key: cord-0739646-qe3d60yh
authors: Bergman, N. K.; Fishman, R.
title: Mobility Reduction and Covid-19 Transmission Rates
date: 2020-05-10
journal: nan
DOI: 10.1101/2020.05.06.20093039
sha: b091701b2505a0a29fdb502390e05ef8cd9661ed
doc_id: 739646
cord_uid: qe3d60yh

Assessing the contribution of mobility restrictions to the control of Covid-19 diffusion is an urgent challenge of global import. We analyze the relation between transmission rates (estimated effective reproduction numbers) and societal mobility levels using fine-grained daily mobility data from Google and Apple in an international panel of 87 countries and a panel of all states in the United States. Reduced form regression estimates that flexibly control for time trends suggest that a 10 percentage point reduction in mobility is associated with a 0.04-0.09 reduction in the value of the effective reproduction number, R(t), depending on geographical region and modelling choice. According to these estimates, to avoid the critical value of R = 1, easing mobility restrictions may have to be limited to below pre-pandemic levels or delayed until other non-mobility related preventative measures reduce R to a level of 0.55-0.7 in Europe, a level of 0.64-0.76 in Asia, and a level of 0.8 in the United States. Given gaps in data availability and inference challenges, these estimates should be interpreted with caution.

By some estimates, more than a third of the global population have been subjected to severe mobility restrictions since the start of the Covid-19 pandemic. Numerous governments around the world have resorted to such "lockdowns" as their primary strategy of limiting the transmission of infection, at enormous economic and social costs. As costs escalate, and transmission rates appear to decline in some countries, a growing debate has emerged regarding when and how lockdowns should be eased, and whether it is possible to do so without unleashing additional waves of infection. An assessment of the relation between mobility restrictions and transmission rates can be of substantial value in helping to navigate this policy dilemma and in understanding the determinants of diffusion.

Several papers have estimated the declines in transmission rates (effective reproduction numbers) that occured following lockdowns and other non pharmaceutical interventions (NPI) by using detailed case-level data in specific countries or regions (Pan et al, 2020; Lipsitch et al, 2020; Salje et al, 2020; Roux et al, 2020) . These studies provide highly informative evidence from a small number of localized contexts (mainly Wuhan and France) that are highly heterogeneous, which perhaps explains their mixed conclusions. The extent to which these findings can be globally extrapolated remains unclear. An additional challenge faced by these "before-after" assessments is the difficulty of separating the effects of the NPIs under study from other time trending factors that can reduce transmission rates. Flaxman (2020a; 2020b) and Kučinskas (2020) make valuable progress on this front by estimating the effects of NPIs on the effective reproduction numbers using a panel of 14 European states, finding results regarding the association between NPI and transmission rates that are sensitive to the manner in which the regression model is specified. In addition, these analyses are limited to a single world region and a small number of countries.

Here, we use publicly available data to empirically estimate the relation between transmission rates (effective reproduction numbers) and mobility restrictions using a large, international 87-country panel, as well as a panel covering all states in the United States. We then discuss the implications for easing or tightening mobility restrictions. Our assessment employs a reduced-form regression analysis based on fine-grained mobility data provided by Google and Apple, estimates of daily transmission rates at the country level from Kučinskas (2020), and 2 daily estimates of transmission rates at the U.S. state level from Systrom and Vladeck (2020). 4 In contrast to existing studies, we focus on the association between transmission rates and mobility data rather than government NPIs because evidence suggests an imperfect correspondence between NPIs, and in particular lockdowns, and mobility, perhaps explaining the inconclusive estimated impact of lockdowns (see e.g., Gupta et al., 2020) . The international data cover 87 countries over the period February 21st to April 11th while the panel of U.S states spans the period March 13th to April 11th.

A visual inspection of the country level data suggests mixed patterns. In Spain, for example ( Figure 1 , top panel), reductions in transmission rate seem to coincide with steep reductions in mobility, although transmission continues to decline even after mobility stabilizes at a low level.

In South Korea, in contrast ( Figure 1 , bottom panel), transmission rates have declined to a much greater extent, and only initially coincide with relatively modest reductions in mobility, implying a weaker relation between the two.

