Cross Border Mobility Responses To Covid 19 In Europe New Evidence From Facebook Data
Summary
A research article by Docquier et al., published in Globalization and Health (2022) 18:41, on cross-border mobility responses to COVID-19 in Europe. The authors use Facebook data on daily cross-border movements from the 29th of February 2020 to the 28th of February 2021, with regression and machine learning models, to compare the effect of non-pharmaceutical interventions with infection threats. The abstract reports that containment policies matter more for cross-border traffic than international travel bans or case and death counts at destination. The data section focuses on 45 country pairs involving 30 contiguous European countries and reports that aggregate traffic decreased from 720,000 to 130,000 between end of February and early April 2020. The article ends with a numbered reference list.
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“Cross Border Mobility Responses To Covid 19 In Europe New Evidence From Facebook Data.”
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Docquier et al. Globalization and Health (2022) 18:41
https://doi.org/10.1186/s12992-022-00832-6
RESEARCH Open Access
Cross-border mobility responses to
COVID-19 in Europe: new evidence from
facebook data
Fré Docquier1 , Nicolas Golenvaux2 , Siegfried Nijssen2 , Pierre Schaus2* and Felix Stips1
Abstract
Background: Assessing the impact of government responses to Covid-19 is crucial to contain the pandemic and
improve preparedness for future crises. We investigate here the impact of non-pharmaceutical interventions (NPIs)
and infection threats on the daily evolution of cross-border movements of people during the Covid-19 pandemic. We
use a unique database on Facebook users’ mobility, and rely on regression and machine learning models to identify
the role of infection threats and containment policies. Permutation techniques allow us to compare the impact and
predictive power of these two categories of variables.
Results: In contrast with studies on within-border mobility, our models point to a stronger importance of
containment policies in explaining changes in cross-border traffic as compared with international travel bans and
fears of being infected. The latter are proxied by the numbers of Covid-19 cases and deaths at destination. Although
the ranking among coercive policies varies across modelling techniques, containment measures in the destination
country (such as cancelling of events, restrictions on internal movements and public gatherings), and school closures
in the origin country (influencing parental leaves) have the strongest impacts on cross-border movements.
Conclusion: While descriptive in nature, our findings have policy-relevant implications. Cross-border movements of
people predominantly consist of labor commuting flows and business travels. These economic and essential flows are
marginally influenced by the fear of infection and international travel bans. They are mostly governed by the
stringency of internal containment policies and the ability to travel.
Keywords: Cross-border mobility, Covid-19, Containment policies, Non-Parmaceutical interventions
Background disrupting infection chains. Many countries introduced
Covid-19 is a disease induced by severe acute respira- coercive measures and disincentives to limit within- and
tory syndrome coronavirus 2 (SARS-CoV-2). The first cross-border mobility of people in the hope of reducing
known cases of Covid-19 were registered in December the virus propagation. Whether these policies were effec-
2019 in Wuhan (China), but the virus rapidly spread into tive or not remains an open question, and there is much
many countries, leading to a global pandemic that has to be gained from better understanding the evolution and
held the world captive for many months. As until recently determinants of people’s mobility during Covid times.1
no effective vaccine or medication was available, govern- There is strong evidence that within-border (or inter-
ment policies were mainly targeted towards tracing and nal) people’s mobility declined during the Covid-19 cri-
sis. Existing literature relies on big data provided by
*Correspondence: pierre.schaus@uclouvain.be
2
Institute for Information and Communication Technologies, Electronics and
Applied Mathematics (ICTEAM), Université catholique de Louvain, 1 We understand mobility as “the movement of human beings in space and
Louvain-la-Neuve, Belgium time” [1]. This broad definition is in line with the mobility measure that we
Full list of author information is available at the end of the article use in our quantitative analysis, as that includes all types of movement.
© The Author(s). 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
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from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative
Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made
available in this article, unless otherwise stated in a credit line to the data.
Docquier et al. Globalization and Health (2022) 18:41 Page 2 of 17
private cellular phone companies,2 and documenting spa- and international) travel bans enacted during the Chi-
tial movements in real time. [2] uses Vodafone data for nese Lunar New Year holiday helped reduce the spread of
Italy, Portugal and Spain, and finds that women and the virus, and [9] argue that an appropriate coordination
younger people show the largest drop in mobility. [3] com- would considerably improve the likelihood of eliminating
bines telco data with household surveys to highlight a community transmission throughout Europe. By contrast,
sharp decline in short-distance mobility, as proxied by others expressed skepticism about the epidemiological
daily time spent at parks, retail and recreation, grocery, consequences of travel bans, arguing that the impacts of
transit locations, and workplaces. Using mobility data these restrictions are not well understood [10] or poorly
from the analytics company SafeGraph, [4] finds that the effective [11–15] once patient zero has already spread the
decline in mobility in New York and in four other U.S. virus across regions.
cities is mostly driven by the fear of infection, rather than Without taking any position on the fact that cross-
by legal restrictions. Although it also finds a significant border mobility should be limited or encouraged, we use a
impact of non-pharmaceutical interventions (NPIs) such unique database on daily mobility of European Facebook
as closing nonessential businesses, sheltering in place, and users to shed light on the evolution of cross-border move-
school closures, the dominant role of infection threats is ments of people during an entire pandemic year, and to
confirmed by [5], who relies on Google mobility data. compare the effects of coercive policies with those related
By contrast, there is scant evidence of the impact to the fear of infection. Our results contrast with those
of Covid-19 on cross-border (or international) mobility, obtained for internal mobility. The following sections suc-
which is due to the absence of high-frequency data on bor- cessively describe our data sources, methods and findings.
der crossings.3 In this paper we aim to fill this research gap
by addressing the following research questions: (i) How Data
has the Covid-19 impacted cross-border movements of Border crossings
people? (ii) Are these changes due to coercive measures Data on daily cross-border mobility is obtained from Face-
(such as containment policies or international travel bans) book (denoted by FB, henceforth) for the period from
or by the fear of contracting the virus? the 29th of February 2020 to the 28th of February 2021
Understanding the determinants of cross-border mobil- [16]. The database documents cross-border flows of FB
ity responses to Covid-19 is important for economic users with location services enabled, who travel from an
and epidemiological reasons. Cross-border movements of origin to a destination country by any means of trans-
people predominantly consists of labor commuting flows portation (car, train, air, etc.) during each 24-hour time
and business travels. Economically speaking, labor mobil- period4 . Only daily flows with a minimum of 1,000 movers
ity is a key ingredient for growth and competitiveness in are reported in the dataset. All flows below 1,000 are
normal times. And in a pandemic context, restrictions set to zero in order to minimize re-identification risk of
placed on how workers move around can slow down eco- FB users. This means that our outcome variable is left-
nomic recovery prospects, by making it more difficult censored. To limit the impact of censoring, we focus on
for businesses to hire productive workers. They can also 45 country pairs (involving 30 contiguous European coun-
induce severe economic impacts on cross-border work- tries) characterized by at least 25% of uncensored values
ers and their families. Epidemiologically speaking, the of daily traffic during the period of observation. This
role that mobility is playing in the spread of the disease selection limits the ability to generalize our results but
is still unclear. Using SafeGraph data for New York city is necessary to limit the impact of censoring, and allow
and for other U.S. cities, [6] find that (internal) mobility smooth estimation with Machine Learning methods. Fur-
increased the spread of the disease in the early stage of ther limiting the impact of censoring, we use the 7-day
the pandemic. [7] also finds a strong association between centered rolling average of daily flows.
internal movements and mortality using Google mobility Although FB data has high coverage, FB users are not
data for the UK. In the same vein, [8] shows that (internal a random sample of the population. This raises concerns
about representativeness. Figure A.1 in Appendix mit-
igates these concerns by showing a strong association
2 By big data, we mean extremely large data sets that may be analyzed between daily movements of FB users and the (estimated)
computationally to reveal patterns, trends and associations, especially those number of daily border crossings in the pre-Covid-19
related to human behaviors and interactions, according to the Oxford
Languages (https://languages.oup.com/google-dictionary-en/).
