The base-rate fallacy is about to become a daily nuisance when it comes to processing outbreak data in highly vaccinated societies. Here's a cautionary tale.
PS: None of this is proof that Delta is nothing to be worried about. I am certainly worried about it. Its early days. But sometimes statistics can look more scary than they really are.
What if I then told you that in fact 99 of the 100 people at that party had been fully vaccinated. Well these facts together tell you that 1 person was unvaccinated and got infected and 1 of the 99 vaccinated people got infected. In other words the vaccine was 99% effective.
In fact it would be a *routine occurrence* that fully vaccinated individuals make up half of new infections. Indeed there will shortly come a day when *the vast majority* of new infections will be fully vaccinated people.
So as long as ~91% of the adults exposed in the early days of the outbreak in Israel were fully vaccinated, this alarming news is actually perfectly consistent with the Pfizer vaccine being no less effective against Delta than it was against old school covid.
Today the Wall Street Journal has the following alarming news. In the recent surge of cases in Israel involving the Delta variant, half of all newly infected adults had been fully vaccinated. I almost cried when I read that.
But hang on. Isn't almost everyone fully vaccinated in Israel? Thought experiment. Suppose I told you there was a superspreader party attended by 100 people and half of those infected had been fully vaccinated. Does that make you worry about vaccine effectiveness?
In general if you know that a fraction r of a population is vaccinated and from that population equal numbers of vaccinated and unvaccinated people have gotten infected from some event, then (1-r)/r is the relative probability of infection vaccinated versus unvaccinated.
Why is that? Let q be the fraction of individuals exposed to the virus by the event, and let p_v and p_u be the probability of becoming infected conditional on exposure for vaccinated and unvaccinated respectively. Then we have
q*p_v*r = q*p_u*(1-r)
i.e.
p_v/p_u = (1-r)/r
Remember that my 83% was just an estimate. But more importantly, another detail from this outbreak in Israel is that it started with some large clusters in schools. Certainly the fraction of adults in a school context who are vaccinated is much larger than the baseline.
(I can't find the exact percentage but I know from the NYT that ~60% of the overall population is fully vaccinated, I "know" from Wikipedia that adults make up ~72% of the Israeli population and I recall that vaccination of children in Israel has barely begun.
If you are like me you have been dismayed at the recent news about waning vaccine efficacy. What used to be 95% protection is now measured to be much lower.
But these estimates are seriously confounded. A simple calculation shows the problem.
We could make more guesses but instead lets reverse engineer it. What value of r would give us back the effectiveness estimates of 90% that we saw in the early vaccine trials (before Delta)?
(1-r)/r = .1
yields r = .91
I just finished an 8 year stint as theory co-editor of the American Economic Review (two 3-year terms, extended by 1 year plus 1 year mopping up the leftovers). Ask me anything
#econtwitter
In basketball is a point scored in the first minute worth as much as a point scored in the last second? You would think so since the winner is the team with the most points regardless of when they are scored. But I don’t think so...
I would like to say congratulations to
@franciscopoggi
, amazing new PhD from Northwestern who has just accepted a job at Mannheim where he will begin what will be a great career as an economic theorist.
its interesting how people seem to view risks as complements rather than substitutes. "i am already doing X unmasked so of course i am fine with also doing Y unmasked."
The reason is simple: people who have chosen not to be vaccinated are also much less likely to be tested. This means that a disproportionate number of cases will be detected in vaccinated individuals, skewing the apparent ratio.
One thing to know is that the AER is very decentralized. There are 10 co-editors and they all do things their own way. Nobody is a given a how-to-be-an-AER-editor slide deck when they start. So it all depends on which co-editor you are assigned. /4
Its easy to understand what happened in the FIDE Candidates Chess tournament based on some interesting strategic incentives in round-robin winner-take-all tournaments.
You all probably already thought of this but a remarkable thing about the past year is that yeah we were all separated and isolated but still never before have so many people shared the same (significant, memorable, life-changing) experience for such an extended time.
Tragic news for
@PennStateEcon
,
@berkeleyecon
, and the world of economic theory: John Morgan’96 passed away last week.
I didn’t know John well, but admired his prolific record, his breadth of interests, and his energy. This is a loss for us all.
