November 13, 2004

Cascades in Affirmative Action; Sander Data

Richard Sander of UCLA has written an article on the effects of affirmative action, and has posted his data on a webpage. It is an empirical article with an unusual angle, addressing the question of whether a student who is admitted to a school but knows he has gotten in by non-standard means and will be in the bottom 10% of the class should accept admission or go to a school where he would be average instead. This is a general point, whether a student gets special admission because of the color of his skin or because his father has political connections, but it is especially relevant to affirmative action because students admitted to it are so likely to be at the very bottom of their class.

Law schools are an especially good case to analyze, because law graduates go on to take the bar exam, so we have an independent measure of success. It has long been known in law school circles that many elite law schools have lower bar pass rates than average law schools, and that within an elite law school, law school grades are a good predictor of whether a student will pass the bar. A student at the bottom of his elite law school class will flunk the bar, where if that same student had gone to an average law school he would have passed it. That is because the elite law school teaches courses in a different style and to a different level, suited to their average or top students and not to their bottom students.

Anyway, Sander's article-- which I have not yet read, and post for reference-- looks at how many black students pass the bar exam now and how many would pass if there were no affirmative action programs. Without affirmative action programs, fewer black students would go to law school, but their chances of passing the bar would be better.

I've thought of trying to model the "cascade" effect which is part of this. If we had no affirmative action, black students would still go to law school-- they just would not go to as good law schools as they do now. The student who under affirmative action goes to Harvard would go to UCLA instead; the UCLA student would go to Iowa, and so forth. Thus, when Harvard started using affirmative action, that meant UCLA did not get as high-quality black students as it did before. If UCLA wanted even to maintain the number of black students it would have in a race-neutral world, it would have to use affirmative action, setting lower admission standards for blacks than for whites. This, in turn, would reduce the number of black students at Iowa, and the cascade would go down to the very bottom law school. If schools value having black students, affirmative action by a school imposes a negative externality on all the schools below it. (Though, on the other hand, a school that does not care about race gets a positive externality: Harvard's choice of the UCLA black student means some smarter white student has been denied admission by Harvard, and *that* student will go to UCLA.)

I think it could be the case that even if we accept that it is good for an individual school to have more black students, that every school but the very top one would be worse if schools are free to use affirmative action, because of this cascade effect. Every school would like to be the only one to use affirmative action, but when all do it, only the top school ends up better off. Probably the modelling result would be that in the affirmative-action equilibrium, every school but the top school has the same percentage of blacks but with lower ability than if racial discrimination were not practiced by anybody-- almost a Pareto-worsening from the point of view of the schools.

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November 05, 2004

Do Markets Cure Consumer Mistakes? Schwartz paper

Yesterday Alan Schwartz of Yale Law was here to give a talk.
His subject was a good one. People make dumb mistakes. They
are not always "rational" in the economic sense. Some of
these mistakes can be viewed as having poor information--
for example, buying astrology predictions even though they
won't come true. Other mistakes are in processing
information-- putting good money after bad into a business
that won't succeed, for example, because of the fallacy of
sunk cost. We have always known people make mistake, but
recent research, "behavioral economics", has focussed more
on the precise kinds of mistakes that get made.

But does the tendency to make this kind of mistake actually
result in bad decisions? The market has some tendency to
cure mistakes. If I put my antique chair up for auction, for
example, then even if my information as to its value is
poor, I will still get a price for it that reflects the good
information of other people. If I am buying things, then
sellers will endeavor to make sure I understand that the
apparently good offers of their competitors are actually bad
for me.

Schwartz's paper modelled this, in one particular way. He
used a search model, where some people shop and others just
look at one seller's offers, and where one product is best
for sophisticated people and another for mistake-prone
people. It is a tricky problem to get a handle on, though.

Another way to model the situation is with an advertising
model. Suppose no consumer searches, but sellers send them
advertisements, and that some consumers are sophisticated
but others are mistake-prone. Sellers will send three kinds
of messages. First, there will be offers aimed at the
sophisticated buyers. Second, there will be offers aimed to
fool the mistake-prone buyer. Third, there will be offers
aimed to tell the mistake-prone buyer about the deceptive
offers. I'm afraid this model would get rather
complicated, since each seller would want his offer to be
just slightly better than what the buyer is likely to get
from some other seller. Also, someone may well have worked
out this idea years ago. But it has some realism to it, I

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October 11, 2004

The Trust Game

I just heard a good presentation by James Cox of Arizona on his experimental work trying to figure out exactly how altruism works. The basic game in this literature is the Trust Game, one version of which goes as follows:

There are two subjects, a Sender and a Responder. Each is given $10.

The Sender can keep his entire $10 or send X to the Responder. If he sends X, then it is tripled for the Responder, who receives 3X.

The Responder then can keep his entire pile of money, or send Y back to the Sender.

