Summary: The Series I savings bond is a US government bond offered to US citizens, with purchases limited to $10k per person per year. It pays interest set by a formula based on the official inflation rate, with a built-in lag. If inflation from November '21 to March '22 follows historical patterns, bonds purchased in December '21 and redeemed after 15 months will pay ~4.62% interest annualized. If inflation is higher (as it has been recently), the bonds will pay more; if it's lower, they will pay at least 3.56% interest when redeemed after 12 months.

All of those potential rates are a percentage points higher than any other bond that is even remotely as safe; this is because of the way the inflation adjustment rule works. Specifically, the inflation adjustment for the next six months is set based on what inflation was in the last six months. As a consequence, a Series I purchased between now and April 30 will pay its first 5-6 months of interest at 7.12% annualized (so 3.56% in 6 months), and then reset to some other rate that will depend on future inflation. If you don't want to stay invested after that, it's possible to redeem the bonds after 12 months.

If getting ~3-6% annualized interest on $20k of a US government bond is a thing that you want, then this might be the best way to do it.

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The Series I savings bond is a US government bond that is offered directly to US citizens, with purchases limited to $10k per person per year. (Apparently, there's a way to purchase an additional $5k

I replicated my estimation of population-average IFR for Africa-ex-South-Africa (henceforth "Africa"), using the same methodology as my India calculations. Africa is significantly demographically younger than either India or the US -- the top quintile of age in Africa starts at 39, India at 49, and the US at 61.

I estimate that the age effect creates an Africa population-average IFR 20% that of the US rate (i.e., a US rate 4.94× greater), assuming age-uniform infection rates and no difference in medical care. This effect is driven by the reduced population share of age>70 in Africa (just 18% that of the US).

My work is here, and here's the primary chart:

In my India analysis, I wrote:

The effect of medical care differences on IFR-by-age curves is of first-order importance to this analysis; as an example, if lack of care were equivalent to 12 years in fatality-rate terms, it would triple India population-average IFR to 0.75%. (...)

A corresponding statistic is that if lack of care were equivalent to 18 years in fatality-rate terms, it would raise Africa IFR to the US level of 0.63%. My tentative hypothesis is that Africa Covid-19 fatality is likely of less concern than regions with meaningfully older populations.

If you'd like to redo these calculations for a population of interest to you, you're welcome to clone the sheet and copy your own numbers into the "Africa pop by age raw" tab. PopulationPyramid.net has easily-formatted CSVs on many countries / regions, but you

Abstract:

India's demographic average age is younger than that of the US. This implies that the strongly age-varying Covid-19 infection fatality rate (IFR) could cause a lower population-average IFR in India than in an older nation such as the US, all other factors being equal (spoiler: they're not).

I estimate that the age effect creates an India population-average IFR 39% that of the US rate (i.e., a US rate \(2.58\times\) greater), assuming age-uniform infection rates and no difference in medical care. This effect is driven by the reduced population share of age>70 in India (just 35% that of the US).

I do not attempt to model age-varying infection rates (which I expect would slightly decrease India fatality rates relative to the US), do not attempt to model selection pressure on patients' immune systems (which I expect would make India fatality rates modestly lower), and do not model environmental factors such as air pollution (which I expect would make India fatality rates higher).

Finally, this predicted effect is extremely sensitive to the IFR-by-age curves; if shortages in medical capacity cause higher IFR in the 45-69 age groups (representing 22% of population), India population-average IFR could be many times greater. I believe this sensitivity (which will also be present in developing economies experiencing Covid-19 outbreaks in the future) should urgently motivate research into IFR by age under triage and shortage conditions.

I recently read a preliminary analysis of estimated Covid-19 infection and fatality numbers in India which suggested an observed IFR in India significantly lower than estimates of US IFR.

I wrote in January about vaccines and public health, and I wanted to retract my bottom-line recommendation about which vaccine to get -- if you have a choice -- in Hong Kong. Appointments opened to residents 16+ yesterday, so this post is coming a bit late, but oh well. Here we are.

If you're in Hong Kong and have choices, my personal recommandation is that you get an appointment for the BioNTech (Pfizer) vaccine as soon as possible. (If you are in Hong Kong and have a HKID, the link to book a vaccine in English is here -- click the red "Book Vaccination" box at the left.)

In the rest of this post, I'll describe how my thinking has changed on the argument I expressed in my January post.

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When I wrote in January, I was looking at a massive shortfall in vaccine demand in the US and assuming that it couldn't happen here in Hong Kong. In hindsight, I was extremely wrong.

