery stores and pharmacies of -4.9 percentage points or -0.4 SD (95% CI between
-0.28 and -0.10). We also find evidence for a small increase in the number of hours spent at
home of 0.08 SD (95% CI between 0.03 SD and 0.13 SD). Our static models do not detect
significant effects on mobility in workplaces and transit stations.
16
4.2 Dynamic effects
Next, we use event study models to assess parallel trends and examine how compulsory
face masks affect mobility patterns over time.
29
In Appendix D, we present results from
the fully dynamic specification (Equation 2), which allows us to assess the parallel trends
assumption. The absence of apparent pre-treatment trends suggests that our identification
strategy is valid.
We use the semi-dynamic specification (Equation 3) to investigate potential over-time effects
of compulsory face mask policies. Figure 2 below summarises the results from the semi-
dynamic model. We do not find evidence to suggest that compulsory face mask policies
affect mobility in public spaces over time. There is a significant decrease in mobility te
day compulsory face mask policies are introduced. This decrease is equal to -2.4 percentage
points or -0.14 SD (95% CI between -0.24 and -0.04), which is small in magnitude and
comparable to the static DD estimate. We do not detect any significant effects on mobility
for any other days following the policy change.
In Appendix E we examine over-time effects for mobility patterns in specific public spaces as
well as time spent at home. We find that mobility in grocery shops and pharmacies decreases
by between -7.7 percentage points (-0.31 SD) and -2.2 percentage points (-0.1 SD) within
the first five days of the policy change, which is consistent with static DD estimates. This
effect, however fades out over time. We find only sporadic evidence for a positive over-time
effect on mobility in places of work (for instance, a 2.8 percentage point (0.15 SD) increase
on the 3
rd
day following the change, and a 3.6 percentage point (0.19 SD) increase on the
4
th
day). However, point estimates are imprecise and rarely distinguishable from zero. In
terms of hours spent a home, we find a small increase within the first four days (between 0.14
29
All event study models include controls from our preferred static DD model specification: state-specific
public holidays, the daily number of new COVID-19 cases in each state (lagged by one day), and dummies for
several policy changes that are likely to affect community mobility (lock-down rules being relaxed, secondary
schools and retail re-opening).
17
and 0.17 SD). We find no significant effects on mobility patterns in transit hubs. Overall,
our results suggest that compulsory face mask policies only affect mobility in the very short
term, with no detectable medium-term effects.
Figure 2: Semi-dynamic event study estimates
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-4 0 4 8 12 16 20
Days relative to face mask policy
Anticipatory effects Phase-in effects
(set to zero)
Average mobility
Note: This graph shows the estimated over-time effect of compulsory face mask policies
on average mobility in public spaces (groceries and pharmacies, workplaces, and transit
stations) for 22 days after the policy change. Point estimates are obtained from a semi-
dynamic event study model, where all treatment leads are set to zero and the panel
is “trimmed” such that it is balanced in time periods (days) relative to the policy
change. The model includes controls from our preferred static DD model specification:
state-specific public holidays, the daily number of new COVID-19 cases in each state
(lagged by one day), and dummies for several policy changes that are likely to affect
community mobility (lock-down rules being relaxed, secondary schools and retail re-
opening). Vertical lines represent cluster-robust 95% confidence intervals.
4.3 Robustness checks
We conduct a number of robustness checks. First, we run the fully-dynamic specification
using a “binning” approach [Abraham and Sun, 2018], where we replace the first and last
switch-on-switch-off leads and lags with switch-on-stay-on indicators (see Equation 4). As
18
shown in Appendix F.1, the main results hold using this alternative event study specification.
Second, we address the potential problem of negative weighting in the static DD setup by
using a control group of states that are never exposed to the treatment, but plausibly face
the same time effects as the treatment group [Borusyak and Jaravel, 2017]. To this end,
we drop all observations from April 27
th
onwards. The four states that made face masks
compulsory before April 27
th
now consitute the treatment group and the remaining twelve
sates are part of the never-treated control group. As shown in Appendix F.2, we also do not
find evidence that compulsory face masks affect community mobility using this alternative
specification. Finally, we address the potential concern that our null-results are an artefact
of too-few clusters [MacKinnon and Webb, 2018]. We show that the main results hold when
using a “sub-cluster” wild bootstrap procedure (see Appendix F.3) and robust standard
errors clustered at the state-week level (see Appendix F.4).
