Following on from yesterday's post on the economics of COVID-19 policy, let's consider what the optimal period of lockdown would be. In doing so, I'll show why anyone who wanted a longer lockdown, and anyone who wanted the lockdown lifted earlier, are both unable to provide compelling evidence to support their arguments. Let's put aside the question of whether a lockdown should be used at all, and start from a position of a lockdown having been imposed - how long should the lockdown go on for?
In my ECONS102 class next semester, in the very first week we'll talk about a framework for determining the optimal quantity of something, using marginal analysis. Marginal analysis involves considering the marginal benefits and marginal costs, and in this case we're considering the optimal length of lockdown.
The general model is outlined in the diagram below. Marginal benefit (MB) is the additional benefit of one more day of lockdown. The benefits of lockdown include primarily the reduction in public health costs, including morbidity and mortality as a result of COVID-19 infection. In the diagram, the marginal benefit of lockdown is downward sloping - the first day of lockdown provides the greatest benefit in terms of reduced infections (and associated costs). Extra days provide more benefits, but compared with the first day, the marginal benefit is less - that's because, once 'the curve starts to flatten', each day in lockdown prevents fewer additional infections than the previous day.
Marginal cost (MC) is the additional cost of one more day of lockdown. The costs are primarily economic - reduced output for the economy, associated with lower incomes (in total and distributed unevenly in the population). The marginal cost of lockdown is upward sloping - most businesses can survive a few days of lockdown, but the longer the lockdown continues, the more businesses close up permanently, and this process likely accelerates over time.
The 'optimal length' of lockdown occurs where MB meets MC, at Q* days. If the lockdown was longer than Q* days (e.g. at Q2), then the extra benefit (MB) of those additional lockdown days is less than the extra cost (MC), making us worse off overall. If the lockdown was shorter than Q* days (e.g. at Q1), then the extra benefit (MB) of an additional lockdown day is more than the extra cost (MC), so keeping the lockdown going for one more day would make us better off overall.
So, has New Zealand got it right? Are we getting out of lockdown too soon, or too late? The problem is that it is virtually impossible to tell (which is why I said that both sides lack compelling evidence). If you believe that the lockdown is too short, you must believe that we are at Q1. An extra day (or more) of lockdown would save more public health costs than the economic costs it would inflict. If you believe that the lockdown is too long, you must believe that we are at Q2. An extra day (or more) of lockdown would cost more economically than the public health costs it would save.
To come to either conclusion, you would have to be able to assess the economic costs and the public health costs of both alternatives - what would happen with, and without, the lockdown continuing. As I briefly mentioned yesterday, and will be apparent to anyone who has been following the emerging and ever-updating research on the modelling of the pandemic, the current models of the pandemic largely fail to agree on anything. To get an estimate of the marginal benefit of an additional day of lockdown, you need to know not just how many infections would be averted tomorrow, but how many through the remainder of the pandemic as a whole (since an infection averted tomorrow, means one fewer person who can infect others in the future, etc.). The uncertainty in the models renders that a fairly fruitless exercise. And that's before we even consider the uncertainty in the marginal benefits (and the potential for interaction between the two, because an infection averted tomorrow could actually improve the economy overall - consider the infection of an essential worker, as one example).
So, 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. So, anyone claiming they know the answer is really talking out of a lower orifice. While there is definitely an optimal lockdown length, and we can define what it would be in theory, in practice this isn't a question that can be answered with any certainty - we don't have the data, and we don't have the models, to do so.
And in situations of high uncertainty like this, it might be tempting to invoke the precautionary principle - to be cautious and avoid making a decision with the potential for long-term negative consequences (essentially, this was one approach that Mulligan et al. noted in the article I linked to yesterday - 'buying time'). However, it isn't clear whether it would be better to be precautionary in relation to public health costs (and err on the side of having a lockdown that lasts too long), or to be precautionary in relation to the economic costs (and err on the side of having a lockdown that is too short).
I definitely don't envy the decision-makers on this one. This is genuinely one of those times where, no matter what decision is made, there will be a large number of vocal critics, who can't prove their argument is correct, but equally can't be proven wrong either.
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