/Covid-19 and the option value of waiting

Covid-19 and the option value of waiting

As the lockdown softens, many are willing to go back to normal. However, the deadly example of San Francisco 102 years ago, when many residents refused to keep up protective measures against the Spanish flu, reminds us of the risks of euphoria following the end of lockdown.

Risks are exacerbated because of proposals to deal with the epidemic by following a ‘natural’ herd immunity strategy. Herd immunity occurs when large parts of the population (the herd) are able to resist a disease, resulting in protection also for the other part. Herd immunity can be achieved if either a large proportion of the population receives protective vaccines (herd immunity by vaccination) or a large proportion of the population becomes infected and consequently develops immunity (natural herd immunity, hereafter NHI).

Proponents of the NHI strategy stress its advantages, revolving around minimizing disturbance to economic activity, and downplay its disadvantages, namely its potential toll in human lives. An alternative strategy, called “the hammer and the dance” (Puyeo 2020), consists in applying harsh social distancing measures to reduce the spread of the disease (‘the hammer’), and controlling it by testing and tracing until eventually a vaccine is found (‘the dance’). While with the current pandemic, many countries have adhered to the latter strategy, recurring pleas to abandon it have been voiced.

The choice between these two strategies involves a hard trade-off between economic activity and human lives. One the one hand, the impact of diminishing economic activity cannot be dismissed. Losing income has severe costs, in particular to those  with weaker social protection nets. Further, as firms go bankrupt, productive capacity is destroyed which will considerably extend the period of economic hardship and it will be some time before equally efficient firms appear after the disease is under control (Furman 2020, Wren-Lewis 2020). Hence, if a disease is not very severe there are good reasons to let the epidemic follow its natural course.

In the case of Covid-19 however, the effects and severity of the disease are still largely unknown. And whenever there is great uncertainty about one of the alternative strategies, option theory tells us that there is value in waiting to have the uncertainty resolved before committing to one alternative, in particular if that choice has irreversible consequences.

The option value of waiting

Option theory was developed to analyse investments (Dixit and Pindyck, 1994), but its basic principle can be illustrated with mundane facts. Consider two youngsters looking to start a family, who just met each other and are pleased with their first impressions. Should they immediately move in together? Separations, while possible, typically entail non-negligible emotional and material costs, which create irreversibilities in the decision of moving in together. Most would advise against doing it immediately and would instead suggest dating for some time in order to receive more information about each other and about their potential fit.

The choice between NHI and ‘the hammer and the dance’ is similar. Even if countries can revert from a NHI strategy, fatalities and injuries are irreversible. By choosing ‘the hammer and the dance’, countries wait for more information about Covid-19 before making a decision. And the option value of waiting can be significant given the extremely high level of uncertainty of the Covid-19 epidemic, as discussed below.

Uncertainty about the basic reproduction number

The basic reproduction number (R0) is the average number of secondary infections produced by an infected person in a population where everyone is susceptible and there are no containment measures. R0 tells us the speed at which the virus spreads through the population1 and the proportion of the population that needs to be immune to achieve NHI. As we currently do not know R0 of Covid-19, we cannot tell which proportion of the population needs to become infected and immune to reach NHI.

The R0 for Covid-19 is likely a number between 2 and 4 (Hausmann 2020). If, on average, each infected person infects two others (R0 = 2), at least one-half of the population needs to become infected and immune to attain NHI. However, if each infected person infects four others (R0 = 4), three-fourths of the population need to become infected and immune to reach NHI.

Knowing R0 is vital because, as discussed below, different values for R0 lead to different estimates of the fatalities and injuries associated with a NHI strategy (Baldwin 2020).

Uncertainty about the infection fatality rate

The infection fatality rate (IFR) is the ratio of the number of deaths to actual infections. It gives an indication of the severity of the disease by measuring its death toll. The IFR of the seasonal flu is about 0.05%. More than four months after the epidemic started, we still do not know if the IFR of Covid-19 is 0.5%, 1%, or 2% (i.e. 10, 20 or 40 times higher than that of the seasonal flu).

The estimated number of fatalities under a NHI strategy depends both on the R0 and the prevailing IFR. With a R0 of 2 (each infected person infects two others), and an IFRs of 0.5%, 1% or 2%, the NHI strategy translates into no less than 2’500, 5’000 or 10’000 fatalities per million people. Evidently, fatalities will increase if the R0 is higher. For a R0 of 4, the same IFRs will lead to fatalities that are 50% higher, that is up to 15,000 fatalities per million in the 2% scenario. As a benchmark, fatalities in both the EU and the US are currently at 270 per million2. Under a NHI strategy, even seemingly low IFRs can translate into shockingly large death tolls given that the virus spreads through a major portion of the population. As shocking as those numbers may be, the possibility that Covid-19 is 40 times more deadly than the seasonal flu cannot yet be ruled out

Uncertainty about the infection injury rate

Being exposed to and recovering from Covid-19 does not necessarily bring one back to good health. Recovery from a critical Covid-19 condition can leave one with irreversible damage to the lungs, kidneys, and other organs (Ferreira 2020). We do not yet know the proportion of the population that will suffer serious impediments to their health after exposure and survival to Covid-19, but increases in this proportion have private and social consequences. Unhealthy individuals may become less productive and earn a lower income for the rest of their working lives. They may also have to heavily rely on social insurance programs.

