Douglas W. Allen published a study Covid-19 Lockdown Cost/Benefits: A Critical Assessment of the Literature in the International Journal of the Economics of Business. September 29, 2021. H/T Raymond  Excerpts in italics with my bolds and some added images

Abstract

An examination of over 100 Covid-19 studies reveals that many relied on false assumptions that over-estimated the benefits and under-estimated the costs of lockdown. The most recent research has shown that lockdowns have had, at best, a marginal effect on the number of Covid-19 deaths. Generally speaking, the ineffectiveness stemmed from individual changes in behavior: either non-compliance or behavior that mimicked lockdowns. The limited effectiveness of lockdowns explains why, after more than one year, the unconditional cumulative Covid-19 deaths per million is not negatively correlated with the stringency of lockdown across countries. Using a method proposed by Professor Bryan Caplan along with estimates of lockdown benefits based on the econometric evidence, I calculate a number of cost/benefit ratios of lockdowns in terms of life-years saved. Using a mid-point estimate for costs and benefits, the reasonable estimate for Canada is a cost/benefit ratio of 141. It is possible that lockdown will go down as one of the greatest peacetime policy failures in modern history.

Overview

The term ‘lockdown’ is used to generically refer to state actions that imposed various forms of non-pharmaceutical interventions. That is, it is used to include mandatory state-enforced closing of non-essential business, education, recreation, and spiritual facilities; mask and social distancing orders; stay-in-place orders; and restrictions on private social gatherings.

‘Lockdown’ does not refer to cases of ‘isolation,’ where a country was able to engage in an early and sufficient border closure that prevented trans-border transmission, followed by a mandated lockdown that eliminated the virus in the domestic population, which was then followed by perpetual isolation until the population is fully vaccinated. This strategy was adopted by a number of island countries like New Zealand.1 Here I will only consider lockdown as it took place in most of the world; that is, within a country where the virus became established.

The report begins with an examination of four critical assumptions often made within the context of estimating benefits and costs. Understanding these assumptions explains why early studies claimed that the benefits of lockdown were so high, and also explains why the predictions of those studies turned out to be false. Then I examine the major cost/benefit studies in roughly chronological order, and focus on the critical factor in these studies: distinguishing between mandated and voluntary changes in behavior. Preliminary work on the costs of lockdown is reviewed, and finally a simple cost/benefit methodology is used to generate several cost/benefit ratios of lockdown for my home country of Canada.

In no scenario does lockdown pass a cost/benefit test; indeed, the most reasonable estimates suggest that lockdown is a great policy disaster.

Discussion

Over the course of the Covid-19 pandemic, there has been no public evidence that governments around the world have considered both the benefit and cost sides of their policy decisions. To my knowledge, no government has provided any formal cost/benefit analysis of their actions. Indeed, the steady press conferences and news releases almost entirely focus on one single feature of the disease. Although the focus of government announcements has changed over the year, from ‘flattening the curve’, number of Covid-19 deaths, number of Covid19 cases, hospital capacity, and variant transmissions (especially the delta variant), there has seldom been any official mention of the costs of the actions taken to address these concerns.

The counterfactual number of cases/deaths

If lockdown reduces the transmission of the virus, the natural question to ask is ‘by how much?’ In other words, ‘but for the lockdown’ what would the level of infection/transmission/deaths be? What is the counterfactual to lockdowns?

Early in the pandemic the Neil Ferguson et al. (2020) model appeared to drive many lockdown decisions and was widely covered in the media. Figure 1 reproduces a key figure of that paper (Table 2, p. 8), and shows the results of various types of lockdown on occupied ICU beds. The symmetry, smoothness, and orderly appearance of the functions is a result of the mechanical nature of the model. This type of figure is found, in one form or another, in most papers based on a SIR model.

In Figure 1 the black ‘do nothing’ line is the counterfactual, while the other lines are various types of lockdowns. The harsher the lockdown, the ‘flatter’ the case load, with the blue line being the strongest lockdown. The difference between the black line and another line is the benefit of that particular lockdown in terms of cases delayed. Clearly the exponential growth of the ‘do nothing’ counterfactual leads to enormous differences, and makes lockdown look better.