As discussed in detail below, there are significant challenges in empirically estimating the transmission-mobility relation, including omitted variable biases, limited data quality, and endogenous policy and individual-level responses to infection rates which affect societal mobility levels. Given the absence of data on other forms of preventative behavior, we attempt to alleviate some of these concerns by including a host of temporal and country-level fixed effects in the regressions to absorb some of these unobserved factors, but emphasize that a great deal of caution must be exercised in interpreting our estimates as causal. We also emphasize that there is no straightforward way to infer policy prescriptions from the correlations we estimate, as policy induced changes in mobility may impact other variables which influence transmission rates. For this reason, our results do not provide definitive conclusions, but should be viewed as a first step that utilizes publicly available measures of mobility levels and transmission to study a question of enormous social import.

Our current point estimates from the international cross-country panel suggest that a 10 percentage point (p.p.) reduction in mobility is associated with a 0.06-0.09 reduction in the value of the effective reproduction number, R ( t ), depending on geographical region and modelling choice. Estimates from the U.S. state-level panel suggest that a 10 percentage point 4 Available at rt.live (p.p.) reduction in mobility is associated with a 0.04 reduction in the value of the effective reproduction number, R ( t ).

Although the magnitude of the estimated impact of mobility restrictions are relatively modest in size, they also imply that in order to avoid allowing R ( t ) to exceed unsustainable levels, easing of mobility restrictions may have to be limited or delayed until further declines in R are achieved through other means. These include non-mobility related social distancing and other non-pharmaceutical interventions (NPIs), or potentially, through environmental changes such as warming or increased UV radiation (Carleton, 2020) which may reduce transmission rates.

Indeed, assuming an additive model for the impact of mobility and non-mobility related suppression methods on transmission rates, to avoid the critical value of R = 1, our estimates suggest that R ( t ) may have to be reduced to levels of about 0.55 -0.7 in Europe, 0.64 -0.76 in Asia, and approximately 0.8 in the United States before mobility levels are fully restored to pre-pandemic levels. 5

The principal measure of mobility used in this analysis is taken from the Covid 19 Community Mobility Reports provided by Google. As an alternative measure, we also use the Mobility Trends Reports provided by Apple. The Google data utilize anonymized location-based information to assess changes in the number of visits to several categories of locations in a given day and country, as compared to a baseline value for that day of week. The categories 6 include retail and recreation, groceries and pharmacy, parks, transit stations, workplaces, and residential. Similarly, the Apple data report the " relative volume of directions requests" sent 7 using the Apple Maps application, compared to a baseline volume on January 13th, 2020. The 5 To the extent that there are interaction effects between various methods of transmission suppressionfor example, if mask usage reduces the impact of increased mobility on Rrequired reductions in transmission rates will be lower. This issue is the subject of ongoing work. 6 The baseline period is the median value for the corresponding day of week, calculated during the 5-week period Jan 3-Feb 6, 2020. 7 https://www.google.com/Covid19/mobility/ 4 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 Apple data differentiate between three types of direction requests: driving, walking, and transit.

Google data is available for 131 countries, whereas Apple data is available for 63 countries. Figure 2 plots Google data on visits to workplaces over time, averaged in six world regions. Figure 3 plots the six measures of Google mobility data over time, averaged over Europe.

Both Google and Apple data are updated continuously. The present analysis utilizes Google data for the period February 15th -April 11th and Apple data for the period January 13th -April 23rd. 8

The preferred indicator of Covid-19 transmission rates is the effective reproduction number R ( t ), which measures the number of individuals an average infected person infects during the period of infection. In the present analysis, we make use of two independent sets of estimates of R ( t ), one at the country level and one for U.S. states.

Country level estimates are provided by Kučinskas (2020) between January 23rd and April 21st for 111 countries (temporal coverage varies by country and begins after 100 cases are confirmed). To construct this proxy, Kučinskas (2020) uses data on new cases, recoveries, and deaths and backs out estimates of R ( t ) on the basis of disease models. Importantly, the data (and the estimates) are smoothed with Kalman-filtering techniques. This means that discrete, high frequency movements in the actual effective reproduction number will be difficult to observe in these estimates. In addition, the estimates do not account for the delay between actual infection and official diagnosis. As such, they reflect lagged infection rates, with a lag size that combines the delay between infection and Covid-19 testing and the time between testing and official reporting of test results. In our analysis we assume an overall lag of seven days to account for an incubation period of approximately 4-5 days (Qun ) and a 2-3 day lag between testing and the official recording of positive test results. 9 8 Apple data extended beyond Google data at teh day of data download. 9 Qun Li et al. 2020 report an average incubation period of 5 days and Linton et al. report a median incubation period of 4-5 days.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

