Assume you use prevention efforts P to reduce a harm H, a harm which depends on those efforts via some function H(P). If you measure these in the same units, then at a prevention optimum you should minimize
What do you suppose P is as a function of lockdown duration? If it's not linear, then percentage change in duration doesn't give percentage change in P.
If, for example, much of cost P was incurred before mid-April (via multiplier effect of early job losses), then percentage change in lockdown duration overestimates dP/P in your polls.
I think there are in fact three local optima: (1) completely squashing the virus (2) just enough measures to avoid hospitals being overrun ("flattening the curve") and (3) not doing anything except for things like hand-washing, and accepting the death toll. It is intuitive for me that a small policy variation from each of them would result in a net loss. A lot of the debate comes down to which local optimum you believe to be the global one. Right now many western countries cannot agree internally on what to pick and compromise between (1) and (2), with obvious sub-optimal results. Your analysis shows that US are on the side of (2) with respect to the local maximum between (1) and (2), but does not resolve the underlying debate. "Pick one and implement it, it would be strictly better" of course is also a good position that we should hear more often. (2 is also really difficult to reach exactly)
Inhttps://www.overcomingbias....your use of Cutler-Summers concerns gross, not marginal, effects. These gross results are the basis for your marginal estimates.
I'm doing a marginal analysis, looking at small chances near the status quo. It is much harder to judge the costs and effects of much larger changes.
Yes my example is faulty.
The relevant harm from the epidemic is the (expected) harm that would have occurred *without preventive efforts*, not the actual direct harm that has occurred in the context of the actual preventive efforts.
For your case of H = 2*Exp(-30*P), I find the min of H+P at P=0.1365, where both the ratio and elasticity are equal to 4.094.
No, the left hand side is an elasticity, which is invariant under any proportional transformation of either of its variables.
We could of course look at H and P in individual U.S. states, if we had the data on that.
Very little of the shortfall is caused directly by people getting sick, almost all of it is caused by people trying to avoid getting sick. Few people have got sick, and most of those didn't work.
I thought we should think of P and H as being measured in, say, $. You don't seem to have done so in the polls, so apologies if the following doesn't apply.
The factor of 50 _sounds_ bad, but it seems to depend on the units used: The right hand side is invariant under change of units, while the left hand side is not. So while the equality is clearly what we should be aiming for, the interpretation of how much we deviate from said equality is a bit tricky. Not only does the interpretation of your factor of 50 change if we measure costs in cents/different currencies instead of dollars, we should even expect different deviations if we look at individual states instead of the US as a whole. I think this makes that metric hard to interpret & use in practice.
What ratio would you still deem acceptable (for the US, measured in $)? Why?
How are you estimating P (the cost of efforts at prevention)? It can’t be just the shortfall of the economy below the previous trend line, because some of that economic harm is caused by the virus, rather than by efforts to prevent harm from the virus. Disentangling H and P looks quite challenging.
Yes. And you did the same. It all leads to an interesting discussion that illuminates a number of points.
You tell me to be careful of some things, but offer no reason to think I haven't already been careful about those things.
Also be careful not to confuse time intensity of effort and cost for total effort and cost. Example here is a short intense shutdown that eliminates the virus and enables all costs to end soon.
Also be careful of non-linearities. Example here is the enormous economic "fear" cost that kicks in at a relatively low level, partly due to a hyped up media. Another example is health costs jumping due to hospitals being overwhelmed.
There are also timing issues. Eg. Border closures are useful when the virus is at a very low level within the border, typically at the start and end of an outbreak. It's pretty obvious that the best response was to close borders immediately and then selectively open them to trusted partners after a few weeks, and/or with strict quarentine processes.
Different places and regions at different times can have very different optimal actions. P+H (P) fluctuates hugely with time and place.
In general, it was always a matter of plotting a path through and thinking a few months ahead. Sometimes confusion and everyone doing their own thing is disastrous.
I'm pretty sure almost everyone who disagrees with me about covid agrees on the principle of minimizing P+H(P).
For a methodological individualist, it's definitely possible to reject the axiom that 'we should maximize effective utility'. Etymology of 'should' actually implies that conclusion. Also, it's easy for a utilitarian to conclude that rejecting open utilitarianism maximizes utility.