Given the prediction that lockdowns would lower deaths by one-half, the authors made a dramatic recommendation: ‘We therefore conclude that epidemic suppression is the only viable strategy at the current time. The social and economic effects of the measures which are needed to achieve this policy goal will be profound.’ (Ferguson et al. 2020, p. 16). In retrospect it is remarkable that such a conclusion was drawn. The authors recognized that the ‘social and economic effects’ would be ‘profound,’ and that the predictions were based on the ‘unlikely’ behavioral assumption that there would be no change to individual reactions to the virus. However, given the large counterfactual numbers, presumably they felt no lockdown cost could justify remaining open.

Problems with the ICL model were pointed out immediately:

i) the reproduction number (Rt) of 2.4 was too high;
ii) the assumed infection fatality rate (IFR) of 0.9% was too high and not age dependent;
iii) hospital capacity was assumed fixed and unchangeable; and
iv) individuals in the model were assumed to not change behavior in the face of a new virus.

All of these assumptions have the effect of over-estimating the counterfactual number of cases, transmissions, and deaths.

The exogenous behavior assumption

A major reason for the failure of SIR models to predict actual cases and deaths is because they assume no individual in the model ever changes behavior.9 The implication of ignoring individual responses to a viral threat are dramatic. Atkeson (2021) used a standard SIR model (with exogenous behavior) that included seasonal effects and the introduction of a more contagious variant in December 2020 to forecast daily U.S. deaths out to July 2023. The results of this standard model were typical: the model made apocalyptic predictions on deaths that were off by a factor of twelve by the summer of 2020. However, he then used the same model with a simple behavioral adjustment that allowed individuals to change behavior in light of the value of Rt. The new forecast of daily deaths based on this single addition completely changed the model’s predictive power. The model now tracked the actual progression of the daily deaths very closely.

The fact that individuals privately and voluntarily respond to risks has two important implications. First, it influences how any counterfactual outcome is understood with respect to the lockdown. When no voluntary response is assumed, models predict exponential caseloads and deaths without lockdowns. If lockdowns are imposed and cases coincidently fall, the actual number of cases is then compared to a counterfactual that never would have happened.11 Therefore, not accounting for rational, voluntary individual responses within a SIR model drastically over-states any benefit from lockdown.12

Second, any empirical work that considers only the total change in outcomes and does not attempt to separate the mandated effect from the voluntary effect, will necessarily attribute all of the change in outcome to the mandated lockdown. Once again, this will over-estimate the effect, and quite likely by an order of magnitude.

The assumed value of life

Economic value is based on the idea of maximum sacrifice. Thus, when it comes to the value of an individual’s life, this value is determined by the actual individual. In practice, what is measured is the marginal value to extend one’s life a little bit by reducing some type of harm, and then use this to determine a total value of life.

One problem with using the VSL for estimating the benefits of saving lives through lockdown is that it measures the total value of life based on a marginal value. Thus, using a VSL (which is based on observing ordinary people not at the point of death) as a measure of the value of a life of someone about to die, is likely to provide an over-estimate of the value of the life.

In many Covid-19 cost/benefit studies, however, there is another more serious problem with how the VSL is used. Namely, it is often assumed that

i) the VSL is independent of age, and
ii) that the VSL is equal to around $10,000,000.

Both of these claims are not true.

To assume that the VSL is constant implies that individuals are indifferent between living one more day or eighty more years. Figure 2 shows more reasonable estimates, with the value of a child being seven times the value of an 85 year old. The VSL of $2,000,000 for an 85 year old is based on the assumption that life expectancy is still ten years. For someone who is 85, in poor health with multiple serious illnesses, the VSL would be much lower.

