That is the topic of a new paper by Farboodi, Jarosch, and Shimer, published version in here. They favor ” Immediate social distancing that ends only slowly but is not overly restrictive.” Furthermore, they test the model against data from Safegraph and also from Sweden and find that their recommendations do not depend very much on parameter values.
Here is an excerpt from the paper:
…social distancing is never too restrictive. At any point in time, the effective reproduction number for a disease is the expected number of people that an infected person infects. In contrast to the basic reproduction number, it accounts for the current level of social activity and the fraction of people who are susceptible. Importantly, optimal policy keeps the effective reproduction number above the fraction of people who are susceptible,although for a long time only mildly so. That is, social activity is such that, if almost everyone were susceptible to the disease, the disease would grow over time. That means that optimal social activity lets infections grow until the susceptible population is sufficiently small that the number of infected people starts to shrink. As the stock of infected individuals falls,the optimal ratio of the effective reproduction number to the fraction of susceptible people grows until it eventually converges to the basic reproduction number.
To understand why social distancing is never too restrictive, first observe that social activity optimally returns to its pre-pandemic level in the long run, even if a cure is never found. To understand why, suppose to the contrary that social distancing is permanently imposed, suppressing social activity below the first-best (disease-free world) level. That means that a small increase in social activity has a first-order impact on welfare. Of course, there is a cost to increasing social activity: it will lead to an increase in infections. However,since the number of infected people must converge to zero in the long run, by waiting long enough to increase social activity, the number of additional infections can be made arbitrarily small while the benefit from a marginal increase in social activity remains positive.
Recommended, one recurring theme is that people distance a lot of their own accord. That means voluntary self-policing brings many of the benefits of a lockdown. Another lesson is that we should be liberalizing at the margin.
If I have a worry, however, it has to do with the Lucas critique. People make take preliminary warnings very seriously, when they see those warnings are part of a path toward greater strictness. When the same verbal or written message is part of a path toward greater liberalization however…perhaps the momentum and perceived end point really matters?
For the pointer I thank John Alcorn.