3 The recent OECD migration outlook reveals that issuance of new visas and
permits in OECD countries plummeted by 46% in the first half of 2020 (by
72% in the second quarter), as compared with the same period in 2019. 4 A number of recent studies such as [17, 18] use data extracted from FB
However, international migrants and refugees account for a tiny proportion, advertising API to identify migrants and model migration patterns. Note that
not a say a negligible proportion, of daily cross-border movements of people our data source is different as we only have access to aggregate bilateral
between European countries. Daily flows predominantly consist of counts, without further details on movers’ characteristics. The advantage of
commuting workers and business travels. our data source is, however, that it is available on a daily basis.
Docquier et al. Globalization and Health (2022) 18:41 Page 3 of 17
period, which are presented in Appendix Table A.1.5 outset of the pandemic (denoted by day 0). We thus use
However [19] shows that FB users are over-represented the relative deviation in bilateral traffic between day 0 and
T −T
in the population aged 20-40, with a high level of edu- day t, τijt ≡ ijtTij0 ij0 , as a variable of interest instead of
cation and an above-average income level. It means that focusing on the level of traffic Tijt itself. Modelling rel-
groups of individuals under 20 or over 65 and those with ative deviations is also helpful to avoid over-fitting large
lower income/education levels are under-represented in corridors at the expense of small corridors, and mitigates
FB data. Although people under 20 and over 65 form a tiny representativeness issues even if the scale factor (φ) varies
minority of the population under investigation (i.e., com- across country pairs.
muters and business travelers), this is a limitation of our Figure 1 portrays these relative deviations in the aggre-
work. FB users are more likely to belong to the richest and gate level of traffic between all country pairs included in
healthiest parts of the movers’ population. our sample. The curve largely mirrors the three phases of
Let us denote by Mi→jt F the count of FB movers from the pandemic, depicting a stark drop in traffic in March
country i to country j at day t. When focusing on con- 2020, a recovery during the spring and summer peri-
tiguous countries (i.e., the pairs of countries that exhibit ods, and a new contraction in the post-summer period.
the largest numbers of daily cross-border movements by Between end of February and early April 2020, the aggre-
far, and that are the least affected by censoring rules), gate traffic level decreased from 720,000 to 130,000,
the number of movers from i to j is almost identical to implying a 82% drop. Aggregate traffic never fully recov-
the number of movers from j to i at each day t (i.e., ered to the February levels in our period of observation.
F
Mi→jt ≃ Mj→it
F ). The reason is that border crossings This also holds true during the summer vacation period
predominantly consist of back-and-forth movements of when international travels were largely liberalized. The
commuting workers and business travelers, who move for pace and strength of these changes vary across the three
short periods and for economic reasons6 . This is also the phases of the pandemic. The drop in March 2020 was
case in the summer vacation period when considering a strong and sudden, while the summer peak and the post-
7-day centered rolling average of daily flows. This means summer contraction were more gradual.
that Mi→jtF F
and Mj→it are reflecting the same reality, and Aggregate fluctuations mask large differences across
say nothing about the primary direction of the flows. For country pairs. Bilateral traffic returned to its pre-Covid
this reason, we define the level of bilateral traffic of FB level in a minority of cases. For the majority of corri-
users between countries i and j as: dors, however, the traffic level has not fully recovered.
F
Tijt ≡ Max Mi→jtF F
, Mj→it , (1) This is illustrated in Fig. 2, which depicts the evolution
of people’s traffic in corridors involving four open coun-
and see it as a proxy for the scaled sum of the two tries, namely Luxembourg, Switzerland, Italy, and Serbia.
unobserved unidirectional flows between the two coun- Luxembourg is the country with the highest share of
tries, φ(Mi→jt + Mj→it ), where the scale factor φ denotes cross-border workers in Europe. Given the economy’s
the fraction of FB users in the actual number of movers high reliance on cross-border workers, the Luxembourg
(denoted by Mi→jt and Mj→it ). Using the maximum as government has never implemented international travel
weighting scheme has the advantage to limit the impact restrictions during the pandemic. Luxembourg experi-
of censoring in the case movers in one of the two direc- enced a significant drop in traffic in March 2020, whatever
tions are below the threshold. As TijtF = T F , we can get
jit the partner country. After one month of lockdown, traf-
rid of the dyadic dimension of the data, treat each country fic levels recovered pretty quickly until reaching a plateau
pair as a one-dimensional observation, and divide the size at about -25% since June 2020. Switzerland is the coun-
of the sample by two. In the methodological section, how- try with the largest number of cross-border commuters in
ever, we explain how priors about the primary direction of Europe. This country experienced a larger drop during the
the flows can be used to improve the quality of fit of our first lockdown, and a slower recovery. Furthermore, the
models. variability across corridors is considerably greater than in
To avoid dealing with re-scaling issues, we express traf- Luxembourg.
fic counts as relative deviations from their initial or pre- Italy has been severely impacted by the pandemic, and
Covid-19 levels – in our case, the levels observed at the responded with national and international travel bans.
We observe similar patterns of contraction and recov-
ery during the first two quarters of 2020, followed by a
5 We also find a strong association between the number of FB users and
population size at the regional level. Results are available upon request. substantial increase in traffic during the holiday summer
6 Note that we only observe the total number of movers within a day, and period, and a second lockdown-type contraction in the
neither the duration of their stay nor the direction of the movement. The vast
majority of movers cross the border twice as they return to their origin
post-Summer period. Finally, the patterns observed in Ser-
country within a day or so. This is why we model cross-border traffic and use bia are less conclusive as they are more severely affected
a trick below to account for the presumed direction of the flows.
Docquier et al. Globalization and Health (2022) 18:41 Page 4 of 17
Fig. 1 Aggregate Traffic Deviations from Pre-Covid Levels. Source: Facebook data on daily border crossings. Notes: Y-axis represents the average of
τijt , the percentage change (times 100) in the 7-day moving average traffic compared to t = 0 over all destinations. The weights are the traffic levels
observed in pre-Covid-19 period (i.e., t = 0)
by censoring rules. Serbia is an important origin and tran- influenced by seasonal effects, epidemiological risks, and
sit country for migrants and refugees entering the EU. policy measures implemented in the countries. We now
Overall these patterns illustrate the need to account for turn to the description of the data sources used to proxy
corridor-specific heterogeneity when analyzing the deter- epidemiological conditions and the stringency of national
minants of bilateral traffic. Variations are likely to be policies.
Fig. 2 Traffic Deviations from Pre-Covid Levels for Selected Corridors. Source: Facebook data on daily border crossings. Notes: Y-axis represents τijt ,
i.e. percentage change (times 100) in corridor 7-day moving average traffic compared to t = 0 in corridor ij
Docquier et al. Globalization and Health (2022) 18:41 Page 5 of 17
Fig. 3 Evolution of the average value of Covid cases and government policy measures. Source: Oxford Covid-19 Government Response Tracker
(OxCGRT). Note: The values of each indicator is scaled between 0 and 1, and the average is computed using the 30 countries included in our sample
Explanatory features For all features and days, Fig. 3 displays the cross-
We link variations in cross-border traffic during the pan- country mean level of each containment index over
demic to daily changes in epidemiological conditions and time. Values close to one represent higher Covid-19
containment policies in the countries involved. We proxy cases/deaths or more stringent responses. As containment
the severity of the pandemic with the daily numbers of policies were implemented in most countries during the
new Covid-19 cases and new Covid-19 related deaths in second half of March 2020, maximum values are observed
each country using data from [20]. With regard to con- during this period. Testing and contract tracing were
tainment measures, we use data on daily policy responses implemented more heterogeneously across countries and
from the Oxford Covid-19 Government Response Tracker peaked in the summer of 2020. Reported number of new
(OxCGRT) [21]. The latter database consists of 18 ordi- Covid-19 related cases/deaths were much greater during
nal indicators capturing the levels of nonpharmaceutical the second wave and peaked at the end of the year 2020.7
interventions (NPIs). Based on our priors as to which poli- Figure 4 shows the cross-country correlations between
cies likely affect mobility, we choose to include the eight each of the explanatory variables and the relative devi-
mobility-related measures that form the “containment and ations in average traffic (i.e. deviation of the country-
closure policies” block (denoted by C1-C8 in the database) specific mean level of traffic with all potential partner
as well as proxies for the intensity of testing and contact countries in the sample). Containment policies are pos-
tracing (denoted by H2 and H3). We rescale all sets of itively correlated with each other, and moderately cor-
predictors between 0 and 1, and align them with the def- related with epidemiological conditions, which allows us
inition of the outcome variable using the centered 7-day
7 Epidemiological conditions are likely to subject to measurement errors. For
rolling average at each day.
example, testing and tracing practices played an important role in determining
the number of detected cases.
