Category: Economics

Sometimes correlation does too imply causation

Correlation, as we all know so well, does not imply causation. But sometimes it comes damn close.

For example: Parents of daughters are more likely to divorce than parents of sons. When I wrote and then rewrote about this odd fact in Slate, I got hundreds of emails from readers protesting that daughters might not cause divorce. Maybe some third factor causes both divorce and daughters.

There’s even a clear candidate for that factor: Stress. It’s well established that in many species, stressed populations produce unusually many female offspring. If the same is true in humans, then perhaps both daughters and divorce are the products of exogenous stress.

The problem with that theory is that it’s arithmetically implausible. To explain even a small correlation between daughters and divorce, you’d have to make pretty extreme assumptions about the effects of stress.

For example: Suppose half of all parents are stressed, stressed parents have 55% girls and a 50% divorce rate, and unstressed parents have 45% girls and a 25% divorce rate. Those are much stronger effects (especially on the boy/girl ratio) than anyone could actually believe. Nevertheless, even with these strong assumptions, we get a 36.25% divorce rate among parents of girls and a 38.75% divorce rate among parents of boys—not a very big difference. So the stress theory just doesn’t hold water.

The general point is that before you attribute a correlation to some mysterious (or non-mysterious) third factor, it’s worth pulling out an envelope, flipping it over, and jotting down some numbers. If your numbers have to be ridiculous to get the result you want, you probably need a different theory.

Quantum Game Theory

Let’s play a coordination game: You and I are each asked a single question, either “Do you like cats?” or “Do you like dogs?”. Our questions are determined by independent coin flips. We both win if our answers differ, unless we’re both asked about dogs, in which case we both win if our answers match.

Here’s a pretty good strategy we could agree on in advance: We’ll contrive to always differ. Whatever we’re asked, I’ll say yes and you say no. That way we win 3/4 of the time.

Can we do any better? No, if we live in a world governed by classical physics. Yes, if we live in the world we actually inhabit—the world of quantum mechanics.

All we need is a pair of entangled particles, easy enough to create in the laboratory. If I get the cat question, I’ll measure my particle’s spin (which is either up or down) and answer “yes” or “no” accordingly. If I get the dog question, I’ll do the same thing, but first I’ll rotate my measuring apparatus by 90 degrees. You do the same, but start with your measuring apparatus rotated 45 degrees from
mine.

The thing about entangled particles is that the outcomes of these measurements are correlated in a very particular way, and remain so forever, even if the particles are separated. In particular, our answers will differ about 85% of the time unless we both make “dog” measurements, in which case they’ll agree about 85% of the time. Overall, then, we’ll have about an 85% win rate. Those particular correlations would be impossible to achieve with any set of measurements if our electrons obeyed the laws of classical physics.

(More precisely, our win rate is cos2(pi/8).)

I took this example from a beautiful paper by Richard Cleve, Peter Hoyer, Benjamin Toner and John Watrous. (The paper has a lot of other cool examples too.) The moral is that game theory changes dramatically when players have access to quantum technology—which might sound very science fictiony at the moment but probably won’t in another couple of decades.

A social experiment

Even outer-space aliens can see the effects of communism.

Koreas

Also check out North Korea’s creepy Ryugyong Hotel, built at a cost of some 2% of GDP the hotel towers over Pyongyang but it’s a shell that has never been completed because of stuctural problems due to poor quality. The North Koreans have gone so far as to remove it from some maps but there is no hiding the 7th tallest building in the world!
Ryugyong2

Thanks to Mahalanabois for the picture and Ted Frank for the hotel recommendation.

More on Vaccines

Though Alex has already blogged about the Kremer/Snyder paper on vaccines versus cures, there are, I think, a couple of comments worth adding.

According to Kremer and Snyder, monopoly sellers would rather sell cures than vaccines. To get this result, they need some heterogeneity: we all have different probabilities of getting sick (though we all find it equally costly to get sick).

