Abstract
We propose a flexible model of infectious dynamics with a single endogenous state variable and economic choices. We characterize equilibrium, optimal outcomes, static and dynamic externalities, and prove the following: (i) A lockdown generically is followed by policies to stimulate activity. (ii) Re-infection risk lowers the activity level chosen by the government early on and, for small static externalities, implies too cautious equilibrium steady-state activity. (iii) When a cure arrives deterministically, optimal policy is dis-continuous, featuring a light/strict lockdown when the arrival date exceeds/falls short of a specific value. Calibrated to the ongoing COVID-19 pandemic the baseline model and a battery of robustness checks and extensions imply (iv) lockdowns for 3-4 months, with activity reductions by 25-40 percent, and (v) substantial welfare gains from optimal policy unless the government lacks instruments to stimulate activity after a lockdown.
Highlights
We propose a generic framework to analyze optimal lockdown policies and we derive a series of results that seem to have gone mostly unnoticed in the recently burgeoning literature focusing on the intersection of epidemiology and economics
We show that a framework with a single endogenous state variable, the share of the population that has contracted the disease at some time in the past, constitutes a tractable and accurate approximation of infectious dynamics in models with additional state variables
We refer to a “lockdown” as a situation where the government wishes to depress economic activity below the level chosen in equilibrium
Summary
Of these steady-state properties the government’s activity level early on in an epidemic, when a lockdown is in place, decreases with re-infection risk Another key result of our analysis concerns the optimal policy when a cure like a vaccine or effective treatment is anticipated to arrive deterministically such that time constitutes another state variable. Our paper presents a battery of extensions and robustness checks and contrasts various epidemiological and economic environments: Laissez faire vs optimal policy; observable vs unobservable infection status; lockdowns vs forced openings; stochastic vs deterministic arrival of a cure; permanent vs temporary immunity, generating either a disease-free steady state or an endemic equilibrium; or, stationary epidemiological environments vs environments with changing characteristics.
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