Our investigations of the potential impact of different approaches to reporting show the usefulness of an internationally agreed standard for assessing the impact of the pandemic. However, in the absence of such a standard we use national official estimates of Covid-19 mortality to understand the impact of lockdown policies. Data is supplied by the Our World in Data programme (Beltekian et al. 2020).
An initial task was to estimate the overall impact which policy responses could plausibly have had on Covid-19 mortality. To achieve this we undertook regression analysis examining the extent to which variation in Covid-19 deaths across all 37 OECD countries might be explained by socio-economic and demographic differences which no government could reasonably be expected to address during the timescale of a pandemic. A number of such exogenous determinants have already been highlighted in the literature. Of these one of the most clearly established mortality risk factors is a positive association with age; all other things considered, older sufferers are more likely to die from contracting Covid-19 than are younger people (Dowd et al. 2020). Therefore, across countries, populations which include a greater proportion of elderly people are likely to report higher death tolls. Similarly, those living in closer proximity to others may be more likely to pass on and contract the respiratory disease, hence variation in population density across nations may be a determinant of Covid-19 deaths (Rocklöv and Sjödin 2020). Beyond simple average population density, the degree to which populations are clustered in large urban centres may influence Covid-19-related mortality (Stier et al. 2020). Health outcomes might also differ because of within-country variation in wealth (Marmot 2005) which we capture in our regression by controlling for the Gini coefficient of income inequality for each country. Richer nations are likely better placed to limit the spread of pandemics (e.g. Hosseini et al. 2020), hence we use per capita GDP as a regressor to net-out cross-country differences owing to wealth. Finally, previous studies (e.g. Fraser et al. 2004) have highlighted that early detection may play a crucial role in halting virus spread, hence it seems plausible that countries which were exposed to Covid-19 earlier in the pandemic, and that therefore had less time to prepare, faced worse consequences. To account for this, we use the regressor “warning days”—the length of time (in days) between the WHO declaring that the Covid-19 outbreak was a “Public Health Emergency of International Concern” on 30th January 2020 and the country recording its 100th confirmed case (WHO 2020c).
The linear regression we use, details of which are presented alongside full results in Online Appendix 3, is deliberately simple and we are not claiming that the model necessarily captures causal relationships. However, even after including the list of exogenous factors which have been hypothesised to be major socio-economic and demographic drivers of cross-country variation in mortality rates, over 75% of the cross-country variation in Covid-19 mortality differences remains unexplained. Covid-19 deaths vary greatly across countries due to factors beyond socio-economics and demographics; the major remaining determinant is the policy responses implemented by national governments of which the most obvious difference is when different countries implemented lockdown.Footnote 8
To investigate the impact of lockdown upon cross-country variation in Covid-19 mortality we calibrate country-specific SEIR models. SEIR models have a long history of development (Li and Muldowney 1995) with applications across a variety of infectious diseases including measles (Bolker 1993), HIV (Shaikhet and Korobeinikov 2016) and Ebola (Lekone and Finkenstadt 2006). More recently SEIR models have also been applied to Covid-19 (e.g. Annan 2020; Flaxman et al. 2020; Pei et al. 2020). However, as far as we are aware, ours is the first study to use the SEIR modelling framework to examine the effects of lockdown timing across multiple countries in the same study, and the first to combine these results with financial forecasts to obtain cross-country implied price of life estimates.
Price of life estimates derived in this paper are of critical importance given that government intervention has the ability to save life, yet trades-off against other goods. For example, closing schools is expected to reduce the transmission of infectious disease, hence decreasing the number of lives lost in a pandemic by imposing a human capital cost on today’s children (Viner et al. 2020). Likewise, there is evidence that the more stringent the government intervention to reduce the spread of coronavirus, the fewer lives that have been lost (Stojkoski et al. 2020). This too is not free: we all pay with restrictions on our basic freedoms. Beyond coronavirus, governments spend money and introduce legislation which imposes significant costs on society in a variety of sectors: healthcare (NICE 2012), road safety (DfT 2016), and safety at work legislation (HSE 2016). Governments also often have to consider multiple policy options for issues of environmental concern, be that considering pollution (Ackerman and Heinzerling 2002), climate change (Stern 2007) or biodiversity loss (Ellis et al. 2015). Here too, lives can be saved and lost as a consequences of policy decisions. Hence understanding how governments should value life is of critical concern. Indeed, a significant section of relevant policy documents is occupied by discussion of the value which a government should place on statistical life when evaluating policy (e.g. The Green Book; H.M. Treasury 2018).
