I hold this truth to be self-evident: It is downright crazy to try to distribute vaccines without using prices. I said as much last week.
The question then becomes: How should those prices be implemented?
Method I: Distribute vaccine rights randomly and let people trade them. This suffers from the fact that you can’t know how much the vaccine is really worth to the people you’re bargaining with, which is a barrier to efficient bargaining.
My immediate instinct (which I still think is a pretty good one) is (after pre-vaccinating certain key groups like first responders and health care workers) to give everyone a choice: You can have your vaccine now, or you can have a check for (say) $500 and your vaccine in six months. This suffers from the need to get the price right (presumably involving some trial and error) but I stand by it as far far better than the Soviet-style central planning we’re about to actually get.
But now Romans Pancs has done far better than I have, by actually thinking about the details of the optimal auction design and getting them right. His paper is here. (You’ll need to sign up for a free account before downloading.) Anyone who actually cares about getting vaccines distributed efficiently should start by reading this paper.
I haven’t finished the paper yet, but I notice it mentions a couple of my favorite economists!
If not enough people are willing to take the vaccine to achieve herd immunity, perhaps the price should be negative–pay people to get vaccinated. People who advocate fiscal stimulus should be on board too.
Maybe the price could even vary as saturation increased: The first to receive the vaccine would pay handsomely for it, the price would fall as more more took it, and eventually people would receive vaccine and check. Under the (plausible) assumption that reluctance to get vaccinated varies inversely with income, the distributional impact could be progressive, at least as far as first-order effects are concerned.
One obvious objection to variable-pay proposal is that it incentivizes hold-outs. I’m just suggesting that the optimal rate of vaccination reward increase may be above zero.
Supplement: Gallup recently found that only 63% of Americans are willing to get a COVID vaccine. The question wording specifies receiving an FDA-approved vaccine for free. Note that the poll was conducted a week after the Pfizer’s announcement of 90% success rate.
https://news.gallup.com/poll/327425/willingness-covid-vaccine-ticks.aspx
Keith (#2): I’m pretty sure that early places in line will be underpriced — because I’m pretty sure that a) I’d pay at least $500 to get vaccinated in January instead of February and b) come February, I won’t be vaccinated.
I am not sure this is looking at things in quite the right way. The lockdowns and restrictions are largely there to protect the vulnerable. If we vaccinate the vulnerable, we can relax the restrictions. The quickest way to relieve restrictions is to vaccinate the vulnerable first.
If we argue from a position that there should be no restrictions and everyone can make their own choice, we are certain that this will lead to more deaths. A pensioner may well take $500 to wait, but may still die from the disease. More fool you, we may say, but this is a choice the Govt. has not taken completely, although I don’t know what restrictions are in the USA.
In UK, there are quite severe restrictions for social interactions, less so for work related and schools are open. Hospitality is hit hard. You can go out to eat but not to drink. This has led to the major discussion of whether a scotch egg is a substantial meal, allowing you to have a drink in a pub.
Anyway, the upshot is we are all really keen to lift these restrictions. It seems to me that once the vulnerable are protected, we can relax them. We could allow infection rates to rise without the large number of deaths. We cannot do that if only low risk people get vaccinated. Pensioners may well prefer to take the $500 and wait, but that means we either sacrifice them to the virus, or we wait to relax restrictions.
A compromise is perhaps to vaccinate the most vulnerable first (say those with a risk of >1%). Then auction the rest once restrictions are relaxed. If we remove the vulnerable, the overall risk to the rest of the population is similar to the risk of flu to the entire population. Very approximately, the risk of death for each age group is about 10 x that for flu.
Will the vaccine be free to all in US?
If you think that we should “pre-vaccinate certain key groups like first responders and health care workers”, then it sounds like you support a hybrid distribution system with an initial stage of Soviet-style central planning followed by a later stage of market distribution. On what basis are you deciding which “key groups” should fall under the Soviet-style central planning system and who should fall under the market distribution system?
Sorry to put this totally off topic thing here, but given the interest in math here I though people might be interested.
It concerns the 1 in a quadrillion chance that Biden got the votes he did. The analysis is here, page 3a in the appendices (about 20 pages in).
https://www.supremecourt.gov/DocketPDF/22/22O155/163048/20201208132827887_TX-v-State-ExpedMot%202020-12-07%20FINAL.pdf
Now. please correct me if I am wrong, but did he just prove that Biden did not get the same number of votes as Clinton, with a confidence of more than 1 in a quadrillion? I think we all knew that before.
He also proves that the mail in votes and the in person votes were not random samples from the same population. Again, no surprises there. It is a bit shocking that this has been presented before the supreme court.
We have seen miscarriages of justice arising from the abuse of statistics in criminal trials, and Steve has covered some here. So whilst off topic, it is within the theme of the blog and a totally apolitical point.
Here’s sort of a problem I see for this.
