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\begin{fmbox}
\dochead{Research}

\title{Cross-border Mobility Responses to Covid-19 in Europe: New Evidence from Facebook Data}


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\appendix

\section{Appendix -- Figures and Tables}

\subsection{Representativeness of Facebook data} \label{sec:represent}
A critical question relates to the representativeness of FB data. On average, comparison between the number of FB users and population size by country reveals that the number of FB users with \textit{location services enabled} represents 5.6\% of the population in Europe, on average. However, this fraction is rather uniform across countries, which suggests that FB data might be representative of the population as a whole. This does not mean, however, that data on FB users are representative of the population of cross-border movers, as using internet connection or activating location services abroad can be costly \cite{spyratos2019}. To address this point, we produce estimates of the number of daily cross-border inflows in the pre-Covid period, and compare them with FB data. We collect data on commuting flows from the Labor Force Survey for 2019,\footnote{Labor Force Surveys are provided by Eurostat. We use data on commuting by NUTS2 region, and allocate commuters aged 15 to 64 by destination on the basis of contiguity links with other countries. When a NUTS region shares several contiguity links, we share the number of commuters proportionately to the level of income per capita in the destination country. To identify daily movements, we assume that each commuter spend 4 days per week in the place of work, and multiply LFS number by $4/7$.} data on air passengers as of March 2019,\footnote{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.} and estimates of immigration flows from \cite{abel2019}.\footnote{The latter are available until the year 2015; we multiply them by 1.5 to proxy the level in 2019. To identify daily movements, we divide annual inflows by 360.}

\begin{center}
[Table \ref{tab:Traffic} about here]
\end{center}

Overall, Table \ref{tab:Traffic} shows that migration flows account for a tiny (say negligible) proportion of daily movements, implying that FB data mostly capture commuting flows and business travels, as well as holiday-maker's moves in vacation periods. This implies that the largest flows are observed between contiguous countries and business partners. Combining corridors available in our sample and corridors involving non-EU countries, Figure \ref{fig:repres} shows that FB data as of the first week of March 2020 are highly correlated with estimates of actual flows in the year 2019, which suggests that FB data might also be representative of cross-border movements.

\begin{center}
[Figure \ref{fig:repres} about here]
\end{center}

\subsection{Parameters of the ML methods} \label{sec:parameters}

We describe in this section the parameters of the different ML models used in this paper. In order to tune the models, a boosting sample corresponding of 70\% of the whole dataset is used (from the 29\textsuperscript{th} February 2020 until the 16\textsuperscript{th} November 2020). We use the following parameters:
\begin{itemize}
    \item \textit{K Nearest Neighbors.} The models uses 5 neighbors and it has the distance metric as weight function.
    \item \textit{Gradient Boosting.} The Gradient Boosting model has least square regression as loss function, a learning rate of 0.1 and a number of estimators of 100 (which is equivalent to the number of boosting stages to perform).
    \item \textit{Multi-Layer Perceptron.} The MLP Regressor has 2 hidden layers of 100 neurons each. The activation function for the layer is the rectified linear unit function. It uses an adam solver with minibatches of size 50.
\end{itemize}

\subsection{Additional figures and tables} \label{sec:addtabfig}

Some additional figures and tables cited in the core of the text are found below.

\begin{center}
[Figure \ref{fig:Weights} about here]
\end{center}

\begin{center}
[Table \ref{tab:PredErrorFixedEffects} about here]
\end{center}

\begin{center}
[Table \ref{tab:FeatureRanking} about here]
\end{center}

\begin{center}
[Table \ref{tab:LagRanking} about here]
\end{center}

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\begin{figure}[ht!]
\centering
\caption{Daily traffic estimates (X-axis) and FB data (Y-axis) by corridor (1 March 2020)}\label{fig:repres}
\includegraphics[width=\textwidth]{Fig_Repres.jpg}
\scriptsize 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 \cite{abel2019} 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.
\end{figure}

\begin{figure}[ht!]
\centering
\caption{Distribution of Weights}  \label{fig:Weights}
\includegraphics[width=\textwidth]{Weights.pdf}
\scriptsize 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 \cite{abel2019} for the year 2015, assuming a conservative 50\% growth in the flows between 2015 and 2020. Notes: Countries on X-Axis are ordered as $country_{i}$ $country_{j}$, thus linked to $\omega_{i\rightarrow j}$. The opposite weight $\omega_{j \rightarrow i}=1-\omega_{i \rightarrow j}$ refers to the weight of $country_{j}$ $country_{i}$.
\end{figure}