In the case of coronavirus, there are already studies which aim to assess the economic value of particular policy interventions by reducing the number of lives lost. Hale et al. (2020) ask: how much of one year’s consumption would an individual be willing to forgo in order to reduce the mortality associated with Covid-19, suggesting the answer lies in the range one-quarter to one-half depending on exact mortality rates. Underpinned by assumptions about the rate of transmission and how policies may affect this, Greenstone and Nigam (2020) show the economic benefit of social distancing measures in the USA to be very substantial—about $8 trillion. Similarly, Thunström et al. (2020) use initial global estimates for the basic reproductive rate, and assume decreases to transmission from policy intervention from studies on Spanish flu, to go further. They conduct a cost–benefit analysis for similar measures, again in the USA, showing that the net benefits exceed $5.2 trillion. Gandjour (2020) and Holden and Preston (2020) conduct similar cost–benefit style analyses for Germany and Australia, respectively, both highlighting that lockdown comes out net positive. Here we ask a different but related question. Not whether lockdown makes economic sense, but rather what the timing of interventions reveal about the relative prices different governments place on their citizens’ lives. We focus on 9 countries with very different mortality rates and intervention timing—if there are discrepancies between countries for the price of life, they are most likely to be shown in this set of countries. In China, lockdowns were implemented on a province-by-province basis on very different dates. Therefore, at the country-level our GDP calculations would be incomparable with other nations. To overcome this challenge, we additionally parameterise an epidemiological model for Hubei, the province worst hit by the pandemic. We use the results from Hubei in our price of life calculations to maintain comparability across countries.
To be clear, the implied price of life should not be regarded as comparable to the Value of a Statistical Life (VSL).Footnote 9 Specifically, VSL is a concept from normative economics—how much consumption should governments be willing to trade-off for an increase in the number of lives saved. This is a question which can be answered through stated-preference methods as has been done elsewhere (e.g. Alberini 2005; Carthy et al. 1999; Jones-Lee 1974). Rather, the implied price of life we calculate can be seen as an answer to the positive economics question of how governments actually do price lives saved in terms of consumption lost when making policy decisions.
Calculating the Implied Price of Life
The key insight is that as the pandemic progressed governments continually had to decide when the moment was right to introduce a lockdown. Earlier lockdowns would save more lives, but likely impose greater immediate costs upon the economy. Likewise, delaying lockdown also delays the point at which a government becomes either morally or legally responsible for addressing the costs which such restrictions impose upon business. Therefore, ex-ante the expectation was that earlier lockdown meant greater financial cost. Ex-post, it seems governments may have been somewhat wrong to make that assumption as longer-term earlier lockdowns actually appear to be associated with shorter overall lockdown length, as is clear in Online Appendix 4, which in turn result in lower long-term economic costs (Balmford et al. 2020). Nonetheless, early imposition of lockdown imposed the certainty of cost, while a delay held out the possibility that the epidemic may turn out to be less severe than expected. Gambler governments chose to delay rather than act.
The chosen date of lockdown reveals a government’s preferences regarding the trade-off between avoided deaths and GDP losses.Footnote 10 Relative to the chosen lockdown date, a later lockdown would have cost more lives, but reduced the financial impact. In its choice of lockdown date a government implicitly accepted the associated GDP loss rather than bear a greater death toll. Earlier lockdowns would have had the reverse effect; saving more lives but at a greater cost to the economy. In choosing not to enter lockdown earlier, the government rejected the higher financial cost of earlier lockdown in favour of more deaths. Hence, we are able to calculate both accepted and rejected prices for human lives: upper and lower bounds for the implied price of life in each country.Footnote 11
A criticism of this method may be that decision makers at the time were unaware of the benefits of lockdown for public health. The evidence, however, points to the contrary. For example, it was reported in the print media at least as early as 7th March that the lockdown in Wuhan was showing signs of slowing the spread of coronavirus (Qin 2020). Within the UK there is evidence that scientific advisors notified the UK government of the benefits of lockdown two weeks prior to its imposition (Barlow 2020).Footnote 12
Calculations of the implied price of life for each country require two data points. First, the differential effect on human lives lost from a marginal change in lockdown date. Second, the marginal effect on GDP from the same change in lockdown date.
