# when are rational expectations a threat to causal inference?

Consider the impact government policy has had on deaths from COVID19. I think the potential relationships are

If the relationships are as given in the above diagram, and I regress covid deaths at t+1 on policy at t-1, is the ONLY threat to causal inference that policy maker's rational expectations of covid deaths at t+1 is affecting policy choice at t-1? Specifically, do I not need to worry about the bi-direction of the relationship between policy and the epidemic because the relationship between the epidemic and covid deaths is one directional and government policy affects covid deaths only indirectly via the epidemic?

I think it is fairly safe to assume that: 1) policy does not affect covid deaths directly, but only through its impact on the epidemic. 2) the epidemic causes covid deaths, but not vice versa. 3) the relationship between policy and epidemic runs both ways. 4) nations choose their own policies and experience their own epidemic.

nb: I am investigating 5 measures of government policy aggregated to the national level, but for clarity referred to them as "policy"

• 'Government policy' assumes as instituted per a sole entity (not a city, or state, but federal, and at the latter, the department of health in line with the executive branch) all producing a co-ordinated uniform policy. If only that were true in select countries. May 16, 2020 at 18:38
• Some government policies appear to affect the pandemic, others (such as lockdowns) don't. There is debate on this. Also, governmental policy can absolutely affect non-pandemic-related deaths as well (e.g., lockdowns definitely causing people not to pursue needed medical treatment). I think I'd draw a few more bidirectional arrows than you have there. May 16, 2020 at 18:52
• The pandemic at $t$ cannot affect government policy at $t-1,$ surely: causes must precede effects. May 16, 2020 at 19:26
• In the extreme, imagine an omniscient policy maker: their optimal policy choice at t-1 would be influenced by their perfect knowledge of their country's epidemic at t+1. More realistically, policy makers in countries where their epidemic got a late start might be able to anticipate their country's future epidemic based on the experiences of "similar" countries that happened to start their epidemics earlier. May 16, 2020 at 20:00
• Perhaps. But given the abysmal performance of every single COVID model I've ever heard of, that seems unlikely. May 16, 2020 at 20:00

I think I would add another node for policy at $$t+1,$$ so as not to violate the fundamental law of cause and effect (causes must precede effects). Let $$E(t)$$ be the epidemic at $$t,$$ $$D(t)$$ be COVID deaths at $$t,$$ and $$G(t)$$ be government policy at $$t.$$ The real question is whether we will allow modeling (accurate or not) to affect government policy. I think we should, since that's obviously happening. So I would propose this alteration to your model:
So this is saying that government policy at $$t+1$$ has inertia (arrow $$G(t-1)\to G(t+1)$$), and that modeling of the epidemic (as well as actual data) and the deaths affect government policy at $$t+1.$$ COVID deaths are only immediately affected by the epidemic, as you said.