5 Discussion
There is an ongoing debate about whether to introduce policies requiring the general public
to wear protective face masks. A key concern is that individuals could feel safer as a result
and, due to risk compensating behaviour, increase their mobility. This could undermine the
most important public-health advice to contain the spread of COVID-19 – which is to reduce
mobility and maintain social distancing [Greenhalgh et al., 2020]. We provide first empirical
evidence on the impact of compulsory face mask policies on community mobility. We do not
find evidence to suggest that, in Germany, compulsory face mask policies affect mobility in
public spaces (groceries and pharmacies, workplaces and transit hubs).
When examining mobility in specific locations, we find a short-lived reduction in the number
of visits to groceries and pharmacies and a short-lived increase in the number of hours spent
at home (respectively within five and four days of the policy change). We find no significant
19
over-time effects on mobility in workplaces and transit hubs. Our overall interpretation
of the results is that compulsory face mask policies in Germany did not affect community
mobility. We do not examine how compulsory face mask policies affect important individual
behaviours such as hand-washing and social distancing. However, the findings presented
here should to some degree alleviate policy makers’ concerns about compulsory face mask
policies leading to an increase in community mobility.
Even though compulsory face mask policies have been introduced in several countries, we
currently lack systematic evidence on the effect of face masks on human behaviour. A recent
small-scale field experiment implemented in Berlin before face mask became compulsory,
finds that masks increase physical distancing by 9cm on average [Seres et al., 2020] - thereby
providing no evidence of risk compensating behaviour. The authors hypothesise that this
is due to others perceiving face masks as a signal of a larger preferred physical distance by
the wearer. Even though this signalling effect most likely disappears in a setting where face
masks are compulsory, we also do not find evidence for risk compensation at the community
level.
There are two potential mechanisms which could explain our main finding that compulsory
face mask policies have no discernible effect on community mobility. First, it might be
that there is simply no risk compensating behaviour when it comes to face masks. Second,
it might be that any risk compensation (which would increase mobility) is outweighed by
increased salience or the hassle factor (which would decrease mobility). In terms of mobility
in specific locations, we find a negative but short-lived effect on the number of visits to
groceries and pharmacies - where face masks are required. Given that the effect occurs
immediately and fades out very quickly, we believe that the hassle factor provides a better
explanation than increased salience (where negative effects would arguably persist over time).
This explanation has intuitive appeal. As face masks are uncomfortable to wear, individuals
initially make fewer visits to locations where face masks have to be worn, until they adapt to
20
the new circumstances. One reason why we observe an effect for groceries and pharmacies
but not for transit hubs could be that it is easier and less costly for individuals to change
the frequency of visits to grocery shops, but that this is more difficult for transit. As we do
not have access to individual-level data, we are unfortunately not in a position to test these
hypotheses.
Our results are limited in three main respects. First, we are only able to observe the effect
of compulsory face mask policies in the medium-term (up to three weeks after the policy
change). It is possible that there are changes to community mobility in the long run that
we are not able to detect. However, our results suggest that any changes in mobility fade
out within days of the policy change and it is unclear if one would expect additional changes
in behaviour after an initial adaptation. Second, one concern with the Google COVID-
19 Community Mobility Reports is that the data are based on Google Account users who
opted-in to Google’s Location History feature. It is therefore likely that these data are from
a non-random sub-sample of the German population. Whilst we have no data on the number
of people using this feature, Germany has a very high smartphone penetration. Over 98%
of people under 50 years of age and 80% on average use a smartphone with Android as the
main operating system.
30
An additional concern is that the accuracy and coverage of the
data vary across sub-national units (e.g. between urban and rural areas) in a systematic
manner that is associated with the timing of the policy change.
