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A Simple Planning Problem for COVID-19 Lockdown

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  • Fernando E. Alvarez
  • David Argente
  • Francesco Lippi

Abstract

We study the optimal lockdown policy for a planner who wants to control the fatalities of a pandemic while minimizing the output costs of the lockdown. We use the SIR epidemiology model and a linear economy to formalize the planner's dynamic control problem. The optimal policy depends on the fraction of infected and susceptible in the population. We parametrize the model using data on the COVID19 pandemic and the economic breadth of the lockdown. The quantitative analysis identifies the features that shape the intensity and duration of the optimal lockdown policy. Our baseline parametrization is conditional on a 1% of infected agents at the outbreak, no cure for the disease, and the possibility of testing. The optimal policy prescribes a severe lockdown beginning two weeks after the outbreak, covers 60% of the population after a month, and is gradually withdrawn covering 20% of the population after 3 months. The intensity of the lockdown depends on the gradient of the fatality rate as a function of the infected, and on the assumed value of a statistical life. The absence of testing increases the economic costs of the lockdown, and shortens the duration of the optimal lockdown which ends more abruptly. Welfare under the optimal policy with testing is higher, equivalent to a one-time payment of 2% of GDP.

Suggested Citation

  • Fernando E. Alvarez & David Argente & Francesco Lippi, 2020. "A Simple Planning Problem for COVID-19 Lockdown," NBER Working Papers 26981, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:26981
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    1. Diamond, P. A. & Maskin, Eric, 1981. "An equilibrium analysis of search and breach of contract II. A non-steady state example," Journal of Economic Theory, Elsevier, vol. 25(2), pages 165-195, October.
    2. Facundo Piguillem & Liyan Shi, 2022. "Optimal Covid-19 Quarantine and Testing Policies," The Economic Journal, Royal Economic Society, vol. 132(647), pages 2534-2562.
    3. repec:aei:rpaper:1008560098 is not listed on IDEAS
    4. Andrew Atkeson, 2020. "What Will be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," Staff Report 595, Federal Reserve Bank of Minneapolis.
    5. Robert J. Barro & José F. Ursua & Joanna Weng, 2020. "The Coronavirus and the Great Influenza Epidemic - Lessons from the "Spanish Flu" for the Coronavirus's Potential Effects on Mortality and Economic Activity," CESifo Working Paper Series 8166, CESifo.
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    More about this item

    JEL classification:

    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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