As is well known, a major limitation shared by all proxies based on confirmed case counts is that they are likely to substantially underestimate the true number of cases in the population. To the extent that the ratio of confirmed to actual cases is constant within countries (even if not between countries), however, this will not bias the R estimates. Further, Kučinskas (2020) argues that the estimation method is "robust in the sense that the estimates of R remain fairly accurate even when new cases are imperfectly measured, or the true dynamics of the disease do not follow the SIR model".

For the state-level analysis in the United States, estimates of R (t) at the state level are provided by Sysrom and Vladeck (2020), which adjusts the estimates for state-level testing capacity and for the delay in test reporting.

The sample studied in our international analysis makes use of Google mobility data and includes observations from 87 countries over the period February 21st to April 11th. When using Apple mobility data, this sample consists of 56 countries observed between February 21st and April 21st. In both cases, data coverage is uneven across countries, starting when the confirmed number of cases reaches 100 in each country. 

We employ standard panel-regression techniques to estimate the association between transmission rates (proxied by the R estimates described above) and mobility measures. The regressions include country specific fixed effects (intercepts) to flexibly account for all 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10. 1101 time-invariant country attributes, thus basing estimates of the relation between transmission rates and mobility on the correlation between these two variables over time within countries. 10 We prefer to study the association between mobility data and transmission rates rather than to estimate the effects of lockdown and other government NPIs for two main reasons. First, changes in mobility are not fully dictated by government orders. Voluntary reductions may precede such orders, and in some cases, orders may not be fully enforced and obeyed.

Second, current estimates of transmission rates do not have sufficient temporal resolution to enable detecting high frequency changes in response to discrete events such as lockdowns.

In addition to the inherent limitations of the precision with which transmission rates are measured, a significant challenge in estimating the transmission-mobility relationship is the likely presence of time varying behavioral, environmental, and epidemiological variables that can also affect transmission rates and which are difficult to observe. Behavioral variables can include hygienic practices, mask usage rates, and dimensions of social distancing not captured by mobility (such as, for example, maintaining minimal distance between individuals and maximal room occupancy rates). Epidemiological models predict transmission rates to respond to the diffusion of the virus in the population. As one example, in standard SIR models, effective reproduction numbers rates decline over time with the fraction of susceptible individuals in the population. Environmental factors may include temperature, UV radiation, and humidity (Carleton et al, 2020) . Failing to control for these variables in the regressions may reduce the precision of the estimates, and may also bias them whenever these variables are correlated with mobility (and affect transmission rates).

An additional concern in analyzing the relation between infection rates and mobility levels is the endogenous nature of mobility behavior. In particular, mobility rates are influenced by individual choice as well as by policy directives (such as lockdown easing and tightening), which may in turn be influenced by disease transmission rates and rising case counts.

For the above reasons, panel-regression estimates relating within-country variation in infection rates to levels of mobility may be subject to bias and should be interpreted with a good deal of caution. Unless all potential confounders are observed, or exogenous variation in mobility is 10 For the state-level analysis in the United States, all regressions include state-level fixed effects. 7 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10.1101/2020.05.06.20093039 doi: medRxiv preprint utilized, the estimates are not amenable to causal interpretation. We note, however, with the appropriate caution, that many of the unobserved confounders would tend to bias our estimates on the relation between mobility and transmission rates upwards, as variation in these confounders likely served to reduce transmission rates in tandem with mobility restrictions (examples include increased mask usage and hygiene).