But what if you introduce the opposite kind of heterogeneity? (That is, we all have different costs of getting sick, even though we all face the same probability of getting sick.) Then it’s a nice little exercise for your students to show that the cure and the vaccine are equally lucrative monopolies (ignoring the positive externalities of the vaccine).

A more important observation: In the Kremer/Snyder setup (still ignoring positive externalities), it’s a good thing for sellers to invest in cures rather than vaccines. The reason cures are more profitable is that they in essence allow perfect price discrimination. So with cures, there’s no deadweight loss due to monopoly; with vaccines there is.

The analysis changes if you assume, say, that a vaccine prevents a four-day illness, but a cure only cuts two days off your illness. Then vaccines might or might not be socially preferable to cures—but in that case, willingness-to-pay for vaccines versus cures would double. This gives sellers an incentive to produce vaccines. The incentive isn’t perfect, but it goes in the right direction.

The Microeconomics of Social Security Privatization

Social security privatization has a little-discussed benefit, done properly it is equivalent to a cut in marginal tax rates. A problem with the current system is that there is little relationship on the margin between taxes paid and benefits received. On average, of course, those who pay more taxes get more benefits (although not proportionately there is a subsidy to low-earners). But because the rules are complex and based on average earnings over a long period of time there is little connection between your social security taxes on an additional hour of work and your social security benefits for that additional hour.

To see why this is important consider the difference between social security and an IRA. If a worker works an additional hour, earns $10 and puts $1 into the IRA he knows the $1 will produce a benefit 30 years down the line when he retires. The $1 contribution to the IRA is not a tax, it’s consumption, a benefit of working extra hours. On the other hand if a worker earns $10 and $1 is taken and paid into social security there is no clear connection to retirement benefits. Social security payments, therefore, are taxes – and like other taxes they deter work effort and create a dead weight loss.

Privatizing social security, or in some other way creating personal accounts, would reestablish a link between marginal payments and marginal benefits and thus would be equivalent to a cut in tax rates.

The insight goes back to my colleague Jim Buchanan and his 1968 paper “Social Insurance in a Growing Economy: A Proposal for Radical Reform.” National Tax Journal, Vol. 21 (December 1968): 386-95

See also Tyler, Arnold Kling, Victor Davis and Brad DeLong who have been discussing the political issues of social security privatization.

Prediction Markets Have Arrived!

Donald Luskin writes:

There is now no question whatsoever that the Bush re-election futures contract at Tradesports.com is being manipulated. Yesterday the price of the futures were sold down from about 55 (indicating the market’s estimate of a 55% probability of Bush’s re-election) to 10 (indicating a 10% probability) with a single 10,000-lot order entered by a single trader. An order that size represents twice the normal volume of an entire typical day’s trading. Within moments after the order was completed, the price recovered back to the low-mid-50’s.

According to sources at Tradesports, yesterday’s order was entered by the same individual who has heavily sold the Bush futures three times over the past month. The first instance was on September 14, when this trader sold the futures down from the mid-60’s to 49.6. The second instance was in the middle of the second presidential debate on October 8, when the futures were sold down from the high 50’s to 51.5. The third instance was right after the third presidential debate on October13. As the debate began the futures were priced at 57, and by the end of the debate they had risen to 60. Then a few moments later they were beaten down to 54 in a matter of minutes.

Luskin hints that George Soros might be at work. Wouldn’t that be cool! What I see as most interesting is a) an order twice the normal volume of an entire day’s trading had virtually no influence on the market price and b) prediction markets are now so widely followed that someone finds it worthwhile to try to manipulate them.

Should Luskin be worried that his candidate is being sold down? Not at all. A surprising result in these markets is that manipulators subsidize information traders. Think about it this way, by definition manipulators aren’t trying to predict the true outcome so they are likely to take losses and the more they try to manipulate the bigger the losses. Now if the manipulators are taking losses who is making money? The information traders! Manipulators, therefore, encourage and support the information traders. Manipulation isn’t impossible but it’s surprising how little information other trader’s need to not only avoid the manipulation but to profit from it.

