Bryan Caplan  

Nobel Prize-Winner Makes Intermediate Error

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In Globalization and Its Discontents, Nobel prize-winning economist Joseph Stiglitz tells us:

Behind the free-market ideology there is a model, often attributed to Adam Smith, which argues that market forces - the profit motive - drive the economy to efficient outcomes as if by an invisible hand. One of the great achievements of modern economics is to show the sense in which, and the conditions under which, Smith's conclusion is correct. It turns out that these conditions are highly restrictive. Indeed, more recent advances in economic theory... have shown that whenever information is imperfect and markets incomplete, which is to say always... then the invisible hand works most imperfectly. (p.73)

If Stiglitz wrote "whenever information is imperfect and markets incomplete, which is to say always... then the invisible hand might work imperfectly" he would be dead-on. But he makes the far stronger claim that imperfect information implies inefficiency. This is provably wrong. Standard theorems demonstrate that perfect information (plus other assumptions) implies efficiency. They do not demonstrate that imperfect information implies inefficiency.

OK, so where's my proof? To refute the claim that imperfect information always implies inefficiency, all I have to do is produce a homework problem with imperfect information and perfect efficiency. As Gerard Debreu might have said with his French accent, "That's completely trivial."

My counter-example: Suppose that the value of a used car to a current owner is uniformly distributed on the interval from $0 to $100. (That is a fancy way to say that every dollar value from 0 to 100 is equally likely). These cars would however be worth three times as much to someone else. The catch: Current owners know the true worth of their car; buyers only know the average value of cars on the market.

What happens? If the buyers bid $50, then every car worth $50 or less gets sold. The average value to the original owners: $25. The average value to the new owners: $75. Profit: $25. Competition forces the buyers to bid more. So they bid up to $75. Average value to original owners: $37.50. Average value to new owners: $112.5. Profit: $37.50. Competition ultimately pushes the price up to $150. Average value to original owners: $50. Average value to new owners: $150. Profit: $0.

Despite imperfect information, laissez-faire manages to squeeze every penny of value out of this misnamed "market for lemons."

If I've lost you, this is a slight variant of a standard homework problem. In the usual problem, the numbers are rigged to make the market outcome disastrous; in my variant, the numbers are rigged to make the market outcome perfect. Which is closer to the truth? Contrary to Stiglitz, "the great achievement of modern economics" is to show that this is an empirical question beyond the purview of pure theorists.

Stiglitz is hardly the first economist to get this wrong. Lots of intermediate textbooks do the same. But that's no excuse. When he translates high theory into plain English, even Joe Stiglitz needs to double-check his work.


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COMMENTS (13 to date)

In a purely logical sense, you are mostly correct. But you're making the unstated assumption that buyers won't demand a discount to compensate them for the chance that they'll overpay (i.e. you are assuming there's no value assigned to the risk). In any realistic scenario, the equilibrium price will be lower than the $150 you predict to compensate for the risk stemming from the inefficient information.

You're also making the unstated assumption that transactional costs are zero, but that's excusable. After all, we don't want reality to intrude too far into abstract models.

But the entire question is framed in the (also unstated) assumption that everyone is a purely rational actor. Of course, without this assumption modern economics wouldn't exist as we know it, but the "purely rational" assumption is so far from the real-world truth that I have to wonder why you bother arguing minor points like this one.

It strikes me as a lot like debating how many angels can dance on the head of a pin.

Bill Stepp writes:

First, everyone has access to mortality tables, not just life insurers. See, e,g., http://www.budgetrates.com/mortality.htm.
This doesn't change your conclusions regarding the economics of the insurance market though, I don't think. Even if the public didn't have this data, it wouldn't matter much, as the economics inherent in "the wisdom of crowds" would lead the median insurance applicant to make a financially appropriate bid for every risk class, and rates would quickly converge on those premia, given the the intensely competitive nature of the insurance industry despite the fact that rates are regulated by Uncle's 50 (forget Ocean's 11/12, we're talking a real heist).

You are right that regulation makes the adverse selection problem worse. In fact, I don't think it's a problem on the market at all, as insurers can segment risks and charge accordingly.

Second, regarding the market for used cars/lemons/nonlemons, what does the "true worth" of a car mean? The market for cars is illiquid, lumpy, discontinuous, and characterized by relatively high transactions costs, unlike the market for, say, stocks and bonds, which trade on their discounted cash flows. It makes sense to speak of an "intrinsic value" of a security, with some caveats, but cars?

Deb Frisch writes:

You're wordier than Arnold, but demonstrate the same mindless worship of simplistic assumptions about the rationality of people and markets.

I suppose you're tickled pink that you apparently debunked a fauxbel prize winner.

