Month: July 2008

Summers Vindicated (again)

by  Alex Tabarrok in

For the past week or so the newspapers have been trumpeting a new study showing no difference in average math ability between males and females.  Few people who have looked at the data thought that there were big differences in average ability but many media reports also said that the study showed no differences in high ability.

The LA Times, for example, wrote:

The study also undermined the assumption — infamously espoused by former Harvard University President Lawrence H. Summers in 2005 — that boys are more likely than girls to be math geniuses.

Scientific American said:

So the team checked out the most gifted children. Again, no difference. From any angle, girls measured up to boys. Still, there’s a lack of women in the highest levels of professional math, engineering and physics. Some have said that’s because of an innate difference in math ability. But the new research shows that that explanation just doesn’t add up.

The Chronicle of Higher Education said:

The research team also studied if there were gender discrepancies at the highest levels of mathematical ability and how well boys and girls resolved complex problems. Again they found no significant differences.

All of these reports and many more like them are false.  In fact, consistent with many earlier studies (JSTOR), what this study found was that the ratio of male to female variance in ability was positive and significant, in other words we can expect that there will be more math geniuses and more dullards, among males than among females.  I quote from the study (VR is variance ratio):

Greater male variance is indicated by VR > 1.0. All VRs, by state and grade, are >1.0 [range 1.11 to 1.21].

Notice that the greater male variance is observable in the earliest data, grade 2.  (In addition, higher male VRS have been noted for over a century).  Now the study authors clearly wanted to downplay this finding so they wrote things like “our analyses show greater male variability, although the discrepancy in variances is not large.”  Which is true in some sense but the point is that small differences in variance can make for big differences in outcome at the top.  The authors acknowledge this with the following:

If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women.

So even by the authors’ calculations you would expect twice as many men as women in engineering PhD programs due to math-ability differences alone (compare with the media reports above).  But what the author’s don’t tell you is that the gender ratio will get larger the higher the percentile.  Larry Summers in his infamous talk, was explicit about this point:

…if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean…But it’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.

If you do the same type of calculation as the authors but now look at the expected gender ratio at 4 standard deviations from the mean you find a ratio of more than 3:1, i.e. just over 75 men for every 25 women should be expected at say a top-25 math or physics department on the basis of math ability alone (see the extension for details on my calculation).  Now does this explain everything that is going on?  I doubt it.  As Summers also pointed out it takes more than ability to become a professor at Harvard and if there are variance differences in characteristics other than ability (and there are) we can easily get a even larger expected gender ratio.

Does this mean that discrimination is not a problem?  Certainly not but we need the media and academia to accurately present the data on ability if we are to understand how large a role other issues may play.

Addendum 1: Andrew Gelman points out that perhaps alone among the media, Keith Winstein at the WSJ reported the story correctly.

Addendum 2: The authors show variance ratios of 1.11 to 1.21, I take a VR of 1.16.  If we set the female variance to 1 this implies the standard deviation for female ability is 1 and for male ability 1.077.  Using an online calculator for the Normal distribution you can find that given their standard deviation .0102% of males have ability of 4 or greater (4 female sds) but given their sd only .0032% of females can be expected to have the same level of ability, thus a gender ratio of 3.18.

Note that we are assuming that mathematical ability is normally distributed – we know the data fit this distribution around the mean but we don’t know much about what happens at the very top.

Sherlock Holmes on prediction markets

by  Tyler Cowen in

"When you see a man with whiskers of that cut and the ‘Pink ‘un‘ protruding out of his pocket, you can always draw him by a bet," said he.  "I daresay that if I had put £100 down in front of him, that man would not have given me such complete information as was drawn from him by the idea that he was doing me on a wager.

That is from Adventure of the Blue Carbuncle and of course the link is added by yours truly.  The latest news from the prediction markets, by the way, is that the U.S. basketball team is given about a 75 percent chance of taking home the gold medal.

The cost of mortgage agency bailouts

by  Tyler Cowen in

I’ve read varying estimates of the cost of the mortgage bailout, including a sum of $1 trillion mentioned in The Wall Street Journal.  I have no idea what the number will be (and I’m not ruling out zero, or close to zero) but here is how to think about the costs:

1. Reimbursing agency debt holders is a transfer, not an economic cost.  No resources are destroyed by the reimbursement.

1b. The previous bad lending involves a cost — in this case too many homes — which already has been incurred.  This is not a cost of the bailout per se.

2. If government taxes the citizenry to raise money for the bailout, those taxes involve a deadweight loss.  Maybe 20 percent of revenue raised is a decent estimate of this cost.

3. Bailing out debt holders means that future lenders won’t be as careful as they should be.  This problem dates from LTCM, or even further back, and it gets worse each time.  The result is excess leverage and leverage of the wrong kind, namely to "too big to fail" institutions, which then become even bigger and more leveraged.  I haven’t seen a back of the envelope estimate of how much that really costs, much less a careful estimate, but this is a very important magnitude for calculating the net cost.

4. Often in these plans equity holders are (nearly) wiped out.  So beware all the talk of moral hazard.  The real moral hazard is on the side of future creditors, not the current, possibly-soon-to-be-extinguished equity holders.  They really are getting burned.

