Friday, December 26, 2008

Thoughts on Long Term Climate

The graph shows global temperatures over the past quarter of a million years; the horizontal scale is in thousands of years, the vertical in degrees C. The source is Jouel et. al. 1996. Two things strike me about it:

1. We are in an unusually warm period, and have been for about the past ten thousand years. It has only gotten this warm once before over the period shown.

2. Judging at least by the previous peak about a hundred and twenty-five thousand years ago,and the smaller peaks between, this warm period has already lasted for an unusually long time.

From point 1 one might conclude that current worries about global warming are misplaced—on the long term evidence, we ought to be worrying about cooling. One might also include that arguments about anthropogenic warning are misplaced, since the current warm period started long before modern technological society with its large consumption of fossil fuel.

Point 2 suggests a somewhat different conclusion. The beginning of the long warm period we are still in roughly coincides with the invention of agriculture and the consequent large expansion in human population as we went from hunter/gathering to farming. One can imagine a variety of mechanisms by which that change might have affected climate, some described in a recent blog post at FuturePundit, one of my favorite blogs.

Monday, December 22, 2008

$70/hour Auto Workers

I've just been reading a column by Eric Boehlert in which he complains, at great length, that the media is propagating a false claim that auto workers get paid $70/hour. He writes "Simply put, GM's labor costs are not synonymous with hourly wages earned by UAW employees. Many in the press have casually used the two interchangeably. " He offers nine quotes from media sources, but only one, from National Review, actually makes the claim he is objecting to. One other makes a claim about how much the average auto worker makes per year. The rest put their numbers in terms of total compensation, wages plus pensions and benefits, or similar terms.

A good deal of Boehlert's indignation is based on the fact that labor costs as calculated include pension and medical benefits to currently retired workers. He regards this as obviously wrong, since the money isn't being paid to the current workers. But it isn't that simple. The cost of pensions is incurred when the worker is employed but paid—assuming, as I gather is the case, that these are not prepaid plans with fixed benefits—when he retires. If labor costs only count what is currently paid to current workers the cost of pensions will be left out, substantially understating both the benefit to the auto worker and the cost to the company.

Ideally, the calculation should be done using costs when incurred. But pension and medical costs are not known when they are incurred, since at that point the company does not know when the worker will retire, how long he will live thereafter or what his medical costs will be. So the choice is either to use a current estimate of the future cost of benefits to current employees or a current figure for current cost of benefits to past employees. Neither gives a reliable figure for the future cost currently being incurred and it is not obvious which is better.

The one problem I can see with estimating the labor cost per hour using current expenditures for both current and past workers is that the number of employees and their terms of employment change over time. If, as seems likely—I haven't checked—the number of employees is substantially less than it was in the past, then dividing current pension payments by the current number of workers gives too high an estimate for the per worker cost being incurred for pensions to current workers. On the other hand, if pension terms now are more generous than they were for many of the currently retired workers, that would bias the numbers the other way. Similarly for medical costs--if we assume they will be higher in the future than they are now, then using current costs paid underestimates future costs currently incurred.

All of those are details and none of them were mentioned in Eric Boehlert's column. At the simplest level, and assuming the companies aren't trying to include both pension costs incurred and pension costs paid, which would be double counting, he is wrong. What he regards as a blatant deception is a better estimate for the real cost per hour of employing auto workers than it would be if corrected in the way he wants it to be.

Wednesday, December 17, 2008

The Rabbi and the Norse King

Leo Rosten, in his (delightful) The Joys of Yiddish, tells the following story:

An official brought the chief rabbi of a town before the Court of the Inquisition and told him, "We will leave the fate of your people to God. I am putting two slips of paper in this box. On one is written 'Guilty.' On the other is written 'Innocent.' Draw."

Now this inquisitor was known to seek the slaughter of all the Jews, and he had written "Guilty" on both pieces of paper.

The rabbi put his hand inside the box, withdrew a slip of paper—and swallowed it.

"What are you doing?" cried the Inquisitor. "How will the court know—"

"That's simple," said the rabbi. "Examine the slip that's in the box. If it reads 'Innocent,' then the paper I swallowed obviously must have read 'Guilty.' But if the paper in the box reads 'Guilty,' then the one I swallowed must have read 'Innocent.'"

It's a clever trick, but I had heard it before:

… it was determined, with the consent of all parties, that lots should be thrown into a box, and the Greeks and Varings should draw which was first to ride, or to row, or to take place in a harbour, or to choose tent ground; and each side should be satisfied with what the drawing of the lots gave them.