Vaccine winners curse: when it turns out to be surprisingly easy to get a vaccine appointment you infer that people value them less than you do. Only this time it makes you want it even more!
Editors have a lot of power and the second-most important quality in an editor is the willingness to use that power. The first-most important quality is to use it for good and not for evil. To the extent I did any good it was by being decisive and accepting lots of papers.
@Jeffely
Did you feel like you had a special power to steer the direction of econ theory discourse and learning? (And, which way did you steer it?)
Or did you feel like you were mainly channeling outside pressures / consensus / objective judgments of research quality?
PS measured protection against severe disease seems to be holding. And this makes sense because everyone with severe disease gets tested, removing the counfounder. (the second term in square brackets goes away and the factor reduces to exactly 1)
Friends: a colleague is writing a children's book about Janet Yellen. Janet Yellen herself is excited about the project. My colleagues are looking for a publisher who would be interested. Any suggestions?
Its difficult to give general advice, everyone has their own strengths and the best advice would be to play to your strengths. One thing I would say specifically for theorists and for the AER is to try really hard to say things in words and avoid conspicuous notation. /3
My colleague Konrad Mierendorff died on Saturday August 7th 2021 after a fall on the
#Wasenhorn
, Switzerland. Konrad was a gifted Economist, both as a researcher and a teacher. He loved the mountains and was on his own journey into Alpine climbing. 1/5
The AER had a length restriction that they didnt really enforce. I personally enforced it, although somewhat inconsistently. (Senior authors I would just send it back, junior authors I might look the other way.) /3
@Jeffely
Papers are getting longer and longer (100+ pages, including appendices, is becoming a new norm). Publication process takes years. What can we do about it?
I will start by saying that I rarely (never?) used that as a criterion even at the AER. One of the unique challenges of being a theory co-editor at the AER is to abandon the idea that *qualitatively* (or "horizontally") there is some special standard for AER theory papers. /2
Another piece of advice, again specifically for theory and for the AER. Keep it simple and emphasize the idea. Be willing to cut corners in terms of generality if it makes the idea easier to communicate. 2/3
Not "the very best" because that would be only 1 paper in 8 years. The AER says that it publishes ~7% of all submitted manuscripts. So I published all papers in the 93rd percentile among those that I received.
ANNOUNCEMENT: I head next week to
@UChicago
for 5 days (Nov. 8-12) at the request of its storied Department of Economics to present our theory that all of economics is based on the wrong version of the differential calculus.
Importantly, this error afflicts Inflation & the CPI.
Today March 21 2021 I played tennis with my wife. The players on the neighboring court hit their ball onto ours. I reached down and picked it up, with my bare hand, and threw it back to them.
Trust your taste, decide whether the paper is good or not and have the courage to make a simple, decisive, and unapologetically subjective recommendation based on that judgement. Don't (ok found one!) waste effort making up reasons why.
I am looking for a professional web designer to redo my webpage . if you are one or you know anyone who might be interested in the job please message me.
@Princeton
Hassan Sayed, a fifth year PhD candidate in economics, and Achinthya Sivalingan, a SPIA MPA second year, have been arrested, evicted, and permanently banned from the
@Princeton
campus, thereby preventing them from finishing their degrees.
I dont think the publishing process is perfect but there are lots of frictions and I think that with respect to those it could be reasonably said to be second best. So there aren't any easy things to fix that would be very impactful. /2
@Jeffely
@ben_golub
What is an easy thing to fix in the publishing process that would be very impactful? What is a hard thing to fix that nevertheless is absolutely necessary? Thank you, Jeff!
Teams are continuously working an effort/win probability trade-off over the course of the game. A point scored at the beginning gives a full 48 minutes to smooth the adjustment in response. A team cannot retroactively increase past effort in response to a point at the buzzer.
Today the Supreme Court ruled that partisan gerrymandering is not something that the judicial system can regulate.
So the States need good systems to prevent it. This is a game theory question. I have one idea here but more work is needed
Economics PhD Candidate Francisco Poggi’s research interests include Microeconomic Theory & Law and Economics. Learn more about
@franciscopoggi
& other Northwestern Job Market Candidates at
the problem with this is that authors just move stuff to the "online" appendix. questions:
1. is the online appendix part of the paper?
