Protecting Children

If you watch mass media and believe what you see, you think the reason to require masks on school children, the reason to vaccinate them, is to protect the children. It’s a lie. Over the entire period of the pandemic fewer than five hundred children under 18 have died in the US, well under one in a hundred thousand of the population — about half as many as died from pneumonia. The IFR, the chance that someone who is infected with Covid will die of it, is about 1/100,000 for ages 5-14, somewhat higher for older teens. The reason to keep children from getting Covid is to protect the adults those children could pass the disease on to. Any  reduction in deaths of the children themselves is a minor side benefit.

But dying children make better news stories, more emotionally moving arguments, than statistics on infection rates.

The Equity Premium Puzzle: A Suggested Solution

Most investors are free to invest in either stocks or bonds, so one would expect the return of both investments to be similar. It is an obvious argument, at least to an economist, but the conclusion does not appear to be true. In the U.S. over the past century, stocks have consistently outperformed bonds. This is the Equity Premium Puzzle.

A variety of explanations have been offered. The most obvious is that the return of stocks, both individual stocks and stock portfolios, is more uncertain than the return of bonds, at least over the short run, so risk averse investors would be willing to accept a lower return on bonds in exchange for lower risk. Attempts to estimate how risk averse investors would have to be to explain the observed premium, however, produce implausible answers: 

To quantify the level of risk aversion implied if these figures represented the expected outperformance of equities over bonds, investors would prefer a certain payoff of $51,300 to a 50/50 bet paying either $50,000 or $100,000.[1]

A variety of other explanations have been offered but none appears to be generally accepted.

I have another one.

Imagine a market where many investors are insider traders on a small scale, in an economic but not necessarily a legal sense. I know more than the market about the firm I work for. You know more than the market about a firm you have repeatedly had dealings with. He knows more than the market about a technology he has worked with extensively that will affect the performance of several firms.

Each person invests some of his money where he has an edge, buys a stock that is going to go up or sells short one that is going to go down. By the standard analysis of insider trading, he makes an above market return. Because he is risk averse he wants to diversify his investment, so part of his money goes into other investments. His marginal return is the return he can get without inside knowledge, his average return is a suitably weighted average of that and his insider return. Bond investments only have to do as well as his marginal investments, so the return on bonds is lower than the average return on stocks.

When I first came up with the idea, someone I described it to offered a proof that it could not be true, one that at the time seemed convincing. My argument implies that everyone, the investor without inside knowledge and the investor with inside knowledge making marginal investments,  is getting less than the average return. Why can’t he buy a random collection of stocks, in the limit a millionth of a percent of the stock of every company, and so guarantee himself the average return?

That proves too much, only that my explanation of the equity premium puzzle is inconsistent with rational behavior by investors but also that an insider cannot profit by his inside knowledge: If some insiders are getting an above average return, everyone else must be getting, on average, a below average return, and anyone who is could get an average return by buying stock at random.

The solution to the paradox is that it is not possible for every uninformed investor to end up with an equal share of every company on the market because some of those shares, the shares of companies particularly likely to go up, belong to insiders. That explains both how it is possible for insiders to make an above average return and why my explanation of the Equity Premium Puzzle is not inconsistent with investor rationality.

Whether it is the correct explanation, of course, I do not know.

Comments welcome.

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[1] Mankiw, N. Gregory; Zeldes, Stephen P. (1991). "The Consumption of Stockholders and Nonstockholders". Journal of Financial Economics. 29 (1): 97–112.

 

Three Comments on the Recall Election

1. Larry Elder's decision to prominently announce his plan to replace Senator Feinstein, when and if she leaves office during her term, with a Republican, was tactically stupid. Elder is going to win the second half of the election, so what matters is the first half. Raising the possibility that recalling him will cost the Democrats their senate majority will surely increase the number of Democrats willing to vote to retain; Republicans were already going to vote to recall. That single decision may decide the election.

