dcw planet

This post is a mea culpa. A year ago, I knew that the U.S. poverty rate -- the portion of people in households with incomes low enough to qualify as officially poor -- has been stuck at around 10% for the last 30 years. I also knew that real GDP per capita -- the amount of stuff that the average American consumes each year -- had just about doubled over that same time. (From $18k in 1970 to $35k in 2000; those are inflation-adjusted figures from the Economic History Services.) I assumed that the explanation for the apparent discrepancy between these two facts was simple: the U.S. government had revised the poverty threshold upward over time, as we as a society had come to expect that everyone eat lunch out, that siblings should not have to share bedrooms, and that every family requires two cars.

I was wrong. I first discovered I was wrong when I finally bothered to look up historical poverty line figures and determined that the 2003 value ($9393 for a single person) is exactly the same as the 1967 value when adjusted for inflation. The government hasn't been changing the goal-posts after all.

So how is it possible that our society has gotten twice as wealthy, but we still have just as many poor people? The answer is that, while average incomes have doubled, the lowest incomes haven't budged. The situation is illustrated by the chart below, which shows the evolution of inflation-adjusted household income for each quintile of the population separately. (This cart is generated from U.S. census bureau data.)



The lowest-earning 20% are represented by the red line, the next-lowest-earning 20% by the orange, and so on, up to the highest-earning 20% represented by the purple line. Notice that the red line is essentially flat, indicating that, as mentioned above, the incomes of the poor remain essentially unchanged. And it's not just the poor who have fared worse than the average. The incomes of the next 20% have gone up a bit, but still have nowhere near doubled. As we move up through the higher income quintiles, each one exhibits larger gains than the last. The incomes of the top 20% really did double, and if we were to plot the incomes of the top 5% or top 1%, we would see that they did even better.

It's important to understand that no mathematical necessity arising from our segregation of the population into quintiles dictates that gains must be distributed in such an unequal way. We could have doubled average income, for example, by doubling the income of each quintile; such a distribution of gains would have cut the poverty rate approximately in half. Nor does any economic necessity require that the rich get richer faster than anyone else. Although these government time-series don't go back far enough to show it, the incomes of the lowest 20% must have increased significantly before 1970. (In 1940, average income was below the current poverty line, so the lowest 20% of incomes must have been far lower, and increased dramatically in the 30 years that followed.)

A number of explanations for this sad phenomenon have been proposed. Certainly membership in trade unions, which aim to increase the bargaining power of the lower classes, has declined precipitously over the last 30 years. (Of course, this explanation begs the question of why, if unions provide such significant benefits, union membership has declined so precipitously.) Also during this time, changes in technology have increased the productivity of capital and of skilled workers far more than they have increased the productivity of unskilled workers. So the difference in the distribution of gains between the period 1940-1970 and the period 1970-2000 may reflect the different sorts of technological process that were made in the two eras.

It is worth pointing out that the U.S. "imports" a large number of poor people to replace those that climb the income ladder -- the number of generations a person's family has been in the country correlates strongly with income. Seen in this light, our constant poverty rate doesn't look so bad, since it means that we are giving new generations of immigrants the chance to better themselves as previous generations lift themselves out of poverty. Conservatives -- at least those that can stomach immigration -- tend to emphasize this effect. I have not yet attempted to calculate what proportion of poverty it could explain. While I do not doubt that this effect does account for a part of the poverty rate, it does not seem to offer any explanation of the difference in the evolution of poverty between the 1940-1970 and 1970-2000 eras.

Progressives, on the other hand, tend to view the contrast between our growing wealth and our unchanging poverty rate as an indictment of the system. But the historical record should give them pause. The late 1960s, which separate our two eras, mark the birth of the war on poverty and the ensuing great society programs intended to reduce the poverty rate. While one could argue that the poverty rate today would have been even worse in the absence of these programs, the prima facie interpretation of the facts before us would be that these programs have failed. In fact, the controversial sociologist Charles Murray, in his book Loosing Ground, makes an occasionally persuasive argument that at least some aspects of these programs incentivized the poor to take decisions that tended to perpetuate their poverty.

Clearly this is an important riddle, and I hope to come back to it as I uncover and analyze more data.

Political compass is web site on a mission to educate its readers about the varieties of political thought. They argue that, instead of locating political beliefs on a line that goes from left to right, we should locate political beliefs in a two-dimensional plane. The east-west axis of their plane represents support for government intervention in economic matters, while the north-south axis of their plane represents support for government intervention in social and moral matters. On their web site, you'll find a fun quiz; using your answers to the quiz, which is anonymous and takes only about 10 minutes to complete, they will pinpoint your location in the political plane. I encourage everyone who reads this to go take the quiz. Here is a picture of their plane, with a dot that represents my own quiz result:



One can, of course, extend their logic and argue that, in fact, many more axes are required to accurately depict a person's politics, and therefore that we all exist in a hyper-dimensional political space. While this is undoubtably correct, the more interesting question is: how many axes are required to depict the politics of the vast majority of people? As far as I can tell, in answering this question the web site's ogranizers have actually erred in the other direction. As best I can determine, just one axis appears to suffice to accurately depict the politics of nearly everyone.

