The approach taken in New Zealand to dealing with Covid-19 may result in unnecessary loss of life. The outbreak of a hitherto unknown disease poses an important new risk to humans, so it is appropriate to devote resources to mitigating this risk. These risk mitigating resources mean some output is foregone. In other words, our lives are going to be somewhat more risky and people will be somewhat poorer, than would have been the case without this new disease.
A key question for public policy is where to strike the balance between reduced risk and foregone economic output. One way to guide the optimal allocation of risk reducing efforts is the concept of “value of a statistical life” which simply summarizes the collective willingness to pay for a reduction in risk. Someone paying more for a safer car, with other features equal to a less safe car, or taking a lower wage for an otherwise similar but safer job (conversely, if ‘danger money’ is part of the pay for a risky job) exhibits the behaviour summarized in ‘value of statistical life’ (VSL) estimates. The VSL used in New Zealand is about $5 million.[1]
So a simple comparison suggests that actions to save, say, 200 lives would be sensible if they involved foregone output of less than one billion dollars. Unfortunately, people misinterpret such thinking, and set it up as a contest between health and the economy. This sort of contest metaphor comes through in a popular tweet by the New York governor, Andrew Cuomo:
“If it’s public health versus the economy, the only choice is public health. You cannot put a value on human life.” (Andrew Cuomo, Twitter, March 24, 2020)
Great politics. Lousy policy.
If we overinvest in saving some lives we underinvest in saving others. Excessively costly interventions designed to save some lives can end up causing more deaths.[2] Instead, socially optimal risk reduction should aim to reduce risk from a new source of danger to the point where the marginal cost per life saved is the same as for other risk reducing activities.
I experienced violation of this principle at first-hand about 20 years ago when I was working on a project evaluating landmine clearance. The Thai army were clearing the minefield that my fieldwork was based on, using mechanical clearance with a variety of devices like heavy rollers, flails, magnets and so forth. To be very, very, very sure of driving risk of unexploded landmines as low as possible, they went over the same plot of land 16 times with their various mechanical operations. Each extra one of these 16 passes over the same ground added to the cost, while the marginal reduction in risk got less and less. On the road outside the field, no one riding motorbikes wore helmets, and usually two adults, a baby and a farm animal were all perched in precarious positions. Of course, this was highly dangerous. Reallocating some of the resources used in the multiple mechanical operations in the minefield into road safety initiatives like policing road rules or subsidizing crash helmets would have saved more lives.
The approach in New Zealand to Covid-19 is like the Thai army with the landmines. After some vagueness about strategy, it is now stated as “elimination”. The SARS‑CoV-2 virus is now endemic in most countries, so elimination essentially requires that we keep a closed border or strict quarantines until a vaccine is available. So we will forego a lot of exchange possibilities and cut economic output in an attempt to bring one health risk down to zero.
There are at least two grounds for concern about the New Zealand strategy. First, the people making decisions are the same ones who botched the preparation for the arrival of Covid-19 and so there is little reason to have faith in the wisdom of their choices. I say “botched” advisedly and would ask readers to consider the following four facts:
- Taiwan recorded their first case of Covid-19 on 21 January, a full month before New Zealand’s first case
- Taiwan usually has about three million visitors a year from China, while New Zealand gets about 400,000. The gap is even bigger in terms of visitors to China (who posed a risk of spreading the disease upon their return)
- Taiwan has not had a lock-down
- Yet despite earlier exposure and much greater risk due to more travel to and from China, Taiwan has just 22 cases per million of Covid-19 while the rate in New Zealand is currently 17 times higher
Similar comparisons could be made with respect to Hong Kong or South Korea, who also provided lessons on management of this new risk. The complacency by politicians and bureaucrats in New Zealand, who had the advantage of an extra month for preparation and much greater distance from China, is staggering. Obviously that chance to respond to the risk in a low-cost manner was missed and so a very costly lockdown has resulted. While we can hope for better decision-making going forward, there is little reason to be confident of this.
In particular, a second concern with the New Zealand strategy is the failure to have informed discussion about trade-offs and optimal risk reduction. The risk from a pandemic obviously differs from my simple example of landmines and road safety in Thailand. For one thing, the risk today may be low, but the future risk may be much higher as the virus spreads. Thus, it is important to consider forward-looking measures of risk.