2. Raising a scandalous accusation against Newsom's wife only a few days before the election — Rose McGowan's claim that Jennifer Newsom tried to persuade her not to accuse Harvey Weinstein of rape — is pretty good evidence that the accusation, if true, cannot be supported with evidence.

3. But I still plan to vote for recall and for Larry Elder, since he is the nearest thing to a libertarian to have any significant chance of becoming governor of California. I doubt he can do much good even if he wins, given the legislature, but he can at least do less damage than Newsom would.

The Ivermectin Mess

Scott Alexander, my favorite source for online information and discussion, has a recent post touching on the Ivermectin controversy. The point of his post, which is mostly about a Rolling Stone article that was wildly inaccurate, is that people on both sides of the political spectrum are too willing to believe whatever fits their prior beliefs. A good deal of the comment thread, however, dealt with the controversy over Ivermectin, which turned out to be interesting.

Ivermectin is a drug approved by the FDA and extensively used for treating problems having nothing to do with Covid, an anti-parasitic drug. There is some evidence that it is useful for treating Covid but apparently not very solid evidence; the FDA says it is not known to help with Covid and that studies are currently being done. True to the usual FDA policy, they disapprove of people experimenting on themselves by using it against Covid before the FDA has approved it for that purpose. Ivermectin is also used to treat animals for parasites, and some people have taken the animal version, a much larger dose, with bad effects. 

Unfortunately, the question of whether it works has somehow gotten linked to political polarization, with people on the right thinking it does, people on the left that it doesn’t. This may be connected to the controversy over vaccination, since the more people believe Covid is treatable, the less the pressure to get vaccinated. The media, not surprisingly, mostly support the left’s view. Much of the reporting is dishonest, representing it as a horse drug dangerous for humans and ignoring the fact that it is also a human drug and that the serious problems are due to people taking the animal version instead of the pill prescribed for humans. That misrepresentation can be found in a tweet, but not the web page, from the FDA. A likely result of the campaign to demonize Ivermectin is to make doctors reluctant to prescribe it even for its approved use, even more for off label use against Covid. That will make people more likely to use the veterinary version, making the problem worse, not better.

Two people in the comments responding to Scott’s piece asserted that Ivermectin had been approved by India. That got me curious, so I googled for information on the subject. The closest I could find to confirmation was a story that two states in India were using it. I then switched my search engine to Duck Duck Go and found a story, from ForbesIndia, which reported that India recommended Ivermectin in its guidelines — along with the statement that WHO and the FDA disapproved of it. I went back to Google and did the same search and was unable to find that article. There were some pro-ivermectin articles but none I found that reported that India had officially recommended the drug and none from a source that a reader, especially a left wing reader, would be likely to take seriously. This at least mildly suggests that Google filters in part on a political basis, which would be disturbing it true.

Since I raised the issue of vaccination ... . My view is that the current vaccines sharply reduce the risk of dying from Covid; I am not sure how good the evidence is that they substantially reduce infection and transmission. Common side effects appear to be minor, ranging from a sore arm to feeling sick for a few days. I therefor expect that it is in the interest of most people to get vaccinated, with the possible exception of people, especially young adults, who have already had Covid. The result of vaccination becoming a political issue is almost certainly to reduce the number of people who get vaccinated, which is unfortunate. It also produces a lot of self-righteous posturing on both sides, as became strikingly clear to me when I put my previous blog post on FaceBook.

Vaccination Arithmetic

A good deal of the current discussion of vaccination takes it for granted that it is in almost everyone's interest to get vaccinated, hence that failure to get vaccinated is evidence of false beliefs or irrational behavior. To see why this is not true for everyone, it is worth looking at some numbers.

According to the CDC, the estimated infection fatality rate is 0.05 percent for 18-to-49-year-olds. I start my calculations with someone who is certain to get infected and has a life expectancy of thirty years. Thirty years is 262,800 hours, so the reduction in life expectancy is .0005x262,800=131 hours.

