have larger populations and smaller areas (i.e., higher population density). On the other hand, higher population density is found to attenuate the negative impacts of stricter NPIs, as evidenced by the positive (negative) estimated coefficient on the interaction of the NPI measure with population (area). Columns 4 and 6 show that these interaction effects are driven by the lower-income country subsample, and the interaction terms for cities in high-income countries are of opposite signs.<sup>18</sup> These opposing effects lead to the further question of whether, on net, higher population density is associated with larger or smaller economic impacts of the Covid-19 pandemic across cities.

# **_3.3 Examining between-city differences in economic trajectories_**

To understand the effect of population density (and other city characteristics) on city trajectories in the _cross-section_ , we first develop a conceptual measurement framework for quantifying losses, both at various points in a city’s trajectory following the onset of the pandemic and in aggregate (i.e., the total loss of economic activity or total loss of light).<sup>19</sup> In this framework, we start from the assumption that, in the absence of the Covid-19 shock, the intensity of a city’s (seasonally adjusted) nighttime lights would have continued to follow its own pre-Covid-19 trend growth path, as defined using the monthly lights data for the period April 2012 – December 2019. Given this, we then compare the observed post-Covid-19 onset, seasonally adjusted, value of a city’s nighttime lights against this counterfactual growth path. For any given month, a negative disparity between a city’s actual and counterfactual light intensity is then defined as the loss of light associated with the pandemic for that month.

Based on this measure, we define the initial impact of the pandemic ( **I** ) as the loss of light experienced during the first month where the number of Covid-19 cases is greater than zero, depth ( **D** ) as the largest absolute loss of light for a month experienced within the time span between the arrival of Covid-19 in a country and December 2020 (when an effective vaccine was developed), and current ( **C** ) as the loss of lights in December 2020.<sup>20</sup> Hence, I, D, and C capture impacts at different points in a city’s post-Covid-19 onset trajectory. Finally, we also calculate the total loss of lights ( **TLL** ), defined as the sum of lost lights, relative to the counterfactual growth path, across all months from the first month of the disease to December 2020. This provides a measure of the cumulative economic impact of the Covid-19 crisis.

Based on this framework, we then estimate the correlation between population density and I, D, and C. Dividing our global sample into cities in high-income and lower-income countries, we find that population density is positively correlated with _less_ loss of lights (i.e., smaller cumulative economic impact), **but only in cities in lower-income countries** . The correlations in Figure 5 show that more densely populated cities tended to suffer _smaller_ impacts of the Covid-19 crisis in terms of TLL, the depth of the shock, and the city’s position in December 2020. _Prima facie_ , this suggests that, for cities in lower-income countries, high population densities have attenuated the impacts of the crisis.

> 18 The results in table 1 also reveal that the effect of the economic support index on a city’s nighttime lights is not significantly affected by either its population or area. And this is the case also for both the high- and lowerincome country subsamples of cities.

> 19 This conceptual framework builds on that used by Roberts (2021).

> 20 We limit the cross-sectional analysis in this subsection to the period before the development of effective vaccines in December 2020 to exclude the impacts of revised expectations of recovery. For example, economic activity may have reacted on beliefs that richer regions would obtain the vaccine first, thus influencing recovery. This is consistent with the sharp uptick in lights for cities in high-income countries seen in panel A of figure 7.

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