Yet another trillionaire protesting the return to Clinton era taxes

And this guy's practically swimming in money.

Lucky pennies and constrained roulette

In a recent post about progressive taxation, Jonathan Cohn says the following about economic fairness:

One is that it fails to account for the power of luck. Almost by definition, people who are successful have benefited from some measure of good fortune. That fortune can take the form of obvious, material advantages -- like access to advanced technology and good schools. Or it can take the form of more subtle, but still important, assets for moving forward in life--like good health or loving parents.

There's no arguing with the basic thrust here, but it presents a very narrow view of luck. You can get a broader and more interesting view if you think in terms of probability distributions.

The idea of luck is closely tied to the idea of beating the odds. Having an unlikely positive outcome is more or less equivalent to the informal concept of being 'lucky,' but this often leads into one of those areas of probability that give people trouble.

There's a natural and entirely rational impulse to look for explanations when we see something unlikely. Unfortunately, there's also a natural tendency to get confused when we go back and assign probabilities after the fact.

One of the best known examples comes from Burton Gordon Malkiel in his classic A Random Walk Down Wall Street. Malkiel draws an analogy between a successful investment fund manager and a lucky coin-flipper.

Imagine a coin flipping competition. You start with a thousand coin-flippers. Every round consists of one flip. At the end of every round, those who came up tails leave the game. The contestants go from 1,000 to 500 to 250 to 125 to 63 to 31 to 16 to 8.

"By this time, crowds start to gather to witness the surprising ability of these expert coin-flippers. The winners are overwhelmed with adulation. They are celebrated as geniuses in the art of coin-flipping, their biographies are written and people urgently seek their advice. After all, there were 1,000 contestants and only 8 could consistently flip heads."

As presented here, this seems absurd but if you spend some time watching CNBC or browsing the business section of your local book store, you'll realize it's not exaggerated.

Related to the lucky coin-flipper is the grand prize winner.

We have a roulette wheel numbered 1 to 100, 100 spaces on the table and 100 players. On a first come, first serve basis, each player picks a number. Whoever is sitting on the number that comes up gets everyone's chips.

The winner can argue that he or she had some special skill at number picking, and that's entirely possible, but there's no way of confirming that claim by looking at the results of the game. Someone had to win and whoever won could make the same argument.

Just as it's not difficult to find lucky coin flippers, it's also easy to find CEOs and business leaders who benefited greatly from landing on the right number.

Consider Michael Eisner.

Eisner was CEO of Disney from 1984 to 2005. By any standard it was a good run, marked by growth, major acquisitions, prestigious and popular products. Eisner deserves credit for a lot of good decisions, but the single biggest factor behind Disney's resurgence came from a turn of the roulette wheel.

In the late Eighties, with the format war settled and VCR reaching saturation levels, parents discovered that the easiest (and often the only) way to keep a small child quiet was to pop in a video (I recall Robert Altman saying in an interview that Popeye was his most profitable film for just this reason). Suddenly Disney was sitting on the most valuable film library in the world.

It is true that Eisner pushed to speed up release of some of the studio's classics, but the home video division had started years before he got there and given the size of the market that opened up, it's hard to believe that even the most cautious of executives would have held back the films much longer.

Michael Eisner simply found himself sitting on a lucky number.

If a sock puppet had been appointed CEO of Disney in 1984, the home video market for kid-friendly shows would still have exploded and the company still would have made a mint. It might not have managed a Little Mermaid or a Lion King but it still would have had a fantastic run and you'd have no trouble finding numerous books exploring the business genius of Argus McArgyleSock.

In praise of orifice-derived numbers

HCZ founder Geoffrey Canada in an interview with City Limits Magazine:

You have set a 65 percent "tipping point" as a universal goal for your programs, after which you think success becomes inevitable. How did you determine that 65 percent was the tipping point?

Why that number? Why that number and not 70, 80 percent? There's no science there. You don't go look up, find the tipping point of a poor community—there's no science there. You take your best educated guess...

I'll tell you what my belief is, and what's my underlying logic. Kids do what their friends do. If your friends smoke, you smoke. If your friends drink, you drink. That's just the way things are. Kids do what they're around. If you're around kids who fight, you better learn how to fight. If you get a whole bunch of kids doing positive things instead of negative things, should you expect that to have an impact on other kids? Absolutely. But there's no science.

If the question is, is there science, has someone done a randomly controlled double-blind study? No, no. But ask anybody. You want the Harlem Children's Zone on your block, working with the kids on your corner, or not? You don't need a random study to decide what the answer to that is. You ask people, when a shooting happens, do you want folks from the Harlem Children's Zone to go in there and make sure no one else gets shot or not? You live in Harlem, guess who you're calling? You're calling me.

