The COVID-19 death rate (deaths over population) is strikingly unevenly distributed across Europe. Figure 1 arranges the countries of Europe in descending order by the recorded COVID-19 deaths per million, as of April 9th, 2020. Atop the list are Spain and Italy, with COVID-19 death rates of 330 and 302 deaths per 1 million, respectively. Spain's COVID-19 death rate exceeds similarly developed economies of Germany (31 per million) and Austria (33 per million) by more than a factor of ten. Few if any epidemiological indicators distinguish the countries of Europe by such an extent.
[ INSERT FIGURE 1] Several plausible hypotheses might account for this puzzling cross-national variation in COVID-19 death rates, including the capacity of a healthcare system to manage and survive infected persons, the timing of epidemic seeding from exported cases, the timing and intensity of non-pharmaceutical interventions, and the share of elderly population. Reported age-specific case-fatality ratios (deaths over observed infections) and age-specific death rates (deaths over population) lend intuitive support for the elderly share hypothesis (Verity et al, 2020 , Liu et al, 2020 , Huang et al, 2020 .
Consider the example of Italy. Table 1 shows age-specific COVID-19 deaths and death rates for Italy, as of April 9, 2020. The risk of death is manifestly increasing in reported age intervals. Of the 16,654 recorded persons that perished from COVID-19, 95% were ≥ 60 and 83% were ≥ 70. The COVID-19 death rate is more than 40X higher for persons ≥ 60 years of age (877 per million) as compared to persons < 60 years of age (45 per million). Of the 44 deceased persons under the age of 40 in Italy, 29 presented with a serious pre-existing disease (Instituto Superiore di Sanità, 2020) .
[ INSERT TABLE 1] Absent individual-level or age-specific death rates for all European countries, the age-gradient of COVID-19 death rates in Italy suggests that the share of elderly population in a country ought to be a good predictor of COVID-19 death rates cross-nationally. However, the COVID-19 death rate and the share of elderly population ≥ 65 are statistically uncorrelated (r = 0.163, p = 0.399). Taking the natural log of both variables still results in statistical independence (r = 0.104, p = 0.591). Even if one expands the definition of elderly share to persons ≥ 75 years of age, the relationship is statistically insignificant (r = 0.207, p = 0.282). Only at the share of population ≥ 85 years of age does the relationship to the COVID-19 death rate become moderately correlated and significant (r = 0.541, p = 0.003). However, with this last definition of elderly (≥ 85 years) we drift from the observed distribution of COVID-19 deaths (at least in the Italian example) and therefore risk loss of validity.
In the next section, we first explain the statistical and theoretical inadequacies of the elderly share variable as a proxy for elderly frailty. After that, we advance the less confounded metric of elderly longevity -life expectancy at 65. We discuss how elderly longevity is linked to health frailty. In Section 3, we present bivariate results showing how life expectancy at 65 adequately accounts for the puzzling distribution of death rates across Europe and might also be partially involved in the timing of a country's epidemic (as indicated by the first COVID-19 death). Next, we present least squares regression results, introducing statistical controls of hospital bed capacity and a proxy for epidemic seeding risk, inbound international tourists.
2 Metrics of at-Risk Elderly Population
COVID-19 disproportionately afflicts the elderly, especially the elderly with underlying health conditions. Frailty is a term used to capture a range of age-related conditions that impair the elderly. Frail populations are prone to dependency, and less likely to withstand a health shock (Hoogendijk et al, 2019; Theou et al 2018 , Vetrano et al, 2018 Denfeld et al, 2017) . The share of population ≥ 65 years of age is an imperfect proxy for elderly survival and consequent frailty because it is confounded by other components of population size and mortality selection. Among many other examples, the numerator in the share of population ≥ 65 partly reflects elderly survival but may also reflect the parental fertility of the present elderly relative to the fertility of subsequent cohorts. With respect to mortality selection, frail populations are less resistant to health shocks, decreasing their survival probability. At a population level, this results in a relative increase of death resistant or health robust individuals with age (Vogt and Missov 2017; Vaupel et al, 1979) . Consider two similarly economically developed countries with varying survival to age of 75, the standard threshold for premature death. Suppose that one country has high and the other low risk of premature death from all causes. Other things held equal, persons surviving to 75 in the high-risk all-cause mortality country are more positively selected on the underlying ability to death resist than counterparts in the low-risk all-cause mortality country. Given mortality selection, elderly persons over the age of 75 in the high-risk country are more likely to withstand adverse health shocks than similarly aged persons in the low-risk country because they are different on the unobserved trait of underlying frailty.