In that regard, it is mainly the BIG SCARY NUMBER approach to political decision-making that has been evident, rather than a careful discussion about trade-offs. When announcing the lockdown, the Prime Minister claimed that if strong action was not taken against the spread of the SARS‑CoV-2 virus, New Zealand’s health system would be overwhelmed and tens of thousands would die:
“If community transmission takes off in New Zealand the number of cases will double every five days. If that happens unchecked, our health system will be inundated, and tens of thousands of New Zealanders will die”[3]
There is very little critical scrutiny of this claim, which seems to be based on modelling done by public health academics at the University of Otago. No empirical data from New Zealand on key parameters informed this modelling, which used an off-the-shelf European model (http://covidsim.eu). It is unknown whether the spread of the virus in a low-density, younger population like New Zealand is the same as in high density, public transport-reliant Northern Hemisphere populations, that are older, and have worse respiratory health to start with.[4] At best, these models are informed projections. It is also the case that across the six scenarios modelled by the Otago academics, the average number of forecast deaths was just over 8000 (mean 8,300, median 8,600).[5] So Prime Ministerial claims that “tens of thousands will die” are vague at best and alarmist at worst.
Moreover, the projections have not been presented in a way that empowers people to make considered judgements. We are shown big numbers of projected deaths, with no context to interpret them. Deaths are bad, more deaths are worse, so it feeds into the narrative that there is no alternative to the approach taken. This approach to public policy tends to disempower people who are not privy to the epidemiological models.
Of course this is unwarranted, as ordinary people make decisions about trade-offs all the time and typically use careful judgement when doing so. One contribution I want to make with this essay is to show that it is entirely possible to recast these projections of forecast Covid-19 deaths in terms of reductions in life expectancy, and there are four advantages of doing so:
- Life expectancy is intuitive to most people, as a measure of the lifespan that can be expected by the average person;
- The calculated impact on life expectancy can be used for risks that change in the future, such as if controls on spread of SARS-CoV-2 fail;
- Life expectancy summarizes the impact on everyone in New Zealand, and is naturally weighted in the sense that the people who will suffer the consequences the longest (the young) contribute more to the average value; and,
- Life expectancy is affected by health shocks and by income shocks and so it naturally allows analysis of trade-offs without needing so-called contests between health and the economy which may initially seem incommensurable.
In terms of this last point, a key fact being ignored in New Zealand discussions is that poorer people and poorer societies have lower life expectancy. The actions being taken to deal with the Covid-19 risk are making New Zealand poorer, and so will reduce life expectancy. While there has been some discussion of possible ‘micro-level’ side-effects of the lockdown, such as potentially more suicides but fewer traffic accidents, it will be at the ‘macro-level’ via income effects on life expectancy that the major effects will occur.
It turns out that life expectancy in New Zealand is more sensitive to changes in real income than is so for many countries. Using World Bank data on real GDP per capita (in purchasing power terms) and life expectancy, from 1990 to 2017, the income-elasticity of life expectancy for New Zealand is estimated as 0.171±0.009.[6] In other words, a ten percent decrease in real per capita GDP reduces life expectancy by 1.7 percent. The most recent period life tables for New Zealand report that male life expectancy was 79.5 years and female life expectancy was 83.2 years, so 1.7 percent of the average of those two values is 1.4 years. In other words, if real per capita GDP in New Zealand falls by ten percent due to the lockdown and other effects associated with Covid-19, life expectancy would be predicted to fall by 1.4 years.
In contrast to the powerful effect of real income growth on life expectancy in New Zealand, comparator countries show smaller effects. The income elasticity of life expectancy for the United States is 0.120±0.007, and for the United Kingdom it is 0.147±0.013.[7] Moreover, while variation in real per capita GDP explains 96% of variation in average life expectancy for New Zealand, it explains only 92% and 85% for the US and the UK. One possible reason for a stronger effect of income in New Zealand is that we may ‘free ride’ to a certain extent; we do not bear big development costs of pharmaceuticals and other life extending treatments but get to benefit from them at relatively low cost due to efficient purchasing arrangements, such as via Pharmac, that help turn income growth into bigger increases in life expectancy.