I've seen the quiz results for many of my friends and acquaintances, and nearly all lie along the line that runs from the south-west (Democratic) to the north-east (Republican) quadrants. All the mainstream politicians I've seen classified on their site lie along this axis. The politicians in the remaining quadrants are either those that everyone recognizes as outliers (e.g. Joseph Stalin in the north-west quadrant) or those that no one recognizes at all because they are too obscure (e.g. Michael Badnarik in the south-east quadrant).

My own lonely quadrant would probably be called Libertarian by most Americans. I don't particularly like that word, since in my mind it conjures up visions of gun-toting wackos in the Montana wilderness. (Not that those people aren't libertarians. They are just crazy libertarians.) British readers might call the inhabitants of my quadrant classical liberals, which sounds nicer but means nothing to most Americans. Continental Europeans would call us neoliberals, which is a word that, in European political discourse, conjures up visions of heartless Dickensian villains.

I don't really understand why my quadrant is so nearly empty. It seems to me an entirely consistent belief system: government should interfere neither in peoples' economic arrangements, nor in peoples' social and moral arrangements. In this view, government plays the role of a referee, who has no interest in a particular outcome, but intervenes when the players can't agree on the rules of the game. Isn't that more consistent than believing that government should intervene in economic but not moral matters, or vice-versa?

Inhabitants of my quadrant oppose a lot of what the left wants: minimum wage laws and affirmative action come to mind. We also oppose a lot of what the right wants: drug prohibition and decency standards come to mind. Many Libertarians even oppose a lot of what the left and right agree on: limits on prostitution and strict immigration controls come to mind. Not that I oppose high wages, or decent behavior, or think that prostitution is an advisable career choice; I just don't think it's right to impose these values at the point of a gun.

At the core of laissez-faire politics lies the notion that our government and our society can and should be separate entities. Governments, by their very nature, deal in coercion. A government's power over its citizens ultimately derives from its ability to lock them up, or worse. Societies, at their best, operate by free cooperation. Charismatic politicians should have to lead by the force of their ideas, and leave the weapons of government power in the hands of boring technocrats.

You have a new baby. Congratulations! In 18 years, your young genius will surely attend a prestigious college. Being certain of this future expense, and being the prudent financial planner you are, you resolve to put a small amount of cash into a drawer each month for next 18 years. You expect that, 18 distant years from now, the accumulated funds will reduce what you will have to pay out of your running budget while your child attends college.

Ten years on, you need to replace your aging car, and, while you certainly qualify for a car loan, you actually have enough money in the drawer to buy a new car outright. Congratulations on your diligent saving! Raiding the trust fund for the car is actually prudent, you reason, since you would have to pay interest on the loan, while the money in the trust fund is interest-free. Of course, you realize, the trust fund will have to be re-paid, so you replace any cash you take out of the drawer with a piece of paper on which you have written the amount of your withdrawal.

After 18 years of diaper-changing, temper-tantrums, piano lessons, homework, school dances and test prep courses, your young genius is indeed accepted into a prestigious college. You open the drawer an find... a lot of pieces of paper.

Is the trust fund real? Don't be too hard on yourself. You love your child and you're good for the money, so certainly in that sense the trust fund is real. On the other hand, you didn't achieve your goal of reducing the money that must come out of your running budget during the next four years to pay for your child's college education. Whether you prefer to think that you are paying the college directly, or that you are paying back the trust fund which in turn pays the college, won't make an iota of difference in the amount that must now come out of your paycheck each month.

Democrats and Republicans love to argue about whether the social security trust fund is real. As my parable illustrates, their arguments are entirely beside the point. Receipts from the payroll tax have, for quite some time now, exceeded social security payments to retirees, and are expected to continue to do so until about 2015. The idea was that, by levying a larger payroll tax than was required to pay retirement benefits before 2015, we would reduce the taxes that would have to be levied after 2015 to pay to for the glut of baby boom retirees.

But that excess cash wasn't put into a vault. And indeed, it wouldn't have been fiscally prudent of the government to leave it sitting in a vault while issuing interest-paying bonds to cover large budget deficits. (What would really have been prudent is for the government to loan the excess cash to interest-paying debtor nations while not running large budget deficits. But that is water under the bridge...) So the excess cash was spent, but carefully accounted for. The social security trustees know how much the government owes them and they are counting on it being paid back. If it were not paid back, a significant tax increase would be required to make up for the missing funds. On the other hand, since the government also doesn't have the money in a vault, in order to pay it back a significant tax increase will be required.