Docquier et al. Globalization and Health (2022) 18:41 Page 6 of 17
Fig. 4 Correlation Matrix of the different variables. Source: Own computations. Notes: Unilateral traffic growth for each country i is the relative
deviation in aggregate traffic involving country i, nj=1 Tijt , as compared to the pre-Covid-19 period (t = 0)
to include both sets of variables jointly in our regression cancellations of public events, restrictions on public gath-
and machine learning models. However, the fact that con- erings, requirements to stay at home, and restrictions on
tainment policies are correlated with each other raises internal movements. Two interesting observations arise
concerns of multicollinearity, and motivates the usage from these partial correlations. First, the negative cor-
of a limited number of synthetic policy indices. These relation between measures of epidemiological intensity
indices are obtained by conducting a Principal Compo- (Covid-19 cases and deaths) and changes in total traf-
nent Analysis (PCA) of all policy measures (C1-C8, and fic are rather low. This might suggest that, in contrast
H2-H3) over the entire sample of observations, and by with studies on within-border mobility, the fear of being
extracting the first two components. The first component infected might play a less important role in explaining
mainly represents the C1-C8 measures which are strongly changes in cross-border movements. Second, among con-
correlated with each other while the second component tainment policies, the implementation of international
corresponds to a higher variance for the H2-H3 mea- travel bans is far from being the most strongly corre-
sures. We will compare the results obtained when using lated covariate. This suggests that travel bans might be
a comprehensive specification, including all (collinear) effective in limiting non-essential travels, but less effec-
explanatory variables, with those obtained when using a tive to limit labor commuting flows and business travels,
parsimonious specification, including the two synthetic which represent the overwhelming majority of daily bor-
PCA components as predictors. der crossings between European countries (see Table A.1).
Turning to the main correlations of interest (i.e., cor- By contrast, cancellations of events and constraints on
relations between the relative deviations in cross-border internal movements and gatherings are highly correlated
traffic and each predictor), the figure displays a moder- with traffic variations, possibly because such constraints
ate negative correlation with containment policies, as well better proxy changes in economic activity and incentives
as low and positive correlations with testing and trac- to move. In the following section, we describe the regres-
ing policies. The strongest associations are obtained for sion and machine learning methods used to test these
Docquier et al. Globalization and Health (2022) 18:41 Page 7 of 17
hypotheses using bilateral traffic growth as a dependent models rely on different ML regressors, each based on a
variable. distinct type of technique. We assess the predictive perfor-
mance of each model using the very same (and standard)
Methods cross-validation ML methodology. The goal of the study
Mobility patterns identified in the previous section might is not to design a forecasting model, but rather to iden-
result from various factors such as travel bans, sanitary tify the main determinants of mobility, and to investigate
measures influencing economic costs and incentives to whether these different approaches generate converging
move for work and business (e.g. sectoral lockdown, work- findings. Therefore, instead of the validating our model
from-home practices) or for leisure (e.g. shops, restaurant on a particular sub-period (as is usually done to evalu-
and bar closings), or the fear of the virus itself. Our goal ate a time-series model), the observations composing the
here is to identify the determinants of the relative devi- cross-validation folds are randomly chosen within the full
ation in daily traffic of people between country i and sample. All models are implemented in Python via the
country j (τijt ), considering all NPIs and epidemiological Skicit-learn library [28].
daily indicators (xit and xjt ) during the Covid-19 crisis.
Our models are also used to predict the effects of epi- Approaches with or without directional priors
demiological restrictions, NPIs and mobility restrictions Ideally, mobility models aim to characterize the evolution
on traffic counts. of the unidirectional flow of people (Mi→jt ) from an ori-
We combine two analytical methods, Econometric gin country i to a destination country j at day t, or of
Modelling (EM) and Machine Learning (ML). EM and ML their
relative deviation
from the initial reference period
techniques are generally used for different purposes. In M −Mi→j0
μi→jt ≡ i→jt Mi→j0 , based on a set of features available
EM, gravity models are used to explain human mobility for the same time period. Without loss of generality, the
flows between two countries.8 EM models require impos- general functional form fM of such a model can be written
ing one analytical specification for the response func- as:
tion, which governs the derivatives of the dependent with
respect to covariates. In the gravity specification, a large μi→jt = fM (xit , xjt , dij , dt ) + ηi→jt (2)
set of fixed effects are included to capture relevant con-
founders, and allow for identification of potential causal where xit represents the set of origin-specific determi-
effects based on the so-called within variation. ML tech- nant, xjt is a set of destination-specific determinants, dij is
niques are at the other extreme of the bias-variance trade- a set of bilateral dummies capturing time-invariant bilat-
off. They do not require strong analytical assumptions and eral resistance (including initial Mi→j0 , distance, language
allow, by design, to explore a larger set of regression func- proximity, cultural proximity, etc.), dt a set of day dum-
tions including linear or polynomial combinations of the mies capturing weekdays and seasonal trends (e.g. holiday
covariates. This increase of the so-called model capacity season, general feeling of risk when traveling, etc.), and
comes with two drawbacks. First, the models are more ηi→jt an error term. In our case, the vectors of explana-
complex and are usually not easy to interpret. Contrary tory variables xit and xjt capture the set of NPIs and
to EM, ML techniques might computationally suffer from epidemiological variables, and should also be interpreted
the inclusion of large sets of control fixed effects. Second, as variations from period 0 since xi0 and xj0 are equal to
there is always a risk of overfitting the training data and zero in the pre-Covid-19 period.
the identification of causation links is usually not an objec- With FB data, the primary direction of the cross-border
tive per se. Despite these difficulties, we use both EM and flows is unknown, which implies that Mi→jt and Mj→it
ML to identify converging messages, and the triangulation cannot be distinguished a priori. Instead, we observe the
of results can serve to strengthen our evidence base. relative deviation in bilateral traffic, τijt , and we have to
We use four models exploring a broad range of learning estimate the function fT linking bilateral traffic to the set
techniques: (i) A gravity model based on the linear regres- of explanatory features without being able to distinguish
sion method [23]; (ii) A K-nearest neighbors method between origin- and destination-specific determinants. A
(KNN), which predicts the dependent variable by inter- learning approach without directional priors writes as:
polation of its nearest observation neighbors in the train- τijt = fT (xit , xjt , dij , dt ) + ηijt (3)
ing set [24]; (iii) A Gradient Boosting method (GBoost),
whose predictions are based on a set of decision tree mod- It is possible, however, to discipline the model with pri-
els [25]; (iv) A Multi-layer Perceptron (MLP), which is a ors about the direction of the flows. As bilateral traffic
classic neural network approach [26, 27]. The last three is a proxy for the sum of unidirectional flows (Tijt ≃
φ(Mi→jt + Mj→it )), relative deviations in Tijt can be
8 Gravity models aim to predict bilateral flows between two entities based on
their size, on their economic characteristics, and on the distance between
expressed as a weighted sum of the relative deviations in
them [22]. unidirectional flows: τijt = ωi→j,0 ×μi→jt +ωj→i,0 ×μj→it ,
Docquier et al. Globalization and Health (2022) 18:41
where @;-;),0 = 1—aj;-+i,9 is the pre-Covid-19 share of uni-
directional cross-border flows from country i to country
j in total traffic between the two countries. Estimates for
@j-+j are constructed using pre-Covid-19 data on com-
muters, air travels and international migration, and then
used as priors to discipline the model (these shares are
depicted in Figure A.2 in Appendix).
We can thus create two sets of weighted features,
namely X;, for origin-specific effects, and x4, for
destination-specific effects, defined as follows:
Xin = Gi jorit + Oj i0xje
d
Xijt = i joxjt + Oj i0%it-
The model with directional priors is obtained after
replacing (xjz, xj) in Eq. (3) by (xe xd
ijv d). It writes as:
tie =f (XoeXtoo diode) + nfl. (4)
If the true model for unidirectional flow (fi(.)) was lin-
ear, plugging weighted covariates in the estimated model
for bilateral traffic (fr(.)) would allow retrieving the true
origin- and destination-specific coefficients of interest
accurately. Although this is not the case when fiy(.) is
non linear, using weighted covariates might improve the
quality of fit or facilitate the interpretation of the results.