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\renewcommand \thetable{\thesection .\arabic{table}}
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\begin{table}[ht!]
\centering
\caption{Estimates of the average count of daily cross-border outflows in 2019}\label{tab:Traffic}
\scriptsize
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} lcccccccc }
\toprule
\addlinespace[0.5ex]
 & \multicolumn{4}{c}{\textbf{Daily count estimates}} & & \multicolumn{3}{c}{\textbf{As percent of Total}}  \\
 \cmidrule{2-5} \cmidrule{7-9}
 & Commuters & Air pass. & Migrants & Total & & Commuters & Air pass. & Migrants \\
 \midrule
\addlinespace[0.5ex]
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 \\ \hline
EU15 & 1911359 & 2765826 & 7428 & 4684613 & & 0.408 & 0.590 & 0.001 \\  \hline
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 \\
\addlinespace[0.5ex]
\bottomrule
\end{tabular*}
\begin{tablenotes}
  \linespread{1}
  \item\hspace*{-\fontdimen2\font}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 \cite{abel2019} for the year 2015, assuming a conservative 50\% growth in the flows between 2015 and 2020.
\end{tablenotes}
\end{table}


%\begin{table}[ht!]
%\caption{Model Error Comparison with and without directional priors\strut}
%\label{tab:PredErrorOmega}
%\scriptsize
%\setlength\tabcolsep{0pt}
%\setlength\extrarowheight{0.25ex}
%\begin{threeparttable}
%\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{8}{c} }
%\toprule
%& \multicolumn{4}{c}{\textbf{Panel A: With priors}}
%& \multicolumn{4}{c}{\textbf{Panel B: Without priors}}  \\
%
%\cmidrule{2-5} \cmidrule{6-9}
%
%& Linear & KNN  & G-Boost & MLP & Linear & KNN  & G-Boost & MLP  \\
%
%\midrule
%avg MAE & 0.134 & 0.020 & 0.049 & 0.038  & 0.135 & 0.020 & 0.050 & 0.041 \\
%std MAE & (0.005) & (0.001) & (0.001) & (0.003)  & (0.005) & (0.001) & (0.002) & (0.003) \\
%\addlinespace
%avg RMSE & 0.203 & 0.047 & 0.077 & 0.064  & 0.210 & 0.045 & 0.081 & 0.068 \\
%std RMSE & (0.009) & (0.005) & (0.002) & (0.005)  & (0.010) & (0.06) & (0.006) &  (0.006) \\
%\bottomrule
%\end{tabular*}
%\smallskip
%\begin{tablenotes}
%  \linespread{1}
%  \item\hspace*{-\fontdimen2\font}Notes: The table compares the performances of the 4 different approaches with the directive priors (Panel A: Supervised) and without the directive priors (Panel B: Unsupervised). Both day and corridor indicator variables are used by the models. These MAE and RMSE result from a 10-fold cross-validation on the whole dataset.
%\end{tablenotes}
%\end{threeparttable}
%\end{table}


\begin{table}[ht!]
\caption{MAE comparison of the different models with and without day/corridor dummies}
\label{tab:PredErrorFixedEffects}
\scriptsize
\setlength\tabcolsep{0pt}
\setlength\extrarowheight{0.25ex}
\begin{threeparttable}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{8}{c} }
\toprule
& \multicolumn{4}{c}{\textbf{Panel A: No dummies}}
& \multicolumn{4}{c}{\textbf{Panel B: Day dummies}}  \\
\cmidrule{2-5} \cmidrule{6-9}
& Linear & KNN  & G-Boost & MLP & Linear & KNN  & G-Boost & MLP  \\
\midrule
\addlinespace[0.5ex]
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) \\
\addlinespace
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) \\
\addlinespace[0.5ex]
\midrule
& \multicolumn{4}{c}{\textbf{Panel C: Corridor dummies}}
& \multicolumn{4}{c}{\textbf{Panel D: Corridor \& Day dummies}}  \\
\cmidrule{2-5} \cmidrule{6-9}
& Linear & KNN  & G-Boost & MLP & Linear & KNN  & G-Boost & MLP  \\
\midrule
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) \\
\addlinespace
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)   \\  \addlinespace[0.5ex]
\bottomrule
\end{tabular*}