5. If the government dallies in executing the bailout, borrowing costs for the entire economy will rise.  A bailout has to be swift and decisive, assuming you want to do it.  Yet a swift and decisive bailout will likely involve errors of detail.

6. Doing a justified bailout this time makes it harder next time to avoid an unjustified bailout.  The bailout mentality is contagious in the political arena.

7. The transfer to the debt holders is generally regressive, at least under the likely assumption that the marginal taxpayers are less wealthy than the debt holders.  Of course some of the debt holders are foreign governments, which adds another element to the mix.

8. When it comes to the mortgage agencies, there is no real choice but to bail out the debt holders.  The alternative is a run on the dollar and collapse of faith in U.S. government securities and the end of the world.

Markets in everything, Japanese edition

by  Tyler Cowen in

The DVD is called Miteiru dake (Just Looking),
and it features various talent/models just staring straight ahead.
That’s right, the models on the DVD do very little other than stare
straight at the camera. According to the website, the idea is to get
young males who aren’t used to socializing with women to become more
accustomed to making eye contact and/or handle the fact that a sentient
being sits across from them and awaits interaction. The DVD hopes to
cure those afflicted with shyness so that they may rejoin society.

Here is more information, with an embedded video at the link.  Thanks to Justin Mancinelli for the pointer.  Of course the market offers real variety:

The result,
from what one can see on the website, is strangely disconcerting. A
girl will stare back at you for an extended period of time,
expressionless and periodically blinking (the blinks are eerily
profound). Once in a while the model will utter a phrase like "ohayoo"
(good morning) or make a move to say something, but for the most part
there is just an uncomfortable silence. Most of the women on the DVD
are jimusho-based talento (most have blogs on Ameba
and other DVDs of their own to sell), but there are also foreign women,
young girls, and older women thrown in the mix to give the viewer
experience in handling long, uncomfortable silences with those of
different races and ages.

Why don’t Americans like foreign movies?

by  Tyler Cowen in

Tyler Cowen…argues that movies are about
familiarity. "A feeling of comfort has to be there" for a movie to
succeed, he says. That is the reason that "Americans don’t like foreign
movies," Mr. Cowen says. A Bollywood movie with Indian cultural themes
and actors sells tickets with the Subcontinent’s three-million strong
diaspora in the U.S., but not with the average American.

And will India embrace Hollywood?

…some predict that as India liberalizes, the movie landscape may
alter. "If India becomes like Bangalore then more Indians will start
watching Hollywood," Mr. Cowen explains, referring to the whiz-bang
technology capital of India, populated by upper- and middle-class
youth. As more Indians get wealthier, their tastes will reflect that
currently exhibited only by the upper classes.

Here is the whole article, most of which is about Bollywood.  Here is earlier coverage on the same theme.

The economics of newspapers

by  Tyler Cowen in

The soon-to-be-working for the Center for American Progress Matt Yglesias writes:

The New York Times is known for its hard news coverage, but
he observes that from a business perspective it’s primarily a fashion
and food publication that runs a small political news operation on the
side. One issue of T Magazine, he says, pays for an entire NYT

And, of course, I would add that the broader logic of the internet
is toward disaggregation of content — the fact that newspapers cover
such a wide array of content has to do with the economics of printing
and distributing bundles of newsprint. In the future, fashion ads
probably won’t be able to cross-subsidize any bureaux anywhere. On the
other hand, there may be a corrupting impact of some of this
cross-subsidization — I can’t help but suspect that the importance of
real estate advertising to papers may have distorted their coverage of
the housing bubble on the way up. 

The best two sentences I read this morning

by  Tyler Cowen in

In this paper, we present a simple model of housing bubbles that
predicts that places with more elastic housing supply have fewer and
shorter bubbles, with smaller price increases. However, the welfare
consequences of bubbles may actually be higher in more elastic places
because those places will overbuild more in response to a bubble.

That’s from Ed Glaeser, Joseph Gyourko, and Albert Saiz.  Here is the paper, ungated here, here is Mark Thoma’s commentary.

Move on — this isn’t true here

by  Tyler Cowen in

I have a simple model of how some people — but by no means all — process political issues.  Occasionally the real force behind a political ideology is the subconsciously held desire that a certain group of people should not be allowed to rise in relative status.

Take the so-called "right wing."  I believe that some people on the right do not like those they perceive as "whiners."  They do not want these whiners to rise in relative status.  That means they must argue against the whining and also they must argue against the presuppositions behind the whining.

If the whiners say that times are bad, the rebuttal is that times are pretty good or times will become better again.  But if the whiners want to increase government benefits (perhaps there is a victim to whine about), we hear about the need to tighten our belts and all the talk about good times is, at least temporarily, muted.  Fiscal discipline is now in order.