To partially alleviate concerns stemming from unobservable within-country time variation, our analysis includes a host of fixed effects and time trends that may capture some of the unobserved variation. As mentioned above, all regressions estimated include country (or state) specific fixed effects. The regressions also flexibly control for temporal trends using individual date fixed effects, at either the global or regional level. Such fixed effects absorb the 11 potentially confounding influences of any time varying factor that behaves in a similar manner globally or regionally. In another check, we flexibly control not for calendar time, but for fixed effects of) the number of days which have elapsed in each country since the 100th case was confirmed. This allows us to absorb the potentially confounding effects of, for example, dynamical factors related to the ecological evolution of the pandemic in the absence of interventions. In a final test, we allow the regressions to include a separate (linear) time-trend for each country. We remain acutely aware, however, that none of these approaches can fully address the possibility that our results are biased by unobserved confounders, and emphasize the need for caution in interpreting them.

Formally, we estimate the following baseline regression:

where T is a proxy for Covid-19 transmission rates in country c (in region r ) on date t as described above, and M is one of the mobility measures described above, measured seven 11 Countries in the sample belong to six world regions.

8 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10.1101/2020.05.06.20093039 doi: medRxiv preprint days before the date at which T is observed. The regression include country fixed effects , α c date fixed effects at either global (eq.1) or regional (eq.2) levels, or country specific time β t trends (eq.3). Because transmission and mobility may exhibit temporal autocorrelation within countries, all standard errors are clustered at the country level.

Finally, since mobility measures are strongly correlated temporally within countries (Figure 3) , separating out the effects of each type of mobility indicator demands statistical power that is unlikely to be provided by the current sample. Our main regression models therefore include a single measure of societal mobility as the explanatory variable. We focus on the Google workplace mobility measure, being a natural proxy for economic activity. In an exploratory analysis reported below, we also estimate models that simultaneously include the various components of mobility levels (workplace, residential, transit, etc).

The data exhibit significant downward trends in both mobility and estimated transmission rates. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10.1101/2020.05.06.20093039 doi: medRxiv preprint sample period of state-level reproduction numbers, R , begins only in mid-March, and so we cannot rule out higher levels of R -similar to those observed in Europe and Asia-prior to that.

Changes in average mobility levels mask a good deal of country-level heterogeneity. Figure 4 plots our two principal mobility measures and estimated R values for sixty countries that have at least 30 days of both mobility and transmission data. The bottom panel of Figure 6 provides a parallel graph for U.S. states on the same two dates.

Here too, during the initial stage of the pandemic in the United States, transmission rates are high, mobility levels have not yet declined, and there is no discernable cross-sectional relation between the two. In contrast, by April 18th, transmission rates and mobility levels decline significantly across the United States, and display a clear positive correlation .

However, cross-sectional correlations of this kind can easily be confounded by numerous other sources of heterogeneity (even if such heterogeneity could be lower across U.S. states than across countries). It is for this reason that, in order to estimate the relation between R and mobility, the analysis below focuses on variation within countries over time. Table 1 provides results of regressions (1)-(3), using estimates of the effective reproduction number ( R ) from Kučinskas (2020) as the outcome variable, and a seven-day lagged measure of workplace mobility from Google data. Google mobility data is coded here as the fraction decline from baseline levels. The coefficients should therefore be interpreted as the associated 12 12 For example, a 10 percentage point reduction in mobility is coded as -0.1.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10. 1101 decline in the effective reproduction number associated with a 100 percentage point (p.p) decline in mobility.

All specifications include country fixed effects (intercepts) to account for all cross-country differences in transmission stemming from time invariant country characteristics. To account for time trends, the specification in Column 1 includes global date fixed effects and the specification in Column 2 includes region-by-date fixed effects. As an alternative, the specification in Column 3 flexibly controls for the number of days elapsed in each country since it confirmed its 100th

Covid-19 case, using fixed effects for each value of this lapse. The specification in Column 4 includes country-specific linear time trends.

Across the four specifications reported in Table 1 , we estimate a positive and statistically significant relation between effective reproduction numbers, R , and Google mobility levels, indicating that increased mobility is associated with increased transmission. The coefficient on lagged mobility ranges from 0.93 to 0.59, depending on the specification. The estimates imply that a ten percentage point drop in the Google mobility measure is associated with a decline of between 0.06-0.09 units of R , depending on the specification used . Figure 7a plots the country-level fixed effects estimated in specification (1) in Table 1 . The figure provides a ranking of the reduction in transmission rates that is unexplained by mobility suppression. As can be seen, countries in Asia appear to be particularly successful in reducing transmission rates using non-mobility suppression methods. The figure also plots the fixed 13 effects of a variant of specification (1) which uses region, as opposed to country, fixed effects.