No one knows how much lower New Zealand’s real GDP per capita will be as a result of the lockdown and other steps taken to deal with the risk of Covid-19. So to help people think about the trade-offs, I present a range of values: if real GDP per capita falls by five percent, that would translate into a fall in life expectancy of 0.7 years; ten percent would be 1.4 years lower life expectancy, and with a 15% fall in real income then life expectancy would be reduced by 2.1 years. Some readers might object that these effects are on some unidentified people sometime in the future, but exactly the same point can be made about the forecast deaths from the epidemiological models. Moreover, the current calculation has the benefit of being based on actual New Zealand data, rather than just on assumed values.
Before turning to the life expectancy effects of various forecasts of deaths due to Covid-19, it is helpful to provide some context to trends in life expectancy in New Zealand. One way to do this is to use (backward-looking) cohort life tables. The most recently available show that for males born in New Zealand in 1942, life expectancy is 75.1 years. This is 4.5 years longer than for the cohort born a decade earlier in 1932 and 10.5 years longer than for the cohort born in 1922. For females from the same cohorts, who live longer than males on average, the rise in life expectancy has been about four years per decade.
Cohort studies cannot tell us about the more recently born, who are only part way through their lifespan, unless projections for future age-specific mortality rates are used. Instead of these projections, period life tables are often used to summarize mortality experiences of people of all ages, drawn from different cohorts, at a point in time. New Zealand’s 1985-87 life tables show male life expectancy was 71.1 years, which rose to 74.4 years in 1995-97 and 78.3 years in 2005-07. The latest period life tables from Statistics New Zealand, for 2012-14, have male (female) life expectancy at birth of 79.5 years (83.2 years). So these data show male life expectancy rising by about 3.1 years per decade, and a little bit less for females.
The period tables underestimate improvements over time because they use mortality rates in a single era but as today’s young people age they will benefit from the lower age-specific mortality rates in the future resulting from on-going improvements in medical technology. For my purposes, an average of the two types of life expectancy trends is fine. So the background to the life expectancy implications of Covid-19 is that life expectancy in New Zealand has been increasing by about four years every decade. So if it takes you ten minutes to read this, it is really only six minutes of your remaining life gone.
What do the big scary numbers for forecast Covid-19 mortality look like, in terms of life expectancy? I start by considering the latest data for deaths due to influenza and pneumonia; in 2017 there were 869 deaths in New Zealand from this cause, with 83% of them for people aged 80 and above. The reason to use these as a base is not to argue that Covid-19 is “just the flu” because most evidence (even without systematic testing to get unbiased infection rates) suggests that Covid-19 is far worse than the flu. However, there is likely to be considerable substitution in deaths between the flu and Covid-19, especially as New Zealand is entering the flu season while the Northern Hemisphere was leaving flu season as Covid-19 struck. For example, one reason suggested for why Italy has such a high Covid-19 death rate is that the flu season there was relatively mild and so people who survived the flu season, but may not have in other years, were still alive to be struck down by Covid-19.[8] Moreover, most of the people who die of Covid-19 have other health conditions, and there is considerable variation in reporting, in terms of whether someone dies of Covid-19, or with Covid-19.
In order to model life expectancy implications of a “one flu-shock unit” increase in deaths, I take age-specific mortality rates from the 2012-14 period life tables, and raise them so as to increase deaths by 870, with the same age pattern as the influenza deaths. For simplicity, I just do this exercise for male life expectancy, which would fall from 79.5 years to 79.3 years. This shock can also be considered in terms of infections, based on an estimated infection fatality rate for Covid-19 of 0.66%, that takes account of censoring and measurement error.[9] So a one-flu shock increase in deaths due to Covid-19 maps to 132,000 New Zealanders being infected with the SARS-CoV-2 virus. If so many people were infected (and detected), it seems very likely that the lockdown would extend for much longer. I summarize the life expectancy effects of this shock size and other shock sizes in the following table:
| Extra deaths | Life expectancy | Change from base | |
| 1 × flu-shock | 870 | 79.3 years | -0.2 years |
| 2 × flu-shock | 1750 | 79.2 years | -0.3 years |
| 4 × flu-shock | 3500 | 78.9 years | -0.6 years |
| Median Otago forecast (»10×flu shock) | 8560 | 77.9 years | -1.6 years |
If deaths due to Covid-19 were to be twice as many as the annual toll from flu, average life expectancy would fall by 0.3 years. To put this in context, this would undo the amount of recent progress in raising life expectancy that typically occurs in less than one year. If the Covid-19 impact would have been four times the usual flu shock, which would involve 3500 extra deaths, life expectancy would fall by 0.6 years (equivalent to the progress made in raising life expectancy that occurs in less than two years). It is worth noting that this level of deaths would give New Zealand a Covid-19 death rate that is more than twice as high as the current Covid-19 death rate in Spain, which seems an unlikely outcome.
