Is it worthwhile for governments to make investments that have a very small chance of curbing the spread of COVID-19? Tsjalle van der Burg, Lara Carminati and Celeste Wilderom (University of Twente) take the hypothetical case of improving ventilation in schools, concluding that the benefits of avoiding lockdown are so great that even investments with a low probability of success are worth it.

In March this year the Dutch government introduced the social distancing rule, which warns that individuals must keep 1.5 metres apart from each other in public life to slow the spread of COVID-19. This was supported by scientific experts. The government did not, however, introduce measures for which there was no convincing evidence. For example, WHO and Dutch health organisation (RIVM) experts said there was no scientific proof that the virus could spread through aerosols to a significant extent. Consequently, the government did not consider improving ventilation in schools, gyms or care homes.

However, a number of less influential experts have suggested that aerosols and ventilation systems can play a role in the spread of the virus. Would it have been wise for the government to act as if there was a (small) chance that ventilation could be an important element in reducing the spread of the virus? For example, it could have acted on the assumption that there was a 10 percent chance that ventilation was an important factor.

Since June, the number of experts suggesting that aerosols seem to play a significant role has increased. Despite uncertainty about whether effective ventilation systems could curb the spread of COVID-19, the Dutch government promised on 1 October to give schools financial support to improve their ventilation systems.

So it is rational to act in a way that has a (very) small chance of achieving the intended effect? By applying solid insights from the portfolio theory and cost-benefit analysis, which are generally accepted among economists, we argue that governments could act upon these small probabilities to curb the spread of COVID-19. Regardless of the specific decision context, very small chances can have very big effects.

The small but real chance of preventing lockdown

First, a hypothetical situation. We assume that a government is considering an investment programme to improve school ventilation systems. The programme might not be of any concrete help in combating the COVID-19 virus. More precisely, the chance that it does not help at all is 98 percent. We assume there is a 2 percent chance that the programme is decisive in preventing a new outbreak of the virus that will lead to another lockdown (as the programme might cause the spread of the virus to remain just below some tipping point). A new lockdown would reduce national income by 100 billion euros. Hence, there is a 2 percent chance that the benefits of the programme are worth 100 billion euros.

In cost-benefit analysis, economists try to estimate the expected value of the costs and the benefits of projects. We assume that the costs of the ventilation programme are known with certainty, so the same holds for its expected outcome. The expected value of the benefits is, by definition, a weighted average of the benefits in the different possible scenarios. More specifically, it is 2 percent of 100 billion, plus 98 percent of 0 billion, which equals to 2 billion. This would imply that the programme should proceed if the costs are lower than 2 billion euros.

The expected values of the costs and benefits are not the only variables at stake, though. The risks related to a project should also be considered in principle. In economic theory, risk refers to the possibility that the outcome is lower or higher than the expected value. For instance, in a situation where a person will certainly earn 100,000 euros next year, there is no risk. However, when there is a 50 percent chance that (s)he will earn 50,000 euros and a 50 percent chance that (s)he will earn 150,000 euros, there is a (serious) risk. In both scenarios, the expected value of the income is the same. Now, some people may prefer the second scenario to the first one; they are called ‘risk-lovers’. However, most people are risk-averse about their income; they do not like the possibility that it is lower or higher than the expected value.

The portfolio theory discusses the decisions of risk-averse private investors in financial assets. The typical investor aims to get high returns on the whole portfolio of assets, and is risk-averse about these returns. The theory posits that the investor can neglect the risks of the individual assets to the extent that their associated risks cancel each other out at the portfolio level. (To be sure, risk relates to what may or may not happen in the future. And when economists say that risks cancel each other out, they are not saying they are sure that the counterbalancing effects will actually occur.) To illustrate: if investment in Volkswagen shares is risky because there is a chance that Volkswagen will no longer be able to compete with Ford in the future, and if an investment in Ford is risky because there also is a chance that Ford will no longer be able to compete with Volkswagen, then an investor who invests in both companies can neglect these individual risks. When the Volkswagen shares go down because its customers turn to Ford, the Ford shares go up, and vice versa, so that the returns to the portfolio remain the same.

The portfolio theory has also been applied to government projects. These are generally evaluated from the perspective of what is good for the country as a whole. Here, we take it that a high national income is good for the country; other factors, such as the distribution of income, or environmental degradation, are neglected. Now, most people are risk-averse with respect to their own incomes, and the national income is the total of the incomes of all the citizens. Therefore, governments aiming to help their people will be risk-averse about the national income.

Fortunately, governmental projects in a country’s portfolio that turn out to have lower net benefits than expected may be counterbalanced by those with higher net benefits than expected. If two conditions are met, the risks can indeed cancel each other out at the portfolio level. The first is that the portfolio is not dominated by one or more large projects in such a way that the associated risks dominate the risk-structure of the portfolio. The second is that there is no interdependence among the projects.

Moore et al. (2017) emphasise that the national income is not only affected by the portfolio of the public projects. It also depends on the portfolio of all the projects and events that affect national income. The question is whether the risk of the project and the risks of the other elements of the larger portfolio cancel each other out. The authors argue that the risk associated with a small project whose net benefits are not positively related to national income becomes cancelled out at the portfolio level, so that the project risk is no longer a disadvantage.

Now, let us go back to the school ventilation project. The chance that it will have a zero effect is remarkably high; it is even 98 percent. The question here is how to evaluate this risk. The ventilation project is relatively small. The correlation between the risk of the project and national income is not positive. This is related to the fact that only two scenarios are possible:

1) Aerosols are a significant factor in COVID-19’s spread. This means the ventilation project has very high benefits. At the same time, the national income is relatively low because the virus has hit the economy.

2) Aerosols do not play a significant role in spreading the virus. This means that the benefits of the ventilation project are zero, while the national income is relatively high. So the correlation between the benefits of the project and national income is negative.

This implies the project reduces the overall risks of the government’s portfolio. This could even be seen as an advantage, but for simplicity we will ignore it now. We are then left with a simple conclusion:

The project risk is not a disadvantage and can be neglected in the decision, which can be based solely on the expected values of the benefits and costs. The expected value of the benefits is 2 billion euros. Consequently, the project can be accepted if its costs are lower than that.

In practice, improving school ventilation would have benefits beyond reducing the spread of COVID-19, such as a better learning environment and less absenteeism due to the flu. Given these other benefits, it follows from the analysis above that even a very small chance that the programme will help prevent another lockdown could then help ensure that the (expected value of the) total benefits are higher than the costs, implying the programme should be implemented.

The way we use portfolio theory and cost-benefit analysis may be relevant to other policies. Consider COVID-19 testing capacity and ‘test and trace’ programmes. Once their capacity is sufficient to deal with large outbreaks, but not with extremely large (unlikely) outbreaks, there may only be a small chance that additional capacity will ever have any benefits. But our analysis could lead to the conclusion that an additional increase in capacity is still rational. Indeed, every small chance to prevent a new lockdown is worth exploring.

The authors would like to thank Elia Smith and Ekaterina Antimirova for their helpful comments. This post represents the views of the authors and not those of the COVID-19 blog, nor LSE.