Accordingly the lots were made and marked. Harald said to Gyrger, "Let me see what mark thou hast put upon thy lot, that we may not both mark our lots in the same way." He did so. Then Harald marked his lot, and put it into the box along with the other. The man who was to draw out the lots then took up one of the lots between his fingers, held it up in the air, and said, "This lot shall be the first to ride, and to row, and to take place in harbour and on the tent field." Harald seized his hand, snatched the die, and threw it into the sea, and called out, "That was our lot!" Gyrger said, "Why did you not let other people see it?" Harald replies, "Look at the one remaining in the box, -- there you see your own mark upon it."

Haraldsaga was written in the 13th century and describes events in the 11th century—Harald, after serving as the commander of the Varengian guard, returned to Norway, became king, in 1066 invaded England and died at the battle of Stamford bridge. So it is unlikely that either Harald or Snorri Sturluson, the author of the saga, got the idea from Leo Rosten or his unnamed rabbi. The most likely explanation is independent invention; it's a clever idea that could have occurred to two different people.

My preferred explanation, however, is that the inquisitor had the bad luck to pick on a rabbi with a taste for reading the Icelandic sagas.

Monday, December 15, 2008

Back of the Envelope

A physics professor my wife knows complains that few of his students have any idea of how to do plausibility calculations, how to figure out whether quantitative claims could be true. My wife suggests that it would be a good topic for a class in elementary school, since such calculations usually require nothing more than arithmetic and demonstrate one reason why arithmetic is useful. It occurs to me that it might also be a good topic for a book.

In physics, economics, and I expect some other fields, these are sometimes referred to as “back of the envelope” calculations, because they can be, sometimes are, done on the back of an envelope destined for the waste basket. They use approximate data, approximate models, and are expected to give the right answer to within about a factor of ten in either direction. Here are a few examples--readers are invited to provide more.

How long cars last: It’s not uncommon to hear complaints about how quickly cars, especially American cars, wear out, sometimes linked to the claim that they are designed to wear out so you will have to buy a new one. Along similar lines, American consumers are sometimes pictured as routinely buying a new car every two years.

If the average car lasts two years, the cars currently on the road represent about two years' production. It is easy enough to look up how many cars are on the road and how many are produced each year; for 2005 the figures (from the Statistical Abstract of the United States) are 137 million automobiles registered and 17 million new cars sold. Dividing the first number by the second tells us that the average car lasts about eight years. Some of those, of course, are made by Japanese or Korean or European firms. But it is easy enough to repeat the calculation for an earlier year, back when most cars driven in America were built in America by American firms.

Population density: One occasionally sees concerns that, as population grows, housing swallows up land needed for farming. To see how plausible they are, I start by estimating the amount of land actually occupied by housing. A large house nowadays has 3000 square feet of floor area, typically on two floors, and is occupied by four people, which means 1500/4 square feet of land per person. That’s surely a high figure, since most people don’t live in houses that large and a considerable part of the population is in urban areas in housing with more than two stories. Round numbers make calculation easier, so call it 200 square feet per person. An acre is 200'x200', so that gives you 200 people per acre. There are 640 acres in a square mile, so (rounding down for simplicity) about 100,000 people per square mile. The U.S. population is about 300 million, so the total area occupied by housing should be about 3000 square miles.

The U.S. is, very roughly, 3000 miles east to west and 1000 miles north to south. So housing occupies about 1/1000 th of its area.

This is a very approximate figure, produced without looking up anything. And it only includes housing, not lawns, streets, grocery stores, and the like. But it is still enough to show that mental images of people packed in like sardines due to too many people in not enough space, along with the associated arguments about how rats behave when there are too many of them in a cage, have to be wrong. There are areas where human construction occupies a large fraction of the land area. But the reason—at least in the U.S.—is not that there are too many people for too little land but that many people, for a variety of reasons, prefer to live in densely populated areas.

One reason for this particular error is that people form their opinion based on what they see around them—and spend most of their time in places where there are people. They are averaging population density over people rather than over acres, asking how densely populated an area the average person lives in rather than how densely populated the average acre is. One way of correcting that error is to observe a sample that is not biased in that way—by, for instance, looking down from an airplane window when flying across the country. What you see is much more likely to be corn fields, mountains, desert or forest than a sea of rooftops.

Asteroid Strikes: The risk of asteroid strikes has two relevant dimensions: How much damage would an asteroid of a given size do and how likely is an asteroid of that size to hit the earth.