The rationale is that the effect of policies depends on
where they are implemented and on the primary direc-
tion of the flows. Suppose w;-.j0 ~ 1 (ie., flows mostly
go from i to /), then an increase in restrictions/stringency
at destination (resp. at origin) makes x4. positive (resp.
Xin positive) and is more (resp. less) likely to reduce the
flow of cross-border movements. Using directional pri-
ors allows approximating origin- and destination-specific
effects without observing the direction of the flows during
the pandemic year.
Permutation feature importance
To identify the main causes of daily mobility variations,
the importance of each feature is computed for the dif-
ferent regression approaches with permutation feature
importance [29]. It has a the advantage of working sim-
ilarly for all regression models considering them as a
black-box models [30]. It is defined to be the decrease in
the regression score when a single feature value is ran-
domly shuffled across observations. More exactly, for a
given model f, it first calculates a baseline score Sy pro-
vided by f when it is fitted, and then evaluated with a
certain metric on the whole sample. Then for each pos-
sible feature x the modified score Sh is computed by
evaluating f on the transformed data set where the values
of feature x are randomly permuted across all observa-
tions. The mean importance of the feature x for the model
f is computed as:
Page 8 of 17
K
y- Sf 7 Shwe (5)
k=1 Sf
1,2
Se K
where K is the number of random permutations realized
for each feature, and SF wk is the Sh score for the k”
permutation.
In order to compare the importance values of the dif-
ferent models in an equivalent manner, the values Jy, are
scaled between 0% and 100% separately for each model
jf. The mean features importance Tf jc are computed over
10 permutations using the negative mean absolute error
(MAE) and the Root Mean Squared Error (RMSE). This
means that the bigger J,, the more permutations of
the feature x degrades the quality of predictions for the
model f and the feature is considered as more importantly
associated with the target variable.
Results
We present our results in two steps. First, we assess
the predictive power of the various models. This implies
comparing learning methods with or without directional
priors and with or without day/corridor control dum-
mies. We compare their predictive performance by using
out-of-sample predictions and computing the MAE and
RMSE. Second, we use the estimated models to rank the
importance of different features relying on permutation
techniques. Using multiple models allows assessing the
robustness of our findings.
Validation of models
We first investigate whether adding priors about the direc-
tion of the flows and/or adding a full bunch of day and cor-
ridor dummies improves the performance of our learning
models. Models without directional priors are described
in Eq. (3), while models with priors use weighted regres-
sors, as described in Eq. (4). A 10-fold cross-validation
over the whole data set (from the 29" February 2020 until
the 28" February 2021) is realized for each model to assess
its performance. Table 1 reports the MAE, RMSE and
their standard error across cross-validation folds obtained
with different learning methods.
It shows that directional priors (@;+;,0 and ji) do
not bring significant additional predictive power under
most learning approaches when day and corridor dum-
mies are not factored in (see Panels A and B). The only
exception is the G-Boost method. On the contrary, when
day and corridor dummies are included (Panels C and D),
adding directional priors slightly improve the quality of fit
with virtually all learning techniques (except with KNN).
In addition, we show below that distinguishing between
origin- and destination-specific effects as in Eq. (4) makes
the interpretation of the results much easier. Therefore,
the model with directional priors will be prioritized in the
rest of the analysis.
Docquier et al. Globalization and Health (2022) 18:41 Page 9 of 17
Table 1 MAE comparison of the different models with or without directional priors and dummies
Linear KNN G-Boost MLP Linear KNN G-Boost MLP
Panel A: No dummies - No prior Panel B: No dummies - Priors
avg MAE 0.194 0.018 0.073 0.051 0.201 0.019 0.042 0.057
std MAE (0.009) (0.001) (0.001) (0.005) (0.005) (0.001) (0.001) (0.003)
avg RMSE 0.285 0.042 0.106 0.083 0.287 0.043 0.064 0.089
std RMSE (0.017) (0.009) (0.003) (0.011) (0.009) (0.005) (0.002) (0.008)
Panel C: Dummies - No prior Panel D: Dummies - Priors
avg MAE 0.135 0.020 0.050 0.041 0.134 0.020 0.049 0.038
std MAE (0.005) (0.001) (0.002) (0.003) (0.005) (0.001) (0.001) (0.003)
avg RMSE 0.210 0.045 0.081 0.068 0.203 0.047 0.077 0.064
std RMSE (0.010) (0.006) (0.006) (0.006) (0.009) (0.005) (0.002) (0.005)
Note: The table compares the performances of the 4 different approaches (Linear, KNN, G-Boost and MLP) with and without directional priors (ωi→j,0 ), and with or without
day/corridor dummies (dt and dij ). Errors are computed from a 10-fold cross-validation on the whole sample
Second, we investigate whether the inclusion of day- based on more complex prediction methods that allow for
specific effects – i.e., 366 time dummies, dt , that are com- non-linear relationships between variables, and account
mon to all corridors and capture unobserved variations for non-stationary variations contained in the matrices of
such as seasonal changes, synchronized fears of infection, o and X d . The KNN always produces the best quality of
Xijt ijt
etc. – and corridor-specific effects – i.e., 45 corridor dum- fit. The error of this approach is minimal when the num-
mies, dij , that are time invariant and capture unobserved ber of neighbors k used to estimate the relative deviations
variations such as the skill level of the cross-border work- in traffic is low (say, 2 or 3). Its impressive performance in
force, linguistic and cultural proximity between countries, 10-fold cross-validation can be explained by the fact that
etc. – improves the predictive power of our models. Again, the model finds a small number of observations for which
we perform another 10-fold cross-validation on different the relative deviations in traffic are similar to those that
versions of each model. Panels C and D in Table 1 includes must be predicted. In general, the closest neighbors are
both sets of dummies jointly, with or without directional observations of the days preceding or following the daily
priors. In the absence of directional priors, the inclusion level of traffic observed in the same corridor.
of day and corridor dummies reduces the MAE and RMSE
by 20 to 30% whatever the learning technique used. When Main sources of variations in cross-border mobility in
directional priors are factored in, the dummies improve COVID times
the performance of the linear and MLP models, whereas In order to identify the government policy indicators hav-
they deteriorate the quality of fit under the KNN and G- ing the greatest impact on relative deviations in traffic,
Boost models. This is because adding day and corridors the importance of each feature is computed for the differ-
dummies drastically increases the number of parameters ent approaches involving directional priors and dummies.
to be estimated, and some ML approaches (like KNN) are Directional priors allow us to distinguish the effects of
known to suffer from the curse of dimensionality. origin-specific features from those of destination-specific
To further explore this issue, Table A.2 in Appendix features. Table 2 presents the results from this exercise.
considers the model with directional priors and adds one Features are ranked by decreasing order on the basis of
set of dummies at a time. The inclusion of 45 corridor- the average predictive power across the four learning tech-
specific dummies always improves the quality of fit. On niques. The column ‘Avg.’ gives the mean value of error
the contrary, the inclusion of 366 day-specific dummies metric averaged over the four models. Panel A provides
deteriorates the performance of KNN and G-Boost meth- the results obtained with the saturated models includ-
ods. This confirms that the gains from adding information ing the large set of corridor and day dummies, which is
about unobserved common time trends, which might the first-best model when using linear and MLP learning
already be captured by the relatively well synchronized techniques. Panel B gives the results obtained with cor-
trends in observed epidemiological conditions and con- ridor dummies only, which is the first-best model when
tainment measures, is outbalanced by the costs linked to using the KNN and G-Boost techniques. Results of Panel
the inflated dimensionality of the computation problem. B will be discussed in the next section. In the top part of
Third, ML techniques always outperform the linear EM the table, the models use all individual features depicted
model. This result was also expected given that ML is in Fig. 3, despite the high level of correlation between
Docquier et al. Globalization and Health (2022) 18:41 Page 10 of 17
Table 2 Feature ranking by origin and destination
Panel A Panel B
Corridor & Day dummies Corr. dum.
