~1100 words, ~6 min reading time.
I’ve been reading and thinking about The Macroeconomics of Epidemics by Eichenbaum, Rebelo, and Trabandt. Here’s my summary:
The paper takes the basic SIR model and adds to it a macroeconomic component. The SIR model is a standard way of modeling the spread of an epidemic. In brief: the number of new infections is affected by the number of people who are susceptible to the illness (have no immunity), and the number who are infected. This paper adds a number of economic models to it. See below:
SIR model – the transmission is independent of economic behavior, but the economy is impacted by transmission. Specifically, if people are sick, they’re less productive. If they die, they will never produce again (obviously).
SIR-Macro model (“Baseline”) – transmission from three channels: shopping (proportionate to amount spent by susceptible and infected populations), working (proportionate to hours worked by susceptible and infected populations), and community (same as SIR model). People are aware of how their behavior affects their probability of infection, and take that into account when deciding to work or shop.
Medical Preparedness model – like Baseline, but the mortality rate is impacted by the # infected. This captures the idea of hitting the health care system’s capacity.
Treatment & Vaccine models – these models are like Baseline, but incorporate the expectation that a treatment (which is usable on the infected, and ensures recovery) or vaccine (which is used on the susceptible to ensure they never become infected) will be discovered.
All but the straight SIR model includes some kind of policy response. The paper models this as a tax on consumption – which would reduce consumption spending and work. Obviously, that’s not what we’re actually doing – but we can use this as an analogy by looking at the results on GDP from the real policies being enacted and the hypothetical consumption tax.
The paper involves a search for “optimal policy” – that is, policy that maximizes utility for the population. This isn’t just “don’t do anything” because, while people account for how their economic activity affects their own risk of infection, they DON’T account for how their activity affects the risk of infection for others.
SIR Model – In the straight SIR model, 8% become infected at the peak, and 70% are eventually infected, and ~0.7% of the population die. There is also a mild recession – about a 2% drop from trend at the trough, and long-lasting economic effects because of those that died.
SIR Macro Model (baseline) – compared to the SIR model, there is a smaller, later peak (only about 5% at peak), and only about 50% of the population are ever affected. So, only about ~0.5% die. In brief: people being aware that they’re more likely to be infected if they go to work or go shopping will encourage people not to, so infections spread more slowly. But, we also get a much larger recession (9% drop in consumption at trough), and it lasts about 3 months longer. In this model, the optimal policy (based on a utility-based CBA approach) would be to increase restriction measures keeping pace with infection, and slowly back off as the % infected dwindles. Doing this would decrease the peak % infected to 2%, and would decrease total infected to about 35% – with 0.35% of the population dying. On the other hand, this leads to a deep recession – about 20% off trend at the trough and it takes about 3 years instead of a year and a half to get back to normal.
Medical preparedness – compared to Baseline, there is a smaller % infected (only about 3%), though there are more deaths (over 1% of population). So, a relevant health care capacity constraint leads people to be more cautious – decreasing infection rates – but not enough to totally offset the higher mortality rates. Because of this, the recession is very deep (- 20% drop in consmption at the trough). An optimal policy involves measures that aren’t much stronger than in the Baseline optimal policy scenario, but come much earlier, and are removed much more slowly. Interestingly, the optimal policy’s effect on the economy is to lengthen, but not deepen the recession. The trough is about the same depth – but the recession starts sooner (because of faster containment policies), and lasts longer – all because of the approach to containment.
Model with treatments – compared to Baseline, a model with treatments expected with a 2% probability each week (but that doesn’t actually materialize) shows almost no change.
Model with vaccines – compared to Baseline, a model with vaccines expected with a 2% probability each week DOES change the optimal policy significantly. Policy should kick in immediately – though not be quite as severe as in the baseline case, and slowly back off over the next 18 months, as the proportion of those with acquired immunity increases. (Policy doesn’t have to be as severe because of the possibility of a vaccine – so policy doesn’t have to do all of the heavy lifting with saving lives.) Interestingly, you end up with deaths with optimal policy here than in the baseline, unless a vaccine actually arrives. (Not that surprising – less severe policy means fewer lives saved by policy. If vaccines don’t cover the difference, then more people die.) The result of optimal policy is a faster, deeper, and longer recession than in the absence of policy – though the recession isn’t as severe as when optimal policy is applied to the baseline case.
Thoughts and Takeaways
First, I have some doubts about the basic economic model. Specifically, they don’t have capital in the model, so they’re probably overstating our ability to get back on track when policy is relaxed. I suspect that adding capital to the model would mute the optimal policy responses somewhat. Also, I’d not pay too much attention to the specific numbers – the calibration is naturally a bit tentative.
The choice of a consumption tax struck me as weird at first, but isn’t too bad, given that we’re stuck with this baseline model.
(1) In every single case, there is a tradeoff between saving lives and saving the economy. However, their model doesn’t account for creative solutions that might be able to decrease transmission without creating significant economic costs on basically everyone. (Example: replacing general social distancing with more focused isolation for those infected or at high risk of it. Practically, we can’t do this in the US right now because we don’t have the testing capacity required.)
(2) In every case, there is some argument for a policy response – but this is only true because people don’t take into account their affect on others’ risk of becoming infected. In as far as people took this into account, then fewer restrictive measures would be justified in the model.
(3) An early, seemingly disproportionate response is justified if (A) we’re worried about the health care system’s capacity increasing mortality, or (B) we’re holding out for a vaccine – but even then, we should start to loosen up as people acquire immunity via the infection/recovery channel.