The game is played only once. The Sender and Responder do not meet face to face, and it is best if the experiment is done double-blind, meaning that the researcher does not find out who sent what (and possibly shame them). All the rules are common information for all the subjects.

If people follow the simplest "homo economicus" behavior, the Sender sends nothing to the Responder. A pure altruist or a utilitarian Sender would send his entire $10, since it would turn into $30 for the Responder.

In practice, some Senders send nothing, and most send a few dollars, and a few send all $10. Most Responders respond with a fraction (often half) of the value they received, but some respond with nothing. On average, Senders don't get back as much as they send, but they are close to breaking even.

This is relevant to the thinking I've been doing on the subject of Gratitude, which Professor Cox calls Positive Reciprocity in this context. He is very interested not just in the Responder, though, but also in the Sender, who needs what is conventionally called "Trust" that the Responder will be properly grateful.

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October 04, 2004

Pager on Criminal Stigma for Employment

I wrote a paper called "Stigma and Self-Fulfilling Expectations of Criminality" and am on the lookout for examples such as this one from the WSJ (free link): " As Background Checks Proliferate, Ex-Cons Face a Lock on Jobs"....

...While Peter Demain was serving a six-year sentence for possession of 21 pounds of marijuana, he did such a good job working in the prison kitchen that he quickly rose to head baker. After his release, the Durango, Colo., resident filled out 25 job applications at bagel shops, coffee houses, grocery stores and bakeries. All turned him down. Some even asked him to leave the premises immediately after learning of his conviction.

It's never been easy for someone with a criminal history to find work, but it is becoming increasingly difficult. More businesses are using criminal-background checks to guard against negligent-hiring lawsuits, theft of company assets and even terrorism. About 80% of big companies in the U.S. now do such checks, up from 56% in 1996, according to a January survey of personnel executives.

Two weeks ago, Wal-Mart Stores Inc., the nation's largest corporate employer with more than 1.2 million workers, said it would conduct criminal-background checks on all applicants in its U.S. stores, beginning in September. Wal-Mart's former policy was to order background checks only for certain personnel, including loss-prevention and pharmacy employees.


"Forty-six million people in this country have been convicted of something sometime in their lives and our economy would collapse if none of them could get jobs," says Lewis Maltby, president of the National WorkRights Institute,a nonprofit human-rights organization founded by former staff of the American Civil Liberties Union. That figure includes everybody in the FBI criminal records database, which includes people convicted of a relatively minor misdemeanor.


Blacks with criminal records also pay a bigger penalty in the job market. According to a study of applicants for low-level jobs conducted by Devah Pager, a Northwestern University sociologist, having a prison record cut by two thirds a black man's chances of getting called back by an employer, while it cut a white man's chances by half.

The explosion in background checks is occurring in part because technological advances have made them faster and cheaper. Businesses commonly pay $25 to $100 per search, and the price is dropping. Several months ago, SecurTest, a Florida- based applicant-screening company, began offering background checks using its own proprietary system that culls public criminal records. The service, which costs about $10 per applicant, focuses mainly on felony-type convictions.

Bottom line: It's now affordable for businesses to do checks for the very sorts of entry-level jobs in which rehabilitated criminals are encouraged to seek employment.

Wal-Mart came under fire last month for two separate incidents in South Carolina in which its employees were accused of sexually assaulting young female shoppers. Both of the accused employees had prior criminal convictions for sexually related offenses. Several weeks after the episodes at Wal-Mart came to light in news accounts, two members of South Carolina's legislature proposed a bill requiring all retailers that sell toys or children's clothing to conduct background checks on potential employees. A spokesman for Wal-Mart says the Bentonville, Ark., company was unaware of the criminal records of the two employees in question.


Wal-Mart says it will use background checks on a case-by-case basis, and that people with a criminal record could still be offered a job. It will all depend on the nature of the crime, how long ago it occurred, and the type of job being filled, the company says.


Such scrutiny has tempted some applicants to lie. When Jeffrey Calwise first got out of prison for unarmed robbery, he disclosed his criminal history on work applications. But after numerous rejections, he decided to fib. The Detroit resident got a factory job making $6.50 an hour, but was later fired after the company performed a background check and discovered his criminal record.

Then, Mr. Calwise decided to begin writing "will discuss at interview" on applications that asked about whether he'd been convicted of a crime. That didn't work, either: He got some interviews, but his explanation didn't get him any jobs.


The U.S. Fair Credit Reporting Act requires employers to give job-seekers a copy of their background report if they are rejected due to a criminal offense. The law also permits applicants to challenge the reports. But companies can always cite different reasons for rejecting someone. Another loophole: Employers aren't required to give a person a copy of the report if they conduct the search themselves, such as by mining publicly available court records.

