Terrence Iverson, Larry Karp, and Alessandro Peri: Optimal Social Distancing and the Economics of Uncertain Vaccine Arrival

I am pleased to be able to share a guest post by my University of Colorado Boulder colleague Alessandro Peri and his coauthors Terrence Iverson and Larry Karp. Below are their words:

Amid the surging COVID-19 pandemic, governments over the past year have faced a difficult policy choice: How much and for how long should they restrict economic activities that cause the virus to spread? From an economic perspective, these lockdown (or social-distancing) policies should balance the economic costs of restricting mobility against the resulting benefit of reduced mortality costs.

A crucial source of uncertainty in this type of analysis is the time needed to develop (and distribute) a vaccine.  While the U.S. ended up approving a vaccine a mere eleven months after the start of the pandemic, the prospects for rapid development were initially murky at best.  In Spring 2020, most experts viewed a one-and-a-half to three year horizon as plausible, and some worried that COVID-19 could turn out to be a disease, like AIDS or the common cold, for which a vaccine would ultimately prove elusive. 

How should policymakers respond to increased optimism about the early arrival of a vaccine? Should it strengthen social distancing policy or weaken it?  To answer this question, we need an adequate model of disease contagion. A widely-used workhorse from epidemiology, now familiar to many economists, is the Susceptible-Infected-Recovered (SIR) model.  It describes how individuals move from being initially susceptible to the virus, to becoming infected, to recovering and developing immunity or dying. 

We use a standard SIR model to show that an earlier expected arrival time for a vaccine can either increase or decrease optimal social distancing, depending on assumptions.  The ambiguity arises because social distancing has two effects: it lowers the stock of infected (a benefit), but it also increases the stock of susceptible who remain vulnerable to future infection (a liability). We refer to the future benefits associated with a reduction in the stock of infected as the “infection channel” and the future liability associated with an increase in susceptible as the “susceptible channel”.  The infection channel causes an earlier expected arrival time to increase optimal social distancing, while the susceptible channel has the opposite effect.

The net effect on policy of the vaccine’s uncertain arrival depends on which of the two channels dominates. Relatively high policy cost or relatively low mortality cost lead to an optimal path for the economy in which infections stay moderately high.  When this happens, the susceptible channel dominates, and an earlier expected arrival time increases optimal social distancing.  Our best guess about the most plausible model assumptions to describe the situation in the United States in early 2021 falls into this category.  An important implication is that U.S. policymakers should restrict economic activities now more than ever since distribution of a vaccine is imminent. 

But there are also plausible settings, e.g. with relatively low social distancing  cost or relatively high mortality cost, where an earlier expected vaccine arrival time makes optimal social distancing policy weaker. In these circumstances, the optimal path of the economy keeps infections low, and the infection channel dominates.  In the U.S., parameters consistent with this relationship may have been plausible early in the pandemic, especially if policy response had been effectively coordinated at the federal level.  Now that U.S. infections are widespread and to a large degree out of control, that situation is implausible. In countries where infection levels have been consistently kept low, including China, Vietnam, and New Zealand, this description of the world is realistic. 

Figure 1: Dots indicate  average infection rate over the first year under two assumptions about  mean arrival time:  52 weeks  on the horizontal axis and 182 weeks  on the vertical axis.   The blue color indicates that a later expected vaccine arrival lowers optimal social distancing. The red color indicates the opposite.

Our paper uses both analytical models (paper-and-pencil math) and numerical models (solved with a computer) to develop the intuition above.  Figure 1 illustrates a key feature of the relation between the level of social distancing policy and the expected time of vaccine arrival. We numerically solve our quantitative model for over 1000 combinations of parameters and for two expected vaccine arrival times, 52 weeks and 182. Each dot in Figure 1 shows, for a single combination of parameters, the first-year average infection level when the expected arrival time is 52 weeks (horizontal axis) and 182 weeks (vertical axis). All of the blue points lie above the 45-degree line, indicating that for the corresponding parameters, a later expected arrival time lowers optimal social distancing, thus increasing infections. The red dots lie below the line, indicating that a later expected arrival time increases optimal social distancing, thus lowering infection. More importantly, the red dots are all very close to the origin.   This shows that earlier expected vaccine arrival leads to stricter social distancing (the red dots) only when the optimal level of infection is kept near zero.

The left and right panels of Figure 2 trace the impact of a ten percentage point increase in early social distancing relative to the original optimum, holding future policy fixed. Economists call these graphs “impulse response functions.”  This figure corresponds to the case where the susceptible channel is strong, so that earlier expected vaccine arrival makes optimal policy stricter. The left panel shows that the stricter social distancing substantially lowers deaths in the short-run, followed by a smaller but longer-lasting increase in deaths.  To explain the dynamics, the right panel shows that while infections initially fall (the blue dashed curve), the stock of susceptible rises (the solid black curve). Individuals who avoid infection in the short run also avoid the benefit of developing immunity and hence remain in the susceptible pool. A higher stock of susceptible is fuel for the fire of future infections. Some of this fuel ignites in subsequent periods, leading to a resurgence in infections and deaths.

Figure 2: Impulse response functions associated with a 10 percent increase in initial-period social distancing relative to the optimal path. Simulations for our baseline model.  The mean arrival time is 156 weeks.

In addition to studying the impact of vaccine arrival beliefs on optimal social distancing, we also use our quantitative model to evaluate recent proposals to move quickly to herd immunity.  We focus on a best-case version of the Great Barrington(“GB”) Declaration, which attracted considerable interest from the Trump administration in late fall 2020.  The proposal encourages governments to focus policy effort on protecting the most vulnerable, while encouraging others to return to normal lives. 

When vaccine arrival remains far off, the proposal might not look too bad.  Indeed, if mean vaccine arrival time is two years, the proposal performs about as well as optimal uniform policy (though still about two trillion dollars worse than optimal targeted policy).[1]  But if vaccine arrival is immanent—as it is in early 2021—then the policy is catastrophic.  With a mean arrival time of six months, 520 thousand more of the vulnerable group (65 and over) die, 380 thousand more of the less vulnerable group (under 65) die, and aggregate (economic + mortality) costs exceeds three trillion dollars.  The assertion in the Great Barrington Declaration that moving quickly to herd immunity will protect the vulnerable is disastrously wrong: the vulnerable cannot be protected when infection levels are allowed to run extremely high.

[1] Targeted policy requires more vulnerable groups to adhere to stricter social distancing; uniform policy imposes the same level of social distancing on all groups, regardless of their risk factors.