\begin{tablenotes}
  \linespread{1}
  \item\hspace*{-\fontdimen2\font}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.
\end{tablenotes}
\end{threeparttable}
\end{table}


\begin{table}[ht!]
\caption{Averaged feature ranking across models and specifications without directional priors\strut} \label{tab:FeatureRanking}

\scriptsize
\setlength\tabcolsep{0pt}
\setlength\extrarowheight{0.25ex}
\begin{threeparttable}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{12}{c} }
\toprule
& & \multicolumn{5}{c}{\textbf{Panel A: Corridor \& Day dummies}}
& & \multicolumn{5}{c}{\textbf{Panel B: Corridor dummies}}  \\

\cmidrule{3-7} \cmidrule{9-13}

\textbf{Features} & & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} & & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} \\

\midrule

\addlinespace[0.5ex]

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\% \\

\textbf{New Covid deaths}	      &  & 3\%   & 10\%  & 100\%     & 0\%   & 28\%   &   & 0\%   & 77\%  & 100\% & 0\%   & 44\% \\

\textit{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\% \\

\textbf{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\% \\

\addlinespace[0.5ex]

\bottomrule

\end{tabular*}

\begin{tablenotes}
  \linespread{1}
  \item\hspace*{-\fontdimen2\font}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.
\end{tablenotes}
\end{threeparttable}
\end{table}


%\begin{table}[ht!]
%\caption{Feature ranking using Index\strut}\label{tab:PCAranking}
%\scriptsize
%\setlength\tabcolsep{0pt}
%\setlength\extrarowheight{0.25ex}
%\begin{threeparttable}
%\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{11}{c} }
%\toprule
%& \multicolumn{5}{c}{\textbf{Panel A: Corridor \& Day IV's}} &
%& \multicolumn{5}{c}{\textbf{Panel B: Corridor IV}}  \\
%\cmidrule{2-6} \cmidrule{8-12}
%\textbf{Features}  & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} & & Linear & KNN  & G-Boost %& MLP & \textbf{Avg.} \\
%\midrule
%\addlinespace[0.5ex]
%\underline{Origin}	        &   &    &   &  &  &  &  &    &    &    &  \\
%\hspace{1ex} Component 1	    & 13\%	 & 75\%	    & 20\%	& 49\%	& 39\%&
%                                & 2\%	& 79\%	& 19\%	& 92\%  & 48\% \\
%\hspace{1ex} Component 2	    & 1\%	& 55\%	& 17\%	& 19\%	& 23\% &
%                                & 8\%	& 41\%	& 17\%	& 38\%  & 26\% \\
%\hspace{1ex} New Covid cases	& 0\%	& 0\%	& 18\%	& 30\%	& 12\% &
%                                & 0\%	&  0\%	&  18\%	&  55\% & 18\%   \\
%\hspace{1ex} New Covid deaths   & 1\%	& 13\%	& 3\%       & 9\%	& 6\%  &
%                                & 0\%	& 2\%	& 2\%	& 23\%	& 7\% \\
%\addlinespace
%\underline{Destination}	        &   &    &   &  &    &  &    &    &    &  \\
%\hspace{1ex} Component 1	& 100\%	& 100\%	& 100\%	& 100\%	& 100\% &
%                            & 100\%	& 100\%	& 100\%	& 100\%	& 100\% \\
%\hspace{1ex} Component 2	& 9\%	& 50\%	& 0\%	& 0\%	& 15\% &
%                            & 1\%	& 36\%	& 0\%	& 33\%	& 17\% \\
%\hspace{1ex} New Covid deaths 	& 5\%	& 14\%	& 6\%	& 11\%	& 9\% &
%                                & 2\%	& 1\%	& 8\%	& 21\%	& 8\% \\
%\hspace{1ex} New Covid cases    & 0\% & 2\%  & 1\%	& 6\%	& 2\%  &
%                                & 0\% & 0\%  & 2\%	& 0\%	& 1\% \\
%\addlinespace[0.5ex]
%\bottomrule
%\end{tabular*}
%\begin{tablenotes}
%  \linespread{1}
%  \item\hspace*{-\fontdimen2\font}Notes: The different features are ranked following the permutation importance method. The ten policy indicators are decomposed on two components by applying two PCA for the origin and destination related features. For each of the approaches, the versions with only corridor IV and the version with day and corridors IV's are presented since they show the best performance. The importance values of each feature is computed over 10 permutations using the negative  mean  absolute  error  (MAE). The origin and destination related features importance are presented separately respectively on the top and the bottom of the table. 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  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 indicator variables.
%\end{tablenotes}
%\end{threeparttable}
%\end{table}