Start with the one case we have good evidence on—the Tunguska event. In 1908 something caused a very large explosion, roughly equivalent to a hydrogen bomb; the current preferred theory seems to be that it was an airburst of a large meteor or comet fragment. It knocked down trees over an area of about 2000 square kilometers. Dropping a hydrogen bomb from time to time at some random location sounds pretty scary; perhaps we were just extraordinarily lucky that it hit Siberia instead of Manhattan. A simple back of the envelope calculation can tell us about how lucky we were.

The earth is a globe with a radius of about 4000 miles, roughly 7000 kilometers. The area of a sphere is 4π times the radius squared, making the surface area of the earth about six hundred million square kilometers. So the area over which trees were knocked down by the Tunguska explosion represents about 1/300,000 of the area of the earth. The current population of the earth is between six and seven billion. If we assume that the area over which trees were knocked down is about the same as the area over which humans would be killed, the average death toll from a Tunguska event would be about 20,000. That is a lot of people but hardly a global catastrophe—about half the number killed in the US each year in auto accidents, about one three hundredth of the number killed in the Holocaust.

How likely is a Tunguska event? It is unlikely that one would have occurred in the past century without being observed, given the seismographic effect, which registered as far off as Washington D.C. How much farther back one can push that argument I don’t know, so I will assume that such events happen at a rate of one a century. If so, the average mortality from such events is about 200 deaths/year. Every death matters, but there are a lot of problems in the world that do a great deal more damage than that. There is a good deal left out of these calculations—for one thing I don’t know how the area of damage from a sea strike would compare with that from a land strike or how easily it would be observed if it happened during the past century, and a sea strike is considerably more likely than a land strike. But they are enough to give us a rough scale for the problem.

So far I have considered only things on the scale of the Tunguska event, but we know that there have been, at very long intervals, much larger meteor strikes. One famous one about sixty million years back is sometimes referred to as the Dinosaur Killer, on the theory that its effects killed off the dinosaurs. My geologist wife objects to that label on the grounds that lots of other things went extinct at the same time; the technical term is apparently the K-T event. The evidence for several earlier large strikes with less drastic consequences is preserved as astroblemes, geological structures believed to be the result of asteroids hitting the earth. So let’s guess that they occur at a rate of one every sixty million years. We don’t know how many people would be killed by a strike on that scale, but the upper limit is everyone, so use that for a very rough calculation. Dividing about six billion people by about sixty million years gives us a mortality rate of about a hundred people a year.

Here again, my calculations leave a lot out. Mass extinctions on the scale of the K-T event occur at a rate considerably below one every sixty million years; there are fewer of them than there are astroblemes. That suggests that perhaps I should have divided by 300 million or so instead of sixty million. On the other hand, I have not considered events intermediate between the two categories, infrequent enough to be left out of the historical record and small enough to be left out of the fossil record but still bigger than Tunguska and more frequent than K-T. But I think my calculations are sufficient to show that anual mortality due to asteroid strikes is tiny compared to other sources.

One final question is whether annual mortality is all that matters. Perhaps we ought to consider not only individual lives but the survival of our species and our civilization. Seen from that standpoint, if an asteroid strikes really does kill everyone the cost, as evaluated by those presently living, might be considerably larger than the number of lives lost. My own guess is that even something on the scale of the K-T event wouldn't wipe out either our species or our civilization, but I might be wrong.

A correspondent points to the signs currently appearing on the tables of local restaurants, explaining that, because of the water shortage, they will only bring drinking water if you ask for it. The obvious question is whether the amounts involved are large enough to matter. It's straightforward to estimate how much water is being saved per person per year. You can go from that either to an estimate of the size of the local reservoir and the number of people it serves, or the amount of water used for some other purpose, such as watering lawns or flushing toilets, or—with a little searching—to per capita water consumption in the U.S., and compare the numbers.

Readers are invited to suggest further examples of such calculations. They should involve claims that people might make and care about and that can be evaluated without any expert knowledge, using information lots of us already have or can easily find. Bonus points for an example that would work for a twelve-year old.

Virtual Off Campus

A very long time ago, when I graduated from high school, going to college meant an almost complete break with one’s previous life. There might be a few people from your high school going to the same college. One or two of them might be friends or at least acquaintances. But for the most part you were being dropped into an entirely new world.

It was an opportunity to abandon forever, or at least until your next visit home, the nickname you had been given in second grade. It was an opportunity, with luck, to change your image, the picture of who and what you were held by those around you. But there was was also the frightening prospect of a world where you had no friends, where nobody knew you, where you would have to rebuild in months the social networks that you built, or had built around you, over the past many years.

That was before the Internet. For college freshmen as for the rest of us, the online world provides portable friendships. I can fly to Paris or London, connect to my hotel’s Wi-fi, and continue a conversation started a day or two earlier from San Jose. A new student arrives at college complete with a network of online friends.