Features Linear KNN G-Boost MLP Avg. Avg.
Indiv. features
Origin - C1 School closures 100 69 100 59 82 85
Destin - C1 School closures 94 60 36 85 68 68
Destin - C3 Cancel public events 19 64 77 68 57 57
Origin - C3 Cancel public events 10 100 33 65 52 46
Origin - C7 Restr. Internal movement 0 93 16 100 52 51
Origin - H2 Testing policy 14 7 87 92 50 43
Origin - C4 Restrictions gatherings 50 51 40 54 49 44
Origin - C6 Stay home requirements 92 16 12 59 45 21
Destin - C6 Stay home requirements 17 15 96 54 45 45
Destin - C4 Restrictions gatherings 6 48 70 25 37 42
Destin - C7 Restr. Internal movement 13 66 12 58 37 29
Origin - H3 Contact tracing 5 12 27 44 22 22
Origin - C8 International travel bans 1 1 45 40 22 18
Origin - New Covid deaths 0 7 73 5 21 46
Origin - New Covid cases 11 0 21 52 21 75
Destin - New Covid deaths 6 10 64 0 20 49
Destin - C5 Close public transport 34 6 1 39 20 9
Destin - H3 Contact tracing 31 21 2 14 17 7
Destin - C2 Workplace closing 5 33 7 23 17 21
Destin - C8 International travel bans 0 12 20 32 16 24
Destin - New Covid cases 12 0 43 6 15 38
Origin - C5 Close public transport 18 7 0 31 14 12
Origin - C2 Workplace closing 1 23 10 14 12 23
Destin - H2 Testing policy 9 0 2 10 4 6
Synthetic features
Destin - Component 1 100 100 100 100 100 100
Origin - Component 1 13 75 20 49 39 48
Origin - Component 2 1 55 17 19 23 26
Destin - Component 2 9 50 0 0 15 17
Origin - New Covid cases 0 0 18 30 12 75
Destin - New Covid deaths 5 14 6 11 9 49
Origin - New Covid deaths 1 13 3 9 6 46
Destin - New Covid cases 0 2 1 6 2 38
Notes: The different features are ranked following the permutation importance method. For each approach, we provide results obtained with the model including
day/corridor dummies (cols. 1-5) and the version including corridors dummies only (col. 6). Directional priors are always used to identify the effects of origin- and
destination-specific features. The importance values of each feature is computed over 10 permutations using the negative mean absolute error (MAE). The resulted values are
scaled between 0% and 100% separately for each model. The col. ‘Avg.’ averages the results obtained with the four learning techniques. The features are ranked according to
the average importance of the models including the day/corridor dummies (Panel A). In Panel B, we only report the ‘Avg.’ score without reporting the model-specific results
some of them. In the bottom part of the table, the models We identify, however, several common and interesting
use synthetic containment features derived from a PCA findings. First, school closures in the origin country has
analysis. the largest average impact on the variation in daily traf-
When considering all individual features, the ranking fic. Remember that cross-border traffic predominantly
based on their predictive power varies across models. consists of labor commuting flows and business travels.
Docquier et al. Globalization and Health (2022) 18:41 Page 11 of 17
School closures at origin imply that many parent workers influencing the fear of infection have negligible impacts
are forced to take parental leave and cannot commute to on border crossings.
work. In the same vein, school closures in the destination
country are also paralyzing economic activity in the desti- Discussion
nation country and reduce incentives to move. This result The EM and ML techniques used in this paper allow
is in line with [31], who finds that school closures were highlighting a strong association between the evolution
among the most important predictors of internal mobil- of bilateral traffic between contiguous countries and con-
ity in March 2020. Second, variations in traffic are mostly tainment policies in the destination country as well as
impacted by containment measures. Based on the average school closures in the origin country. Association does
predictive power (col. ‘Avg.’), ten out of the twelve most not imply causation. It could be argued that this statisti-
predictive features involve C-type containment measures cal association is governed by the influence of unobserved
implemented in the origin or destination countries. Third, characteristics affecting both policy changes and mobil-
the fear of being infected in the destination country, as ity simultaneously, or that a reverse causation mecha-
proxied by the destination-specific number of Covid-19 nism operates (i.e. cross-border mobility influences policy
deaths and cases (appearing in bold characters in Table 2) reforms). The fact that our results are robust to the inclu-
are among the least predictive features. Fourth, inter- sion of a large set of day and corridor dummies captur-
national travel bans in origin and destination countries ing unobserved time- and corridor-specific characteristics
(appearing in italics in Table 2) also have a low predictive strongly mitigates the first misspecification concern.
power. We thus conclude that cross-border daily flows are With regard to reverse causation, concerns are mitigated
marginally influenced by the fear of infection and inter- by the use of high-frequency data. We cannot reject the
national travel bans. They are mostly governed by the possibility of a mobility-driven propagation of the virus
stringency of internal containment policies and by fam- requiring new containment measures. However, such a
ily constraints. It is worth noticing that models without mechanism takes time to operate. Mobility shocks at day
directional priors deliver very similar results, as illustrated t do not generate immediate and visible epidemiological
in Table A.3 in the Appendix. consequences, and policy responses are also implemented
In addition to school closures, the top panel of Table 2 with a certain delay. By contrast, our estimates suggest
suggests that the most important containment measures that containment policies are immediately associated with
are the cancellation of public events, restrictions on gath- changes in cross-border mobility. This prudently sup-
erings, restrictions on internal movements and stay-home ports the existence of a causation effect of containment
requirements. In addition, the twelve most predictive fea- measures on mobility.
tures include 5 destination-specific and 7 origin-specific An opposite argument that goes against the reverse cau-
measures. However, as illustrated in Fig. 4, these mea- sation issue is that it also takes time for information about
sures are highly correlated at the national level. Hence, epidemiological conditions to be assimilated by potential
instead of feeding the model with correlated features, the movers. Hence, the fear of infection could be better prox-
bottom part of the table uses synthetic indices of contain- ied by the lagged numbers of Covid-19 cases and deaths.
ment and sanitary measures. We use a PCA analysis to Our results are preserved and even reinforced when using
reduce the dimensionality of the origin- and destination- lagged proxies for the fear of infection. More precisely,
specific containment measures and we extract the first traffic at day t is very badly predicted by the number
two components of the PCA. Covid-19 cases and deaths observed one or two weeks
Remember that the first PCA component can be inter- before the date (see Table A.4 in the Appendix). Hence,
preted as an average index of stringency of containment we can reasonably rule out that the low impact of infec-
measures (i.e. C1-C8 indices); the second component cap- tion fears at destination is driven by a misspecification
tures testing and tracing policies (i.e. H2 and H3). The problem.
results clearly reveal that the stringency of containment In the same vein, it could be argued that fears are
measures in the destination country has, by far, the great- strongly synchronized across countries and captured by
est predictive power. The average stringency of contain- the day dummies. These concerns are mitigated by the fact
ment measures at origin is the second most predictive that removing the day-specific dummies does not alter
power, with an average importance equal to 40% of that our conclusions. In Panel B of Table 2, day dummies are
of the destination country. This comforts the idea that excluded. The only significant change is that the num-
cross-border daily flows of people mostly involve eco- ber of Covid cases in the origin country has a greater
nomic/essential movements which can only be influenced predictive power, possibly implying that people in sick
by changes in incentives to move or coercive mobility con- leave self-isolate and stop moving. However, the predictive
straints. In line with the top part of the table, variables power of international travel bans (in italics) and fears to
Docquier et al. Globalization and Health (2022) 18:41 Page 12 of 17
be infected at destination (epidemiological conditions at their mobility decisions to epidemiological threats. Bor-
destination are in bold characters) remain low when using der crossings can only be controlled with internal coercive
both individual and synthetic features. Again, the strin- policies.
gency of containment measures in the destination country
has the greatest predictive power by far. Appendix A: Appendix – figures and tables
Finally, one may fear that our results can be affected by A.1 Representativeness of facebook data
the quality of data as well as their comparability across A critical question relates to the representativeness of
countries (see [32] for a discussion of the strengths and FB data. On average, comparison between the number
weaknesses of data sources on Covid-19). Data on Covid- of FB users and population size by country reveals that
19 threats and NPIs (such as the number of new cases the number of FB users with location services enabled
and deaths) are likely to be subject to country and time represents 5.6% of the population in Europe, on average.