Again, a clear ranking emerges in regions' ability to reduce transmission rates using non-mobility suppression methods, with Asia most successful, North America least successful, and European countries in between. 14 Figure 7b plots the time fixed effects estimated in specification (1), which reflect the average daily reduction in transmission that is unexplained by mobility reduction or by non-time varying country specific factors. As can be seen, the time fixed effects decline over time, indicating 13 The top 5 countries on this list-i.e., with the lowest fixed effects-are South Korea, Cambodia, Japan, Vietnam, and Taiwan. 14 The omitted regional fixed effect is Europe.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10. 1101 increased global suppression of transmission rates stemming from measures unrelated to variation in mobility (these measures could potentially include increased usage of masks, increased hygiene, favorable weather trends, etc). Table 2 repeats the analysis in Table 1 but uses the Apple driving mobility measure to proxy for mobility levels. Results are similar to those in Table 1 and indicate positive and statistically significant relations between R and mobility in all four specifications. The estimates imply that a ten percentage point drop in the Apple mobility measure is associated with a decline of 0.08 -0.09 units of R , depending on the specification used. Table 3 examines the relation between transmission rates and mobility levels in an analogous manner, but uses the state-level panel dataset in the United States. Transmission rates are taken from Systrom and Vladeck, 2020, and mobility is measured either by Google workplace mobility, or Apple driving mobility indicators. All regressions include state-level fixed effects and either date fixed effects or state-level time trends. As can be seen, similar to the global analysis, the results in the United States indicate a positive relation between transmission rates and mobility levels. Focusing on Column 1, which is most similar to our benchmark global model (i.e., with country and date fixed effects), the estimates suggest that a 10 percentage point reduction in mobility levels is associated with a 0.04 decrease in the value of R . The size of the effect is rather similar to that in the benchmark global estimate (0.06) despite the fact that the estimates of R ( t ) used in the two regressions are derived by independent methods and researchers. Table 4 repeats the global estimation model separately in five different geographical regions using Google mobility data. As can be seen, the positive relation between transmission rates 15 and mobility levels is concentrated in the regions of "Europe" and "Asia and Pacific". We find a positive, but weaker and marginally insignificant (p=0.11) relation in South America. No statistically significant relation between transmission rates and lagged mobility is observed in 15 We classify countries into six geographical regions: Africa, Asia and Pacific, Europe, Middle East, North America and South/Latin America. As there are only two countries in North America, we do not run the regression separately for that region.

12 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10.1101/2020.05.06.20093039 doi: medRxiv preprint the Middle East or Africa, perhaps owing to the relatively small number of observations within these regions. 16 We next conduct an exploratory analysis of how infection rates relate to the various mobility measures provided by Google and Apple. Results should be interpreted with caution given the high levels of temporal correlation between the various location-based Google mobility measures (workplace, residential, parks, retail and recreation, transit, grocery and pharmacy) as well as the high correlation between the search-type Apple mobility measures (driving, transit, walking). Table 5 reports estimates of regression (1) and (2), respectively, that include as independent variables all six location-based measures of Google mobility (with date and date-by-region fixed effects, respectively). Columns 3 and 4 report the analogous specifications that simultaneously include all three search-type Apple measures.

Focusing on the first column of the table, the results provide suggestive evidence that increased mobility in "work places", "retail and recreation", "transit stations", and "residential areas" are positively associated with transmission rates. Coefficients on the Google location-based measure should be interpreted in relation to an omitted location category defined as the complement to the union of the six locations defined by Google. Similarly, the results in Column 1 indicate a negative relation between increased population mobility in "parks" as well as in "grocery and pharmacy". Adding regional date fixed effects does not change the sign of the coefficient but reduces statistical precision, leaving only the coefficients on "Retail and Recreation", "Transit Stations", and "Residential Areas" as significant. The positive coefficient on "Residential Areas" is somewhat counterintuitive. One potential explanation might stem from increased prevalence of infection between members of the same household (see, e.g., Bi et al., 2020) .