The people we need to vaccinate the most tend to be the working poor and lower-middle classes. Why? Because their jobs require them to work more amongst the public than the higher middle and upper classes. The upper classes’ jobs tend to be more likely to be able to be done remotely. So here’s the problem… the upper classes can easily outbid the folks who really need it. You may say “wait wait they know they have lower risk, so they won’t bid as much!” But wait… they have a lot more income! Why wouldn’t they be willing to pay more because they may be more risk averse with more to lose?
So what happens if this is put up for bid is you risk only the people who don’t need it as much getting it… remember vaccinating certain groups first is best for society. I’m not sure the price mechanism works great here when the function of how specify benefits is actually in this case a *reverse* of who’s able and willing to pay. That is, society would likely benefit from vaccinating those who aren’t able to pay due to what they in itself is correlated with.
We need actually to probably pay these poor people to take the vaccine.
Josh: The Romans Pancs paper deals with these issues. Do you have an objection to ths protocol there?
#7. I guess the argument is that for most goods, the price covers most of the costs/benefits, with perhaps a small externality left unaccounted for. Here the externality is a lot of the benefit, and the price only accounts for a relatively small part.
I think a key phrase that goes towards Josh’s problem is this:
“Alice does not pay what she bids. She pays the externality that her bids impose. If her bids do not affect the allocation of the vaccine, and the bids of her heath insurer and others are doing all the work, then she pays nothing.”
The externality here is not the externality of extra disease in the community, but the externality her bid imposes on other people by moving them down the vaccination queue.
I am thinking about how this might work from a UK perspective. It is absolutely key that we are in a position of Govt imposed restrictions which have large economic harm.
The interested bidders are the individuals themselves, the NHS and their employers.
If we assume the Govt would be sensible, and remove lockdowns when the level of risk overall is lower than, say seasonal flu AND makes this clear.
Then most people’s and group’s priorities align with vaccinating the elderly first. Business can then open pretty much as normal. The risks to business from lockdown are greater than staff loss or absence among their younger employees. Businesses should bid for the elderly in order to get lockdown removed as a first priority.
For the NHS, saving lives is more or less what they are for, so they will bid to vaccinate the elderly. Individuals will also bid something for the elderly, even if they don’t care how many die, but they want to get back to work normally and keep their jobs.
Thus, in the face of lockdowns and restrictions, this allocation method should meet the first priority to protect those most at risk so we can get back to work. If this system produces that outcome, then I am fine with it.
Assuming this is the first outcome, then individuals will pay for themselves proportional to their wealth and age and businesses will pay for them according to importance to the business and age. Could this result in greater overall loss than other means of allocation? Possibly. With perfect knowledge it would not, because everyone would bid appropriately. If one group of people were super spreaders then everyone would bid towards vaccinating them. We don’t have perfect knowledge, so the question then becomes do the authorities have more information than the individuals and businesses? Yes, about some things, but not about others. They may be able to identify high risk groups better and target the overall burden of disease, but they do not know about the businesses, so they do not know what trade offs they are making. Nobody knows. Once we have protected the most vulnerable and restrictions are lifted, this becomes much less important.
So, given lockdowns, the system seems fine. There is an academic question (for UK) about whether it would be fine without Govt restrictions. We know that without restrictions the disease will spread. If we do not vaccinate the elderly first, they will die. The question then becomes, would this be worth it? I think Roman and Steve would say “yes” but I am not sure.
But what would Al Roth say?
Harold (#11): If the government is willing to spend political and economic capital in order to maintain the lockdown and protect the elderly, then surely the government (as well as those who currently support the government in prioritising the elderly) would also be willing to bid on behalf of the elderly in order to make sure that the elderly get vaccinated first. As for the government being possibly better informed than everyone else, I would expect the information available to everyone else (e.g., as universities and the press demand to scrutinise the vaccine trial data submitted to the FDA) to improve drastically in anticipation of a vaccine auction.
Josh (#8): As Steven (#9) has pointed out, the vaccine auction is designed to mitigate some of the issues you raise. The unmitigated residual (not directly concerned with vaccine allocation but still possibly of interest to you) is the focus of the papers by Mohammad Akbarpour, Piotr Dworczak, and Scott Duke Kominers: http://web.stanford.edu/~mohamwad/Inequality.pdf and http://web.stanford.edu/~mohamwad/RAM.pdf
Romans (#13) ” the government (as well as those who currently support the government in prioritising the elderly) would also be willing to bid on behalf of the elderly in order to make sure that the elderly get vaccinated first.”
Yes, this was my conclusion, although I did not the consider the Govt as a bidder (except in the guise of the NHS). In the face of lockdowns AND if the Govt will relax lockdowns when elderly are vaccinated, most people’s interests line up with vaccinating the elderly first.