Yikes.

Austin writes:

Bryan,

I understand you are saying that over the long haul, the average car purchaser would make an average of $0 profit. Yeah, as Bill stated, the car market is illiquid, and discontinous, but if you average over long enough time period, it is correct.

I don't see, however, how that shows Stiglitz is wrong. It seems like the more imperfect he information, the more error there will be in car purchasing decisions. Maybe somebody will lose $2000 and another person will make $3000. Of course, you could argue that, averaged over 1 million car purchasers, that the average profit is $0.

Isn't this just variance versus bias? Bad information doesn't necessarily lead to a bias. A bias meaning that the average profit, over a milllion cars, isn't $0. However, with bad information, there could be a huge variance in the profit of each individual car purchaser.

dsquared writes:

Bryan, "most" modifies "imperfectly" in that sentence; it isn't working as part of an adjectival phrase "most imperfectly".

Bill Stepp writes:

From the link to the homework problem:
"Insurance companies know more about you than you do about yourself. They have actuarial tables. You don't."

As I pointed out above, everyone has access to actuarial tables, mortality and morbitity statistics. They are compiled from publicly available information and are widely published in books, which are available in libraries, for example, the College of Insurance library, and I'm sure in many others. They are also on the internet.

More importantly, an insurance company never has more information about an insurance applicant than he does. That's why an agent asks his prospective client about his health as well as what activities he engages in. An agents will ask if he is he a rock climber, a hang glider, a parasailor, a parachutist, etc. An insurance company will write to the applicant's doctor(s), and conduct a background check. Even a healthy insurance applicant can be rejected for lots of reasons, including "moral turpitude" and lying on an insurance application.

But even background checks and underwriting sometimes fails to weed out poor risks, or price them appropriately. In 1993, a small business owner applied to the Northwestern Mutual insurance company for a big life policy (I think it was $15 million) and was declined because he refused to take a chest X-ray. He then was approved by Prudential, which waived the X-ray requirement. He was later diagnosed with lung cancer and Pru paid the claim.

Question: guess which life company has higher ratings from Moody's and S&P?

The question shouldn't be about perfection, but; 'compared to what other system?'.

ASG writes:

YAY! ded fisch is back!

What would the love child of Deb Frisch and Lawrence George Lux believe? I shudder to think.

Lawrance George Lux writes:

Restudy of Hayek might be worthwhile. The Market corrects imperfect information through the process of Price competition. This through secondary reentry into the market. The Standard problem you cite, and the one you use, does not factor in the use of Product and material for resale in the Market. lgl

Parke Wilde writes:

Okay, you caught him. The correct conclusion is: "whenever information is imperfect and markets incomplete, which is to say always... then there is no reason to expect the invisible hand to work well." Of course, the invisible hand *could* work well in a make-believe example.

engine_us writes:

One example of yours does not prove him wrong, and I can't see what can be generalized from your example to prove him wrong.

The lack of complete market information explains the distortion in the prices of the cars and this in effect makes Prof. Stiglitz assertion correct.

dietrich writes:

I would like to see what is behind the double ellipses in the crucial sentence, but even assuming that the import doesn’t change, I’m still not sure that you’ve proved your point.

First, you write, “But he makes the far stronger claim that imperfect information implies inefficiency,” and so all you have to do is “produce a homework problem with imperfect information and perfect efficiency.” But even in the elided quotation provided, Stiglitz says that “whenever information is imperfect and markets incomplete,” there will be inefficiency in market operations. You have dropped one of his two conditions. I take incomplete markets to be “situations in which no market may exist for some good or for some risk, or in which some individuals cannot borrow for some purposes.” You have to develop a counterexample with imperfect information, incomplete markets, and perfect efficiency if you wish to counter his claim.

Second, I’m not convinced that you have refuted the straw man target in any more than a sophistical sense (hence, you may unwittingly be right that “that’s completely trivial”). You rely on competition to bring more buyers into the market until there is no profit. But if your example is meant to model a plausible real world situation, then presumably some of the signals to other imperfectly informed consumers that there is a profit to be had will come in the form of completed transactions. Even though they serve a valuable purpose, any such completed transactions will constitute inefficiency as compared with a situation in which buyers have perfect information. And if no such signaling transactions are needed, perhaps the mere process of competition forcing price adjustment, costing time and perhaps money, is inefficient as compared with the ideal scenario? And further, if the market is realistically dynamic so that the zero profit price changes, then the effects of imperfect information may become more deleterious. This does not spell disaster, but none of this spells “perfect efficiency” as compared with the measuring stick of a situation with perfect information.

Nonetheless, it is surprising that the claim would be expressed so strongly.

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