Andr ́ee

# **4.1 Linear analysis of March 22 cases per 100,000 inhabitants**

To analyze the relationship between spatial variation in particulate matter concentrations and COVID-19 incidence, a number of regressions are estimated that control for possible spatial autocorrelation (Anselin, 1988).<sup>13</sup> Importantly, the spread of SARS-CoV-2 manifests itself in hot-spots that result from contact with infective subjects from areas that are in close proximity, and it can show strong geographical patterns that are not structurally related to air pollution levels. The fact that the infection started at different times in different areas together with the exponential and geographical nature of case spread, may lead to spurious associations between the spatial distribution of case hot-spots and pollution levels, particularly if the initial cases occurred in polluted regions by mere chance and then spread to nearby regions.<sup>14</sup> To account for the issue, spatial models include neighboring values of the dependent variable and/or residuals as additional variables. These spatial averages control for the clustering that results from geographical spillovers.<sup>15</sup> These models can be understood as spatial equivalents to the models that are commonly used to analyze time series in which observed values are in part explained by recent observations. While the household composition and population density terms capture more dense social links, the spatial regression components capture the likelihood of contact with infective subjects. In particular, within a hot-spot, neighboring areas have high numbers of cases per 100,000 inhabitants, and the spatial regression terms capture the increased likelihood of having contact with infective subjects within the region. The important empirical question that these models thus seek to answer is whether pollution and case incidence are associated after controlling for the geographical relationships in disease spread.

First, Model 1 estimates a linear regression using all 22 covariates and possible confounders of interest that are summarized in table 3. These include population density, gender, age groups, marital status and household composition, the share of migrants, as well as several population health indicators. Particularly the health indicators are important because PM2 _._ 5 is known to affect population health. This may result in important pre-conditions that lead to more severe COVID-19 disease. Pre-conditions captured by the data include the share of population with a long-term illness (including asthma), the share of people that smoke and admit to guidelines on alcohol use, the share of people diagnosed with obesity or overweight, as well as variables on populations exposed to traffic noise.

> 13. The treatment of spatial autocorrelation and spatial residual correlation took a firm position in quantitative geography after the contributions by Cliff and Ord (1969, 1972). Spatial econometrics as a subfield of econometrics was rapidly developed as a means to analyze sub-country data in regional econometric models (Anselin, 2010). Good introductory books exist, apart from the one referenced in the main text (LeSage and Pace, 2009) is one other. The (Q)MLE is worked out, for example, in (Lee, 2004). The field is still actively developed, with recent advances focusing on time series dynamics and non-linearity (Beenstock and Felsenstein, 2019; Andr ́ee, 2020).

> 14. The first case was detected on February 27 in Loon op Zand in Brabant, but that same night a case was also confirmed in Amsterdam. Within 4 days, 10 cases had been confirmed in 6 cities across 4 provinces with multiple sources of infection, it took till March 23 for lockdown policies to be announced, giving ample time for spread from multiple points, see https://nos.nl/artikel/2325309-beatrixziekenhuisgorinchem-gesloten-om-coronavirus-tien-patienten-in-nl.html

> 15. While the spatial autoregressive models only include the rate of infective subjects in neighboring areas as regressors, the models in fact allow for feedback and spillovers to more distant observations as each area is also a second-order neighbor of itself. See the literature on spatial models cited earlier.

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