Finally, whilst this paper provides important evidence for current policy debates on how to
manage the COVID-19 pandemic, it is unclear if results can be generalised to other settings.
The Google mobility data used in this paper, or other sources of aggregate level GPS data,
could be used to determine the effect of compulsory face mask policies in other countries.
Further research is also needed on the impact of compulsory face mask policies on other
important behaviours such as hand washing and social distancing.
30
https://www.statista.com/statistics/469969/share-of-smartphone-users-in-germany-by-age-group/
21
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24
B Mobility trends
Figure A1 shows mobility trends in specific public spaces as well as in terms of hours spent
in places of residence.
Figure A1: Mobility trends in Germany (other mobility measures)
National lockdown
-80
-60
-40
-20
0
20
40
15feb2020 16mar2020 15apr2020 15may2020
Grocery & pharmacy
National lockdown
-80
-60
-40
-20
0
20
40
15feb2020 16mar2020 15apr2020 15may2020
Workplaces
National lockdown
-80
-60
-40
-20
0
20
40
15feb2020 16mar2020 15apr2020 15may2020
Transit stations
National lockdown
-80
-60
-40
-20
0
20
40
15feb2020 16mar2020 15apr2020 15may2020
Residential
Change in mobility (%)
Note: This graph shows the percentage change in mobility (shown separately for goceries and pharmacies,
workplaces, places of residence, and transit stations) for each day between Feb 15
th
and May 21
st
2020
relative to the baseline mobility for that day of the week. The baseline is the median value for the
corresponding day of the week in the five-week period between Jan 3
rd
and Feb 6
th
2020. Data: Google
COVID-19 Community Mobility Reports.
26
C Static DD estimates for other mobility measures
This section presents estimates from the static DD model (Equation 1) for other location-
specific mobility measures.
Table A2: Effect of compulsory face mask policies on mobility in groceries and pharmacies
(1) (2) (3) (4) (5) (6)
Face mask policy -4.723*** -4.918*** -4.902*** -4.832*** -4.859*** -4.896***
(1.091) (0.963) (0.971) (1.034) (1.051) (0.789)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 957 957 957 957 957 957
R-squared 0.951 0.962 0.962 0.962 0.962 0.984
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Table A3: Effect of compulsory face mask policies on mobility in workplaces
(1) (2) (3) (4) (5) (6)
Face mask policy 2.129*** 1.927** 1.916** 1.275 1.497 0.967
(0.714) (0.810) (0.801) (0.986) (1.017) (0.833)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.974 0.978 0.979 0.979 0.979 0.989
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
27
Table A4: Effect of compulsory face mask policies on mobility in transit stations
(1) (2) (3) (4) (5) (6)
Face mask policy -0.094 -0.620 -0.630 -1.642 -1.614 -1.593*
(1.117) (0.978) (0.988) (1.259) (1.195) (0.907)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.917 0.920 0.920 0.921 0.921 0.948
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Table A5: Effect of compulsory face mask policies on time spent at home
(1) (2) (3) (4) (5) (6)
Face mask policy 0.083 0.257** 0.255** 0.445*** 0.450*** 0.222
(0.220) (0.094) (0.095) (0.134) (0.138) (0.171)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.973 0.975 0.975 0.975 0.975 0.985
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
28
D Parallel trends
This section examines parallel trends using the fully dynamic event study specification (Equa-
tion 2).
Figure A2: Fully dynamic event study estimates for average mobility in public spaces
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-22 -18 -14 -10 -6 -2 2 6 10 14 18 22
Days relative to face mask policy
Anticipatory effects Phase-in effects
Average mobility
Note: This graph shows the estimated anticipatory and over-time effects of compulsory face mask policies
on average mobility in public spaces (groceries and pharmacies, workplaces, and transit stations) for 22
days before and after the policy change. Point estimates are obtained from a fully dynamic event study
model, where the first and last treatment leads are set to zero and the panel is “trimmed” such that it is
balanced in time periods (days) relative to the policy change. Vertical lines represent cluster-robust 95%
confidence intervals.
