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Journal of Geographical Systems

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23-05-2021 | Original Article

The propagation effect of commuting to work in the spatial transmission of COVID-19

Authors: Timo Mitze, Reinhold Kosfeld

Published in: Journal of Geographical Systems | Issue 1/2022

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Abstract

This work is concerned with the spatiotemporal dynamics of the coronavirus disease 2019 (COVID-19) in Germany. Our goal is twofold: first, we propose a novel spatial econometric model of the epidemic spread across NUTS-3 regions to identify the role played by commuting-to-work patterns for spatial disease transmission. Second, we explore if the imposed containment (lockdown) measures during the first pandemic wave in spring 2020 have affected the strength of this transmission channel. Our results from a spatial panel error correction model indicate that, without containment measures in place, commuting-to-work patterns were the first factor to significantly determine the spatial dynamics of daily COVID-19 cases in Germany. This indicates that job commuting, particularly during the initial phase of a pandemic wave, should be regarded and accordingly monitored as a relevant spatial transmission channel of COVID-19 in a system of economically interconnected regions. Our estimation results also provide evidence for the triggering role of local hot spots in disease transmission and point to the effectiveness of containment measures in mitigating the spread of the virus across German regions through reduced job commuting and other forms of mobility.

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Tizzoni et al. (2020) also point to the potential problem of overestimation of mobility flows, such as commuting networks, when mobile phone rather than census data are used.

Other types of region-scale models are, for instance, presented in Bertozzi et al. (2020).

We provide a summary of different methods in the online appendix.

See the online appendix for a stylized simulation model that highlights the concept of (spatial) co-integration and error correction applied to the case of epidemic disease modeling at the regional level.

Different from the approach in Beenstock and Felsenstein (2010), we apply the SP-ECM framework to a univariate and not multivariate case. While the multivariate case allows the researcher to include two long-run residual adjustment terms in the SP-ECM equation, namely one for adjustment processes related to within-group cointegration across variables and a second “spatialized” residual term to account for between-group spatial adjustment processes, we only account for the latter through \(u_{i,t - p}\). Moreover, while the inclusion of between-group adjustment processes often takes place on an ad hoc basis in spatial econometric applications, we provide theoretical priors with regard to the expected time path in the case of epidemic diffusion (see the online appendix).

For instance, Berlemann and Haustein (2020) use two lags (L = 2, M = 2) in the epidemic component of their HHH model for Germany arguing that this lag is sufficient to capture the time-series properties of new infections. However, the authors do not explicitly test their choice against some information criteria for evaluating the model fit.

See the online appendix for conceptual details.

We, though, apply count data models as a robustness check. Details are given in the online appendix.

As discussed in Blundell et al. (2002), a solution to this inconsistency problem would be to apply a quasi-differences GMM estimator, which may, however, suffer from a weak instrument bias if time series are highly persistent.

See https://www.bbsr.bund.de/BBSR/DE/forschung/raumbeobachtung/Raumabgrenzungen/deutschland/regionen/AMR/Arbeitsmarktregionen.html for further details.

Updated data for the most recent definition of commuting zones in Germany in 2016 are obtained from the supplementary online materials available at: https://www.iab.de/389/section.aspx/Publikation/k110222301.

For further information on the IAB gross commuting database, see also http://www.iab.de/infoplattform/pendler.

Summary information on spatial weight matrices is given in the online appendix.

The model’s explanatory power increases with the inclusion of additional lags starting from a simple AR(1) specification but becomes smaller for a lag size larger than L = 4 and M = 4. We thus argue that the latter lag structure is sufficient to capture both the short-run temporal and spatial dynamics of new infections.

Regression results only including commuting-based space–time lags are reported in the online appendix.

The online appendix additionally assesses the robustness of the estimated effects for alternatively specified outcome variables in the linear dynamic panel data model and alternative estimators including a negative binomial (NegBin) panel data model with random and fixed effects. However, since model properties of the NegBin specification are unclear in dynamic panel settings (e.g., related to the initial condition problem in nonlinear models), the obtained (unadjusted) estimates should only be seen as a rough proxy for comparison purposes. All in all, these specifications provide similar (or even higher) estimates for the included space–time lag coefficients for the short-run dynamics and thus underline parameter robustness in the baseline SP-ECM rendering the reported DFE coefficients conservative estimates of the propagation effect of commuting to work.

In the estimation of the long-run specification as shown in Eq. (2), we avoid estimating specifications with higher order spatial weights by assuming strict exogeneity of one of the two included spatial lag terms. The results show that the estimated coefficients remain very stable regardless which spatial lag term is treated as exogenous right-hand side regressor. For the results shown in Table 2, we have maximized the concentrated log likelihood for the general spatial weighting matrix \({\mathbf{W}}\) while included the commuting-based spatial lag term as an exogenous regressor.

The online appendix additionally shows the contribution of the individual model components for the in-sample fit on the basis of proportional reduction in error (PRE) tests.

In addition to imposing higher economic costs, Espinoza et al. (2020) argue on the basis of a historical analysis of earlier epidemics that more extreme mobility restrictions may also bear undesirable epidemiological consequences.

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Title: The propagation effect of commuting to work in the spatial transmission of COVID-19
Authors: Timo Mitze
Reinhold Kosfeld
Publication date: 23-05-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Geographical Systems / Issue 1/2022
Print ISSN: 1435-5930
Electronic ISSN: 1435-5949
DOI: https://doi.org/10.1007/s10109-021-00349-3

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