Our colleague, Robin Hanson, has written a paper explaining the theory (warning, not for the mathematically faint hearted) and an experimental paper showing that the theory works in practice.

Thanks to Newmark’s Door for the link.

Do as I say…

For antiglobalization demonstrators, Nike came to symbolize everything that was wrong with the emerging capitalist world order. Yet this animus toward Nike did create occasional moments of embarrassment. During the famous Seattle riots of 1999, the downtown Niketown was trashed by protestors, but videotape recorded at the scene showed several protestors kicking in the front window wearing Nike shoes. It occurred to many people that if you think Nike is the root of all evil, you really shouldn’t be wearing their shoes.

Here is the link, which offers further arguments against Adbusters magazine. It is an advertisement for a forthcoming book entitled The Rebel Sell, Amazon lists it under its old title.

Alex and the FDA in Forbes

This week’s Forbes (the Nov. 1 issue) has a feature story on Alex’s work to make drug regulation more sensible.

Alex notes that off-label drug uses are largely unregulated. No proof of efficacy is required, and off-label drug prescriptions bring a net health gain; see this paper. Yet to get a new drug approved it must go through, in addition to Phase I trials,

…Phase II and Phase III trials, which typically take years and focus on efficacy as well as safety. The long wait can cost lives and runs up new-drug costs–to an estimated $900 million per successful drug.

Tabarrok says this system makes little sense; the FDA demands costly, time-consuming efficacy tests for some uses and no tests for others. And while the FDA allows off-label prescribing by docs, it strictly limits the drugmakers’ promotion of such uses to doctors and permits none at all to patients.

Alex argues that FDA regulation ought to be reduced, making the regulation of new and old drugs more consistent. But that is not all:

Tabarrok and [Dan] Klein also offer some alternative proposals at FDAReview.org. One is to make all FDA testing optional. Drugs that didn’t go through the process would be labeled “Not FDA Approved.” Under this approach, they say, “the FDA would become a genuinely voluntary institution, much like Underwriters Laboratories.” Another idea is for the FDA to award letter grades, A to D, to claims made by drugmakers, much as it is considering doing for health claims for foods and dietary supplements. The FDA could still have its say, but wouldn’t be able to impose long delays, since a new drug could be marketed at first as “unrated.”

At the least, Tabarrok argues, the FDA should permit drug companies to sell any drug that has been approved by other sophisticated drug regulators, such as those in Canada, Australia or the European Union. Under such a system U.S. patients would get speedier access to new medicines without losing out on safety protection.

Kudos to Alex, the only sorrow is that the on-line version does not reproduce the excellent photo of him in the magazine. But you can see that at your local Borders.

Social security privatization, continued

Brad DeLong writes:

There is a bigger, unmentioned reason to be against private accounts. Ten years down the road or so, there will be pressure on Congress to allow people to borrow against their private accounts, or to withdraw them to buy a house, or to use them to meet unexpected medical expenses. Congress will bow to that pressure–it’s their money, after all. And in the end a lot of people will hit 70 having drained their Social Security private account dry. The rest of us will then have to decide whether to let them starve on the street, or tax ourselves a second time to give them Social Security benefits. As Dick Schmalensee says, “You have to ask yourself not just, ‘Is this good policy?’ but ‘Will this still be good policy after Congress does its worst to it?'” The Medicare drug benefit and the corporate tax boondoggle are powerful evidence that the Bush administration holds no leashes to use to control what this Congress does to policy proposals, while lobbyists can make this Congress roll over and beg.