If you believe your chance of getting infected is only .1, not unreasonable if you regard the current wave as the last of the epidemic, that reduces it to 13 hours. If you are 25, which according to one source gives an IFR of .01, that takes it down to less than three hours. Saving that may not be worth the time and trouble of two injections, a likely few days of not very serious side effects and some small risk of more substantial side effects. The same is more true for younger ages or people in particularly good health.

It may be objected that a .1 probability of getting infected is unreasonably low, but that depends what you believe about vaccine effectiveness. If you are optimistic about vaccines, you should expect the current wave to be the last serious one. If you are pessimistic about vaccines, the risk of infection is much higher but the benefit of vaccination lower.

It may also be objected that I am looking only at death. I don't have, I don't think anyone has, good data on long term effects of getting Covid and recovering. The short term effects range from zero for asymptomatic infection to several weeks in the hospital for almost lethal infection. Including that would reduce the number of people for whom vaccination is not a clear benefit but not, I think, to zero. 

And, on the other side, I am ignoring people who have already had Covid, hence have protection comparable to, perhaps better than, that provided by vaccination. Vaccination apparently increases the protection, but not by much. The CDC estimates  that about a third of the population have had symptomatic Covid, so that is a large group for which the benefit should be reduced by at least an order of magnitude.

I am 76, so a similar calculation implies that I should be vaccinated, and I am. But I do not agree with the claim that everyone should obviously be vaccinated as well.

All of this is in terms of the self-interest of the individual. Vaccination also reduces the spread of the disease, benefiting others, although by how much is not clear. That is an additional argument for getting vaccinated but one whose size is harder to estimate.

Am I Irrational

 A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

— Robert Heinlein, Time Enough for Love

In a number of ways my views and acts are difficult to explain as rational. I will list them:

1. As an economist, I believe in division of labor and the benefits of specialization and yet I find Heinlein’s ideal, quoted above, persuasive. I would like to be that sort of person. To the extent that I am — I think I can claim at least thirteen items on his list — I am proud of it.

2. I recently attended a social event, a dinner for forty or fifty people in the host’s home, with catered food. That felt wrong to me. When we host such events, as we occasionally do, almost all of the food, aside from any nibbles brought by the guests, is cooked by me and my family.

3. At this point in my life I am comfortably well off, yet I still make an effort to save money in small ways. We buy flour from Costco in 25 pound bags, pay attention to prices in the grocery store. I look at the right side of the menu as well as the left when deciding what to order. If we eat out, it is usually at relatively inexpensive ethnic restaurants. Looking for a new one, we ignore anything whose online description is $$$. I could afford to fly business class but never do, save for a few times when someone else was paying for it.

4. We do a lot of things in-house that it would arguably make more sense to do through the market. I build our bookcases in my basement workshop. If a button comes off a shirt or a pants seam comes out or the knee of my jeans wears through, my wife fixes it. At any reasonable per hour value for her time, it would usually be cheaper to hire the work out, perhaps to replace the jeans — I get mine from Haband, not L L Bean. But we don’t.

Arguably this is all irrational behavior, perhaps behavior that made sense at an earlier and poorer stage of life, retained through habit.

But perhaps not.

I am comfortably well off at present, but my income reaches me through an elaborate set of social, legal, and political mechanisms and the world is an uncertain place. Quite a lot of Americans who were comfortably well off in 1928 were no longer so in 1930. The same was true a fortiori for French aristocrats in the late 18^th century, Russian in the early 20^th. Even short of stock market collapse or revolution, there are multiple ways in which I could suddenly find myself in a much worse situation, such as a fraud at my broker’s that emptied my portfolio. Any money saved today through habits of thrift would vanish along with everything else, but the habits would not. Even if I am safe through my lifetime, my children extend my concern decades further, and their pattern of life will be in part modeled on mine.

In the world as it now is, most things I want done can be done better and cheaper by someone else, hence it pays to specialize, earn money doing what I am good at, use that money to get other things through the market. That mechanism makes possible for modern-day people a standard of living enormously higher than a self-sufficient homesteading household could produce with its own labor.

