Effects of a Partially Effective Vaccine

The race to publish COVID-19 related papers is on, and I am already behind. Instead, I will repurpose a paper by Eduard Talamas and myself on networks and infections which is due out in GEB.

It is prompted by the following question: if you are given the option to distribute—without cost to you or anyone else—a perfectly safe but only moderately effective vaccine for a viral infection, should you? That we’ve posed it means the answer must be no or at least maybe not.

Unsurprisingly, it has to do with incentives. When the risk of becoming infected from contact declines, individuals tend to be less circumspect about coming into contact with others. This is risk compensation, first suggested by Charles Adams  in 1879 and popularized by Sam Peltzman in the 1970’s.

Therefore, the introduction of a vaccine has two effects. On the one hand, it reduces the probability that an individual becomes infected upon contact. On the other hand, it decreases individuals’ incentives to take costly measures to avoid contact. If the second effect outweighs the first, there will be an increase in infections upon the introduction of a moderately effective vaccine.

These are statements about infection rates not welfare. Individuals make trade-offs. In this case between the risk of infection and the costs of avoiding it. Therefore, observing that an individual’s infection probability will increase upon introduction of a partially effective vaccine is insufficient to argue against introduction.

In our paper, Eduard and I show that the introduction of a vaccine whose effectiveness falls below some threshold could make everyone worse off, even when each individual is perfectly rational and bears the full cost of becoming infected. If the vaccine is highly effective, this outcome is reversed. This is because risky interactions can be strategic complements. An individual’s optimal amount of risky interactions can be increasing in the amount of risky interactions that others take.

To illustrate, call two individuals that engage in risky interactions partners. Every risky interaction that Ann’s partner Bob has with Chloe affects Ann’s incentives to have risky interactions with Chloe in two countervailing ways. It increases Chloe’s infection probability. But it also increases the probability that Ann is infected conditional on Chloe being infected—because if Chloe is infected, chances are that Ann’s partner Bob is also infected. Given that a risky interaction between Ann and Chloe only increases the probability that Ann becomes infected when Chloe is infected and Ann is not, the combination of these effects can lead to an increase in Ann’s incentives to engage with Chloe and her partners when Bob engages with Chloe.

One might ask, given the huge trove of papers on epidemiological models, this effect must have been identified before and discussed? No, or at least not as far as we could tell. This is because we depart from from a standard feature of these models. We allow agents to strategically choose their partners— instead of only allowing them to choose the number of partners, and then having matches occur uniformly at random.

Going On-line

In response to the Covid-19 virus a number of American Universities are moving instruction on-line. Some see this as great natural experiment to test the efficacy of virtual instruction (NO). Others believe it will speed the pace at which instruction  moves on-line (NO). The focus now is on execution at scale in a short period of time.  We would be better off canceling the rest of term and giving all the students A’s.

Here is what I predict will happen. Students will be dilatory in viewing lectures. Temptation and the difficulty of adjusting to new habits will be obstacles. When the exams approach, some will complain that they are unprepared because virtual is not as good as live, their instructor made a hash of things, the absence of live office hours, etc. etc. The exams will be take home without any proctors. While one’s own spirit is willing, there are doubts about the rectitude of one’s classmates.

On the other hand, during this period of exile, perhaps, there will emerge another Newton.