Abstract
Assuming that there is no other solution than herd immunity in front of the current pandemic, on which groups of citizens should we build this herd immunity? Given the fact that young people face a mortality rate which is at least a thousand times smaller than people aged 70 years and more, there is a simple rational to build it on these younger generations. The transfer of some mortality risk from the elderly to younger people raises difficult ethical issues. However, none of the familiar moral or operational guidelines (equality of rights, VSL, QALY, ...) that have been used in the Western world over the last century weights the value of young lives 1000 times or more than the lives of the elders. This suggests that Society could offer covid protection to the elders by recommending them to remain confined as long as this herd immunity has not been attained by the younger generations. This would be a potent demonstration of intergenerational solidarity towards the most vulnerable people in our community. The welfare gain of this age-specific deconfinement strategy is huge, as it can reduce the global death toll by more than 80% as compared to a strategy of non-targeted herd immunity.
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A similar argument can be made in the context of climate change. Notice however that in that context, wealth differences across generations are taken into account by using a positive discount rate to value the social cost of carbon. Future generations are typically assumed to be wealthier in expectation. The Ramsey rule implies a positive discount rate in that case.
In the different policies that I consider, the changes in mortality risk faced by different age classes remain moderate, so that \(v_i\) can be interpreted as the Value of Statistical Life (VSL), a concept that values marginal changes in the probability to die.
In other words, I adopt a cost-efficiency approach. Contrary to the cost-benefit approach, I don’t arbitrage here between health and wealth.
Pindyck (2020) characterizes the relationship between the herd immunity proportion and the social distancing proportion.
Technically, let \(n_1\) and \(n_2\) denote the size of the two groups, respectively the unlocked one and the confined one. Let x denote the asymptotic proportion of recovered people in a community without social restriction. We assume that after deconfining the second group, some light social restrictions are imposed, yielding an asymptotic immunity proportion X, with \(X<x\). The intensity of these restrictions is selected in such a way that \(X=n_1x/(n_1+n_2)\). In other words, when unlocking the second group with the new social restriction, the proportion of immune people in the population is equal to X, so that no second wave occurs.
Other risk factors such as obesity, diabetes and gender also matter. I prefer to focus on age, as it is probably less controversial. See my discussion in Sect. 4.
Shepard and Zeckhauser (1984) also estimates an inverted-U shaped age-sensitive VSL by using a life-cycle income and consumption model with a mortality risk. Their VSL starts at 500,000 at age 20 to peak at 1,250,000 at age 40, and declines to 630,000 at age 60, in USD of 1978. This may be due to a time-consistency problem. Under this valuation system, protecting the seniors is optimal too.
In reality, the social interaction matrix is not uniform, and old people have less interaction with others. This implies that their susceptibility ratio will asymptotically converge to a larger ratio than for younger generations. I don’t take account of this dynamic effect in this analysis.
Let’s for example consider a 30-year old person. Her covid mortality risk is 80% of 0.02%. Using a VSL of 3 million euros, her covid mortality cost is estimated at 480 euros, which is likely to be much smaller than the social, psychological and financial benefit of her deconfinement.
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Acknowledgements
I thank Ingela Alger, Jim Hammitt, Ulrich Hege, Paul Seabright, Nicolas Treich and an anonymous reviewer for helpful comments. The research leading to these results has received the support from the ANR Grants Covid-Metrics and ANR-17-EURE-0010 (Investissements d’Avenir program).
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Gollier, C. If the Objective is Herd Immunity, on Whom Should it be Built?. Environ Resource Econ 76, 671–683 (2020). https://doi.org/10.1007/s10640-020-00504-2
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DOI: https://doi.org/10.1007/s10640-020-00504-2