Modelling Deaths Across for Different Lockdown Dates
We use a compartmental epidemiological model to simulate the epidemic in each country and in particular to predict the outcomes of the counterfactual scenarios in which lockdown dates are changed. In this type of model, at any moment in time the population of a region or country is distributed between compartments according to disease status, and the function of the model is to describe (and predict) how the population flows between these compartments as the epidemic progresses. In the SEIR model which we are using, there are four compartments corresponding to Susceptible (i.e., not infected, but vulnerable to the disease), Exposed (a latent stage usually lasting a few days, where the victim has been infected but is not yet infectious), Infectious (at which point they can pass the disease on to others), and Removed (meaning they are no longer infectious and may be either recovered from the disease and immune, or else dead). In more complex models, the population may also be subdivided according to age and other factors, with each subdivision being compartmentalised according to disease status as previously described. This would allow for a more detailed representation of the structure of society and the progress of the epidemic as it spreads through the population, but such detail would greatly increase computational demands (especially for large ensembles of simulations as we are using here) and is not necessary for this work. For a full description of the model we are using, see Annan and Hargreaves (2020) and also House (2020) where the underlying model equations were originally presented. The flow of the population between the compartments depends on parameters which we estimate by fitting the model to observational data for each country. This model fitting process follows the standard Bayesian paradigm of defining prior distributions for uncertain parameters, running the model numerous times with parameters sampled from these priors, and calculating the likelihood on the basis of how well the model outputs match the specific observational data that we are using. This process (using a Markov Chain Monte Carlo approach) is described in detail in Annan and Hargreaves (2020). This approach requires around 15,000 model simulations for each experiment (i.e. country) and the results are represented by an ensemble of model simulations that samples our posterior probability distribution.
One critical parameter of the model, which has been widely discussed in the literature and media, is the reproductive number or R, which is the number of new cases that each infectious case generates in a fully susceptible population. If R is greater than 1, the epidemic initially exhibits exponential growth until it infects a sufficiently high proportion of the population that the remaining susceptible fraction substantially shrinks. If R is less than 1, the epidemic decays, again exponentially. In our estimation procedure, we assume that all uncertain model parameters are fixed in time apart from R, which is treated as piecewise constant. We consider three discrete periods within which R is constant. First, there is an initial period prior to “lockdown” controls being imposed by governments. A new, lower value for R is then assumed to apply during the period of strict controls, with a third value applying after the controls are significantly relaxed. Country specific lockdown dates that we use are detailed in Online Appendix 4. In reality, R and other model parameters are likely to vary somewhat during these periods but this piecewise constant approach has been widely used and captures the dominant features of the system (e.g. Flaxman et al. 2020).Footnote 13
Due to serious limitations in the testing and reporting of case numbers, we rely exclusively on daily reported death numbers for the calibration of our model. Again, this is a common approach which is justified on the basis that the reporting of deaths is usually far more consistent and reliable than case numbers which depend strongly on testing capacity and policy. An alternative approach would be to use the number of excess death. While this may better reflect the number of deaths caused by Covid than reported death statistics, daily excess death data are not available. Moreover, the key results in the model are driven by changes in the rate of infection, hence even if death numbers in a particular country are underestimated due to systematic biases, this will not usually bias the estimates of model parameters. Therefore to calibrate the models we use daily reported deaths from Our World in Data up to 9th June (Beltekian et al. 2020), and later suggest how accounting for excess mortality would alter our estimates.
The prior estimate for R after the release of lockdown is taken to be N(1,0.22) which represents our assumption that the policies are intended to be as open as possible while keeping the epidemic controlled. In many cases, there are insufficient data to constrain this prior estimate strongly, and therefore it plays a greater role in our results than the priors used in earlier phases of the epidemic. Estimates of all the R values, as well as our priors, are detailed in Online Appendix 5. Lockdown clearly reduces the infection rate across the board. Easing lockdown allows the infection rates to increase again.