biases due to multiple reasons (e.g. changes in testing However, this fraction is rather uniform across countries,
strategies, seasonal effects, variations in reporting delays which suggests that FB data might be representative of
or in the classification of Covid-related deaths, etc.). It is the population as a whole. This does not mean, however,
worth emphasizing, however, that the Permutation Fea- that data on FB users are representative of the population
ture Importance technique that we use is, by construction, of cross-border movers, as using internet connection or
robust to noise.9 In addition, the systematic use of bilat- activating location services abroad can be costly [33]. To
eral and time dummies (dij and dt ) allows us to mitigate address this point, we produce estimates of the number
the biases caused by unobserved variations in the quality of daily cross-border inflows in the pre-Covid period, and
of data across country pairs and periods. compare them with FB data. We collect data on commut-
ing flows from the Labor Force Survey for 2019,10 data
Conclusion on air passengers as of March 2019,11 and estimates of
Existing literature shows that people within-border mobil- immigration flows from [34].12
ity has drastically declined in times of Covid-19, primarily Overall, Table A.1 shows that migration flows account
because of the fear to be infected in parts of the pop- for a tiny (say negligible) proportion of daily movements,
ulation. To the best of our knowledge, our study is the implying that FB data mostly capture commuting flows
first to analyze the effect of Covid-19 and related contain- and business travels, as well as holiday-maker’s moves
ment measures on people’s cross-border movements. In in vacation periods. This implies that the largest flows
line with the findings above, we also document a sharp are observed between contiguous countries and business
decline in cross-border mobility in general, especially dur- partners. Combining corridors available in our sample and
ing the first lockdown and in the second and third waves of corridors involving non-EU countries, Figure A.1 shows
the pandemic. However, these variations in cross-border that FB data as of the first week of March 2020 are highly
mobility are mostly induced by local containment policies correlated with estimates of actual flows in the year 2019,
in the destination country, and school closures in both which suggests that FB data might also be representative
countries. The fear of infection and international travel of cross-border movements.
bans have little influence on cross-border movements.
The likely reason is that cross-border daily flows of A.2 Parameters of the mL methods
people are predominantly made of commuting workers We describe in this section the parameters of the different
and business travelers who move for economic/essential ML models used in this paper. In order to tune the mod-
reasons. These economic flows are observed between els, a boosting sample corresponding of 70% of the whole
contiguous countries, and account for 99% of interna- dataset is used (from the 29th February 2020 until the 16th
tional movements of people when compared with the November 2020). We use the following parameters:
flows of migrants and refugees. Their magnitude varies
• K Nearest Neighbors. The models uses 5 neighbors
with the economic costs and incentives of moving, which
depend on lockdown measures and on the stringency of and it has the distance metric as weight function.
internal containment policies. In addition, international 10 Labor Force Surveys are provided by Eurostat. We use data on commuting
travel bans do not apply to commuters and businessmen. by NUTS2 region, and allocate commuters aged 15 to 64 by destination on the
Although there is no consensus on the fact that these basis of contiguity links with other countries. When a NUTS region shares
several contiguity links, we share the number of commuters proportionately
flows contribute to the propagation of the virus, policy- to the level of income per capita in the destination country. To identify daily
makers must be aware that economic movers hardly adapt movements, we assume that each commuter spend 4 days per week in the
place of work, and multiply LFS number by 4/7.
11 We use monthly statistics on Air passengers from Eurostat by airport of
departure, and allocate them by destination using FB data. To identify daily
movements, we divide monthly flows by 30.
9 It could be further supplemented with a leave-one-out sensitivity analysis on 12 The latter are available until the year 2015; we multiply them by 1.5 to proxy
countries [32]. the level in 2019. To identify daily movements, we divide annual inflows by 360.
Docquier et al. Globalization and Health (2022) 18:41 Page 13 of 17
Table 3 Estimates of the average count of daily cross-border outflows in 2019
Daily count estimates As percent of Total
Commuters Air pass. Migrants Total Commuters Air pass. Migrants
AUT 159678 169395 441 329514 0.484 0.514 0.001
BEL 133742 241103 729 375574 0.356 0.641 0.001
DNK 44732 45719 77 90528 0.494 0.505 0.000
FIN 22532 21311 195 44038 0.511 0.483 0.004
FRA 396457 417902 670 815029 0.486 0.512 0.000
DEU 472160 361659 2770 836589 0.564 0.432 0.003
GRC 1714 24700 4 26418 0.064 0.934 0.000
IRL 23892 108689 61 132642 0.18 0.819 0.000
ITA 139103 115605 952 255660 0.544 0.452 0.003
LUX 152407 4829 76 157312 0.968 0.030 0.000
NLD 102000 267917 296 370213 0.275 0.723 0.000
PRT 55785 87144 157 143086 0.389 0.609 0.001
ESP 79857 346395 36 426288 0.187 0.812 0.000
SWE 51000 87565 91 138656 0.367 0.631 0.000
GBR 76300 465893 873 543066 0.140 0.857 0.001
EU15 1911359 2765826 7428 4684613 0.408 0.590 0.001
BIH 17017 21296 0 38313 0.444 0.555 0.000
BGR 52571 33019 42 85632 0.613 0.385 0.000
HRV 36557 28639 33 65229 0.560 0.439 0.000
CZE 122160 62294 156 184610 0.661 0.337 0.000
EST 10642 18674 6 29322 0.362 0.636 0.000
HUN 100196 62174 217 162587 0.616 0.382 0.001
LTU 2414 14435 0 16849 0.143 0.856 0.000
NOR 8232 50767 178 59177 0.139 0.857 0.003
POL 205314 135350 109 340773 0.602 0.397 0.000
ROU 65550 81892 207 147649 0.443 0.554 0.001
Sources: Numbers of daily commuters are extracted from Eurostat data by Nuts2 region in 2019; Numbers of air passengers are extracted from Eurostat monthly statistics on
air passenger transport in February 2019; Data on international migrants are extrapolated from [34] for the year 2015, assuming a conservative 50% growth in the flows
between 2015 and 2020
Fig. 5 Daily traffic estimates (X-axis) and FB data (Y-axis) by corridor (1 March 2020). Sources: Numbers of daily commuters are extracted from
Eurostat data by Nuts2 region in 2019; Numbers of air passengers are extracted from Eurostat monthly statistics on air passenger transport on March
1, 2020; Data on international migrants are extrapolated from [34] for the year 2015, assuming a conservative 50% growth in the flows between
2015 and 2020. FB data are the Facebook data on daily border crossings on March 1, 2020. Note: All variables are expressed in logs
Docquier et al. Globalization and Health (2022) 18:41 Page 14 of 17
Fig. 6 Distribution of Weights. Sources: Numbers of daily commuters are extracted from Eurostat data by Nuts2 region in 2019; Numbers of air
passengers are extracted from Eurostat monthly statistics on air passenger transport on March 1, 2020; Data on international migrants are
extrapolated from [34] for the year 2015, assuming a conservative 50% growth in the flows between 2015 and 2020. Notes: Countries on X-Axis are
ordered as countryi countryj , thus linked to ωi→j . The opposite weight ωj→i = 1 − ωi→j refers to the weight of countryj countryi
• Gradient Boosting. The Gradient Boosting model has function for the layer is the rectified linear unit
least square regression as loss function, a learning function. It uses an adam solver with minibatches of
rate of 0.1 and a number of estimators of 100 (which size 50.
is equivalent to the number of boosting stages to
perform). A.3 Additional figures and tables
• Multi-Layer Perceptron. The MLP Regressor has 2 Some additional figures and tables cited in the core of the
hidden layers of 100 neurons each. The activation text are found below.
