...if the marginal benefit of lockdown is highly uncertain, and the marginal cost is also uncertain, then we really have no way of knowing for sure whether the lockdown has been too long, or too short.Of course, I'm not the only one thinking about the issue of how long an optimal lockdown should last, although as I also noted in that post, the quality of work is highly variable. In the main, it is because the researchers aren't systematically thinking through both the benefits and the costs of lockdown (most are focused on one or the other). However, I have taken note of a number of papers that seem to address the question of the optimal lockdown length using a suitable framework of both costs and benefits.
For instance, this NBER Working Paper by Fernando Alvarez (University of Chicago), David Argente (Pennsylvania State University), and Francesco Lippi (Einaudi Institute for Economics and Finance), investigates:
...the problem of a planner who has access to a single instrument to deal with the epidemic: the lockdown of the citizens... The planner's problem features a tradeoff between the output cost of lockdown, which are increasing in the number of susceptible and infected agents, and the fatality cost of the epidemic.Notice that this is pretty much the same trade-off I outlined in my post (although I didn't frame it in exactly their terms). Using a combination of a simple epidemiological model and a simple economic model, Alvarez et al. study (emphasis is theirs):
...how the optimal intensity and duration of the lockdown depend on the cost of fatalities, as measured by the value of a statistical life, on the effectiveness of the lockdown (the reduction in the number of contacts once the citizens are asked to stay home), and on the possibility of testing, i.e. to identify those who acquired immunity to the disease. We show that if the fatality rate (probability of dying conditional on being infected) is increasing in the number of infected people, as is likely the case once the hospital capacity is reached, the policy maker motive for lockdown is strengthened.Their findings are not at all surprising, and depend on their parameter assumptions:
In our baseline parameterization, conditional on a 1% fraction of infected agents at the outbreak, the possibility of testing and no cure for the disease, the optimal policy prescribes a lockdown starting two weeks after the outbreak, covering 60% of the population after 1 month. The lockdown is kept tight for about a full month, and is subsequently gradually withdrawn, covering 20% of the population 3 months after the initial outbreak. The output cost of the lockdown is high, equivalent to losing 8% of one year's GDP (or, equivalently, a permanent reduction of 0.4% of output). The total welfare costs is almost three times bigger due to the cost of deaths...One other interesting point is this:
...the elasticity of the fatality rate to the number of infected is a key determinant of the optimal policy - we found that when the fatality rate is flat the optimal policy is to have no lockdown.In other words, lockdowns make the most sense when the fatality rate is high and increasing in the number of infected - that is, when the fatality rate has a non-linear relationship with the number of infected.
Alvarez et al. used the value of a statistical life in their calculations, as a measure of the health benefits of a lockdown. Weighing up costs and benefits requires a common metric be used, and economists often use dollars (which is why the value of a statistical life is important - it provides a dollar value that can be used as a measure of the value of lives saved or deaths averted).
An interesting alternative is proposed in this working paper by Richard Layard (London School of Economics) and co-authors. They use a measure of 'WELLBYs' - a wellbeing equivalent of the QALY (Quality-Adjusted Life Year), which is often used as an evaluation tool in health policy. Essentially, one year of perfect life satisfaction is worth one 'WELLBY', while one year with life satisfaction of 5/10 is half a 'WELLBY'.
Having converted the benefits and costs of the lockdown into the WELLBY metric, Layard et al. show that the UK lockdown should be lifted around 1 June. Of course, their analysis has a huge number of assumptions that are pretty heroic - I wouldn't take their headline results as a strong endorsement of a date for lifting the UK lockdown. And of course, any analysis based on life satisfaction is ignoring the strong theoretical problems of life satisfaction measurement (as noted in this post). However, the overall framework of considering costs and benefits of the lockdown is important, even if you don't believe the measurement using WELLBYs.
Finally, both the Alvarez et al. and Layard et al. papers outline trade-offs between public health benefits and economic costs of the lockdown. However, not going into lockdown can have economic costs as well, as this working paper by Martin Bodenstein (Federal Reserve Board), Giancarlo Corsetti (University of Cambridge), and Luca Guerrieri (Federal Reserve Board) notes. They use a more sophisticated economic model and epidemiological model than the Alvarez et al. paper. In particular, their economic model distinguishes between a core economic sector and another sector, while their epidemiological model distinguishes three groups (one associated with each economic sector, and one non-working group). They are able to show that:
...by affecting workers in this core sector, the high peak of an infection not mitigated by social distancing may cause very large upfront economic costs in terms of output, consumption and investment.So, the simple trade-off between economic output and lives saved may not be quite so simple. Of course, we are still early on in properly understanding the trade-offs associated with the coronavirus lockdown, and clearly we're not going to be able to evaluate the optimal lockdown length until well after the lockdowns have been lifted. However, the methods and measurement necessary to better understand this problem for future pandemic outbreaks are developing quickly.
[HT: Marginal Revolution for all three papers: here, here, and here]
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