Brad also takes on whether the government could finance the transition to a more private system by borrowing (also read Bruce Webb’s comment, number two in the list). After all, government debt would be higher but government long-term implicit obligations are lower. Would this simply be a wash? (Arnold Kling believes “yes”). I am skeptical. When it comes to government, measured nominal flows tend to be sticky. So say our government increases its borrowing today but lowers its SSA obligations for tomorrow. Even if the transaction can balance without a current increase in interest rates, the increased rate of borrowing (or taxation) will tend to stick in the long run. Plus there is a time consistency problem. If the new debt is placed smoothly, government has an incentive, ex post, to accept some new unfunded liabilities for the future. Knowing this in advance, the bond market will be suspicious about the new debt offering.

What should we do? Here is my previous post on social security privatization.

Vaccines and the Media

Dueling articles on the flu vaccine shortage today in the Washington Post and NYTimes. The Times article is much better. As Russ Roberts, points out you have to wade far into the Post article before you get to a decent explanation of the shortage. The Times article correctly pinpoints low prices, liability and regulation early on (the same factors I wrote about here).

In recent decades, many drug companies in the United States abandoned the manufacture of vaccines, saying that they were expensive to make, underpriced and not profitable enough. Flu vaccine can be a particular gamble, because the demand for it varies from year to year and companies throw away what they do not sell because a new vaccine must be made each year to deal with changing strains of the virus. Some companies dropped out because of lawsuits, and others because they determined that it would not pay to retool aging vaccine plants to meet regulatory standards.

Vaccines: The Long Run

Yesterday I discussed some of the reasons for the current shortage. Today, I will discuss an important paper by Michael Kremer and Christopher Snyder. Kremer and Snyder argue that for the same cost and effectiveness drugs are more profitable to produce than vaccines. As a result, private incentives bias the market against vaccines.

A well known reason is that some people free rider on vaccine provision. When you are vaccinated, I benefit from one less possible transmitter. As a result, some who benefit do not pay. Drugs, in contrast, offer more excludable benefits thereby increasing demand and profits.

Drugs also provide a very natural method for firms to, in effect, price discriminate.

A simple example suffices to illustrate this point. Suppose there are 100 total consumers, ninety of whom have a ten percent chance of contracting the disease and ten of whom have a 100 percent chance. Suppose consumers are risk neutral and are willing to pay 100,000 to be cured of the disease if they contract it. A monopolist selling a vaccine could either charge 100,000 and sell to the ten high-risk consumers or charge 10,000 and sell to all 100 of them. Either way, the monopolist’s revenue is 1,000,000. A monopolist selling a treatment would, in expectation, sell to the nineteen consumers contracting the disease (all ten of the high risk consumers as well as an average of nine consumers from the low-risk group) at a price of 100,000 for a total revenue of 1,900,000, almost twice the revenue from a vaccine.

Damn, that’s clever. I wish I had thought of that.

Having praised Kremer and Snyder I now must say that I am not convinced that the forces they discuss matter very much. First, if the pharmaceutical market is competitive and vaccines pay then they will be produced even when drugs would be more profitable to a monopolist. K&S underestimate the competitiveness of the pharmaceutical market.

Second, my suspicion is that nature and science combine to make it the case that some diseases at some times are better treated by vaccines and other diseases by drugs. K and S’s model works best if there are many cases where drugs and vaccines are close cost-substitutes. Firms then choose drugs even when vaccines would have been more desirable. I think, in contrast, that cost differences will usually exceed the profit differences. On the margin, K and S are correct but suppose vaccines had been subsidized would we today have an AIDS vaccine? I doubt it.

I’m not necessarily against their conclusion, however, that vaccines should be subsidized relative to drugs. It’s sad to say, therefore, that as discussed yesterday we currently do precisely the opposite.

Is tit-for-tat the best strategy in games?

Remember tit for tat? I will cooperate if you do, but otherwise I defect. Many consider this to beeconsidered the best way to play in repeated prisoner dilemma situations. But the old wisdom is being revised:

…the Southampton team submitted 60 programs. These, Jennings explained, were all slight variations on a theme and were designed to execute a known series of five to 10 moves by which they could recognize each other. Once two Southampton players recognized each other, they were designed to immediately assume “master and slave” roles — one would sacrifice itself so the other could win repeatedly.