I liked this answer.

As a statistician, I am frequently asked quantify difficult-to-measure variables and estimate parameters for decision processes. In these situations I can always find some rational-sounding process for deriving a metric, but I can't always vouch for its robustness or even its relevance and there's a good chance all it will do is give the recipient a false sense of security. Some things just don't readily lend themselves to these approaches.

People like the notion of processes being data-driven. They feel safer knowing that there methodologies and statistics behind the decisions that affect them. Unfortunately a suspect methodology and a statistic that doesn't measure what it's meant to can do tremendous damage. If I'm ask to produce metrics when I don't have faith in the analyses or in our ability to measure what's relevant, then as a statistician, the best and most responsible answer I can give is often, "Hell, I don't know. What sounds reasonable to you?"*

There's a lot to be said for an arbitrary number that's reasonable to the people who actually work in the field, particularly if that number is also a good and useful rule of thumb. Of course, it could turn out to be a poor estimate of what you're after but the same holds for the results of bad data and analyses and it's a great deal easier to drop a number when it doesn't come with pages of impressive-looking but meaningless tables.






* I'm not going to wander off into a discussion of informative priors here, but these woods are filled with Bayesians so there's a good chance someone will pick up the scent.

LA Weekly doesn't just bury the lede; they hide the body

(It's Sunday so I'm taking a break from bitching about bad statistics so I can bitch about bad journalism.)

LA Weekly's Jonathan Gold is the first food writer to win a Pulitzer and for a first, it was a remarkably uncontroversial award. Gold has been widely recognized for his sharp, funny prose and his knowledgeable and discerning approach to criticism.

(That has nothing to do with the topic of the post but I wanted to start with something nice.)

With the exception of Gold, the Weekly offers pretty much the standard free-weekly fare, specializing in starkly-lit heroes-and-villains stories with obligatory swipes at the mainstream media (particularly peevish and resentful when focusing on their competition).

One of the problems with writing this sort of story is that, if you're going to stay true to the narrative you invariably have to leave out something funny and/or interesting because it undercuts your case.

For example, if you were writing a story about a sleazy conman slandering respectable businesses, you wouldn't be able to include a quote that made one of those respectable businesses look completely street-rat crazy. That's too bad, because it must be difficult to ask a journalist to pass up anything as memorable as this (from Felix Salmon, who almost never leaves out the good stuff):

On Monday, Barry Minkow put out a press release accusing a NYSE-listed company, InterOil, of being “nothing more than hype”. InterOil has had a large short interest for some time, and it seems that Minkow touched a nerve, because InterOil’s senior manager for media relations, Susuve Laumaea, went borderline insane via email in response:

you are a gutless coward of the highest order, a jealous and envious SOB… You are a loser, a non-achiever and a sour-grape. Piss off you good for nothing… Do not be afraid on account of me being a descendant of cannibals … no, no, believe me, I will not cannibalise you or feed you to the swamp crocodiles…

you are known crook, conman, convicted felon, a psychopath and a pathological liar who is jealously envious… You have no sense of common decency. You are neither here nor there among the cream of decent God- fearing humanity. You are a scum of the earth, a creepy-crawlie who should have been locked away and the key thrown away too so that you rot away like the dung heap you are. You are a coward of the highest order… I can’t use you as crocodile feed because you are too poisonous … those alligators will die eating you, cooked or uncooked…

Who gave you the authority to investigate InterOil, you piece of shitty non-entity? You are nothing more than an internet pirate, a low-life manipulator who is out to profit by your dishonest, fraudulent, slanderous and cowardly methods. Up yours.

How could the Weekly leave this out? It's like Beat poetry. It practically demands to be read aloud with dramatic pauses and bongo accompaniment.

Benoît Mandelbrot (1924 - 2010) and Education Reform

From A maverick's apprenticeship:

It was then and there that a gift was revealed. During high school and the wandering year and a half that followed, I became intimately familiar with a myriad of geometric shapes that I could instantly identify when even a hint of their presence occurred in a problem. “Le Père Coissard,” our marvelous mathematics professor, would read a list of questions in algebra and analytic geometry. I was not only listening to him but also to another voice. Having made a drawing, I nearly always felt that it missed something, was aesthetically incomplete. For example, it would improve by some projection or inversion with respect to some circle. After a few transformations of this sort, almost every shape became more harmonious. The Ancient Greeks would have called the new shape “symmetric” and in due time symmetry was to become central to my work. Completing this playful activity made impossibly difficult problems become obvious by inspection. The needed algebra could always be filled in later. I could also evaluate complicated integrals by relating them to familiar shapes.