I was not quite sure how the payments would work out. In the case where NHS, big firms and the elderly themselves all bid for the elderly. Does it effectively work like a second price auction, they all pay only what the “next” highest scoring group’s bids were? In a simple example where there is 1 elderly person, 1 50yo exec, 1 50yo shop worker and 1 student. Elderly gets bids worth 100, exec gets bids worth 10, worker 5 and student 1. I don’t think it is a simple as this, but in very broad terms, do the bidders for the elderly effectively pay 10 between them, and the bidders for the Exec pay 5 between them?
Regarding information, some of it may be available to all, but nearly everyone will not have resources to process it. If it takes a team of dozens of experts working full time to evaluate the evidence that is available, mostly it will be Government that will do this. You are right that there would be demands for this infomation to be public, such as full SAGE reports, but it still requires a lot of resources to comprehend it all. Given competing sources of information, such as Youtube, I suspect a great many will still be ill informed.
Harold (#14): In your example, assuming that there is just one vaccine that arrives early enough to make any difference, your logic is correct. If everyone bid on his or her own behalf, the elderly would win and pay 10. If, by contrast, a hundred private individuals bid 1 on behalf of that elderly person (with the total bid adding up to 100), then the elderly would still win the vaccine but now no one would pay anything because no one is pivotal. Without one of the bids on behalf of the elderly, the aggregate bid on behalf of the elderly would be 99, which is enough to convince the auction to allocate the vaccine to the elderly. In practice, with many vaccination dates, a small bid could move the elderly up or down the queue a little bit, and, so, a small bidder would end up paying something.
Regarding information, all the bidder needs to know is where his valuation ranks (or valuations rank, if he cares about others) relative to the average valuation in the population. In particular, he or she need not know how effective the vaccine is or how wild the pandemic will be three months from now. It suffices to know, say, that the mortality for one’s age group is twice the average mortality and that one values the freedom afforded by the vaccine half as much as the average individual does (e.g., because one is comfortable working and socialising from home).
While I view the auction’s information requirement as rather moderate, I also predict that the kind and the amount of information available to the public would change if an auction were seriously contemplated. The public would want the results from vaccine trials to be publicly available and verifiable by universities and charities, not just by a government agency. Such general transparency would grant additional credibility not just to the vaccines but, incidentally, also to the government’s non-pharmaceutical interventions, such as lockdowns.
Thank you for the explanation. It does clarify the position, and I am glad I have it at least sort of right.
It is a complicated idea to get across. The subtleties are easily lost among the “it is immoral to pay for saving lives” rhetoric.
Regarding information. “In particular, he or she need not know how effective the vaccine is or how wild the pandemic will be three months from now.”
If we took an extreme case, where everybody did not think the vaccine worked, but the Govt. knew with 100% certainty that it did, and in fact the vaccine does work. Everybody except the Govt believed it would just go away. It seems that this contradicts your view that he or she need not know how effective the vaccine is or how wild the pandemic would be in 3 months. This is a reductio ad absurdium argument, but these are sometimes useful tests of principle.
Harold (#16): My interpretation of the the discussion in the rubric “Discount Factors” of Section 3 on page 7 of the current draft is that it takes care of your concerns. It does not matter what the government thinks. Every bidder may have his own model of the progression of the pandemic and the efficacy of the vaccine. If the auction payments are deferred until after the pandemic has played out, truthful bidding remains optimal for every bidder even if the bidders disagree about the “science.”
The basic idea is stolen from the positions auction problem articulated by Hal Varian. Advertisers bid on the advertising positions that appear on a page with Google search results. Positions towards the top are more desirable because they have a higher click-through rate. This rate may be uncertain ex-ante but can be measured precisely after the fact. Then, the positions auction payments can also be assessed and processed also after the fact. The vaccine auction can do the same: the auction payments can be made to depend not on the universally agreed-upon expected efficacy of the vaccine ex-ante but on the realised efficacy.
From the artilce:
> A susceptible individual who is allergic to the vaccine
How the f would anyone know that? The only way of finding that out is to inject and observe that you are breaking out in hives, blood pressure plummeting, throat swelling shut, death
Economists shouldn’t do medicine. They should leave that to the lawyers.
Advo (#18): It is true that lawyers often end up doing all the fun work. Previous allergic reactions and certain autoimmune deceases are known risk factors for future allergic reactions.
“the auction payments can be made to depend not on the universally agreed-upon expected efficacy of the vaccine ex-ante but on the realised efficacy.”
This I had missed. So in my reductio ad absurdum, people should bid their honest evaluation because their confidence in the efficacy is adjusted for later. If it turns out less effective, they pay less (in very general terms).
“The basic idea is stolen from the positions auction problem articulated by Hal Varian.” I think it is fine to say “inspired by” rather than “stolen” :)
Thank you for taking the time to answer my questions. These ideas are difficult to get across to us lay people. Has the advertising position auction been used?