%\begin{table}[ht!]
%\caption{Feature ranking by origin and destination\strut}\label{tab:OriginDestinationranking}
%\scriptsize
%\setlength\tabcolsep{0pt}
%\setlength\extrarowheight{0.25ex}
%\begin{threeparttable}
%\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{11}{c} }
%\toprule
%& \multicolumn{5}{c}{\textbf{Panel A: Corridor \& Day IV's}} &
%& \multicolumn{5}{c}{\textbf{Panel B: Corridor IV}}  \\
%\cmidrule{2-6} \cmidrule{8-12}
%\textbf{Features}  & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} & & Linear & KNN  & G-Boost %& MLP & \textbf{Avg.} \\
%\midrule
%\addlinespace[0.5ex]
%\underline{Origin}	                     &   &    &   &  &  &  &  &    &    &    &  \\
%\hspace{1ex} C1 School closing           & 100\%    & 69\%  & 100\% & 59\%  & 82\% &            % specification with date FE
%                                        & 100\%     & 90\%  & 100\% & 51\%  & 85\% \\           % specification without date FE
%
%\hspace{1ex} C3 Cancel public events 	& 10\%      & 100\%	& 33\%  & 65\%  & 52\% &
%                                        & 7\%	    & 100\%	& 34\%	& 42\%	& 46\% \\
%
%\hspace{1ex} C7 Restr. Internal movement	& 0\%       & 93\%  & 16\%  & 100\% & 52\% &
%                                            & 2\%	    & 80\%	& 31\%	& 90\%	& 51\% \\
%
%\hspace{1ex} H2 Testing policy           & 14\%     & 7\%   & 87\%  & 92\%  & 50\% &
%                                         & 46\%     & 8\%	& 84\%	& 32\%	& 43\% \\
%
%\hspace{1ex} C4 Restrictions gatherings  & 50\%      & 51\%  & 40\%	& 54\%  & 49\% &
%                                        & 22\%	    & 61\%	& 46\%	& 49\%	& 44\% \\
%
%\hspace{1ex} C6 Stay home requirements   & 92\%   	& 16\%  &	12\%& 59\%  & 45\% &
%                                        & 21\%	    & 23\%	& 17\%	& 22\%	& 21\% \\
%
%\hspace{1ex} H3 Contact tracing 	    & 5\%       & 12\%  &	27\%&  44\% &   22\%   &
%                                        & 25\%	    & 0\%	&   30\%&	32\%&	22\% \\
%
%\hspace{1ex} C8 Inter. travel controls 	& 1\%       & 1\%   &	45\%& 40\%  & 22\% &
%                                        & 12\%	    & 12\%	& 44\%	& 5\%	& 18\% \\
%
%\hspace{1ex} New Covid deaths            & 0\%	    & 7\%   &	73\%& 5\%	& 21\% &
%                                        & 1\%	    & 61\%	& 95\%	& 0\%	& 39\% \\
%
%\hspace{1ex} New Covid cases             & 11\%      & 0\%   &	21\%& 52\%  &	 21\%   &
%                                        & 14\%	    & 65\%	& 48\%	& 100\%	& 57\% \\
%
%\hspace{1ex} C5 Close public transport   & 18\%      & 7\%   &	0\% &31\%   &	14\%  &
%                                        & 18\%	    & 5\%	& 0\%	& 26\%	& 12\% \\
%
%\hspace{1ex} C2 Workplace closing        & 1\%	    & 23\%  & 10\%  & 14\%  & 12\% &
%                                        & 10\%	    & 33\%	& 20\%	& 30\%	& 23\% \\          %
%\addlinespace