If the program recognized that another player was not a Southampton entry, it would immediately defect to act as a spoiler for the non-Southampton player. The result is that Southampton had the top three performers — but also a load of utter failures at the bottom of the table who sacrificed themselves for the good of the team…

Our initial results tell us that ours is an evolutionarily stable strategy — if we start off with a reasonable number of our colluders in the system, in the end everyone will be a colluder like ours,” he said.

This, by the way, is how the Soviets used to win chess tournaments. Throw games to the leading Soviet player, and fight especially hard against the leading non-Soviet rivals.

I have not seen the primary information on the games or the program, but I suspect that some caveats are in order. First, simulated game results usually are sensitive to the choice of parameter values. Second, this strategy may be appropriate for genetically-related teams, but otherwise it will not be implemented in the real world without side payments or coercion (both are typically prohibited in the game in question).

Here is the full story, which also provides useful background information for those new to this debate. And thanks to www.geekpress.com for the pointer.

What is the nature of American poverty?

Robert Samuelson is one of my favorite economics columnists:

Many middle-class families achieved large income gains in the 1990s and — despite the recession and halting recovery — have kept those gains. They’re worse because the increase in poverty in recent decades stems mainly from immigration. Until our leaders acknowledge the connection between immigration and poverty, we’ll be hamstrung in dealing with either.

Let’s examine the Census numbers. They certainly don’t indicate that, over any reasonable period, middle-class living standards have stagnated. Mostly, the middle class is getting richer. Consider: In 2003, 44 percent of U.S. households had before-tax incomes exceeding $50,000; about 15 percent had incomes of more than $100,000 (they’re included in the 44 percent). In 1990, the comparable figures were 40 percent and 10 percent. In 1980, they were 35 percent and 6 percent. All comparisons are adjusted for inflation.

True, the median household income has dropped since 1999 and is up only slightly since 1990. That’s usually taken as an indicator of what’s happened to a typical family. It isn’t. The median income is the midpoint of incomes; half of households are above, half below. The median household was once imagined as a family of Mom, Dad and two kids. But “typical” no longer exists. There are more singles, childless couples and retirees. Smaller households tend to have lower incomes. They drag down the overall median. So do more poor immigrant households.

A slightly better approach is to examine the incomes of households of similar sizes: all with, say, two people. In 2003 those households had a median income of $46,964, off about $900 from the peak year (1999) but up almost 10 percent from 1990. For four-person households, the median income in 2003 was $64,374, off about $2,200 from its peak but still up about 14 percent from 1990. Though unemployment and a decline in overtime have temporarily dented incomes, the basic trend is up.

Now look at poverty. For 2003, the Census Bureau estimated that 35.9 million Americans had incomes below the poverty line; that was about $12,000 for a two-person household and $19,000 for a four-person household. Since 2000 poverty has risen among most racial and ethnic groups. Again, that’s the recession and its aftermath.

But over longer periods, Hispanics account for most of the increase in poverty. Compared with 1990, there were actually 700,000 fewer non-Hispanic whites in poverty last year. Among blacks, the drop since 1990 is between 700,000 and 1 million, and the poverty rate — though still appallingly high — has declined from 32 percent to 24 percent. (The poverty rate measures the percentage of a group that is in poverty.) Meanwhile, the number of poor Hispanics is up by 3 million since 1990. The health insurance story is similar. Last year 13 million Hispanics lacked insurance. They’re 60 percent of the rise since 1990.

To state the obvious: Not all Hispanics are immigrants, and not all immigrants are Hispanic. Still, there’s no mystery here. If more poor and unskilled people enter the country — and have children — there will be more poverty. (The Census figures cover both legal and illegal immigrants; estimates of illegal immigrants range upward from 7 million.) About 33 percent of all immigrants (not just Hispanics) lack a high school education. The rate among native-born Americans is about 13 percent.