In the first 57 days of the government vaccination program, 16.3 doses have been given for every 100 persons in Hong Kong, at an average rate of 21,500 doses/day (government source). On Friday at 9am, all residents 16+ became eligible to book appointments, and "about 31,300 new vaccination bookings [were] made online" in the 13 hours before and 11 hours after the opening. I'm not sure whether this is 31k people with 62k appointments, or 16k people with 31k appointments.

Even if it's 62k new appointments in the first-day rush, that's still only 2.4x the daily processing rate (26,100 doses given in the same 24

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The following proposition is paraphrased from Savage 1971 (pdf), the original paper that introduced proper scoring rules way back when. Savage characterized the space of all possible scoring rules two ways -- in the now-common form using a general convex function and its subgradient, and in the equivalent "schedule of demands" form that has a natural interpretation as being given the opportunity to trade into a limit order book.

Proposition 1. Any (strictly) proper scoring rule \(S(p,q)\) can be written as \(S(p,q):=\alpha+S^*(p,q)\), where \(\alpha\in\mathbb R\) is a constant and \(S^*(p,q)\) is the profits-or-losses from trading into a limit order book (with nonzero size available at each price) when your initial position is some \(\beta\), your fair value is \(p\), and the contract value resolves to \(q\).

Proof. Let \(\phi:[0,1]\to\mathbb R\) be a (strictly) monotone-increasing function with \(\phi(0)<0\) and \(\phi(1)>0\). We will interpret \(\phi\) as a limit order book, with prices \(a\in[0,1]\):

• \(\phi(a)\) is the cumulative size offered (available to buy) at or below \(a\).
• \(-\phi(a)\) is the cumulative size bid (available to sell) at or above \(a\).

Given \(\phi\), we want to know the profits or losses (PnL) of trading towards a fair value of \(p\).

Let \(a_0\) be either the point where \(\phi\) crosses \(0\), the first point after \(\phi\) jumps across \(0\), or the last point before \(\phi\) jumps across \(0\). This means that \(a_0\) is

Zvi Mowshowitz's new policy is not to link to the New York Times, and he's willing to entertain the policy of not linking to NYT reporters' Twitters (though hasn't pulled the trigger yet). I understand where he's coming from -- Cade Metz's piece on Scott Alexander was really, really not good.

Scott Aaronson has a numbered list of 14 theses issues and won't talk with Cade Metz, even to explain quantum complexity, without a full explanation on how the piece on Slate Star Codex happened. Also understandable; the article really was quite bad.

Then there's social pressure going around not to read the Times. I think this is a mistake. It is important to understand what rhetoric the paper chooses to use, for the same reason that it's important to occasionally look at what's happening on the other side of a chessboard. I wouldn't claim it's in the top-5 most important things to read to understand the world (or even the top 10), but I believe it's part of a complete breakfast a useful exercise, at least sometimes. Certainly it's a good skill to train.

Today, I was holding a physical copy of the Times's international edition -- mostly by accident -- which was a surprisingly good opportunity to practice the technique of carefully separating substance from spin. The rest of this post is a worked example of this 'careful reading' technique on the front-page article that happened to catch my eye. Let's read the Times!

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Here's the article (NYT paywall, of course, and I don't know if the online edition matches the print international edition, sorry).

First, ignore the headline entirely.

Then, read each paragraph. Read slowly,

In Zvi's 2/11 Covid update, he turned to Metaculus for help. He looked at the numbers. Becase the man is an inveterate trader, he saw odds that were Wrong On The Internet and just couldn't stop himself from creating an account to bet against it. And then he saw the payout structure and decided he was done after making a single prediction.

I spent some time with the Metaculus site and figured out how they borked this one up enough to drive away Zvi Mowshowitz. I'll try to explain it here.

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Here's a presumably current description of the scoring function that I found on the FAQ, slightly abridged:

Your score \(S(T;f)\) at any given time \(T\) is the sum of an "absolute" component and a "relative" component: \[S(T;f)=a(N)\times L(p;f)+b(N)\times B(p;f),\] where \(N\) is the number of predictors on the question.

If we define \(f=1\) for a positive resolution of the question and \(f=0\) for a negative resolution, then \(L(p;f)=\log_2(p/0.5)\) for \(f=1\) and \(L(p;f)=\log_2((1−p)/0.5)\) for \(f=0\). The normalizations \(a(N)=30+10\log_2(1+N/30)\) and \(b(N)=20\log_2(1+N/30)\) depend on \(N\) only.

The "betting score" \(-2\lt B(p;f)\lt 2\) represents a bet placed against every other predictor. This is described under "constant pool" scoring on the Metaculus scoring demo (...)

I'll try to describe that in friendlier terms.

When you make a prediction with \(30n-30=N\) other people, you put your internet points behind two different bets (which get multiplied by 10 to get Metaculus points, but let's skip that for now):

• You bet \(3+log_2(n)\) times against the house, with a