29
Figure A3: Fully dynamic event study estimates for other mobility measures
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-22 -18 -14 -10 -6 -2 2 6 10 14 18 22
Days relative to face mask policy
Grocery & pharmacy
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-22 -18 -14 -10 -6 -2 2 6 10 14 18 22
Days relative to face mask policy
Workplaces
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-22 -18 -14 -10 -6 -2 2 6 10 14 18 22
Days relative to face mask policy
Transit stations
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-22 -18 -14 -10 -6 -2 2 6 10 14 18 22
Days relative to face mask policy
Residential
Anticipatory effects Phase-in effects
Note: This graph shows the estimated anticipatory and over-time effects of compulsory face mask policies
on mobility (shown separately for groceries and pharmacies, workplaces, transit stations, and places of
residence) for 22 days before and after the policy change. Point estimates are obtained from a fully
dynamic event study model, where the first and last treatment leads are set to zero and the panel is
“trimmed” such that it is balanced in time periods (days) relative to the policy change. Vertical lines
represent cluster-robust 95% confidence intervals.
30
E Semi-dynamic estimates for other mobility measures
Figure A4 shows semi-dynamic event study (see Equation 3) estimates for measures of mo-
bility in specific public spaces as well as hours spent in places of residence.
Figure A4: Semi-dynamic event study estimates for other mobility measures
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-4 0 4 8 12 16 20
Days relative to face mask policy
Grocery & pharmacy
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-4 0 4 8 12 16 20
Days relative to face mask policy
Workplaces
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-4 0 4 8 12 16 20
Days relative to face mask policy
Transit stations
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-4 0 4 8 12 16 20
Days relative to face mask policy
Residential
Anticipatory effects Phase-in effects
(set to zero)
Note: This graph shows the estimated over-time effects of compulsory face mask policies on mobility
(shown separately for groceries and pharmacies, workplaces, transit stations, and places of residence) for
22 days after the policy change. Point estimates are obtained from a semi-dynamic event study model,
where all treatment leads are set to zero and the panel is “trimmed” such that it is balanced in time periods
(days) relative to the policy change. Vertical lines represent cluster-robust 95% confidence intervals.
31
F Robustness checks
F.1 Fully dynamic binned specification
The fully dynamic binned model is specified as follows:
Y
st
= α
s
+ β
t
+ µ
g
X
`<−21
D
`
st
+
−2
X
`=−21
γ
`
D
`
st
+
21
X
`=0
γ
`
D
`
st
+ µ
g
X
`>21
D
`
st
+ X
0
st
+
st
(4)
where distant relative periods (| ` |> 21) are binned into g = [−T, −21) and g = (21, T]
and T denotes all available calendar time periods (i.e. dates) in the data. In the binned
specification, the panel is balanced in calendar time periods rather than in periods relative
to the treatment. Only one lead (where ` = −1) is set to zero.
Figures A5 and A6 show, respectively, estimates from fully dynamic “binned” event study
models for measures of average mobility and mobility in specific locations.
32
Figure A5: Fully-dynamic binned event study estimates for average mobility
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21
Days relative to face mask policy
Anticipatory effects Phase-in effects
Average mobility
Note: This graph shows the estimated anticipatory and over-time effects of compulsory face mask policies
on average mobility (groceries and pharmacies, workplaces, transit stations) for 22 days before and after
the policy change. Point estimates are obtained from a fully-dynamic event study model, where the first
treatment lead is set to zero. The most distant leads and lags are “binned” and not displayed. The panel
is balanced in calendar time periods. Vertical lines represent cluster-robust 95% confidence intervals.
33
Figure A6: Fully-dynamic binned event study estimates for other measures of mobility
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21
Days relative to face mask policy
Grocery & pharmacy
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21
Days relative to face mask policy
Workplaces
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21
Days relative to face mask policy
Transit stations
-25
-20
-15
-10
-5
0
5
10
15
20
25
Change in mobility (pp)
-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21
Days relative to face mask policy
Residential
Anticipatory effects Phase-in effects
Note: This graph shows the estimated anticipatory and over-time effects of compulsory face mask policies
on mobility (shown separately for groceries and pharmacies, workplaces, transit stations, and places of
residence) for 22 days before and after the policy change. Point estimates are obtained from a fully-
dynamic event study model, where the first treatment lead is set to zero. The most distant leads and lags
are “binned” and not displayed. The panel is balanced in calendar time periods. Vertical lines represent
cluster-robust 95% confidence intervals.