An issue with lockdown costs

It is common in cost/benefit studies to only use lost GDP as the measure for the cost of lockdown. That is, the reduced value of goods and services caused by lockdown is the only cost of the lockdown considered. For example, US GDP over 2020 fell by 3.5%. If 100% of the fall in GDP (approximately $770 billion) is attributed to the lockdown (that is, the virus directly had no effect on production), then compared to the presumed ‘22 trillion’ dollar savings in lives, lockdown seems like an excellent policy.

This type of comparison, however, is entirely inappropriate.

The VSL is based on the utility of life, and therefore, the costs of lockdown must also be based on the lost utility of lockdown. It has been understood from the very beginning of the pandemic that lockdown caused a broad range of costs through lost civil liberty, lost social contact, lost educational opportunities, lost medical preventions and procedures, increased domestic violence, increased anxiety and mental suffering, and increased deaths due to despair and inability to receive medical attention. If the value of lockdown is measured in utility, then the costs of lockdown must be measured in the same fashion. Excluding the value of lost non-market goods (goods not measured by GDP) grossly under-estimates the cost of lockdown.

Other Costs

Lost educational opportunities. Lost, delayed, or poor education leads to reduced human capital that has life long negative consequences.

Additional effects of school closures. Closing schools creates isolation for children, which is known to increase the risk of mental health conditions.

Increased deaths expected from unemployment. Life expectancy depends on wealth levels. McIntyre and Lee (2020) predict between 418–2114 excess suicides in Canada based on increased unemployment over the pandemic year. 

Increased deaths from overdoses and other deaths of despair. Lockdowns disrupt illegal drug channels, often resulting in a more contaminated drug supply. Lockdowns also increase human isolation, leading to increased depression and suicides.

Increased domestic violence. Chalfin et al. (2021) found that much of the increased domestic violence is related to increased alcohol which increased during lockdown.

Lost non-Covid-19 medical service. In the spring lockdown hospitals cancelled scheduled appointments for screenings and treatments (e.g. London et al. 2020; Garcia et al. 2020), this created fear among individuals who required emergency treatments. Woolf et al. (2020) estimate that in the U.S. about 1/3 of the excess deaths over 2020 are not Covid-19 deaths. 

The opportunity costs of lockdown are widespread across societies, and everyone has faced some type of lockdown consequence. These costs are often non-market and in the future, making them difficult for third parties to measure. They are also unevenly distributed onto the young and the poor who have been unable to mitigate the consequences of lockdown.

These characteristics contribute to the lack of attention given to them, and stand in sharp contrast to Covid-19 case loads and deaths that are measured, highly concentrated, and widely reported.

In light of the nature and measurement problems associated with the costs of lockdown, as of July 2021 no true, standard, cost benefit study has been conducted. All efforts have rested on assumptions and guesses of things not yet known. It will still take time for a systematic, ground-up, attempt to determine the total lost quality of life brought about by lockdown. Even though such studies do not exist, there is still weight to the economic logic that, with negligible benefits and obvious high costs, lockdown is an inefficient policy.

Four stylized facts about covid-19

Atkeson et al.’s (2020) paper ‘Four Stylized Facts About Covid-19’ was a watershed result that appeared six months into the pandemic. Using data from 23 countries and all U.S. states that had experienced at least 1000 cumulative deaths up to July 2020, it discovered important features of the progression of the virus across countries that cast serious doubt that any forms of lockdown had a significant large impact on transmission and death rates.

In particular, they found that across all of the jurisdictions there was an initial high variance in the daily death and transmission rates, but that this ended very rapidly. After 20–30 days of the 25th death the growth rate in deaths fell to close to zero, and the transmission rate hovered around one. Not only did Atkeson et al. find a dramatic drop and stability of the death and transmission rates, but the spread in these rates across jurisdictions was very narrow. That is, across all jurisdictions, after 20–30 days the virus reached a steady state where each infected person transmitted the virus to one other person, and the number of daily deaths from the virus became constant over time.

Atkeson et al. speculated on three reasons for their findings. First, unlike the assumptions made in the SIR models, individuals do not ignore risks, and when a virus enters a population people take mitigating or risky actions based on their own assessments of that risk. Second, again in contrast to the classic SIR model where individuals uniformly interact with each other, actual human networks are limited and this can limit the spread of the virus after a short period. Finally, like other pandemics, there may be natural forces associated with Covid-19 that explain the rapid move to a steady state death and transmission rate.