Take the so-called "left wing."  Some of these people favor a kind of meritocracy.  They feel it is unfair that money so determines access in capitalist society and they do not want the monied class to rise in relative status, certainly not above the status of the smart people and the virtuous people.  It is important to fight for the principle that the desires of this monied class have a relatively low priority in the social ranking.  Egalitarianism is the rhetoric of the day, and readjusting the status of other Americans to the status of this monied class often receives more attention than elevating the very poorest in the world to a higher absolute level.

So when happiness research indicates that money brings more happiness only up to a point, this is a popular result.  That perspective lowers the status of this monied class by showing they really aren’t that happy.  When happiness research indicates that conservatives are relatively happy, however, or that many redistributions don’t make the beneficiaries much happier (in some accounts the money-happiness relationships flattens out at a pretty low level), suddenly happiness research isn’t talked up so much.  Inequalities which do not raise the status of this monied class, such as inequalities in the sphere of beauty or teenage sex, don’t come under so much criticism.

Some on the right wing will stress "individual responsibility" as a value when it lowers the status of the whiners (why whine when it was the victim’s own fault?).  Some on the left wing will stress "individual responsibility" when it is time to punish corporate wrongdoers and thus lower their status.  Not everyone applies (or rejects) this value consistently.

Given this difference in rhetoric, the right wing will be identified with the monied class, even when the left often has more money.  And the left wing will be identified as the whiners, even though the right at times whines as much or more.  You might say that both sides are monied, high human capital whiners, on the whole.  And if you compare them to Burmese rice farmers, the two sides seem somewhat alike.

For the people caught up in these intellectual traps, it all boils down to which groups of whiners they find most objectionable.  And once they choose sides, the wisdom of that choice becomes increasingly clear with time.

Fortunately not everyone has these subconscious motivations.  But even if more people did, it’s not something I would want to whine about.

Assorted links

by  Tyler Cowen in

1. Leopard vs. crocodile

2. How easy is it to disappear?

3. "Lifestreaming"

4. The real Panopticon?: "Subjects tested in a room with a mirror have been found to work harder,
to be more helpful and to be less inclined to cheat, compared with
control groups performing the same exercises in nonmirrored settings.
Reporting in the Journal of Personality and Social Psychology, C. Neil
Macrae, Galen V. Bodenhausen and Alan B. Milne found that people in a
room with a mirror were comparatively less likely to judge others based
on social stereotypes about, for example, sex, race or religion."

Which disciplines are the most and least politically correct?

by  Tyler Cowen in

Here are the data, based on one study; I am surprised that psychology is "tops," with a 58.7% rate of political correctness.  The other "winners" are not hard to predict, though "art" comes in at a surprisingly low 14.6%.  Economics is rated at 4.7%, noting that beneath us lie Marketing, Accounting, Computer Science, Biology, and now into the zero percent category, Finance, Management Information, and Mechanical and Electrical Engineering.  OK, wise guys, give the best single sentence (you are allowed one comma) account of these numbers that you can.

Should we pay doctors to ignore patients?

by  Tyler Cowen in

Here is one interesting proposal for reforming Medicare:

Each fee is meant to reimburse the doctor for the time and skill he
or she devotes to the patient. But it is also supposed to pay for
overhead, and this is where the problem begins. To Medicare, a doctor’s
overhead (or “practice expense”) includes such items as rent, staff
salaries and the cost of high-tech medical equipment. When the agency
pays a fee to a doctor who has performed a CT scan, it is meant to
cover some of the cost of buying or leasing the scanner itself.
Services using more expensive equipment generate higher fees.

…The cost of a CT scanner is fixed, but a doctor earns fees each time it
is used…a scanner becomes highly profitable as soon as
it’s paid for.

In contrast, the doctor-patient visit, which
involves no expensive equipment, offers no significant profit
opportunity. So the best way for a doctor to make money in his practice
is not to spend time with patients but to use equipment as much as
possible.

Get this:

Doctors who do their own CT scanning and other imaging order roughly
two to eight times as many imaging tests as those who do not have their
own equipment, a 2002 study by researchers at the University of North
Carolina found. Altogether, doctors are ordering roughly $40 billion
worth of unnecessary imaging each year…

So what’s the solution? 

For their time, doctors should be given a stipend for each of their
patients. It should be larger for patients with complicated medical
conditions and smaller for those who are healthy, and it should not be
influenced by the number of services or tests a doctor orders.

For
overhead, doctors should be paid an amount that covers the typical cost
of tests and treatments needed to address a patient’s condition. This
strategy – known as “case rate” or “prospective” payment – is standard
in American hospitals. The hospital receives a payment for dealing with
a patient’s underlying condition rather than individual payments for
each test and treatment. This approach offers no incentive to run
unneeded tests, and it has been credited with substantially slowing the
growth in Medicare payments to hospitals.

Of course this penalizes patients with chronic conditions, namely those which show more complications over time than average for the specified class of ailment (e.g., Bill Walton’s foot).  At some margin of unexpected complicatedness, the money runs out and people find it very hard to get their doctor on the phone or for an appointment.  If the relevant alternative is death, this policy is relatively egalitarian; if the relevant alternative is a smooth recovery, this policy is relatively inegalitarian.

I believe this idea deserves serious consideration.

Addendum: Via Mark Thoma, here are other ideas.