34
F.2 Never-treated control group
We re-run the main static DD specification (Equation 1) using a control group of states that
are never exposed to the treatment. Given that all states in Germany eventually implemented
compulsory face mask policies, we create an “artificial” control group. To this end, we drop
all observations from April 27
th
onwards. The four states that made face masks compulsory
before April 27
th
now consitute the treatment group and the remaining twelve sates are part
of the artificial never-treated control group.
Table A6: Effect of compulsory face mask policies on mobility in public spaces (with
never-treated control group)
(1) (2) (3) (4) (5) (6)
Face mask policy 0.860 0.080 0.147 0.136 0.111 -1.090
(1.013) (1.463) (1.495) (1.714) (1.697) (1.455)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 560 560 560 560 560 560
R-squared 0.971 0.971 0.971 0.971 0.971 0.986
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
35
F.3 Wild cluster bootstrap
We employ a wild cluster bootstrap procedure to obtain more accurate p-values. Intuitively,
the procedure generates many bootstrap samples that mimic the distribution from which
the original sample was obtained. It then computes a t-statistic for the coefficient of interest
in each bootstrap sample. The refined p-value is the proportion of the bootstrap t-statistics
that are more extreme than the t-statistic obtained from the original sample [Angrist and
Pischke, 2009].
In a setting with very few treated clusters, the standard wild cluster bootstrap will typically
under-reject the null of no treatment effect when the null is imposed (restricted). The re-
stricted specification is the one from which we obtain the refined p-values reported in the
main results table (Table 1). In contrast, the standard wild cluster bootstrap will over-reject
when the null is not imposed (unrestricted) [MacKinnon and Webb, 2018, Roodman et al.,
2019]. To account for this problem, we also employ the “sub-cluster” wild bootstrap proce-
dure proposed by MacKinnon and Webb [2018], where the wild bootstrap data-generating
process is clustered at a finer level (i.e. state-date level) than the covariance matrix (i.e.
state level).
In Table A7 we report results from static DD models predicting our main outcome (average
mobility), with refined p-values from a wild cluster bootstrap procedure, where the data-
generating process is clustered at the state-date level (and the null is imposed).
36
Table A7: Effect of compulsory face mask policies on mobility in public spaces
(1) (2) (3) (4) (5) (6)
Face mask policy -0.759 -1.075 -1.074 -1.591 -1.500 -1.763**
(0.703) (0.692) (0.700) (0.946) (0.924) (0.605)
[0.366] [0.211] [0.214] [0.211] [0.228] [0.040]
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.965 0.973 0.973 0.973 0.973 0.985
Clusters 16 16 16 16 16 16
Robust clustered standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Wild cluster (state-date level) bootstrap p-values in square brackets.
37
F.4 State-week clustered standard errors
We re-run the main static DD specification (Equation 1) using robust standard errors clus-
tered at the state-week level (rather than the state-level).
Table A8: Effect of compulsory face mask policies on mobility in public spaces (with robust
standard errors clustered at the state-week level)
(1) (2) (3) (4) (5) (6)
Face mask policy -0.759 -1.075 -1.070 -1.588 -1.494 -1.763**
(1.218) (1.228) (1.230) (1.480) (1.513) (0.844)
State FE X X X X X X
Date FE X X X X X X
State-specific holidays X X X X X
Lockdown relaxed X X X X X
COVID-19 cases (t-1) X X X X
Sec. school open X X X
Retail open X X
State * Day-of-week FE X
Observations 960 960 960 960 960 960
R-squared 0.968 0.976 0.976 0.976 0.976 0.987
Clusters 144 144 144 144 144 144
Robust standard errors clustered at the state-week level in parentheses.
*** p<0.01, ** p<0.05, * p<0.1
38