%\underline{Destination}	        &   &    &   &  &    &  &    &    &    &  \\
%\hspace{1ex} C1 School closing           & 94\%	& 60\%	& 36\%	& 85\%	& 68\% &           %  specification with date FE
%                                         & 89\%	& 75\%	& 53\%  & 54\%	& 68\% \\          % % specification without date FE
%
%%\hspace{1ex} C3 Cancel public events 	& 19\%	& 64\%	& 77\%	& 68\%	& 57\% &
%                                        & 36\%  & 66\%  & 72\%	& 53\%	& 57\% \\
%
%\hspace{1ex} C6 Stay home requirements  & 17\%	& 15\%	& 96\%	& 54\%	& 45\% &
%                                        & 32\%	& 21\%	& 96\%	& 30\%	& 45\% \\
%
%\hspace{1ex} C4 Restrictions gatherings & 6\%	& 48\%	& 70\%	& 25\%	& 37\% &
%                                        & 0\%	& 67\%	& 69\%	& 32\%	& 42\% \\
%
%\hspace{1ex} C7 Restr. Internal movement	&  13\%	& 66\% & 12\% & 58\% & 37\% &
%                                            &  7\% &  59\% & 17\% &	31\% & 29\% \\
%
%\hspace{1ex} New Covid deaths               & 6\%	& 10\%	& 64\%	& 0\%	& 20\% &
%                                            & 4\%	& 67\%	& 83\%	& 9\%	& 41\% \\
%
%\hspace{1ex} C5 Close public transport      &  34\%	& 6\%	& 1\%	& 39\%	& 20\% &
%                                            &  15\%	& 3\%	& 0\%	& 18\%	& 9\% \\
%
%\hspace{1ex} H3 Contact tracing 	    & 31\%	& 21\%	& 2\%	& 14\%	& 17\%  &
%                                        & 2\%	& 9\%	& 4\%	& 13\%	& 7\% \\
%
%\hspace{1ex} C2 Workplace closing       & 5\%	& 33\%	& 7\%	& 23\%	& 17\%  &
%                                        & 0\%	& 47\%	& 20\%	& 16\%	& 21\% \\
%
%\hspace{1ex} C8 Inter. travel controls 	& 0\%	& 12\%	& 20\%	& 32\%	& 16\% &
%                                        &  1\%	& 22\%	& 34\%	& 41\%	& 24\% \\
%
%\hspace{1ex} New Covid cases            & 12\%	& 0\%	& 43\%	& 6\%	& 15\%   &
%                                        & 12\%	& 63\%	& 65\%	& 6\%	& 37\% \\
%
%\hspace{1ex} H2 Testing policy           & 9\%	& 0\%	& 2\%	& 10\%	& 4\% &
%                                         & 7\%	& 2\%	& 4\%	& 11\%	& 6\% \\
%
%\addlinespace[0.5ex]
%
%\bottomrule
%
%\end{tabular*}
%
%\begin{tablenotes}
%  \linespread{1}
%  \item\hspace*{-\fontdimen2\font}Notes: The different features are ranked following the permutation importance method. For each of the approaches, the versions with only corridor IV and the version with day and corridors IV's are presented since they show the best performance. The importance values of each feature is computed over 10 permutations using the negative  mean  absolute  error  (MAE). The origin and destination related features importance are presented separately respectively on the top and the bottom of the table. 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  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 indicator variables.
%\end{tablenotes}
%\end{threeparttable}
%\end{table}