The world is an uncertain place. As long as I am alive and without serious injury I have my mind, my hands, my skills. In an uncertain future, there might come a time when I had no access to a market — perhaps not for a day, a month, or, in an extreme case of societal collapse, a lifetime. Modern Americans have lived in a safe world for a very long time, but past performance, as they say, is no guarantee of future returns. There might come a time when I could no longer support myself by teaching, writing, speaking, perhaps a time when I would need to flee my country and find other ways of making a living. Safer not to be a one trick pony.

I conclude that while it makes sense to do most things through the market — I do not grow my own wheat and grind it for flour or spin and weave my own cloth — there is much to be said for maintaining a range of skills, the sort of range Heinlein describes if not his exact list. Just in case.

Insofar as being to some degree a generalist is prudent, it is admirable. Insofar as it is admirable, it is something one feels good about, wishes to demonstrate.  By, for example, feeding forty people out of your kitchen or building your own bookcases.

 

Writing a Novel Backwards

About twenty years ago I wrote Harald, my first novel, started a sequel, decided to work on an unrelated novel instead, wrote a sequel to that, planned a third book in the series. When that project stalled I decided to go back to the abandoned sequel and try to complete it. 

At which point it occurred to me that there was something I should do first. Harald has an implicit backstory, a history of the lands and people before the story starts. To produce a second novel in the same setting I should know that history. 

It was my first novel and it had not occurred to me while writing it that I needed to work out the timeline implied by things characters said, scenes they remembered, bits of dreams. Solving that problem, reconstructing the backstory from fragments of information, felt like historical research — except that the history being researched was fictional. World building, in my experience, feels more like discovery than invention.

I started by going through the book collecting everything in it that had implications for events before the book started, then worked out how to make all of it as nearly consistent as I could manage. It was fun, so I decided to write a blog post about it. 

For example ...

Central to the story is the repeated attempt by an aggressive empire to annex the kingdom of Kaerlia, where most of it happens, four invasions before the book starts, three more during it. Comments by characters imply that the first invasion was  twenty years before the start of the story. Or twenty-five. Or thirty. If I had spotted the inconsistencies before the book was published, as I should have, I would have reduced the disagreements to a more realistic year or two. Since I didn't, I needed to decide what the right number was, interpret the others as careless mistakes. To decide which number to pick ...

My protagonist's grandson appears to be about twelve or thirteen when the story starts. If I assume he was born when his father was eighteen, which is as young as seems plausible, his father would have been conceived about thirty-one years before the story starts. It is clear from details in the text that Harald was not yet married to Gerda at the time of his first battle, probably not for a year or two after, so that battle must have been at least thirty-two years before the story starts. It ended a failed invasion of the empire by the kingdom, so it seems plausible that the first invasion the other way would have been a few years later, putting it about thirty years before the story starts. That also fits the fact that my protagonist, a young adult in his first battle, appears in the book at about the age I was when I wrote it, somewhere in his fifties.

So the first invasion was thirty years before the story starts. Problem solved.

What about the fourth? There are three passages that could all be references to the same battle. One describes Artos, an  important secondary character, as the junior legion commander in a defeated imperial army. By the time we see him he has become the most prominent commander in the empire, which should have taken at least a few years. Another passage implies the death in battle of a woman whose daughter, a young adult, describes someone as sounding like her mother. The context is archery practice, which suggests that she was at least seven or eight before her mother died, which puts the battle she died in at most ten years before the story starts. 

I conclude that all three passages are references to the battle that ended the fourth invasion and that it happened between five and ten years before the opening scene of the book.

Why, for the sequel, do I need the dates of failed invasions? I do not know all the reasons, since I have not written it yet, but I expect parts of the story to involve Belkhan, an imperial province with a history of rebellion. The most recent rising was set off by the Imperial defeat at the end of Harald, which makes it plausible that earlier rebellions were similarly linked to earlier defeats. My objective is to make the whole story, two books, perhaps eventually three, feel like a consistent picture, one where things fit together. 

My main points in this somewhat odd blog post are:

1. I should have done all of this before publishing the novel. So should you if you are writing a novel.

2. But  doing it backwards was fun.