Typically, this article is sympathetic to the ex-cons and doesn't ask why the employer prefers to hire someone else instead of the selected ex-cons here. If there are 46 million people with criminal records, most of them have gotten jobs anyway, and certain employers in the past have been quite willing to hire ex-cons. It is all a matter of supply and demand. When an employer has a choice between an ex-con, or someone identical except for that who wants 20% higher pay, the employer will have to think hard.

The Devah Pager study caught my eye. It finds that blacks lose more by having a criminal record than whites, the opposite of what I suggest in my paper (as a theoretical prediction). That is interesting, because if blacks have less future-wage incentive not to be criminal, that makes high black criminality rates all the harder to explain. It's possible, though. In my theory, that finding would be a hopeful sign: it says that instead of thinking most blacks are criminal and some just don't get caught, employers do reward black men with clean records. This, too, is a point missed by the public: it might be that an employer who doesn't have access to criminal records would be reluctant to hire *any* black youths, but with the comfort of finding no criminal record,he is willing to hire one. If this is true, it would be bad to forbid employers to look at criminal records-- they would respond by not hiring at all rather than by hiring blind.

Professor Pager's article, "The mark of a criminal record." American Journal of Sociology 108(5): 937-975 (2003), looks pretty good. She did an experiment with matched job applicants, a good methodology.

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September 15, 2004

Knightian Risk and Uncertainty: Two-Card Bets

This post is notes mainly for myself (or for others who have heard about this subject) on risk. I've started reading Roger Lowenstein's When Genius Failed, about the collapse of Long-Term Capital Management in 1998. Besides the lessons for finance, thinking, and life generally, Professors Merton and Scholes were involved. On page 62 Lowenstein talks about risk, and that started me thinking.

(1) Consider various bets.

Bet 1-A. I have two cards, the 3 of spades and the 4 of spades. I win $1 if a 3 turns up. Value: $.50 (if you're risk neutral). This is the situation some people (Knight) call "risk", though I hate that terminology since it contradicts the usual meaning of the word in economics. "Definite Priors" is better, or "Certainty about Uncertainty".

Bet 1-B. I have two cards. Both are either 3's, or 4's. I win $1 if a 3 turns up. Value: $.50 (if you're risk neutral). This is the situation some people (Knight) call "uncertainty", though I hate that terminology since it contradicts the usual meaning of the word in economics. "Indefinite Priors" is better, or "Uncertainty about Uncertainty".

Some people think it is impossible to value Bet 1-B, because the investor needs to estimate probabilities of probabilities. I've never understood the problem, though, and am left with the impression that those people are just confused in their thinking. Situations with Indefinite Priors make one's head hurt more, because it's harder to think out of the box, one *does* have to think up some priors, and not thinking hard enough will lead to bigger mistakes, but all that is different from saying that a person can't or won't come up with an estimate of probabilities. I side with Savage against Knight.

The Ellsberg Paradox is essentially that people prefer 1-A to 1-B. The explanation for it that I like is that we don't trust the person on the other side of the bet, so the more wiggle room they have, the less we like it. Maybe they know that, for whatever reason, more people like to bet on 3 than on 4, so they always choose a deck with two 4's instead of one with two 3's. Even more simply, as in the way I specified Bet 1-A, they pick a deck of two 4's and only let me bet on 3. Either way, I'm safer with a deck I know has exactly one 3 and one 4.

(2) Now suppose now that I draw a card 100 times , reshuffling each time, but keeping the same two-card deck each time. The expected value of each bet will be $50.

Bet 100-A will very likely yield me close to $50, though I might get as little as $0 or as much as $100.

Bet 100-B will yield me either $100 or $0, with zero probability of anything else happening.

Bet 100-A will be preferred to Bet 100-B by any risk-averse investor.

(An investor will be indifferent between 1-A and 1-B unless he doesn't trust that the bet is not rigged.)

(If the investor is allowed to change what he bets on-- shifting from 3 to 4 and back-- then Bet 100-B is clearly the best, yielding either $100 or $99 to an investor playing the rational strategy. When learning is possible, starting with bad info is, other things equal, good

Although Bet 100-B is riskier than 100-A, it is much simpler. If I wanted to make precise plans for what to do in the various possible outcomes of Bet 100-B, I would only have to make two plans, for $0 and $100, whereas for Bet 100-A I would need 101 plans.

(3) If I were betting on the outcome of the bets, it would be much easier to bet on Bet 100-B. I could bet that the outcome would be either $0 or $100, and I'd win my bet for sure. In this sense, it is quite possible for a situation with Indefinite Priors to be simpler, safer, and more certain.