Figure 2 compares observed and modelled deaths in the UK, showing deaths on the (exponential) vertical axis over time. Modelled mortality (the solid line) closely matches the actually observed deaths (circles), illustrating that the modelling framework is flexible enough and the methodology sufficiently rigorous that the epidemiological model well replicates the observed patterns in the UK. Indeed, only on 3 days do observed deaths fall outside the 95% confidence interval (shaded area), and all such occurrences are in the post-lockdown period when the number of daily deaths is comparatively low. Similarly, close relationships are displayed for the other countries in the equivalent plots (Online Appendix 6), highlighting that the model well captures the country specific pandemic pathways.
In order to calculate the effects of changing the dates of lockdown, we use the fitted parameter values, and perform simulations in which the date of imposing lockdown is changed—either delayed or advanced by 3 days. We also explore advancing or delaying lockdown by 7 or 12 days, results of which are presented in Online Appendix 7. This approach is similar to that of others (e.g. Flaxman et al. 2020) in which the effects of policies have been analysed. Since we are using a single date to represent the net effect of multiple policies which were introduced across a period of several days, it would be more precise to interpret these scenarios as representing a change in the timing of all such policies by the given number of days. Likewise, we identify the impact of lockdown using within-country variation in the rate of infection. Therefore, to the extent that the stringency of policy interventions vary between countries, our simulations reflect the same country-specific set of policy interventions of the same stringency being implemented either earlier or later. That said, the lockdown is widely believed to be the most important of these measures (Flaxman et al. 2020) and so we consider our interpretation to be a reasonable approximation of the impacts of lockdown and variation therein. Differences in total mortality for each country dependent on date of lockdown are calculated to 24th June 2020. We also calculate the number of deaths that likely would have occurred were no lockdown implemented, again to the 24th June 2020. For illustrative purposes, the graph of predicted daily deaths for the UK under such a scenario is in Online Appendix 8.Footnote 14 In all cases, no correction is made for the possibility that hospitals got overwhelmed, causing an increase in infection-fatality ratios. To the extent that such an outcome would have occurred, yet more lives would have been lost under the delayed- and no-lockdown scenarios.
The Impact of Lockdown Decisions on Lives Lost
Table 3 highlights the likely impacts of lockdown policy. It is clear that the imposition of lockdown likely saved in excess of 14 million lives across the countries we examine. This overall analysis of lockdown is similar to that of Flaxman et al. (2020) and comparison of overlapping results shows that they are in most cases strikingly similar.Footnote 15 However, we caution against over-interpreting the result: it is likely that even without a formal lockdown, people would have socially distanced and engaged in other behaviours to limit Covid-19 deaths. Nevertheless, earlier governmental action would have saved a large numbers of lives, particularly in countries such as the UK and US who acted relatively late. Pre-lockdown reproduction rates are substantially greater than one, hence across all countries, longer delays result in exponentially greater losses of life.
Table 3 The human impact of imposing lockdown, and how that would have varied by earlier or later intervention Economic and Financial Consequences of Lockdown
The previous sub-section presented clear evidence that the choice of when to impose lockdown drastically affects the likely number of deaths. Moreover, there is significant heterogeneity across countries in the number of lives that would have been saved had lockdown been implemented just 3 days earlier or later. How does this heterogeneity translate into the implied price of life across countries?