Of course, a taxpayer couldn't care less whether he is taxed by the social security trustees or taxed by the government in order to pay the social security trustees. In either case, the only way we can pay retirees their promised benefits is to raise taxes just as much as if we hadn't saved at all. I'm not saying we aren't good for it -- given current demographic trends, and comparing the voting records of old and young people, I'm pretty sure we are going to be good for it. I'm just saying that we haven't succeeded in our ostensible goal of creating a cushion that would have allowed us to make good on our promises without raising taxes.

Stay tuned for more retirement financing conundrums.

Recently, Larry Summers, the president of Harvard University, has found himself in hot water for suggesting that the under-representation of women in the highest echelons of science might be due to innate biological differences between the sexes. In the past, others have been similarly chastised for suggesting that the the over-representation of blacks in the highest echelons of many professional sports might arise from innate biological differences among races.

The most amusing aspect of these debates is that almost all the participants are completely off the mark. How different groups perform at a given task on average is entirely irrelevant to predicting which group will contribute the most to that tiny portion of the population who are the very best at the task. Whether men or women are, on average, better at science has no effect on whether the best scientists are men or women. Whether blacks or whites are, on average, better at competitive athletics has no effect on whether the best competitive athletes are black or white. How can this be?

Below is a picture of the bell curve, named for its shape, beloved by statisticians and bemoaned by test-takers everywhere.



It is a picture that shows how often a particular value will be measured. When the line over a value is high, that value is measured often; when the line over a value is low, that value seldom occurs. The shape of the curve, which fits the measured distributions of many attributes and test scores remarkably well, says that medium values occur often, while higher and lower values occur less frequently. Very high and very low values occur, of course, very infrequently.

Most of the area under a bell curve, representing the great mass of the population, lies near the middle value, called the average or mean. The very highest values, obtained by the people who are the very best at the measured skill, are represented by the small area under the far-right tail of the bell curve.

Before we proceed to determine who dominates that far-right tail, you must know that you need two numbers to characterize a bell curve. First, of course, you need to know the middle value, which statisticians represent by the Greek letter μ (mu). But you also need to know how spread out the values are around the middle; visually, that corresponds to how wide or narrow the bell curve is. Statisticians call the width of a bell curve its standard deviation, and represent it by the Greek letter σ (sigma).



Take, for example, measurements of IQ. The average IQ is μ=100, and the standard deviation σ=15. A score over 115 (one standard deviation above the mean) will be measured for around one person in ten. If instead we had σ=5, a score of 115 (now three standard deviations above the mean) would be measured only for around one person in 100,000. As σ decreases, the bell curve becomes narrower and it becomes more difficult to get a score far from the mean. Conversely, as σ increases, the bell curve becomes wider and it becomes easier to get an extreme score.



Now consider two different groups of people, which we will call pink and blue. Suppose we measure the distributions of some characteristic in the two populations, and get the bell curves shown above. I don't know what the characteristic is; perhaps it's height or weight, or perhaps it's interest in science or the score on some math test. You'll notice immediately that the pink population scores, on average, lower than the blue population. It has a lower μ. What you might not notice right away is that the pink population's bell curve is also a little wider than the blue population's. It has a higher σ. That fact isn't important for determining whether a typical pink or blue person is likely to have a higher score. But it is decisive for determining whether the highest scores will belong to pink or blue people. Notice that, despite that fact that the blue average is higher than the pink average, pink dominates the very highest scores, due to its higher standard deviation. Below is a close-up of the far-right tails of the distributions, to make this easier to see.



But surely, you might argue, having a higher μ helps. If blue's average were high enough, there would be more blues than pinks in the region where there are now more pinks than blues. And that is "sort of" true, but only "sort of". It turns out that, as long as you go far enough out in the tails of a bell curve, the population with the higher standard deviation will always dominate. By changing the means, you can change the score where the cross-over occurs, but you can't change the fact that the higher-σ group will eventually, at some point in the far-out tails of the distribution, overtake the lower-σ group.

I don't know whether the pink and blue lines sketched above accurately represent the distributions of scientific ability in the sexes, or of athletic ability in whites and blacks. Such measurements are fraught with peril for the career of any statistician who might think to undertake them. And whatever one chooses to measure, whether it is the right measure of ability is entirely debatable. But I do find it amusing that, for any measure, the suggestion that one sex or race might have a higher μ is enough to elicit a torrent of vitriolic responses, while the suggestion that one group might have a higher σ usually elicits yawns. For the question at hand, it is really σ that counts!

By the way, the mathematical properties of bell curves were first investigated in detail by the German mathematician Carl Friedrich Gauss in the early 19th century. So we should really all have this down by now.