Column 3 provides a parallel analysis to that reported in Column 2, but uses the daily-level panel dataset of U.S. states described above. Estimates of infection reproduction numbers are taken from Systrom and Vladeck (2020) , while state-level mobility indicator levels are provided by Google. Similar to Column 2, results indicate that workplace mobility in the United States is 16 To estimate R , Kučinskas (2020) requires that the number of reported Covid-19 cases exceed 100, implying that countries where infection rates climbed in later time periods are underrepresented in the sample.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 positively related to transmission rates in a statistically significant manner. Further, we find a statistically significant, negative, but small coefficient on the parks mobility measure. All other mobility measures in Column 3 are non-significant.

Columns 4 and 5 of Table 5 use Apple search-type mobility data. Focusing on Column 4, when all three mobility measures are included in the regression, the coefficient on transit related searches is the only measure which is statistically significant, while the other mobility measures based on driving and walking -activities involving less social interactions -are not related to R in a statistically significant manner. However, once regional fixed effects are added, none of the coefficients associated with the three Apple mobility measures are statistically significant, potentially due to their high levels of correlation. As additional data becomes available, we will continue to update these estimates with the hope that increased sample size may allow for greater precision.

We conclude by analyzing evidence for a structural break in the relation between transmission rates and mobility levels during our sample period. This analysis is motivated by the patterns visible in Figure 5 , which show that on average, countries in Europe and the Asia and Pacific region exhibit an initial large decline in both Google workplace mobility levels and R up to mid-March, followed by a relative stabilization in workplace mobility but a continued decline in estimated reproduction numbers. Table 6 repeats the baseline analysis reported in Table 1 , but separately conducted over the time period up to, and following, the week of March 25th. Results in the table provide suggestive evidence for a weakening in the relation between transmission rates and mobility, with larger point estimates and higher significance levels in the three specifications estimated over the former part of the sample period as compared to those in the latter part of the sample period.

We note that mobility levels in a number of countries have begun rising in the latter part of the sample period, as can be seen in the Apple mobility indicators. As transmission rate indicators arrive with a lag, additional data arriving in the upcoming weeks will be of particular interest in tracking the evolution of mobility levels and Covid-19 transmission rates.

14 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 

Given the estimates in Table 1 , a 10 percentage point decline in the Google workplace mobility measure is associated with a 0.06 -0.09 unit decline in the estimated reproduction number R .

Based on these estimates, it is instructive to analyze the share of the overall decline in transmission rates that can be explained by mobility reductions.

Overall, Google mobility rates in Europe declined by approximately 50 percentage points by the beginning of April, which our estimates imply is associated with a reduction in R of 0.3 -0.45 units. The fraction of the overall decline in R that is explained by this mobility reduction depends on the time window chosen for the calculation. By April 11th, the mean value of R across the European countries in our sample had declined to 1.1. Taking the starting date for the 17 calculation as February 21st, when R = 3.4, implies an overall decline in R of 2.3 units, meaning that mobility reductions explain about 13%-20% of this decline. However, data from February is still very sparse, and derived from only a few countries. If we more conservatively choose the starting time of the calculation to be a month later, on March 11th, when R = 2.3-at this point data is available from more than 20 countries, and most of the European mobility reduction has yet to take place-the overall reduction in R is reduced to 1.2 units, so that mobility reductions explain approximately 25% -37% of the decline in R .

Analogously, in countries within the "Asia and Pacific" region the decline in average Google mobility measures-approximately 40 percentage points to date-imply a reduction of 0.24 -0.36 units in R . Again, the fraction of the overall decline in R explained by mobility depends on the time frame chosen. Taking the starting date of the calculation to be March 11 (average R = 2.06), and given the April 11th average value of R of approximately 1.27, we obtain that mobility reductions in Asia explain approximately 30%-45% of the reduction in R .

Our estimates, to a large extent, are estimated during a period when both mobility levels and transmission rates decline. Assuming that the association between mobility and R is similar when the two variables rise, the same coefficients, interpreted at face value, also imply that in Europe, returning from current levels of mobility to pre-pandemic baseline levels-approximately 17 Given the assumption of a seven-day lag between actual and observed R in the international data, the values corresponding to a given date refer to the R estimated seven days afterwards.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. We emphasize again that to the extent that coefficients in Table 1 are overestimates -due, for example, to unobserved confounders not absorbed by our flexible time trends that reduce transmission rates simultaneously with mobility declines -the share of the decline in R that is explained by the decline in mobility would be reduced still further.