(4) Suppose I had to pay $.40 for Bet 1-A or $40 for Bet 100-A. Which would I prefer? Most risk-averse investors would prefer 100-A, because it very likely yields around $50, and is very unlikely to yield less than $40. An old result (due to Samuelson) in finance, though, is that to think Bet 100-A is better for *any* risk averse investor is The Fallacy of Large Numbers, because even independent repetitions of a gamble do not reduce risk, if by risk we mean the standard definition in terms of mean-preserving spreads. Bet 100-A, at cost $40, incurs the risk of a net payoff of $-40. The worst that can happen with Bet 1-A at a cost of $0.40 is a net payoff of $-0.40. Thus, someone who is heavily averse to big down-side risks would prefer Bet 1-A.

The Fallacy of Large Numbers comes up most often in the context of insurance. Insurance companies work not by collecting risks so they average out, but by dividing risks among many small investors. That is why insurance against big earthquakes and hurricanes-- which do *not* average out-- makes sense (or would if we didn't all know that the government will bail out even the uninsured,so it is pointless to pay for insurance).

If I get round to reading more of the book, I may discover how these examples fit into LTCM's collapse. I am hoping this will fit into my research program on consumer and bargaining uncertainty over values, as in "Explaining Incomplete Contracts as the Result of Contract-Reading Costs," "Getting Carried Away in Auctions as Imperfect Value Discovery," and "Strategic Implications of Uncertainty Over One's Own Private Value in Auctions."

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August 31, 2004

Combined vs. Separated Bargaining; Government Drug Purchases

We had a good discussion last week in the law-and-econ lunch on bilateral vs. multilateral bargaining vs price-taking. Here's the story.

Suppose Eli Lilly has a patent monopoly on Zyprexa. Compare four systems:

1. Lilly sets one price and consumers or insurance companies are price takers.

2. Lilly negotiates with each of 5000 insurance companies.

3. Lilly negotiates with each of 50 state governments.

4. Lilly negotiates with just the federal government.

Which would Lilly prefer? ....

The answer is not as simple as it might seem. If Lilly just charges one,
monopoly price that is very inefficient. If Lilly negotiates with one buyer, the
federal government, they will choose the efficient quantity, and some lump-sum
price which splits the surplus (and then the federal government will sell
Zyprexa to consumers at marginal cost). The efficiency gain might be so great
that both Lilly and consumers gain.

Cases (2) and (3) really are no different from each other-- tehy are both
negotiation instead of price taking, but negotiation with lots of buyers instead
of just one. The idea in my price discrimination notes is that if we continue to
split the surplus 50-50, Lilly won't be any better off negotiating with 5000
than it was negotiating with 1. Each of the 5000 insurance companies has (we
woudl assume) irreplaceable consumers-- if company 4322 decides not to buy from Lilly, Lilly has lost the 43,000 customers of company 4322 and can't replace

Our discussion at lunch focussed on psychological things such as the envy of
New York if Mississippi got a cheaper price, on info (how would New York know?)
and on corruption (is it cheaper to bribe 1 big buying agent, or 50 small
ones?). All those things are interesting but separate from the perfect price
discrimination idea. Yet another thing which is separate but practically
important is that there are economies of scale in bargaining. It is not that
having 1 US governmetn negotiate for all 50 states really gives it more
bargaining power, but that the 1 buyer finds it worthwhile to hire a super duper
bargaining team, spending 49 times as much on it as each of the 50 states. Thus, if the Federal-Lilly surplus split was 50-50, the state-LIlly split might be
more like 20-80 for each state because of Lilly's superior bargaining skill.

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August 26, 2004

Designing a Utopian Economy

A good Economic Systems/Ethics question would be how we would want to structure an altruistic economy.

Suppose we could instill virtue into everybody so nobody lied or stole and everybody cared about everybody else's utility-- but people still had private information. What kind of economic system would attain efficiency?

We would not, for example, want everyone to give away their wealth to the poor, because then the poor would become the rich. We would not want everyone to work hard, because they'd work inefficiently hard, without detailed instructions. Some kind of decentralized system would be needed, probably using prices. But what would it be, since we could now, unlike in an Adam Smith world, rely on morality too?

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August 05, 2004

Speed Limits and Safety

I've long been dubious of the 55 mph speed limit. It might save lives, but at a huge cost which someone ought to calculate. BUt I just had a thought that makes me doubt whether it even saves lives.

Consider this. Suppose you are trying to avoid a thunderstorm and you are driving 100 miles. If you drive at 50 mph, you have double the chance of being in the storm that you would if you drove 100 mph. Driving faster is less safe.

Suppose, now, that the main danger on a road is from a drunk driver. The more time you spend on the road, the more time you might run across him and be hit. In this case, too, driving faster is driving safer.

The question, then, is whether the extra danger of more hours on the road from a slower speed is offset enough by the extra safety of being better able to avoid hazards. I don't know the answer.

One background fact that would be useful is how many and how major are accidents in town, at slower speeds, compared to on highways, at higher speeds. I should look that up if I can.

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