Elderly longevity or life expectancy at 65 more effectively captures population survival independently of other demographic dynamics. Given that vulnerability to adverse outcomes increases with age, elderly longevity also has the merit of capturing the accumulation of age-related frailty in a society.
Consider Table 2 The countries of Europe clearly vary in their ability to survive the elderly. Because human frailty increases with age, it stands to reason that similarly economically developed countries with higher elderly longevity might also have higher percentages of elderly requiring the care of others.
The European Commission, Eurostat database contains information on the 1) percentage of persons ≥ 65 that need help with household activities; 2) percentage of persons ≥ 65 that need help with personal care activities, and 3) percentage of disabled persons ≥ 65 that need the assistance of others.
Together, these three variables can form a reasonably good indicator of late life physiological decline requiring the assistance of others. Table 3 presents data on these variables for similarly economically developed European countries 2 arranged in descending order on life expectancy at 65. Notably, the top 3 countries in terms of life expectancy score highest on the elderly frailty index, constituting the average of our three indicators of assistance need. The correlation between our frailty index and life expectancy at 65 is positive and statistically significant (r = 0.631, p = 0.016).
Having discussed how the share of population ≥ 65 is a weak proxy for mortality risk and how elderly longevity is a more adequate metric of elderly survival and consequent frailty, in the next section we evaluate the statistical relationship between COVID-19 death rates and life expectancy at 65.
1 The statistically significant correlation between life expectancy at 65 and the population share of elderly does appear at older age definitions of elderly. The correlation between the natural log of life expectancy at 65 and the natural log of the share at 75+ is r = 0.175 (p = 0.365), and r = 0.570 (p = 0.001) with the share at 85+. This pattern of a rising correlation between life expectancy at 65 and older definitions of elderly share reflects the increasing predominance of the survival component of population size as one graduates up the age structure. 2 Countries with GDP per capita in 2018 above the median GDP per capita across Europe are included. GDP per capita data are from the World Bank.
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Elderly longevity (or life expectancy at ≥ 65) is not only a sound correlate of European variation in the COVID-19 death rate but also a good predictor of the timing of the COVID-19 epidemic in a country. Timing is measured in terms of the first recorded COVID corresponding to the observed COVID-19 death rate (as of April 9th, 2020). Importantly, while these countries vary meaningfully in healthcare system capacity and in the timing and intensity of non-pharmaceutical interventions, the striking spatial variation in COVID-19 death rates across these countries appears statistically and intuitively explainable by elderly survival and consequent frailty.
[ INSERT FIGURE 4] 
Next, we test whether observed relationships between our outcome variables -COVID-19 death rate and date of epidemic timing -and elderly longevity are robust to inclusion of variables that operationalize other candidate hypotheses, namely healthcare capacity and seeding from international tourists. We collected data from the World Bank 4 on hospital beds per 1,000 persons (2015/2016) and the annual count of inbound international tourists (2018). First, we estimate the following least squares model:
where, CovDR is the observed COVID-19 death rate for country i at the time of April 9th, 2020, 
where, all terms carry from equation (1), except for our second response variable, CovDate which denotes the date of the first recorded COVID-19 death in a country. CovDate is equal to 1 on 4 According to World Bank documentation, the hospital beds per 1,000 includes: "Hospital beds include inpatient beds available in public, private, general, and specialized hospitals and rehabilitation centers. In most cases beds for both acute and chronic care are included." With respect to international tourist counts, the World Bank notes: "International inbound tourists (overnight visitors) are the number of tourists who travel to a country other than that in which they have their usual residence, but outside their usual environment, for a period not exceeding 12 months and whose main purpose in visiting is other than an activity remunerated from within the country visited. The data on inbound tourists refer to the number of arrivals, not to the number of people traveling. Thus, a person who makes several trips to a country during a given period is counted each time as a new arrival."