I was cheating but my strange performance never broke any written rule. Everyone else was training towards speed and accuracy in algebra and reduction of complicated integrals; I managed to be examined on the basis of speed and good taste in translating algebra back into geometry and then thinking in terms of geometrical shapes.

Where did my gift come from? One cannot unscramble nature from nurture but there are clues. My uncle lived a double life as weekday mathematician and Sunday painter. My gift for shapes might have been destroyed, were it not for the unplanned complication of my life during childhood and the War. Becoming more fluent at manipulating formulas might have harmed this gift. And the absence of regular schooling influenced many life choices, but ended up not as a handicap but as a boon.

I realize we can't have an educational system focused entirely on the occasional Mandelbrot, but I can't help but wonder how the great man would have fared in the rigid, metric-driven system we're headed toward.

(also posted at Education and Statistics)

"No, I said 'self-select for attitude.'"

One of the many weird aspects of the charter school debate has been the non-exchanges over selection effects. Critics suggest that students who choose to go through the application process will tend to be more motivated, more committed to school, more interested in college, and more open to the idea of a heavier work load and will tend to have more stable, supportive families.

Here's an example:

Some observers, such as the authors of The Charter School Dust-Up, say that KIPP's admission process self-screens for students who are both motivated and compliant, from similarly motivated and compliant—and supportive—families. Parents must commit to a required level of involvement, which rules out badly dysfunctional families.

This would seem to be fairly straightforward. Almost every school could do a good job if it were populated solely by students who worked hard, followed instructions and had the full support of their families. A strong selection effect here could explain away most or all of the positive results observed in KIPP schools. This hypothesis even raises the possibility that KIPP schools are actually doing worse than public schools would under comparable circumstances.

(You'll notice that no mention is made of race, poverty or test scores.)

Now here's how SRI responds:

KIPP schools’ higher-than-expected test score results draw both attention and claims that they “cherry-pick” high-achieving students from poor neighborhoods. This is the first report to closely scrutinize the praise and criticisms associated with KIPP, as well as key challenges facing Bay Area KIPP schools today.

In the three KIPP schools where they were able to draw comparisons, SRI researchers found that students with lower prior achievement on the CST were more likely to choose KIPP than higher-performing students from the same neighborhood, suggesting that, at least at these schools, cherry-picking does not occur.

And here's the much-touted Mathematica report:

Our nonexperimental methods account for the pre-KIPP (baseline) characteristics of students who subsequently enter KIPP schools: not only demographic characteristics such as race/ethnicity, gender, poverty status, and special education status, but also their achievement test results for two years prior to entering KIPP. We examine the achievement levels of the students for up to four years after entering KIPP schools. In our preferred models, we compare these trajectories to the achievement trajectories of a matched set of local public school students who have similar achievement test results and demographic characteristics in the baseline period (typically third and fourth grades) but who do not enroll in KIPP.

Waiting for Superman... to get bored and drop you like a bad habit

From Roger Ebert's review of Waiting for Superman:

We have met five of these students, heard from them and their parents, and hope they'll win. The cameras hold on their faces as numbers are drawn or names are called. The odds against them are 20 to 1. Lucky students leap in joy. The other 19 of the 20 will return to their neighborhood schools, which more or less guarantees they will be part of a 50 percent dropout rate. The key thing to keep in mind is that underprivileged, inner-city kids at magnet schools such as Kipp L.A. Prep or the Harlem Success Academy will do better academically than well-off suburban kids with fancy high school campuses, athletic programs, swimming pools, closed-circuit TV and lush landscaping. [emphasis added]

Probably the most comprehensive study of the KIPP program was done by SRI, which looked at KIPP schools in the Bay Area. Here's one of their findings (again, emphasis added):

As researchers analyzed the student achievement data and KIPP’s approach, they also identified challenges facing Bay Area KIPP schools, including high student attrition rates, teacher turnover, and low state and local funding. For example, 60 percent of students who entered fifth grade at four Bay Area KIPP schools in 2003-04 left before completing eighth grade.

More that any other player in the charter school movement, KIPP has relied on the cheese effect to generate its results. It's a profitable and highly praised business model built entirely of the backs of discarded students.

"5 Myths about Federal Taxes"

From Bob Stoker via John Sides at the Monkey Cage, here are some relevant numbers for the tax debate:

Myth #1: Federal taxes are higher than they have ever been.