\begin{table}[ht!]
\caption{Feature ranking including lagged epidemiological conditions}\label{tab:LagRanking}
\scriptsize
\setlength\tabcolsep{0pt}
\setlength\extrarowheight{0.25ex}
\begin{threeparttable}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{11}{c} }
\toprule
& \multicolumn{5}{c}{\textbf{Panel A: Corridor \& Day dummies}} &
& \multicolumn{5}{c}{\textbf{Panel B: Corridor dummies}}  \\
\cmidrule{2-6} \cmidrule{8-12}
\textbf{Features}  & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} & & Linear & KNN  & G-Boost & MLP & \textbf{Avg.} \\
\midrule

\hspace{1ex} C1 School closing	& 100\%	& 69\%	& 81\%	& 68\%	& 79\% &
                                & 100\%	& 83\%	& 79\%	& 97\%	& 90\% \\

\hspace{1ex} C3 Cancel public events	& 10\%	& 100\%	& 56\%	& 78\%	& 61\% &
                                        & 19\%	& 100\%	& 58\%	& 77\%	& 63\% \\

\hspace{1ex} C7 Restr. Internal movement	& 5\% &	89\%  &	22\% &	100\% &	54\% &
                                            & 4\% & 74\%  & 20\%	& 100\%	& 49\% \\

\hspace{1ex} C6 Stay home requirements 	& 60\%	& 20\%	& 79\%	& 55\%	& 54\% &
                                        & 27\%	& 24\%	& 74\%	& 31\%	& 39\% \\

\hspace{1ex} C4 Restrictions gatherings	& 12\%	& 57\%	& 100\%	& 33\%	& 51\% &
                                        & 5\%	& 74\%	& 100\%	& 32\%	& 53\% \\

\hspace{1ex} H2 Testing policy	& 12\%	& 6\%	& 69\%	& 54\%	& 35\% &
                                & 20\%	& 2\%	& 67\%	& 29\%	& 30\% \\

\hspace{1ex} H3 Contact tracing	& 23\%	& 15\%	& 37\%	& 29\%	& 26\% &
                                & 21\%	& 0\%	& 34\%	& 34\%	& 22\% \\


\hspace{1ex} C5 Close public transport	& 25\% &	11\%  &	7\% &	32\% &	19\% &
                                        & 14\% & 5\%  & 4\%	& 33\%	& 14\% \\

\hspace{1ex} C8 Inter. travel controls	& 0\%	& 7\%	& 30\%	& 28\%	& 16\% &
                                        & 11\%	& 16\%	& 28\%	& 21\%	& 19\% \\

\hspace{1ex} C2 Workplace closing	& 0\%	& 32\%	& 8\%	& 19\%	& 15\% &
                                    & 2\%	& 41\%	& 5\%	& 12\%	& 15\% \\

\hspace{1ex} New Covid cases $t-7$	& 12\%	& 0\%	& 8\%	& 12\%	& 8\% &
                                & 14\%	& 34\%	& 6\%	& 46\%	& 25\% \\

\hspace{1ex} New Covid deaths $t$	& 4\% &	12\%  &	12\% &	0\% &	7\% &
                                & 10\% & 49\%  & 13\%	& 12\%	& 21\% \\

\hspace{1ex} New Covid cases $t$	& 1\%	& 1\%	& 0\%	& 24\%	& 7\% &
                                & 4\%	& 41\%	& 0\%	& 68\%	& 28\% \\

\hspace{1ex} New Covid cases $t-14$	& 4\%	& 1\%	& 9\%	& 8\%	& 6\% &
                                    & 6\%	& 33\%	& 8\%	& 0\%	& 12\% \\

\hspace{1ex} New Covid deaths $t-14$	& 0\%	& 12\%	& 6\%	& 5\%	& 6\% &
                                    & 0\%	& 53\%	& 7\%	& 21\%	& 20\% \\

\hspace{1ex} New Covid deaths $t-7$	& 1\% &	10\%  &	4\% &	3\% &	5\% &
                                    & 8\% & 48\%  & 4\%	& 44\%	& 26\% \\

\addlinespace[0.5ex]
\bottomrule
\end{tabular*}
\begin{tablenotes}
  \linespread{1}
  \item\hspace*{-\fontdimen2\font}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.
\end{tablenotes}
\end{threeparttable}
\end{table}


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