Here too there are advantages and disadvantages. The first day is surely less frightening if you know that, back at your dorm room, lots of friends are waiting for you via email, facebook, or your evening WoW raid. On the other hand, knowing that reduces the need to go out of your dorm room looking for new friends. As one colleague I discussed the matter with suggested, the situation of a student in the dorms in the world of the Internet is rather like that of a student, in the old days, who lived off campus. His classroom life was shared with fellow students; his social life might well not be.

Friday, December 12, 2008

"Accepting responsibility"

"Following the verdict, the Acting Met Commissioner Sir Paul Stephenson said Mr de Menezes' death had been a "most terrible mistake", which he "deeply regretted".

"He was an innocent man and we must accept full responsibility for his death," he said.

I know very little about this particular case or who was or was not at fault, but I was struck by the emptiness of Mr. Stephenson's concept of responsibility. He is not proposing that the police officers who killed Mr. de Menezes be punished in any way—the coroner had instructed the jury that they were not permitted to return a verdict of unlawful killing. He is not proposing that he himself or anyone else in any sense responsible be punished in any way or owe recompense to anyone. He is merely "accepting full responsibility" on behalf of his organization for killing an innocent man.

I am reminded of my reaction at the time of the Waco tragedy when Janet Reno, then Attorney General, made a similar statement on her own behalf. If you accept personal responsibility for actions that led to a substantial number of people, including children, being burned to death while under attack by people whose actions you consider yourself responsible for, the very least you can do is to resign. Subsequent suicide may be appropriate but is not mandatory.

But of course what she actually meant, and what he actually meant, was something closer to "all right already, stop bugging me."

Saturday, December 06, 2008

Android G1 Update

In a recent post I listed a number of pieces of software that did not yet exist for the G1 and, in my view, should. One of them was an ftp program. A few days ago, DroidFtp appeared in the Google market.

There is still no word processor unless you count Google Docs, which requires an internet connection to work, although I gather that is supposed to change at some point. There is a pretty good text processor suitable for making notes, although with no control over font, text size and the like: AKNotepad. And there is a program for reading books, textonphone, complete with access to 30,000 or so, mostly, I suspect, courtesy of project Gutenberg. It allows you to either read online or download the book and read it off your G1. It still has minor flaws—lines of verse, for instance, get run together—and it does not let the reader control text size or similar characteristics. But still a very nice program. And there has been some progress towards a tethering application, although so far the connection is through the USB port, not bluetooth or WiFi.

Still missing: A real word processor, software to link the G1 to a bluetooth keyboard, software to let the G1 serve as a wireless router that would connect notebooks to its 3G connection, and a web browser that can save to, and read from, internal memory. And while file browsers are getting better, further improvement would be nice.

Nature vs Nurture: A Natural Experiment

I have been engaged in a long Usenet thread (much of it here) coming out of my claim that hostility to evolution isn't limited to the religious right, that the left, although unwilling to reject the theory of evolution, is also unwilling to accept implications of evolutionary biology that are politically incorrect. The main thing I've gotten out of the thread is evidence supporting that claim—although, of course, those who provided that evidence may disagree.

But recently someone pointed out an interesting paper which provides evidence on a related question of considerable interest: To what extent are outcomes for a child determined by the environment he is raised in, to what extent by his genes? Children of well off and well educated parents tend to end up richer and better educated than children of parents with the opposite characteristics. Is that because of a superior environment or superior genes?

From 1970-1980, a large number of Korean-American children were placed for adoption by an agency which assigned them at random to adoptive families. That meant that any correlation between characteristics of the families, such as maternal education, socio-economic status, or income, and characteristics of the children as adults, would be due to environment not genetics. By comparing the strength of the relation between characteristics of parents and adoptive children with the corresponding figure for parents and biological children raised by those parents, one can get at least some estimate of how much of the relation comes from which cause.

The conclusion is striking. An increase of one year in maternal education produces an increase of only .07 years in the education of an adoptive child but an effect four times as large on the education of a biological child. Similar results apply to a variety of other characteristics. It looks as though being brought up by well off or well education parents is indeed an advantage, but a considerably smaller advantage than being the biological child of such parents.

One important qualification to that result is to note that all of the adoptive families had to be certified by the adoption agency as suitable to adopt. That would presumably cut off some of the lower tail of the distribution—an alcoholic unmarried mother would be unlikely to qualify. And, they had to be families that wanted to adopt, which again would eliminate some. But at least over the range of environments in the sample, nurture seems to be a good deal less important than nature.

