# 2 Lockdown Cost-Benefit Analyses

Back on Mar. 21 I complained that I hadn’t seen any cost-benefit analyses of the lockdown policies that had just been applied where I live. Some have been posted since, but I’ve finally bothered to make my own. Here are two.

**ANALYSIS #1:** One the one side are costs of economic disruption. Let us estimate that a typical strong lockdown cuts ~1/3 of income of econ/social value gained per unit time. (It would be more due to harm from time needed to recover afterward, and to due to for stress and mental health harms.) If one adds 9 weeks of lockdown, perhaps on and off spread out over a longer period, that’s a total of 3 week’s income lost.

On the other side are losses due to infection. I estimate an average infection fatality rate (IFR) of 0.5%, and half as much additional harm to those who don’t die, due to other infection harms. (E.g., 3% have severe symptoms, and 40% of those get 20% disabled.) I estimate that eventually half would get infected, and assume the recovered are immune. Because most victims are old, the average number of life years lost seems to be about 12. But time discounting, quality-of-life adjustment, and the fact that they are poorer, sicker, and wouldn’t live as long as others their age, together arguably cuts that figure by 1/3. And a standard health-econ estimate is that a life-year is worth about twice annual income. Multiply these together and you get an expected loss of 3 week’s income..

As these equal the same amount, it seems a convenient reference point for analysis. Thus, if we believed these estimates, we should be indifferent between doing nothing and a policy of spending 9 added weeks of lockdown (beyond the perhaps 4-8 weeks that might happen without government rules) to prevent all deaths, perhaps because a vaccine would come by then. Or, if death rates would actually be double this estimate due to an overloaded medical system, we should be indifferent between doing nothing and spending 9 added weeks of lockdown to avoid that overloading. Or we should be indifferent between doing nothing and 4 added weeks of lockdown which somehow cuts the above estimated death rate in half.

Unfortunately, the usual “aspirational” estimate for a time till vaccine is far longer, or over 18 months. And a doubling of death rates seems a high estimate for medical system overload effects, perhaps valid sometimes but not usually. It seems hard to use that to argue for longer lockdown periods when medical systems are not nearly overwhelmed. Especially in places like the US with far more medical capacity.

During the 1918 flu epidemic, duration variations around the typical one month lockdown had no noticeable effect on overall deaths. In the US lately we’ve also so far seen no correlation between earlier lockdowns and deaths. And people consistently overestimate the value of medical treatment. Also, as death rates for patients on the oft-celebrated ventilators is 85%, they can’t cut deaths by more than 15%.

We’ve had about 6 weeks of lockdown so far where I live. A short added lockdown seems likely to just delay deaths by a few months, not to cut them much, while a long one seems likely to do more damage than could possibly be saved by cutting deaths.

Of course you don’t have to agree with my reference estimates above. But ask yourself how you’d change them, and what indifferences your new estimates imply. Yes, there are places in the world that seem to have done the right sort of lockdown early enough in the process to get big gains, at least so far. But if your place didn’t start that early nor is doing that right sort of lockdown, can you really expect similar benefits now?

**ANALYSIS #2:** Consider the related question: how much should we pay to prevent crime?

Assume a simple power-law (= constant elasticity) relation between the cost *H* of the harm resulting directly from the crimes committed, and the cost *P* of efforts to prevent crime:

*H* = *k***P*–*a*, or dln*H */ dln*P* = –*a ,*

where *a* is the (positive) elasticity of harm *H* with respect to prevention *P*. To minimize total loss *L* = *H* + *P*, you set *P* = (*k***a*)1/(1+*a*), at which point we have a nice simple expression for the cost ratio, namely *P*/*H* = *a*.

So, when you do it right, the more effective is prevention at stopping harm, then the larger is the fraction of total loss due to prevention. If 1% more prevention effort cuts 1% of crime, you should lose about the same amounts from harm and prevention. If 1% more prevention cuts 2% of crime, then you should lose twice as much in prevention as you do in harm. And if it takes 2% more prevention effort to cut 1% of crime, you should lose about twice as much in harm as you do in prevention.

This model roughly fits two facts about US crime spending: the elasticity is less than one, and most loss comes from the crimes themselves, rather than prevention efforts. Typical estimates of elasticity are around 0.3 (ranging 0.1-0.7). US governments spend $280B a year on police, courts, and jails, and private security spends <$34B. Estimates of the total costs of crime range $690-3410B.

Now consider Covid19 prevention efforts. In this poll respondents said 3.44 to 1 that more harm will come from econ disruption than from direct health harms. And in this poll, 56% say that more than *twice* the loss will come from econ disruption. For that to be optimal in this constant elasticity model, a 10% increase in lockdown, say adding 12 days to a 4 month lockdown, must cut total eventual deaths (and other illness harm) by over 20%. That seems very hard to achieve, and in this poll 42% said they expect us to see too much econ disruption, while only 29% thought we’d see too little.

(More on Analysis #2 in the next post.)

In this post I’ve outlined two simple analyses of lockdown tradeoffs. Both suggest that we are at serious risk of doing too much lockdown.

**10am:** On reflection, I changed my estimate of the lockdown from 25% to 27% of income, and my estimate of non-death harm from as-much-as to half-as-much-as the death harm. So my reference added shutdown duration is now 4 months instead of 6.

**12pm:** Even if recovery gave immunity for only a limited period, then as long as you were considering lockdown durations less than that period, the above calculation still applies, but now it applies to each such period. For example, if immunity only lasts a year, then these are annual costs, not eventual costs. And that’s only if infection chances are independent each period. If, more likely, it is the same people who at more at risk each year, then in later years gains from lockdowns decline.

**29Apr, 3am:** We are now at 73 comments, and so far *all* of them are about analysis #1, and *none* about analysis #2. Also, tweet on #1 got 18 retweets, tweet on #2 got none.

**29Apr, 1pm:** In two more polls. over half estimate a 10% increase in lockdown duration gives <5% decrease in deaths, for both world and US. Instead of the >20% that would be required to justify allowing twice the damage of lockdowns as health harms. See also results on the cost of masks.

**28May:** I’ve updated the numbers a bit.

**22Oct**: This analysis from March 22, based on happiness, also suggests far more harm from the economy dip than from deaths. And I confirm my analysis with more recent estimates here.

**23Oct:** I’ve just shown that the above condition that =dln*H */ dln*P* = *P*/*H* holds for any function H(P).