Stay-at-home orders and second waves: a graphical exposition
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Stay‑at‑home orders and second waves: a graphical exposition Kent A. Smetters1 Received: 2 July 2020 / Accepted: 27 August 2020 / Published online: 10 September 2020 © International Association for the Study of Insurance Economics 2020
Abstract Integrated epidemiological-economics models have recently appeared to study optimal government policy, especially stay-at-home orders (mass “quarantines”). But these models are challenging to interpret due to the lack of closed-form solutions. This note provides an intuitive and graphical explanation of optimal quarantine policy. To be optimal, a quarantine requires “the cavalry” (e.g., mass testing, strong therapeutics, or a vaccine) to arrive just in time, not too early or too late. The graphical explanation accommodates numerous extensions, including hospital constraints, sick worker, age differentiation, and learning. The effect of uncertainty about the arrival time of “the cavalry” is also discussed. Keywords Virus · Epidemiology · Economics · Quarantine JEL Classification H0 · I0
1 Introduction Integrated epidemiological-economics models have recently appeared (Alvarez et al. 2020; Barro et al. 2020; Dewatripont et al. 2020; Eichenbaum et al. 2020; Hall et al. 2020; Jones et al. 2020; Piguillem and Shi 2020). But they are challenging to interpret due to the lack of closed-form solutions for optimal policy decisions, including the most common focus of the literature: stay-at-home orders (mass “quarantines” herein) and full opening. The classic infectious SIR disease model dates back to Kermack and McKendrick (1927), where agents move through various stages (“compartments”): Susceptible, Infectious, and Recovery. The SIR model has been modified over the year to include an Exposed stage (SEIR) as well as two mutually exclusive infections stages
* Kent A. Smetters [email protected] 1
Wharton and NBER, Philadelphia, USA Vol:.(1234567890)
The Geneva Risk and Insurance Review (2020) 45:94–103
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(asymptomatic and symptomatic) stages (SEIIR). Stock (2020) provides an overview and discusses related estimation challenges. The SIR model and its derivatives have several virus-specific key parameters. The case fatality rate 𝜇 equals total deaths (not recovered) divided by the total number of cases (infections).1 It places an effective upper-bound on the number of deaths as a percent of the (Susceptible) population.2 For COVID-19, the value of 𝜇 has been estimated to be as low as 0.2% to as high as 2%; both estimates likely reflect a fair degree of selection bias. The virus’ reproduction number (R, sometimes called R0) equals the number of people that an infected person in turn infects, on average. A value R > 1 implies that the number of cases increases geometrically over a limited range. In the pre-aware population (before voluntary social distancing), for example, COVID-19’s value of R was estimated to be around 3 in China and the United States, although lower in Scandinavian countries.3 Public policy generally aims to drive the value of R below 1 (Budish 20
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