Pandemic economics: optimal dynamic confinement under uncertainty and learning
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Pandemic economics: optimal dynamic confinement under uncertainty and learning Christian Gollier1 Received: 21 July 2020 / Accepted: 27 July 2020 © International Association for the Study of Insurance Economics 2020
Abstract Most integrated models of the covid pandemic have been developed under the assumption that the policy-sensitive reproduction number is certain. The decision to exit from the lockdown has been made in most countries without knowing the reproduction number that would prevail after the deconfinement. In this paper, I explore the role of uncertainty and learning on the optimal dynamic lockdown policy. I limit the analysis to suppression strategies where the SIR dynamics can be approximated by an exponential infection decay. In the absence of uncertainty, the optimal confinement policy is to impose a constant rate of lockdown until the suppression of the virus in the population. I show that introducing uncertainty about the reproduction number of deconfined people reduces the optimal initial rate of confinement. Keywords Covid · Pandemic · SIR · Rate of confinement · Reproduction number
1 Introduction Academic economists have recently spent a huge amount of energy to better understand the science of pandemic dynamics in the face of the emergence of the covid19. Economists are contributing to the analysis of the covid-19 crisis by integrating economic dimensions to the models, such as the economic cost of social distancing and the statistical value of lives lost. These are key elements necessary for public and private decision-makers interested in shaping strategies and policies that minimize the welfare cost of the crisis. My preferred reading list on this issue as I write this paper is composed of papers by Acemoglu and Chernozhukov (2020), Alvarez et al. (2020), Brotherhood et al. (2020), Favero et al. (2020), Fischer (2020), Greenstone and Nigam (May 2020), Miclo et al. (2020), Pindyck (2020). This investment by the profession is impressive and highly policy-relevant. It raised critical debates about, for example, when and how much to deconfine people, who should remain * Christian Gollier christian.gollier@tse‑fr.eu 1
Toulouse School of Economics, University of Toulouse-Capitole, Toulouse, France Vol.:(0123456789)
The Geneva Risk and Insurance Review
confined longer, the value of testing and tracing, or whether the individual freedom of movement should be limited. One of the most striking feature of the crisis is the deep uncertainties that surrounded most parameters of the model at the initial stage of the pandemic. To illustrate, here is a short list of the sources of covid-19 uncertainties: The mortality rate, the rate of asymptomatic sick people, the rate of prevalence, the duration of immunity, the impact of various policies (lockdown, social distancing, compulsory masks, …) on the reproduction numbers, the proportion of people who could telework efficiently, and the possibility of cross-immunization from similar viruses. Still, all models that have been built over such a short
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