To assess the price of life we require estimates of the financial cost of lockdown on GDP. We first assume that the full cost of any extension to the length of lockdown is felt in the year 2020. Therefore, we estimates the cost to GDP by comparing the last IMF forecasts of national GDP in 2020 prior to the pandemic (from October 2019; IMF 2019) with their most recent forecast for 2020 (April 2020, IMF 2020b).Footnote 16
Further assumptions are needed to understand the cost of a marginal extension to lockdown. The first is the relationship between lockdown length and cost to GDP. In line with the best available evidence, from studies in the US (Walmsley et al. 2020) and thirty pan-global countries (with a focus on European nations, Fernandes 2020), length of lockdown appears to be directly proportional to the percentage GDP loss. Of course, not all of the GDP loss associated with an extended lockdown is the result of the policy decision alone: progression of the pandemic sufficient to warrant a lockdown (extension) would reduce GDP outlook anyway and there is good evidence that people were changing their behaviours to enact social distancing in advance of direct regulations (Gupta et al. 2020). Moreover, it is not just the domestic pandemic which causes GDP losses—some is also driven by the state of the virus in other nations owing to trade (Mandel and Veetil 2020). Hence we must also make an assumption about how much of the loss in GDP in any given country is the result of the lockdown policy, rather than other factors associated with the ongoing pandemic. Andersen et al. (2020), Chronopoulos et al. (2020) and Goldsztejn et al. (2020) have all teased apart the effects of lockdown policy from the wider pandemic. All three suggest that the GDP loss caused by lockdown policy is approximately 15% of the total GDP loss experienced by each country.Footnote 17 We note of course that there are reasons to believe this figure could be an over- or under-estimate of the proportion of cost attributable to the lockdown policy, and that this could also vary somewhat by country given that lockdown policy may have different impacts on different industries.Footnote 18 Nonetheless, we see the 0.15 estimate as offering a reasonable ball-park figure, and so adjust predicted GDP losses as per Eq. 2:
$$\Delta GDP_{ij} = \left( {\frac{{\Delta Lockdown \;length_{i} }}{{Actual \;lockdown\; length_{j} }}} \right) \times IMF\; forecast\; GDP\; loss_{j} \times 0.15$$
(2)
Equation 2 states that the GDP loss caused by changing the length of lockdown by some amount (either 3, 7 or 12 days; denoted \(i\)), in country \(j\), is calculated as the relative change in lockdown length, multiplied by the predicted change in GDP as forecast by the IMF, and the proportion of the loss attributable to the policy decision (\(0.15\)). We adopt the IMF metric for measuring GDP in terms of Purchasing Power Parity International dollars (PPP$) which is held constant such that it is equal to the US dollar. For Hubei, we use the same formula as above, however the IMF only publishes estimates GDP forecasts at the national level. Therefore we partition the effect for Hubei alone by multiplying by the proportion of China’s GDP which Hubei makes up (0.04,651).Footnote 19 The necessary data, and calculated GDP outcomes, are presented in Online Appendix 8.
It is worth highlighting two further implicit assumptions. First, we assume all of the GDP loss a country experiences occurs during the lockdown period. Clearly, countries’ economies were already contracting pre-lockdown, and likely will take a long time to return to normal functioning post-easement. However, our assumption ensures that the implied price of life we calculate is an upper bound. Second, we assume that the date on which lockdown is eased is independent of the date on which lockdown was imposed. This is an open empirical question as it may be that earlier lockdowns halt the spread of the virus quicker, allowing an earlier end to lockdown. If earlier lockdowns result in earlier release this would lower the overall financial burden of lockdown. Hence, again our assumption tends towards an upper bound estimate on the price of life. The additional assumption made for Hubei may underestimate the price of life there: the contraction in China’s GDP is likely most keenly felt in Hubei, the worst hit province. Our estimates of price of life would increase if we adjusted for this.
Aside from the caveat with respect to China, while our assumptions influence absolute estimates of the price of life, the only variables affecting the relative prices across countries are: (1) the number of lives a change in the length of lockdown would save; (2) the original length of lockdown in a country; and (3) a country’s GDP. These key variables are not assumed. To underscore the point, our assumptions cannot substantially influence the implied relative price of life across countries.
Cross-Country Estimates of the Price of Life
To calculate the implied price of life from a change in the length of lockdown of a set number of days, \(i\), for country, \(j\), we link the predicted change in GDP to the change in number of lives lost as in Eq. 3:
$$Implied\;price\;of\;life_{ij} = \Delta GDP_{ij} /\Delta Lives\;lost_{ij}$$
(3)
Our primary focus is for the most marginal change in length of lockdown we calculate: imposing lockdown either 3 days earlier or later than its actual date. Results for different changes in lockdown date, of 7 and 12 days, are presented in Appendices 9 and 10. These show that relative patterns remain unchanged. Table 3 showed that the exponential growth in infections means more lives are lost from a delay, than would be saved by shifting lockdown earlier by the same number of days. In contrast the modelled impact on GDP from moving the lockdown date by a fixed number of days is exactly the same; the only difference is in the sign (earlier lockdowns are a cost to GDP, later lockdowns a benefit). Hence, the implied price of life is higher for moving lockdown earlier as opposed to later. Moreover, as explained previously, by choosing not to impose lockdowns 3 days earlier governments rejected saving more lives when the price was relatively high. Similar logic reveals them to have accepted the implied price of life from a delay; they would rather bear the cost in terms of GDP than as further human lives lost. Results from these analysis are presented in Table 4.