Boeing builds many planes near Seattle, and my hometown newspapers regularly run editorials calling for the U.S. to sanction European countries for subsidizing Airbus. Magazine articles endlessly re-hash the debate over whether low-cost imports from China are good because they help keep inflation low or bad because they destroy American manufacturing jobs. The U.S. steel and textile industries clamber for protection against dumping.

Trade policy is forever in the news. It was in the 1930s, when the U.S. congress, reacting to the Great Depression, passed the Smoot-Hawley Tariff Act severely curtailing trade. It was in the 1840s, when Great Britain fought the Opium Wars to protect its right to sell the drug to Chinese addicts.

A depressing number of debates on the merits of trade go like this: A says "trade benefits consumers by lowering prices." B says "trade harms workers by eliminating jobs." A responds "but everyone, including the displaced workers, benefit from lower prices." B responds "you can't buy anything at all if you don't have income". The assertions of both A and B are obviously correct. There is no way to get beyond these sound-bites without quantifying the dollars saved and wages lost, and no newspaper dares to impose such an analysis on its readers.

There actually is such an analysis, which is done in introductory economics courses around the world. Economists are quite fond of it. Done in the early 19th century by David Ricardo, it was one of the first mathematical models of an economic phenomenon. You draw some lines, measure slopes and intercepts, and obtain an actual answer to the question of whether trade is, in the net, good or bad. I'm quite fond of it myself, but I'm not going to describe it here.

Primarily because of such mathematical analysis, almost all economists are in agreement on the issue of trade policy. From that darling of the right, Milton Friedman, to that darling of the left, Paul Krugman, they will tell you that unfettered free trade is almost always good.

I'm going to show you an entirely non-mathematical way to understand the answer.

Imagine that, instead of selling us a product at a cost lower than domestic producers, a foreign producer were to give us the product. Surely the recipient of a gift isn't made worse off by accepting it? (Well, perhaps if the gift is opium, or a a Torjan horse, but let's stick to airplanes and textiles for the moment.) The situation for domestic producers would certainly look bleak. No one would buy from them. They would go out of business, and their workers would be out of their jobs. Still, even in the short run, the total amount of stuff available for domestic consumption would clearly be the same or greater. All the other stuff that was made before would continue to be made, and the free foreign supply of the product in question would replace the old domestic supply, if not exceed it.

In the longer run, the workers would get different jobs. They would produce other things, perhaps things that previously didn't get produced at all, because they had spent their time producing the old product. Then even more stuff would be available for domestic consumption.

The more realistic scenario is that the foreign producer still wants payment for the good, but less payment than the domestic producer. When a foreign producer undercuts a domestic producer, we haven't quite reached the happy state of getting the good for free, but we are closer, and, therefore, in the net, better off.

You can, if you like, also imagine the even less realistic scenario in which some hyper-mercantilist foreigners give us all the the products we currently produce, for free. Then no one in our country has a job, but we certainly aren't worse off!

I want to be very honest about what this argument proves and what it doesn't. It doesn't prove that every displaced worker is just as well-off in his new job as in his old one. Trade can increase inequality, and if you want to oppose trade you are welcome to claim that it does. But my argument does show that, if dollars saved are counted one-for-one against wages lost, in the aggregate and in the net, tade makes us better off. So if you want to oppose trade, you cannot claim that the costs of lost wages will outweight the gains of lower prices. That is simply and provably wrong. By concentrating on the total ammount of stuff available for domestic consumption, we have been able reach this conclusion without having to seperatly weigh the effects of each dollar of lost wages against the effects of each dollar of consumer savings.

Being able to produce more things with fewer workers lies at the heart of what we mean by economic progress. Seventy years ago, in the United States, we employed about 20% of workers to feed ourselves; today, we employ only about 2% to do so (U.S. census statistics). We are richer precisely because we don't need as many workers to feed ourselves as we used to. In the same way, our country will be richer if, by trade, we can obtain larger quantities of steel and textiles using fewer workers.

Imagine what the world might look like if, at the behest of farm workers, we had undertaken measures to insure that agricultural efficiency not increase, so that just as many of us had to work at keeping ourselves fed as did 200 years ago. Imagine what the world might look like if, at the behest of the luddites, we decreed that all socks be knit by hand. While these imagined worlds might have a certain romantic charm, it wouldn't take very long in a 200-year-old standard-of-living before the vast majority of us opted for progress.

This is my first post to my google blog. I hope my musings will be of interest to family, friends, and perhaps even strangers. I plan to write mostly about social, economic, and political issues that might concievably be of interest to the wider world.

At the moment, I am a professional computer programmer. Five years ago, I was a professional research physicist. I have a strong background in mathematics and economics. My background in history, literature, and philosophy is less strong, but I do very much enjoy those subjects. Basically, I'm a hard-numbers guy who was blessed to have an excellent liberal-arts education in his youth. Many thanks to my teachers!