Optimally Controlling an Epidemic*

Gonzalez-Eiras, Martín; Niepelt, Dirk (11 December 2020). Optimally Controlling an Epidemic* (Discussion Papers 20-19). Bern: Department of Economics

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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-continous, 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.

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