The diffusion of COVID-19 across Italian provinces: a spatial dynamic panel data approach with common factors

ABSTRACT

This study adopts a spatial dynamic panel data model with common factors and a connectivity matrix based on cross-province population flows to help explain the spread of COVID-19 infections across Italian provinces during the period 2020–21. We find that an increase in the infections in a province has a positive and statistically significant effect on neighbours’ infections, which highlights the relevance of spatial spillover effects. This finding is robust to several robustness checks. Furthermore, we investigate cross-provincial transmission heterogeneity using a heterogeneous spatial dynamic panel, which provides novel insights into the diffusion patterns of the disease.

KEYWORDS:

• spatial dynamic panel data
• common factors
• spillovers
• heterogeneity
• COVID-19 pandemic
• Italian provinces

JEL:

• C11
• C23
• I18
• R19

ACKNOWLEDGEMENTS

The thorough comments and suggestions from four anonymous referees are gratefully acknowledged. The comments and suggestions of Davide Fiaschi and Giancarlo Manzi are also acknowledged.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1. Critical values in the CADF test are usually smaller than the common value of –1.96 at the 5% significance level and depend on the sizes of N and T. Generally, they fluctuate between –2 and –3.

2. The common factor term can be treated as exogenous explanatory variables based on the assumption that the contribution of each single province to the cross-sectional averages is small.

3. Alternative measurements of human mobility, based on Facebook Data for Good Program (which exhibit a correlation of 0.79 with Google’s data), suggest that within-province flows (with origin in $i$ and destination $i$) account for most of movements in Italy during our sample period (i.e., 96.5%). On the other hand, the estimated median ratio of the inflows to within-province flows in such a dataset has ranged from 0.5% to 4.5%, with the sample median being about 3.5%. In Table B22 in Appendix B in the supplemental data online, we take a different route to investigate the effect of mobility by differentiating within-province flows from provincial inflows. Thus, we follow Han et al. (2021) and provide complementary results obtained from a modified version of equation (5). In that specification, instead of using Google’s data, we use Facebook Data for Good Program.

4. For more details on the construction of the dataset, the sources employed and descriptive statistics of time-varying predictors, see Table A1 in Appendix A in the supplemental data online.

5. In Figure C1a in Appendix C in the supplemental data online, we report the correlation between the matrix of weekly between-province population flows pre-pandemic and during the pandemic. We show that the directionality and relative importance of between-province movements is quite persistent over time, as it displays an average correlation of 0.96. Figure C1b online reports similar results when using Facebook’s data, obtaining a correlation of 0.99. Finally Figure C3 and Table C2 online report the estimated daily population flows using Enel X data and Facebook data.

6. In Table C1 and Figure C2 in Appendix C in the supplemental data online, we report the cross-correlations among $W$ matrices and plot their sparsity patterns, respectively.

7. Given that the intrinsic nature of the data on daily infections is count, in Table B23 in Appendix B in the supplemental data online, we provide further evidence of the robustness of the role played by spillover effects by considering both Poisson and negative binomial panel count data models.

8. In Figure B1 in Appendix B in the supplemental data online, we report the dynamic cumulative responses up to a period 10 of weeks after the change in each regressor. We find that most of the total impact on infections, up to a 70%, takes place during the four weeks that follow the change in $X_{\mathrm{kt}}$.

9. We compute the average decomposition implied by (1) the Lindeman, Merenda and Gold (LMG) metric, (2) the proportional marginal variance decomposition (PMVD) metric, (4) the Genizi score and (4) the correlation adjusted (CAR) scores.

10. We report the key metrics and statistics of this estimation procedure in Table B20 in Appendix B in the supplemental data online.

11. We restrict our analysis to the period where the shock takes place given that the share of provinces presenting significant spill-in and spill-outs decreases very quickly and makes it difficult to draw conclusions beyond the two-week horizon (see Table B21 in Appendix B in the supplemental data online).

12. To assess the significance of short-run responses to a shock, we draw 1000 times from the empirical distribution of each ${\rho }_i^{\left(d\right)}\sim N\left({\hat{\rho }}_i,{\sigma }_{{\rho }_i}^2\right)$ and compute the mean and standard deviation over the draws for each unit.

13. To operationalize these estimated effects as our dependent variables, we take into account their significance. Thus, if the estimated effect in province $i$ is not statistically different from zero, $\mathrm{spil}{l}_i^{\mathrm{in}}$ and $\mathrm{spil}{l}_i^{\mathrm{out}}$ are set to zero.

Additional information

Funding

This work was supported by the Italian Ministry of University and Research (MIUR) in the framework of PRIN project 2017FKHBA8001 (The Time–Space Evolution of Economic Activities: Mathematical Models and Empirical Applications); and by the Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación MCIN/AEI/10.13039/501100011033 [PID 2020-115135 GB-I00].