The final shock considered is the median of forecasts made by the public health academics at Otago University, of 8560 deaths. Conveniently, this is also equivalent to ten times the usual flu shock. A death toll of this magnitude would reduce life expectancy by 1.6 years. Such a death toll is consistent with about 1.3 million people being infected with SARS-CoV-2, which is almost 30 percent of all New Zealanders. While infection rates are not being tabulated by country, no country has ratios of cases to population above one percent and no country with a population over one million has a case-to-population rate above 0.3 percent (https://www.worldometers.info/coronavirus/#countries). So an infection rate that would give a Covid-19 death toll in New Zealand that was equivalent to ten times the usual flu death toll seems quite far from anything yet experienced anywhere in the world.
With these estimated impacts on life expectancy it is now possible to compare both the health shock and the income shock using the same measuring rod of life expectancy. For example, if the lockdown leads to a ten percent fall in real GDP per capita, we can expect life expectancy to be 1.4 years less than otherwise. This could be justified as a rational investment in risk reduction if it prevented a Covid-19 death toll that would be ten times the usual flu shock. In contrast, if the death toll would otherwise have been four flu-shocks or less (so 3500 or fewer deaths), shrinking the economy by ten percent would reduce life expectancy by 1.4 years, in order to avert a risk that otherwise would have produced a 0.6 year decline in life expectancy. In other words, this mix of risk and response would take almost one year off the expected life span of everyone in New Zealand. The apparent kindness of doing everything possible to limit deaths due to Covid-19 would, instead, be killing more people by making them poorer.
There are no easy choices here. Nevertheless, it is possible to present the trade-offs in ways that can be interpreted by ordinary people, who rightly should have far more input into these decisions than they have to date.
Footnotes:
[1] https://www.stuff.co.nz/national/politics/110753822/is-a-life-worth-47-million
[2] https://link.springer.com/article/10.1023/A:1015635518824
[3] https://www.stuff.co.nz/national/health/coronavirus/120501534/coronavirus-jacinda-ardern-just-made-the-most-consequential-decision-of-her-career-putting-nz-on-house-arrest
[4] There is also a more subtle criticism of the “If that happens unchecked…” phrasing by the Prime Minister. This implies no change in behaviour but we know from the Lucas Critique that when circumstances change, people change their behaviour, so forecasts that are not based on “deep” or “structural” parameters provide poor predictions. The virus reproduction rate is unlikely to be a deep parameter, which is why careful treatments distinguish between R0 – the reproduction number in the absence of behavioural change or immunity, and R‑effective (see https://fivethirtyeight.com/features/coronavirus-case-counts-are-meaningless/). So a forecast that assumes no behavioural change by people seeing an epidemic unfolding is not a plausible counterfactual.
[5] https://www.health.govt.nz/system/files/documents/publications/report_for_moh_-_covid-19_pandemic_nz_final.pdf
[6] Based on a double logarithmic specification, with heteroscedasticity and autocorrelation (one-year lag) robust standard errors and with 96% of variation explained by the regression. Dickey-Fuller tests do not reject the null hypothesis of unit roots in life expectancy (p=0.29) and real per capita GDP (p=0.90) but these two variables are cointegrated (p<0.001 for rejecting the unit root null, for the residuals) and so the regression reflects a stable long-run relationship that is not subject to spurious regression problems.
[7] I use the UK and the US for comparisons because they have income elasticity of life expectancy values recently published in The Lancet (August 18, 2012, p.649), which are higher than for other countries and which have increased over time. That these two countries have higher and rising income elasticities of life expectancy makes the even higher elasticity for New Zealand even more notable.
[8] https://www.bloomberg.com/news/articles/2020-03-31/italy-s-mild-flu-season-may-solve-mystery-of-coronavirus-deaths
[9] https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext