Self-fulfilling Lockdowns in a Simple SIR-Macro Model

This study aims to show that a self-fulfilling (extrinsic) lockdown can occur even in economies where lockdowns are not necessary to keep the number of infected people below a threshold level. We conducted our analysis using a simple epidemiological SIR model modified by Eichenbaum et al. (2020). We derive various extrinsic lockdowns by solving a control problem explicitly. A key mechanism that leads to extrinsic lockdowns is that an anticipated lockdown increases the consumption of susceptible people before the lockdown and raises the number of infected people. Consequently, the anticipated lockdown becomes a self-fulfilling prophecy in the following period. The welfare effect of extrinsic lockdowns is in marked contrast to intrinsic lockdowns. When extrinsic lockdowns are expected to occur, the increased number of infections increases the probability of infection and deteriorates the welfare of susceptible people. The results suggest that an appropriate policy announcement might be key to ruling out undesirable self-fulfilling expectations.