Uncertainty about the body’s immune response

Further, we still do not know if infected people develop immunity to Covid-19 that protects them from reinfection (Iwasaki 2020, Bergstrom and Dean 2020). If natural immunity does not exist (or lasts very little), the NHI strategy is ineffective.

Uncertainty about Covid-19 mutations

The NHI strategy relies on the virus not mutating much. If this is the case, the epidemic will die out when the herd immunity threshold is reached. However, we still do not know if and how much the virus mutates. But in general, the risk of mutation becomes larger, the more people are infected as there are more opportunities for mutation.

Uncertainty about finding treatments and a vaccine

Proponents of a NHI strategy assume that herd immunity by vaccination is not viable. This is not necessarily the case, but time is needed to develop, test, manufacture, and distribute treatments and vaccines. Keeping social distancing measures in place would buy us the necessary time.

Uncertainty about the costs of a lockdown

Proponents of NHI strategies seem to assume that most of the economic costs arise from lockdown. However, people are very likely to change their behaviour in response to Covid-19 even without a lockdown. We know little about these reactions, but there are first estimates indicating that the reduction in aggregate expenditure experienced in Denmark was not much bigger than the one in Sweden, where Denmark had a lockdown in place and Sweden did not (Andersen et al. 2020).

Uncertainty about the costs of not treating other conditions

If the consequences of a disease are serious, the NHI strategy will lead to large number of critical cases which need hospitalization. If the number of hospitalisations is very large, it may overwhelm the capacity of the health system (Gourinchas 2020). As a consequence, the health system may not be able to treat other diseases which will result in additional deaths from such other causes. Furthermore, people with other severe diseases may avoid seeking help from the health system for fear of being infected in hospitals. In more overstretched systems, these effects are more likely.


While we do know much more about Covid-19 now than when the epidemic first started, there is still much to be learnt about its real impacts (Avery et al. 2020, Kresge 2020, Silver 2020, Wu and MacCann 2020). Choosing the best strategy to respond to Covid-19 implies taking into account not only the costs and benefits associated with each alternative strategy, but also the option value of waiting. This is bound to be large given the high uncertainty we are facing. Proponents of the NHI strategy overlook key uncertainties associated with Covid-19. Keeping social distancing measures in place will gain us time to allow uncertainties to be resolved and is hence our best course of action. But, at the same time, we need to invest decisively in collecting data which will provide us with the necessary information to resolve the different sources of uncertainty identified above.


Andersen, A, E Hansen, N Johannesen, and A Sheridan (2020), “Pandemic, shutdown and consumer spending: Lessons from Scandinavian policy responses to COVID-19”, mimeo University of Copenhagen and CEBI, 12 May.

Avery, C, W Bossert, A Clark, G Ellison, and S Ellison (2020), “Policy implications of models of the spread of coronavirus: Perspectives and opportunities for economists,” NBER Working Paper Series 27007, National Bureau of Economic Research.

Baldwin, R (2020), “COVID-19 Testing for testing times: Fostering economic recovery and preparing for the second wave“, VoxEU.org, 26 March.

Bergstrom, C and N Dean (2020), “What the proponents of ‘natural’ herd immunity don’t say: Try to reach it without a vaccine, and millions will die”, New York Times, 1 May.

Dixit, R and R Pindyck (1994), Investment under uncertainty, Princeton: Princeton University Press.

Ferreira, I (2020), “We and the virus: When can we return to a pre-covid situation?”, Interview to Mundo, 24 April.

Furman, J (2020), “Protecting people now, helping the economy rebound later”, in Mitigating the COVID-19 Economic Crisis: Act Fast and DO Whatever It Takes, CEPR Press.

Hausmann, R (2020), “Target R and wait for a vaccine”, Project Syndicate, 23 April .

Gourinchas, P O (2020), “Flattening the pandemic and recession curves”, in Mitigating the COVID-19 Economic Crisis: Act Fast and DO Whatever It Takes, CEPR Press.

Iwasaki, A (2020), “We still know very little about the body’s immune response to the SARS CoV-2”, Interview to Público, 6 April .

Kresge, N (2020), “Virus may spread twice as fast as earlier thought, study says”, Bloomberg, 6 April .

Puyeo, T (2020a), “Covid-19: Why you must act now: Politicians, community leaders and business leaders: What should you do and when?”, Medium, 10 March.

Puyeo, T (2020b), “The hammer and the dance”, Medium, 19 March.

Silver, N (2020), “Covid-19 case counts are meaningless unless you know somethings about testing. And even then it gets complicated”, FiveThirtyEight, 4 April.

Wren-Lewis, S (2020), “The economic effects of a pandemic”, in Economics on the Time of Covid-19, CEPR Press.

Wu, J and A MacCann (2020), “28,000 missing deaths: Tracking the true toll of the Covid-19 crisis”, New York Times, 21 April.


1 If R0 is 2 and there are no limits on the number of people that can be contaminated, after ten rounds of transmission each infected person gives it to more than 1,000 others. If R0 is 3, the figure is 59,000 and if R0 is 4, it is more than one million. 

2 In all countries in which this ratio is reported to be highest (Italy, Spain, Belgium), its current value is still below 800.

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