Mobility-based real-time economic monitoring amid the COVID-19 pandemic

Mobility restrictions have been identified as key non-pharmaceutical interventions to limit the spread of the SARS-COV-2 epidemics. However, these interventions present significant drawbacks to the social fabric and negative outcomes for the real economy. In this paper we propose a real-time monitoring framework for tracking the economic consequences of various forms of mobility reductions involving European countries. We adopt a granular representation of mobility patterns during both the first and second waves of SARS-COV-2 in Italy, Germany, France and Spain to provide an analytical characterization of the rate of losses of industrial production by means of a nowcasting methodology. Our approach exploits the information encoded in massive datasets of human mobility provided by Facebook and Google, which are published at higher frequencies than the target economic variables, in order to obtain an early estimate before the official data becomes available. Our results show, in first place, the ability of mobility-related policies to induce a contraction of mobility patterns across jurisdictions. Besides this contraction, we observe a substitution effect which increases mobility within jurisdictions. Secondly, we show how industrial production strictly follows the dynamics of population commuting patterns and of human mobility trends, which thus provide information on the day-by-day variations in countries’ economic activities. Our work, besides shedding light on how policy interventions targeted to induce a mobility contraction impact the real economy, constitutes a practical toolbox for helping governments to design appropriate and balanced policy actions aimed at containing the SARS-COV-2 spread, while mitigating the detrimental effect on the economy. Our study reveals how complex mobility patterns can have unequal consequences to economic losses across countries and call for a more tailored implementation of restrictions to balance the containment of contagion with the need to sustain economic activities.


Supplementary Information
State space representation of the model Below are the details for the state space representation of equation (8) as specified by the Eqs. (2)-(7), for p = 1, r = 3 and a single monthly variable y M t . This means that the following formulation refers to one lag common factors, which collect the global component f G and discriminate between FB and Google variables f F B and f GOOG . The state space representation of equation (8) articulates as follows: where = ( 1,t , ..., n,t ) and e = (e 1,t , ..., e n,t ) .
The block specific factor structure further implies that:

Expectation Maximization algorithm
The parameters θ of the state space form of equation (8) are estimated by the Expectation Maximisation (EM) algorithm [1,2,3]. The algorithm is a popular solution to problems, for which latent or missing data yield a direct maximisation of the likelihood function intractable or computationally difficult. The basic principle behind the EM is to write the likelihood in terms of observable as well as latent variables and given the available data Ψ v obtain the maximum likelihood estimates in a sequence of two alternating steps. Precisely, iteration τ + 1, with τ = 1, ..., T , would consist of the following steps: • The E-Step in which the expectation of the log-likelihood conditional on the data is calculated using the estimates from the previous iteration θ(τ ) • The M-Step in which the new parameters, θ(τ + 1), are estimated through the maximisation of the expected log-likelihood (from the previous iteration) with respect to θ.
We first estimate µ and µ M by sample means and use the de-meaned data throughout the EM steps. To deal with missing observations inx t we introduce selection matrices [4] W t and W M t . They are diagonal matrices of size n and 1, respectively, with ones corresponding to the non-missing values in x t and y M t , respectively. For the sake of simplicity, we first consider the case without restrictions on Γ, Γ M , A 1 and Q implied by block specific factors. To account for the restrictions imposed by group specific factors, we need to split the parameters in Γ into blocks and repeating the computations for each block. The matrix of loadings for the daily variables assumes the following form: For deriving the matrix of loadings for the monthly variables, let The unrestrictedΓ ur M = (Γ ur M , ..., 30Γ ur M , ..., Γ ur M ) is given by: The restrictedΓ M is given by:Γ The autoregressive coefficients in the factor VAR are: The covariance matrix in the factor VAR has the following form: The autoregressive coefficients in the AR representation for the idiosyncratic component of the daily variables can be written as: Hence, the variance in the AR representation for the idiosyncratic component of the daily variables is: where i = 1, ..., n, M . The conditional expectations (the E-step) in the expressions above are computed using the Kalman smoother on the state space representation of equation (8) with the previous iteration parameters θ(τ ). The initial parameters θ(0) are obtained on the basis of principal components analysis [5].

Supplementary Figures and Tables
Variable Definition

Variables
Lags Factors GOOG lag1 r av , g av , w av , s av

Data representativity
In this section we investigate whether the variables we employed in th work, which are based on phone-tracking movements, are representative and constitute a good proxy for workers travelling and thus commuting on the transport infrastructure; or whether these variables embed information concerning the population densities in different geographical areas.
We study the representativity of Facebook mobility data as a proxy of commuting, by performing a comparison exercises with the 2011 commuting network provided by the Italian National Institute of Statistics (ISTAT), which encodes movements of workers travelling between municipalities, recorded in the last census. We tread carefully in the comparison, first because the commuting network contains information only about residents who travel for working reasons, and second because the information refers to the Italian mobility patterns of 9 years ago. On the other side, this data is not biased towards individuals who own a phone and are registered on social networks, as in Facebook data, therefore we believe it is useful to further validate the representativity of the mobility data observed before entering the lockdown phase. We conduct this further analysis on the Italian mobility network, since it is the only data to us available at present. To make a consistent comparison we filtered out those paths where the number of commuters is less than 10 (indeed Facebook employs this value as threshold to include an observation, see [6]) and retained only municipalities which are present also in our dataset (approx. 1/3 of all Italian municipalities). Besides, we build an averaged graph of mobility over a window of 14 days before the Italian national lockdown of the 10th of March, and we aggregate the network at NUTS3 level. Then, we performed Pearson's correlation test to the following metrics: In-Strength and Out-Strength of nodes, i.e. the number of incoming commuters and outgoing commuters. In all cases we find a significant positive correlation, i.e. 0.74 and 0.62 for In-and Out-Strength respectively, as reported in the left and central panels of Secondly, we further investigate whether commuting patterns observed within provinces in the Facebook dataset are consistent with the provinces' population. This last information has been obtained from the 15th General Census of Population and Housing developed by the Italian National Institute of Statistics (ISTAT). The database contains information, at sub-municipal levels, on the demographic and social structure of the Italian population. In particular for each district, we rely on information on population size, available in the Employment Register created in 2011 in the occasion of the CIS2011 Virtual Business Census and updated annually, starting from 2012 (see [7]) and we aggregate this information at province (NUTS3) level to be consistent with Facebook data. The right panel of Fig. 5 shows a positive and significant correlation between the two measures (0.93). This validates the use of commuting patterns as key features to provide us with a solid background for our nowcasting model.