Table 4 MAE comparison of the different models with and without day/corridor dummies
Linear KNN G-Boost MLP Linear KNN G-Boost MLP
Panel A: No dummies Panel B: Day dummies
avg MAE 0.201 0.019 0.042 0.057 0.179 0.181 0.056 0.059
std MAE (0.005) (0.001) (0.001) (0.003) (0.004) (0.005) (0.001) (0.003)
avg RMSE 0.287 0.043 0.064 0.089 0.259 0.269 0.084 0.090
std RMSE (0.009) (0.005) (0.002) (0.008) (0.008) (0.008) (0.002) (0.004)
Panel C: Corridor dummies Panel D: Corridor & Day dummies
avg MAE 0.156 0.018 0.037 0.048 0.134 0.020 0.049 0.038
std MAE (0.006) (0.001) (0.001) (0.004) (0.005) (0.001) (0.001) (0.003)
avg RMSE 0.231 0.043 0.059 0.086 0.203 0.047 0.077 0.064
std RMSE (0.010) (0.005) (0.002) (0.009) (0.009) (0.005) (0.002) (0.005)
Notes: The table compares the performances of the 4 different approaches with and without the day- and corridor-specific dummies. All models are estimated with
directional priors. Errors are computed from a 10-fold cross-validation on the whole data set
Docquier et al. Globalization and Health (2022) 18:41 Page 15 of 17
Table 5 Averaged feature ranking across models and specifications without directional priors
Panel A: Corridor & Day dummies Panel B: Corridor dummies
Features Linear KNN G-Boost MLP Avg. Linear KNN G-Boost MLP Avg.
C1 School closures 100% 78% 98% 91% 93% 100% 100% 86% 86% 93%
C3 Cancel public events 14% 100% 79% 84% 69% 21% 100% 60% 76% 64%
C6 Stay home requirement 56% 18% 78% 71% 56% 25% 23% 64% 38% 38%
C7 Restr. Internal movement 6% 97% 20% 100% 56% 1% 84% 27% 100% 53%
C4 Restrict gatherings 28% 60% 80% 49% 54% 9% 76% 65% 64% 53%
H2 Testing policy 11% 4% 64% 64% 36% 26% 2% 49% 30% 36%
New Covid deaths 3% 10% 100% 0% 28% 0% 77% 100% 0% 44%
C8 Inter. travel controls 0% 8% 47% 44% 25% 3% 17% 44% 32% 24%
H3 Contact tracing 18% 20% 20% 35% 23% 12% 1% 19% 32% 16%
New Covid cases 11% 0% 46% 35% 23% 11% 76% 63% 87% 59%
C5 Close public transport 26% 7% 0% 43% 19% 15% 0% 0% 31% 11%
C2 Workplace closing 2% 34% 12% 21% 17% 2% 46% 23% 33% 26%
Notes: The different features are ranked following the permutation importance method. For each approach, we provide results obtained with the model including
day/corridor dummies (cols. 1-5) and the version including corridors dummies only (cols. 6-10). Directional priors are not included. The importance values of each feature is
computed over 10 permutations using the negative mean absolute error (MAE). The origin- and destination-specific features importance are aggregated by taking the mean
between the 2. Finally, the resulted values are scaled between 0% and 100% separately for each model. The last column in each panel presents the mean value of importance
averaged over the four models. The features are ranked according to the average importance of the models including the corridor and day dummies
Table 6 Feature ranking including lagged epidemiological conditions
Panel A: Corridor & Day dummies Panel B: Corridor dummies
Features Linear KNN G-Boost MLP Avg. Linear KNN G-Boost MLP Avg.
C1 School closing 100% 69% 81% 68% 79% 100% 83% 79% 97% 90%
C3 Cancel public events 10% 100% 56% 78% 61% 19% 100% 58% 77% 63%
C7 Restr. Internal movement 5% 89% 22% 100% 54% 4% 74% 20% 100% 49%
C6 Stay home requirements 60% 20% 79% 55% 54% 27% 24% 74% 31% 39%
C4 Restrictions gatherings 12% 57% 100% 33% 51% 5% 74% 100% 32% 53%
H2 Testing policy 12% 6% 69% 54% 35% 20% 2% 67% 29% 30%
H3 Contact tracing 23% 15% 37% 29% 26% 21% 0% 34% 34% 22%
C5 Close public transport 25% 11% 7% 32% 19% 14% 5% 4% 33% 14%
C8 Inter. travel controls 0% 7% 30% 28% 16% 11% 16% 28% 21% 19%
C2 Workplace closing 0% 32% 8% 19% 15% 2% 41% 5% 12% 15%
New Covid cases t − 7 12% 0% 8% 12% 8% 14% 34% 6% 46% 25%
New Covid deaths t 4% 12% 12% 0% 7% 10% 49% 13% 12% 21%
New Covid cases t 1% 1% 0% 24% 7% 4% 41% 0% 68% 28%
New Covid cases t − 14 4% 1% 9% 8% 6% 6% 33% 8% 0% 12%
New Covid deaths t − 14 0% 12% 6% 5% 6% 0% 53% 7% 21% 20%
New Covid deaths t − 7 1% 10% 4% 3% 5% 8% 48% 4% 44% 26%
Notes: The different features are ranked following the permutation importance method. The importance values of each feature is computed over 10 permutations using the
negative mean absolute error (MAE). Four new variables are inserted in addition to the ones includes in the regression: 7- and 14-days of new Covid cases and deaths are
included. For each approach, we provide results obtained with the model including day/corridor dummies (cols. 1-5) and the version including corridors dummies only (cols.
6-10). Directional priors are not included. The origin- and destination-specific features importance are aggregated by taking the mean of the 2. Finally, the resulted values are
scaled between 0% and 100% separately for each model. The last column in each panel presents the mean value of importance averaged over the four models. The features
are ranked according to the average importance of the models including the corridor and day dummies
Docquier et al. Globalization and Health (2022) 18:41 Page 16 of 17
Abbreviations the first wave of covid-19 in england and wales. SSM-Popul Health.
EM: Econometric Modelling; EU: European Union; FB: Facebook Inc.; G-Boost: 2021;14:100799.
Gradient Boosting; KNN: K-nearest neighbors method; MAE: Mean Absolute 8. Chen S, Yang J, Yang W, Wang C, Bärnighausen T. Covid-19 control in
Error; ML: Machine Learning; MLP: Multi-layer Perceptron; NPIs: china during mass population movements at new year. Lancet. 2020;395:
non-pharmaceutical interventions; OxCGRT: Oxford Covid-19 Response 764–66.
Tracker; PCA: Principal Component Analysis; RSME: Root Mean Squared Error 9. Ruktanonchai NW, Floyd JR, Lai S, Ruktanonchai CW, Sadilek A,
Rente-Lourenco P, Ben X, Carioli A, Gwinn J, Steele JE, Prosper O,
Acknowledgments Schneider A, Oplinger A, Eastham P, Tatem AJ. Assessing the impact of
The second, third and fourth authors acknowledge financial support from the coordinated covid-19 exit strategies across europe. Science.
ARC convention on “New approaches to understanding and modeling global 2020;369(6510):1465–70. https://doi.org/10.1126/science.abc5096.
migration trends” (convention 18/23-091). https://science.sciencemag.org/content/369/6510/1465.full.pdf.
10. Lee K, Worsnop CZ, Grépin KA, Kamradt-Scott A. A global coordination
Authors’ contributions on cross-border travel and trade measures crucial to covid-19 response.
F.D. and P.S. conceived the presented idea. F.D., N.G., P.S. and F.S. contributed Lancet. 2020;395:1593–95.
to the design and implementation of the research, to the analysis of the 11. Errett NA, Sauer LM, Rutkow L. An integrative review of the limited
results and to the writing of the manuscript. F.D., F.S. and P.S. collected the evidence of international travel bans as an emerging infectious disease
data. F.S. cleaned the data and produced descriptive graphs. N.G. and F.S. disaster control measure. J Emerg Manag. 2020;18:7–14.
implemented the EM and ML modelling. All authors discussed the results, 12. Tian H, Liu Y, Li Y, Wu2 C-H, Chen B, Kraemer MUG, Li B, Cai J, Xu B,
drafted and critically revised the article. The authors read and approved the Yang Q, Wang B, Yang P, Cui Y, Song Y, Zheng P, Wang Q, Bjornstad
final manuscript. ON, Yang R, Grenfell BT, Pybus OG, Dye C. An investigation of
transmission control measures during the first 50 days of the covid-19
Funding epidemic in china. Science. 2020;368:638–42.