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The copyright holder for this preprint . https://doi.org/10.1101/2020.04.14.20065540 doi: medRxiv preprint equal, that a 1% increase in life expectancy at 65 is associated with percent inward shift in the date of epidemic launch. Table 4 reports coefficients for our two estimated least square models. In Model 1, controlling for bed capacity and tourism inflow, we find that a 1 percent increase in life expectancy at 65 is associated with a 14.21 percent increase (95% CI: 9.02, 19.41) in the COVID-19 death rate. In Model 2, we substitute our tourism inflow variable that proxies for epidemic seeding risk for the actual date of first death, CovDate, our response variable in equation (2). Adjusting for the date of first COVID-19 death and hospital bed capacity, we find that a 1 percent increase in life expectancy at 65 increases the COVID-19 death rate by 11.76 percent (95% CI: 5.69, 17.83). In Model 3, controlling for bed capacity and tourism inflow, we find that a 1 percent increase in life expectancy at 65 is associated with inward shift in the date of first COVID-19 death by -1.36 percent (95% CI: -2.17, 0.54).
Here, observe relationships between our COVI-19 response variables and life expectancy at 65, partially out the effects of hospital bed capacity and international tourism inflow.
By substituting the more readily intuitive (but confounded) share of elderly population ≥ 65 for elderly longevity (life expectancy at 65) we adequately statistically match the puzzling distribution of COVID-19 death rates in Europe. This result also obliges the widely observed fact that the risk COVID-19 mortality increases with age (Verity et al, 2020 , Liu et al, 2020 , Huang et al, 2020 . The correlation between the COVID-19 death rate and elderly longevity holds with statistical control for hospital bed capacity and international inbound arrivals, as well as control for the date of the first recorded COVID-19 death. As shown in Appendix Figure Life expectancy at 65 is not only strongly correlated with the COVID-19 death rate, but also moderately correlated with epidemic timing. Importantly this statistical relationship holds when controlling for the more obvious covariate of timing -the seeding of the virus in Europe from inbound international tourists. This is an admittedly more difficult statistical relationship to interpret, but 7 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint . https: //doi.org/10.1101 //doi.org/10. /2020 one possibility is that seeding from visitors abroad sets infection in motion, but that the timing of the first death from infection operates through the frailty profile of the country visited.
From a mortality selection standpoint, in advanced economies the long survival of the elderly is accompanied by the accumulation of elderly frailty. This renders a sizeable segment of the population at-risk to an adverse health event like a lethal respiratory assault. Our index of elderly frailty, emphasizing the proneness of elderly to dependency is positively correlated with life expectancy at 65. In France, Spain and Italy, the three hardest hit countries of Europe, about half to two-thirds of elderly require assistance for basic personal and household care activities. This fact educates that a sizeable percentage of European elderly cannot easily socially distance. They require the intimacy of care, and intimate care or interpersonal proximity is a transmission risk. More proximate, our results imply that the order-of-magnitude higher COVID-19 mortality risk in Italy and Spain may result from patterns of interpersonal contact required to support an increasingly frail elderly population. Moreover, viral spread through the social intimacy that characterizes elderly care is plausibly associated with a higher viral load of initial infection as compared with random contact, a factor implicated in disease severity (Liu et al, 2020) .
Several other characteristics of SARS-Cov2 are relevant to the problem of high mortality risk among the elderly of Europe. First, several studies have shown that the elderly are particularly susceptible to this virus for reasons that are not yet fully understood (Verity et al, 2020 , Liu et al, 2020 , Huang et al, 2020 . Second, a significant percentage of infected persons are asymptomatic (estimates range from 15% -50%), and asymptomatic persons can shed viruses and infect others (Verity et al, 2020) .
Also, a large percentage of symptomatic patients exhibit mild symptoms that can be confused with a more common cold or flu. Third, viral replication has been shown to be highest in the early days of infection, when most people are mildly or asymptomatic (Zhou, Fei et al, 2020) . Thus, in the context of caregiving, people with little or no symptoms can be potent spreaders of the virus to the susceptible elderly and frail. The many stories of outbreak and death in nursing homes testifies to this transmission channel. This necessitates more intense testing of caregivers to break transmission to the elderly and frail.
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(which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.14.20065540 doi: medRxiv preprint NOTE: Life expectancy, international tourists, and hospital beds per capita are log transformed, as are both response variables. Estimated coefficients therefore have the meaning of an elasticity, where a 1% increase in a predictor variable is associated with % change in the response variable. Standard errors in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.
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(which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.14.20065540 doi: medRxiv preprint (1), controlling hospital bed capacity and international tourist inflow. Panel B leverage equation (2), again controlling hospital bed capacity and international tourist inflow.
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(which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10. 1101 /2020 