👍Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement

Published in Journal of Economic Theory, 2022

After writing my SIR paper in March 2020, I got interested in adding more realistic features such as agents’ optimizing behavior and the possibility of imperfect testing such as asymptomatic infections. At that time I was in touch with Tom Phelan, who was at the Cleveland Fed and asked me some questions about my discretization paper. So we started this project. Because the agents’ problem was complicated (agents need to correctly infer the aggregate dynamics as well as form beliefs about their health status), we invited Joel Sobel to work together. All of us worked hard, but none of us were able to prove the existence of a Markov perfect Bayesian equilibrium with a continuum of agents. Then differences in opinions surfaced. Joel (a game theorist) insisted that we should use a continuum of agents, for otherwise it is inconsistent with perfect competition. On the other hand, I (a general equilibrium theorist) was fine with finitely many agents, and my priority was to publish this paper before the pandemic is over. We could not resolve our disagreement, so Joel left the project and Tom and I wrote the paper.

The main theoretical result of this paper is quite interesting. Because the exeternality of infections is caused by the interaction of susceptible and infected agents, which is second order, to the first order agents internalize the effect of infected agents, so lockdown policies are redundant. This supports my earlier claim in the April 2020 VoxEU and May 2020 Fortune opinion pieces that lockdown policies are bad, which I think everybody agrees ex post. After getting rejected from Econometrica, in the interest of getting it published before it’s too late, we sent it to JET.

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