Felix Stips gratefully acknowledges financial support from Luxembourg 13. Kraemer MUG, Yang C-H, Gutierrez B, Wu C-H, Klein B, Pigott DM,
National Research Fund (FNR) under the ACROSS Doctoral Training Unit (grant Group OC-DW, du Plessis L, Faria NR, Li R, Hanage WP, Brownstein JS,
n° PRIDE19/14302992). Layan M, Vespignani A, Tian H, Dye C, Pybus OG, Scarpino SV. The
effect of human mobility and control measures on the covid-19 epidemic
Availability of data and materials in china. Science. 2020;497:493–97.
The datasets supporting the conclusions of this article are available in the 14. Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, Piontti
Zenodo repository Cross-border-Mobility-Responses-to-Covid-19-in-Europe, APY, Mu K, Ross L, Sun K, Viboud C, Xiong X, Yu H, Halloran ME,
https://doi.org/10.5281/zenodo.4719559 Longini Jr IM, Vespignani A. The effect of travel restrictions on the spread
of the 2019 novel coronavirus (covid-19) outbreak. Science. 2020;368:
Ethics approval and consent to participate 395–400.
No ethics approval or consent required. 15. Askitas N, Tatsiramos K, Verheyden B. Estimating worldwide effects of
non-pharmaceutical interventions on covid-19 incidence and population
Consent for publication mobility patterns using a multiple-event study. Sci Rep. 2021;11(1972):
Not applicable. 41598–02181442.
16. Inc. F, Facebook Data for Good. https://dataforgood.fb.com/. Accessed 19
Competing interests Feb 2021.
The authors declare that they have no competing interests. 17. Rampazzo F, Bijak J, Vitali A, Weber I, Zagheni E. A Framework for
Estimating Migrant Stocks Using Digital Traces and Survey Data: An
Author details Application in the United Kingdom. Demography. 2021;58(6):2193–218.
1 Crossing Borders, Luxembourg Institute for Socio-Economic Research (LISER), https://doi.org/10.1215/00703370-9578562.
Esch-sur-Alzette, Luxembourg. 2 Institute for Information and Communication 18. Alexander M, Zagheni E, Polimis K. The impact of hurricane maria on
Technologies, Electronics and Applied Mathematics (ICTEAM), Université out-migration from puerto rico: Evidence from facebook data. Popul Dev
catholique de Louvain, Louvain-la-Neuve, Belgium. Rev. 2019;45(3):617–30.
19. Ribeiro FN, Benevenuto F, Zagheni E. How Biased is the Population of
Received: 3 May 2021 Accepted: 25 March 2022 Facebook Users? Comparing the Demographics of Facebook Users with
Census Data to Generate Correction Factors. In: 12th ACM Conference on
Web Science. WebSci ’20. New York: Association for Computing
Machinery; 2020. p. 325–34. https://doi.org/10.1145/3394231.3397923.
References Accessed 01 Dec 2021.
1. Zhang A, Wang A. Human Mobility and Smart City. Sch Community 20. Dong E, Du H, Gardner L. An interactive web-based dashboard to track
Encycl. 2021. https://encyclopedia.pub/entry/6764. Accessed 12 04 2022. COVID-19 in real time. Lancet Infect Dis. 2020;20(5):533–34. https://doi.
2. Caselli F, Grigoli F, Sandri D, Spilimbergo A. Mobility under the COVID-19 org/10.1016/S1473-3099(20)30120-1.
pandemic: Asymmetric effects across gender and age. IMF Econ Rev. 21. Hale T, Webster S, Petherick A, Phillips T, Kira B. Oxford COVID-19
2020;70(1):105–38. Government Response Tracker, Blavatnik School of Government. Data
3. Chetty R, Friedman J, Hendren N, Stepner M, Team, The Opportunity retrieved from Oxford Oxford Covid-19 Government Response Tracker
Insights. The Economic Impacts of COVID-19: Evidence from a New Public (OxCGRT) Github page. 2020. https://github.com/OxCGRT/covid-policy-
Database Built Using Private Sector Data. Cambridge: National Bureau of tracker. Accessed 25 Apr 2021.
Economic Research; 2020, p. w27431. https://doi.org/10.3386/w27431. 22. Beine M, Bertoli S, Fernández-Huertas Moraga J. A Practitioners’ Guide to
4. Goolsbee A, Syverson C. Fear, lockdown, and diversion: Comparing Gravity Models of International Migration. World Econ. 2016;39(4):496–
drivers of pandemic economic decline 2020. J Public Econ. 2021;193: 512. https://doi.org/10.1111/twec.12265. _eprint: https://onlinelibrary.
104311. https://doi.org/10.1016/j.jpubeco.2020.104311. wiley.com/doi/pdf/10.1111/twec.12265. Accessed 16 Feb 2022.
5. Maloney WF, Taskin T. Determinants of Social Distancing and Economic 23. Letouz E, Purser M, Rodriguez F, Cummins M. Revisiting the
Activity During COVID-19: A Global View. Rochester: Social Science Migration-Development Nexus: A Gravity Model Approach. Hum Dev Rep
Research Network; 2020. https://papers.ssrn.com/abstract=3599572. Off (HDRO), U N Dev Program (UNDP), Hum Dev Res Pap (2009 to
6. Glaeser E, Gorback C, Redding S. How Much does COVID-19 Increase present). 2009. https://mpra.ub.uni-muenchen.de/19227/.
with Mobility? Evidence from New York and Four Other U.S. Cities. 24. Peterson LE. K-nearest neighbor. Scholarpedia. 2009;4(2):1883. https://doi.
Cambridge: National Bureau of Economic Research; 2020, p. w27519. org/10.4249/scholarpedia.1883. Accessed 24 Mar 2021.
https://doi.org/10.3386/w27519. 25. Friedman JH. Greedy Function Approximation: A Gradient Boosting
7. Basellini U, Alburez-Gutierrez D, Del Fava E, Perrotta D, Bonetti M, Machine. Ann Stat. 2001;29(5):1189–232. Publisher: Institute of
Camarda CG, Zagheni E. Linking excess mortality to mobility data during Mathematical Statistics. Accessed 24 Mar 2021.
Docquier et al. Globalization and Health (2022) 18:41 Page 17 of 17
26. Hinton GE. Connectionist learning procedures. In: Kodratoff Y, Michalski
RS, editors. Machine Learning. San Francisco: Morgan Kaufmann; 1990. p.
555–610. https://doi.org/10.1016/B978-0-08-051055-2.50029-8.
27. Glorot X, Bengio Y. Understanding the difficulty of training deep
feedforward neural networks. In: Proceedings of the Thirteenth
International Conference on Artificial Intelligence And Statistics. Sardinia:
JMLR Workshop and Conference Proceedings; 2010. p. 249–56. ISSN:
1938-7228.
28. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O,
Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A,
Cournapeau D, Brucher M, Perrot M, Duchesnay E. Scikit-learn: Machine
learning in Python. J Mach Learn Res. 2011;12:2825–30.
29. Altmann A, Toloşi L, Sander O, Lengauer T. Permutation importance: a
corrected feature importance measure. Bioinformatics. 2010;26(10):
1340–7. https://doi.org/10.1093/bioinformatics/btq134.
30. Molnar C. Interprtable machine learning: Leanpub; 2018. https://leanpub.
com/interpretable-machine-learning.
31. Vannoni M, McKee M, Semenza JC, Bonell C, Stuckler D. Using
volunteered geographic information to assess mobility in the early phases
of the covid-19 pandemic: a cross-city time series analysis of 41 cities in
22 countries from march 2nd to 26th 2020. Glob Health. 2020;16(1):1–9.
32. Stoto MA, Woolverton A, Kraemer J, Barlow P, Clarke M. COVID-19 data
are messy: analytic methods for rigorous impact analyses with imperfect
data. Glob Health. 2022;18(1):2. https://doi.org/10.1186/s12992-021-
00795-0. Accessed 09 Feb 2022.
33. Spyratos S, Vespe M, Natale F, Weber I, Zagheni E, Rango M.
Quantifying international human mobility patterns using facebook
network data. PloS ONE. 2019;14(10):0224134.
34. Abel GJ, Cohen JE. Bilateral international migration flow estimates for 200
countries. Sci Data. 2019;6(1):1–13.
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