Turning to the United States, the estimates based on the state-level analysis imply that a 10 percentage point decline in the Google workplace mobility measure is associated with a reduction of 0.04 units (S.E. 0.01) in the value of R . As during the sample period average reproduction numbers in the United States fell by approximately 0.5 units, this estimate suggests that the decline in mobility in the United States can explain approximately 40% of the overall decline in R . This estimate, obtained using within country variation and a different source and methodology for estimating R , is rather similar to that obtained in Europe and Asia.

Understanding the determinants of Covid-19 transmission rates is one of the most pressing policy questions facing society. This paper provides an empirical analysis of this question, utilizing comprehensive data at global scale to analyze the association between mobility levels and transmission rates. As such, it provides an important complement to detailed epidemiological modelling of the spread of Covid-19. It will be valuable to revisit the estimates provided in this paper as mobility levels and Covid-19 transmission rates continue to vary in the coming months and as additional data become available.

16 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 Figure 3 : Average measures in Europe in Europe of Google mobility data, by mobility indicator type, by mobility indicator type, over time.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. . Figure 4 : Country plots of R ( t ), Google (visit to workplaces) and Apple (driving searches) mobility indicators over time. Only countries for which there are at least 30 days of both mobility and R ( t ) data are included. R ( t ) is plotted against the left axis. Mobility changes from baseline (in percentage points, see data section) are plotted against the right axis.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 Figure 4 (cont.): Country plots of R(t), Google (visit to workplaces) and Apple (driving searches) mobility indicators over time. Only countries for which there are at least 30 days of both mobility and R(t) data are included. R(t) is plotted against the left axis. Mobility changes from baseline (in percentage points, see data section) are plotted against the right axis.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020 . . https://doi.org/10.1101 Figure 5: Plots of R ( t ), Google (visit to workplaces) and Apple (driving searches) mobility indicators over time, averaged for Europe and Asia. R ( t ) is plotted against the left axis. Mobility changes from baseline (in percentage points, see data section) are plotted against the right axis.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. .

: Top: Estimated country fixed effects from regression (1), sorted from smallest to largest by country. Bottom: region fixed effects from a version of regression (1) which replaces country fixed effects with region fixed effects.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. 28 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. 30 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 10, 2020. 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 10, 2020. Date Fixed Effects Regional Regional Regional Regional Regional (2020) in Columns 1-5. Each column report results from a separate regression. All regressions include country fixed effects. Standard errors, clustered by country, are reported in parentheses. Stars indicate statistical significance (* p<0.1,** p<0.05,*** p<0.01).

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 10, 2020. Table 5 : Joint estimation of all mobility indicators. Dependent variable: estimates of R from Kučinskas (2020) in Columns 1,2,4,5 and from rt.live in Column 3. Each column reports results from a separate regression. Columns 1,2,3: Google mobility indicators. Column 4,5: Apple mobility indicators, with all mobility indicators lagged seven days (other than in Column 3). All regressions include country fixed effects (column 3 includes state fixed effects). Standard errors, clustered by country (or state), are reported in parentheses. Stars indicate statistical significance (* p<0.1,** p<0.05,*** p<0.01).

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 10, 2020. 

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 10, 2020. . https://doi.org/10. 1101 

Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study

Ultraviolet radiation decreases COVID-19 growth rates: Global causal estimates and seasonal implications

Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries

Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update

Tracking Public and Private Response to the COVID-19 Epidemic: Evidence from State and Local Government Actions. No. w27027

Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia

Epidemiological characteristics of novel coronavirus infection: A statistical analysis of publicly available case data

Association of Public Health Interventions With the Epidemiology of the COVID-19 Outbreak in Wuhan, China

Association of public health interventions with the epidemiology of the COVID-19 outbreak in Wuhan, China

COVID-19: One-month impact of the French lockdown on the epidemic burden

Estimating the burden of SARS-CoV-2 in France

Documentation available at: rt.live

Updated understanding of the outbreak of 2019 novel coronavirus (2019-nCoV) in Wuhan, China

Evolving epidemiology and impact of non-pharmaceutical interventions on the outbreak of coronavirus disease