The bottom line: The American middle class is doing better than many commentators would have you believe. And while I don’t think we should neglect the welfare of Hispanics, in many cases the correct comparison is with their native countries, not with other U.S. statistical aggregates.

Addendum: Here is a good piece on how the federal government defines poverty.

Vaccines: The Short Run

President Bush was correct when he said that liability risk is one factor in the recurrent shortage of vaccines. Based on a post by Mark Kleiman, suggesting that flu vaccines are immune from liability due to the Vaccine Injury Compensation Program, Brad De Long called Bush’s claim an “eternal lie.” To his credit, Kleiman (but not DeLong) quickly retracted his post when others pointed out that the VICP applies only to pediatric vaccines.

Liability is not the only issue, however. Costly FDA regulations and requirements, for example to remove thimerosal from vaccines despite no evidence of safety problems, have pushed firms out of the industry. See this paper in the The Independent Review (I am an assistant editor) for more on these regulations and their consequences.

A further problem is that the federal government is the major purchaser of vaccines, although not the flu vaccine, and it uses its monopsony powers and the law to require companies to sell at low prices. Firms have left the industry because they are squeezed on one end by regulation and on the other by low prices and, for vaccines like the flu vaccine not covered by VICP, potential liability. Note that even if the prices are high enough to earn the company a modest profit the point is that they are not high enough to make it worthwhile to make a surplus of vaccine that can be sold in the event of a contamination problem, as has happened this year. If the firms can’t price high during a shortage then there is no incentive to plan for a shortage.

Even without legal price caps there are significant disincentives to high prices. Here is a CDC spokesperson (link to audio file) on recent price increases:

Shame on the people who are price gouging. This is a reprehensible thing to be doing. I think an immoral thing.

Is it any wonder that firms don’t want in on this market?

Henry Miller, a former head of the FDA’s biotechnology division, summarizes well:

The fundamental problem is that government regulatory policies and what amounts to price controls discourage companies from investing aggressively to develop new vaccines. Producers have abandoned the field in droves….Although their social value is high, their economic value to pharmaceutical companies is low because of vaccines’ low return on investment and the exposure to legal liability they bring manufacturers….

Moreover, the FDA has a history of removing safe and effective vaccines from the market based merely on perceptions of excessive side effects — a prospect that terrifies manufacturers.

We need a fundamental change in mind-set: The rewards for creating, testing and producing vaccines must become commensurate with their benefits to society, as is the case for therapeutic pharmaceuticals.

Read Henry’s article for more on dealing with the problem today, (he notes, for example, that it may be possible to dilute current stocks and still maintain good effectiveness). Also, as Tyler reported last year, simply targeting vaccines to at-risk people is not necessarily the best approach. A better approach is to target super-spreaders, people who may not be at great risk themselves but who can and will spread it to many others.

Tomorrow: Vaccines: The Long Run.

Fastest Flip-Flop Ever?

Here from last night’s debate, is President Bush making a good case against government-run health care:

I think government- run health will lead to poor-quality health, will lead to rationing, will lead to less choice.

Once a health-care program ends up in a line item in the federal government budget, it leads to more controls.

And just look at other countries that have tried to have federally controlled health care. They have poor-quality health care.

Our health-care system is the envy of the world because we believe in making sure that the decisions are made by doctors and patients, not by officials in the nation’s capital.

And what does he say less than two minutes later?

We’ve increased VA funding by $22 billion in the four years since I’ve been president. That’s twice the amount that my predecessor increased VA funding.

Of course we’re meeting our obligation to our veterans, and the veterans know that.

We’re expanding veterans’ health care throughout the country. We’re aligning facilities where the veterans live now. Veterans are getting very good health care under my administration…

True, you can’t blame him much for the flip-flop – it’s what the public wants to hear. How many people even noticed the glaring contradiction? I suppose that on this issue I’d rather have flip-flop than all flop.