Table 4 Implied price of life in different countries (PPP$) Obviously, estimates for prices countries were willing to pay (accepted) are lower than estimates for the prices countries rejected. In almost all cases the estimates of the price of life are below thresholds typically used to estimate the VSL in cost–benefit analyses. Hence, ex-post, it is highly likely lockdown enhance social welfare.Footnote 20 As with progression of the pandemic, there is huge heterogeneity in the price of life across countries. Comparing across countries those who pursued an early lockdown strategy reveal they are willing to pay a high price to save their citizen’s lives, only rejecting prices above $1,000,000. The highest implied prices are in Korea (> $11,000,000) and New Zealand (> $6,000,000), both countries who acted swiftly to suppress the pandemic.Footnote 21 However, those countries which imposed lockdown relatively late-on in their respective pandemics were clearly only willing to pay far less to protect lives. Belgium, Italy and the UK reject prices of life around $100,000.
Clearly, delayed action in the face of exponential growth cost lives, and implied low price of life in those countries imposed lockdowns relatively late in the pandemic. Two comparisons make this cross-country variation in the implied price of life particularly clear. First, the accepted price of life in China ($108,000) is about 25% higher than that for an American ($87,000). This is despite our methods meaning the calculated price of life for China is likely an underestimate.Footnote 22 Second, compare the acceptable price of life in Germany ($525,000) with that in the UK ($67,000). The price of life for a German is nearly an order of magnitude greater than that for a British citizen. That vast difference is despite the two countries being very similar in terms of GDP per capita. These relative implied price of life comparisons are particularly pertinent. Our methodology uses ex-post estimates of the number of lives saved to infer what government policy implies for the price of life. Yet, these governments were clearly making the decisions ex-ante. Nonetheless, these governments were making lockdown decisions at around the same time (except Hubei which was far earlier), with nearly identical information sets. Thus any differences in relative estimates would hold true even if the pandemic had proved to be far less deadly than it actually is.
Moreover, this heterogeneity in the price of life is not explained by different values for life. Indeed, the implied prices are often far lower than official VSL estimates—seemingly, cash flowing through the market is worth much more than value passing through wellbeing, at least to some countries. The low rejected prices also imply that very few Quality Adjusted Life Years (QALYs) are assumed to be saved by governments in reducing Covid-19-related mortality; otherwise delays to lockdown seem nonsensical. For reference, in the UK the National Institute for Health and Clinical Excellence views a QALY costing between £20,000 and £30,000 as good value (NICE 2012).
As we mentioned when discussing Table 2, those countries with high reported Covid deaths, tend to be countries with high ratios of excess mortality to reported death, i.e. there is substantial under-reporting. To examine the extent to which our estimates change when we account for this under-reporting, we focus on the set of countries for which we have reliable estimates of that ratio, and where under-reporting appears prevalent. These countries are: Italy, the UK and the USA. The estimates reported in Table 5 are calculated by dividing the estimates of the price of life by the ratio of excess mortality to reported deaths (from Table 2). The intuition behind this is that our estimates of lives saved by lockdowns (used in Table 4) are based upon reported death data, and hence should be scaled upwards by the degree of under-reporting of deaths. Implicit in this correction is the assumption that the ratio of excess death to reported death is constant within a country throughout the pandemic. It is possible that the ratio declines during the tail of the pandemic when Covid cases and deaths are less common, and tests more available. Nonetheless, our correction offers what is currently the most comparable cross-country figure.
Table 5 Implied price of life in different countries after correcting for under-reporting (PPP$) Table 5 shows that for those countries which under-report Covid-19 deaths, implied price of life is substantially reduced, highlighting once again that earlier lockdowns would have increased social welfare tremendously. For example, in the UK, the country for which we estimate a relatively high rate of under-reporting of Covid-19 deaths, the adjusted rejected price of life is just $65,000 (equivalent to just over £50,000). The accepted price of life is lower still, at $40,000 (£32,000).