The study, as so far described, is limited to particular, readily measured, characteristics of the adoptive parents. Having a well educated adoptive mother doesn't have much effect on how much education you get. But having an adoptive mother who cares a lot about her children and pays them a lot of attention might.

To test that possibility the author of the paper looked at the relation between characteristics of siblings. Adoptive siblings, like biological siblings, are brought up in the same household, but, unlike biological siblings, are not genetically related. So if some households are much better places to be brought up in than others, one would expect the result to show up in the relation between (say) years of education of adoptive siblings.

There is such a relation, but it is only a little stronger, relative to the corresponding relation between biological siblings, than in the parent/child case. An extra year of education by an adoptive sibling predicts, on average, an extra .09 years of education, for a biological sibling an extra .29. The effect is stronger for income: .16 vs .29.

A further limitation in the study is that it does not distinguish a relation between biological parent and child or biological siblings due to shared genetics from one due to pre-natal environment. Arguably, better educated and higher income mothers are in better condition during pregnancy, which could result in better children for (pre-natal) environmental reasons rather than genetic reasons. That does not affect the absolute level of the effect for adoptive children but might make the genetic contribution to the difference between adoptive and biological look larger than it really is.

Monday, December 01, 2008

Executive Compensation and the Economics of Insurance

One of the things legal rules do is to allocate risk, so one of the subjects covered in teaching the economic analysis of law is the economics of risk allocation, conventionally put in terms of the economics of insurance. Designing optimal rules in this context is hard, because there are three different objectives and no reason to expect the rule that is best for achieving one to be best for the others.

The first objective is risk spreading—for familiar reasons, many people prefer a certain income of (say) $50,000 a year to a coin flip between $10,000 and $90,000, even though the average outcomes are the same. Insurance provides a way of converting the riskier outcome into the less risky.

The second objective is optimum incentives for controlling risk. Often, although not always, the same person who starts out bearing the risk is the one in the best position to take precautions against it. From this standpoint insurance is the problem, not the solution. Once I have insured my house or factory for its full value, the incentive to me to take costly precautions to make it less likely to burn down is low. In the extreme case, where an insurance company has been so imprudent as to insure something for more than its full value, the chance of a fire may become very large indeed. This is the problem described in the literature as moral hazard, not because taking risks is immoral but because “moral” in this context has an older meaning close to “psychological.” The hazard is due to the incentives of the actors, the moral not the physical characteristics of the situation.

The third objective has to do with the fact that the choices we make signal—imperfectly—information about our private information. That I want to buy lots of life insurance today is evidence that I know something the insurer doesn’t about my chances of living to tomorrow. That is a reason for him not to sell it to me, or only at a high price. The same argument applies, although less strongly, to anyone who wants to buy insurance against any risk that he has better information about than the seller. Wanting to buy is evidence that the risk is higher than average, a fact which the seller will take into account in pricing the insurance.

That is a problem if you face an average or below average risk but still, because of risk aversion, want to insure against it, provided you can do so at a price not much greater than the actuarial value of the insurance, a problem known in the literature as “adverse selection.” The classic example is the market for lemons. Sellers of used cars know more about them than buyers, so the fact that I want to sell my car signals that it is likely to be a lemon, so I get offered a lemon price, which makes it even less likely that I will sell it if it isn’t a lemon.

The same set of problems applies to executive compensation. One obvious way of better aligning the interests of executives with those of stockholders is to require the executives to be stockholders. To align the interests in the long term as well as the short, one could require executives not only to hold a sizable fraction of their personal wealth as stock in the company they work for but also to hold it under rules that prevent them from selling the stock or hedging it for some substantial period of time.

Arguably, this would be a good way of controlling not only moral hazard but adverse selection as well. An executive whose private information implied that hiring him would be bad for the company—perhaps because he planned to keep the job only until a better offer, expected shortly, came through, or because he planned to supplement his income at the expense of the stockholders—would have a good reason not to take the job on those terms, which is a second reason to insist on those terms when offering it.

On the other hand, requiring executives to invest a large fraction of their wealth in the stock of the company they worked for would be a very bad way of spreading risk. If the company did well, both the executive’s salary and his stock portfolio would go up. If it did badly, both would go down. Better, from that standpoint, to spread the risk by owning stock in some company, practically any company, other than the one he works for.

In some contexts, some employees are paid with stock options that can only be exercised after a set period of time; I do not know if there are any precautions to prevent the employee from hedging his bet by selling the stock short before the time has expired. I also do not know to what extent the tactic described above is, or can be, implemented for executive compensation more generally. Clearly there are reasons both for doing it and against.

Comments welcome, especially from anyone who knows more than I do about the actual terms of the usual employment contracts for top executives.