2. is it refereed?
if the answer to either of those questions is yes then this is simply a policy that papers should 75 pages or less.
📢 **REStud Page Limit**
With effect from 1st July 2022, a page limit policy applies to all submissions. Papers should be under 45 pages. Online appendices should not exceed 30 pages. A “grace period” is in place until 15th August 2022. For more details:
In the original randomized trials, efficacy was found to be about 95%. That is, the ratio of vaccinated cases to unvaccinated cases was 1/20.
Now we have only observational data. But using observational data can make that ratio look much larger even though it isn't.
There are good papers and less-good papers. But to answer your question, a good general-interest test is whether you can write a 100-word abstract that makes someone want to read it.
The base-rate fallacy is about to become a daily nuisance when it comes to processing outbreak data in highly vaccinated societies. Here's a cautionary tale.
Indeed, as more and more of the population gets access to vaccines the unvaccinated population is a larger and larger concentration of those who are just unwilling to get vaccinated, presumably the same people who won't get tested.
I took an idiosyncratic approach to "timeliness." For rejections I was pretty fast. In exchange for that I allowed myself to take my time on papers that had a reasonable chance to be accepted. /2
Even the crappiest model can be made into a martingale (and better version of itself) by real-time simulating future results and reporting the average of its future probabilities.
There's a case for taking the 'over' on the needle. It builds in tabulation errors, which we don't expect but definitely happen (see NC)! And we haven't increased our confidence to reflect that we just had this election. Won't be any Miami-Dades tonight
War of information between a totalitarian government and a democracy is asymmetric, and not just because of the differences in their capacity to launch information attacks (which is probably a superficial difference anyway)
Department of Economics PhD Candidate Matteo Camboni’s research interest is Microeconomic Theory, Economics of Information, Economics of Organizations, Political Economy. Learn more
@matteo_camboni
& other Northwestern Economics Job Market Candidates at
And so the typical dynamics of a round-robin winner-take-all tournament is that whoever takes an early lead will benefit from this effect and with a little luck quickly jump out to a large and insurmountable lead.
i'll bet that height and ability to shoot free throws are uncorrelated or slightly positively correlated in the overall population and yet they are negatively correlated among professional basketball players.
Then the term in square brackets is
1 + (40)* (1/5) = 1 + 8 = 9
That is the measured protection will 9/20 rather than 1/20. Note that 9/20 = 45% which translates to a measured vaccine efficacy of only 55%, without any change in the true efficacy.
“We are all just prisoners here of our own device” used to be a clever turn of phrase using a subtle form of the verb. Today it’s just a cliche use of the noun.
Hey
@doronravid
your webpage has a link to the "best hummus in Israel" but the page is in Hebrew. Where do I go to find the best hummus in Israel (I will be in Tel Aviv and briefly Jerusalem).
Simple way to eliminate the incentive to foul at the end of basketball games: on a non-shooting foul a team that is in the bonus can *choose* whether to take the shots or keep possession with a new clock. makes the "bonus" actually a bonus and not a penalty.
A simpler way to write this expression is
p [ 1 + (m/s)*t ]
Because this shows that the true protection level p = 1/20 will be multiplied by a number bigger than 1, the number in square brackets.
Let's suppose that unvaccinated individuals will only get tested when they have severe symptoms. Then the measured vaccine protection is
(p*s + p*m*t)/s
where t is the probability that a vaccinated individual gets tested when she has a mild or asymptomatic infection.
So... collect all games where such a review happened in the first minute (5 minutes, quarter whatever) and compare the frequencies of {win, lose, tie at end of regulation} between the subset in which the point was awarded versus the subset in which it was not.
New rule: you're not allowed to criticize any pollster or polling aggregator unless you pre-register your own forecast. Use this thread to predict the following:
1—% chance of R Senate win
2—% of R House win
3—# of R Senate seats
4—# of R House ""
5—GA-Sen result
6—AZ-Gov result
Of course these are just example numbers for p and m/s and for t. But they are in the ballpark and the point is that it's not hard to see how the illusion of waning efficacy can come from this simple logic.
So while on average I was reasonably fast, for papers that made it through I was probably overall pretty slow. I had a few papers that I accepted on the first round.