Voluntary versus mandated lockdown channels

There are, by my count, over twenty studies that distinguish between voluntary and mandated lockdown effects. Although they vary in terms of data, locations, methods, and authors, all of them find that mandated lockdowns have only marginal effects and that voluntary changes in behavior explain large parts of the changes in cases, transmissions, and deaths.

A reasonable conclusion to draw from the sum of lockdown findings on mortality is that a small reduction (benefit) cannot be ruled out for early and light levels of lockdown restrictions. There is almost no consistent evidence that strong levels of lockdown have a beneficial effect, and given the large levels of statistical noise in most studies, a zero (or even negative) effect cannot be ruled out. Maybe lockdowns have a marginal effect, but maybe they do not; a reasonable range of the decline in Covid-19 mortality is 0–20%.

An alternative cost/benefit methodology

Professor Caplan (2020) has suggested a thought experiment that provides a solution for the cost measurement issue. Rather than attempt to measure a long list of costs and add them up, Caplan proposes a method that exploits our willingness to pay to avoid the harms of lockdown. If lockdown imposed net costs of $1000 on a person, then that person would be willing to pay up to $1000 to avoid lockdown. Caplan, however, poses the matter in terms of time rather than dollars.

Professor Caplan’s thought experiment addresses the total costs of all covid prevention as perceived by each person living under it, and therefore is an appropriate utility based cost measure to hold up against the value of lives saved through lockdown: X is the number of months a person is willing to pay to avoid lockdowns, other things equal.

For any random individual, X could take on a wide range of values. For some this past year has been horrific, and perhaps they would have preferred it never happened. Perhaps they suffered violence or abuse that was fueled by frustration and alcohol while locked down during a long stay-at-home order. Or perhaps they lost a business, a major career opportunity, or struggled over a long period of unemployment and induced depression. For these people, X equals 12 — they would have paid 12 months of their life to have avoided this past year. Others might have been willing to pay even more.

For the vast majority of populations, Covid-19 was not a serious health risk. Lockdowns provided no benefits and only costs. Thus, for the vast majority, X likely takes on a value in the order of a few months.

As of March 2021 the pandemic had lasted one year, and by assumption the average Canadian had lost two months of normal life due to lockdown. The population of Canada is 37.7 million people, which means that 6,283,333 years of life were lost due to Canada’s lockdown policy. This number of years can be converted into ‘lives’ using average life expectancy.

The average age of reported Covid-19 deaths in Canada over the first year of the pandemic was 80. In Canada an average 80 year old has a life expectancy of 9.79 years. This means that the 6,283,333 million years of lost life is equivalent to the deaths of 643,513 80 year olds. As of March 22, 2021 Canada had a total of 22,716 deaths due to Covid-19 (or 222,389 lost years of life).

Conclusion

After more than a year of gathering aggregate data, a puzzle has emerged. Lockdowns were brought on with claims that they were effective and the only means of dealing with the pandemic. However, across many different jurisdictions this relationship does not hold when looking at the raw data.

A casual examination of lockdown intensity and the number of cumulative deaths attributed to Covid-19 across jurisdictions shows no obvious relationship. Indeed, often the least intensive locations had equal or better performance. For example, using the OurWorldInData stringency index (SI) as a measure of lockdown, Pakistan (SI: 50), Finland (SI: 52), and Bulgaria (SI: 50) had similar degrees of lockdown, but the cumulative deaths per million were 61, 141, and 1023. Peru (SI: 83) and the U.K. (SI: 78) had some of the most stringent lockdowns, but also experienced some of the largest cumulative deaths per million: 1475 and 1868.

These unconditional observation puzzles are resolved by the research done over the past year. The preconceived success of lockdowns was driven by theoretical models that were based on assumptions that were unrealistic and often false.

The lack of any clear and large lockdown effect is because there isn’t one to be found.