According to the Congressional Budget Office (CBO), the opposite is true. Budget analysts typically measure the federal tax burden as a proportion of GDP because this accounts for the amount of our economic output that is devoted to paying federal taxes as the economy grows or contracts. Federal taxes from all sources were 14.8% of GDP in 2009 and are projected to be 14.6% of GDP in 2010. See the CBO report, "The Budget and Economic Outlook: An Update," August 2010, Table 1-2 (pdf).

By comparison, the lowest tax burden during Ronald Reagan's Presidency was 17.3% of GDP. Under President Bush federal taxes reached their low point at 16.3% of GDP. See the CBO historic budget tables: http://www.cbo.gov/budget/data/historical.pdf

Myth #2: People at the top of the income distribution pay more than half of their incomes in federal taxes.

According to the Tax Policy Center, the average federal tax rate in 2009 (including income taxes, payroll taxes, estate taxes, and corporate taxes) among the top 20% of the income distribution was 22.9%. Among the top 1% of the income distribution, 26.1%; among the top 0.1 of the income distribution, 27.9. The top one tenth of one percent of the income distribution paid an average federal tax rate of less than 28%.

Myth #3: Poor people don't pay taxes.

It would be more accurate to say working poor families with several children don't pay federal taxes. According to the Tax Policy Center, the average federal tax burden on the bottom 20% of the income distribution is negative...that means, people in this income range typically get more money back from the federal government than they pay in federal taxes. However, this is a consequence of the Earned Income Tax Credit (EITC) and the Child Tax Credit. For most families the most generous benefits are provided by the EITC and you must work to receive this credit. The current value of the credit is $5,657 for families with three or more qualifying children. Although modest EITC benefits are available to childless taxpayers, the credit is much more generous for families with children. When the generous benefits that are provided for working poor families are aggregated with others in the bottom 20% of the income distribution, the overall federal tax rate for this group is negative.

Myth #4: Federal marginal tax rates always go up as income increases.

The marginal tax rate is the rate that is applied to the last dollar of taxable income. Although it is generally true that federal marginal tax rates increase with income (because the personal income tax is progressive), this is not always true. The FICA tax that supports Social Security and Medicare is a significant portion of the federal tax burden for many taxpayers. The part of the FICA tax that supports Social Security (a 6.2% tax on earned income that is paid by employees and employers) has an income cap (currently $106,800). Earned income above that cap is excluded from the tax. Beyond this, at present unearned income is entirely excluded from the FICA tax (though this is scheduled to change for the part of the FICA tax that supports Medicare under provisions of the federal health care reform). Because most calculations of the federal tax burden include both the employer's and employee's share, moving earned income just above the cap reduces the federal marginal tax rate by 12.6%. Here is a history of FICA tax rates from the Social Security Administration.

Myth #5: Only affluent people pay federal taxes.

It is true that people in the top 20% of the income distribution provided 67.2% of federal tax revenues in 2009. However, they receive 54.3% of cash income. Despite this however, most American households pay a share of the federal tax burden. Although 47% of households paid no federal income taxes, two-thirds of these households did pay social insurance taxes to support Social Security and Medicare. The "deadbeats" who paid neither tax were mostly elderly people and people with annual incomes below $20,000. See again the analysis of the Tax Policy Center:

Punch, brothers! punch with care!

Conductor, when you receive a fare,
Punch in the presence of the passenjare!
A blue trip slip for an eight-cent fare,
A buff trip slip for a six-cent fare,
A pink trip slip for a three-cent fare,
Punch in the presence of the passenjare!

CHORUS

Punch, brothers! punch with care!
Punch in the presence of the passenjare!

If you don't recognize these lines, you should probably go here before going any further. If you do catch the reference, be warned. Some news stories are like Sam's jingle and unfortunately this is one of them:

"Pat Sajak: Should Public Employees Always Be Allowed To Vote?"

MBA thinking , gestalt and the death of humanities

The following comes from Stanley Fish:

What he didn’t know at the time is that it had already happened, on Oct. 1, when George M. Philip, president of SUNY Albany, announced that the French, Italian, classics, Russian and theater programs were getting the axe.

For someone of my vintage the elimination of French was the shocker. In the 1960s and ’70s, French departments were the location of much of the intellectual energy. Faculty and students in other disciplines looked to French philosophers and critics for inspiration; the latest thing from Paris was instantly devoured and made the subject of conferences. Spanish was then the outlier, a discipline considered stodgy and uninteresting.

Now Spanish is the only safe department to be in. Russian’s stock has gone down, one presumes, because in recent years the focus of our political (and to some extent cultural) attention has shifted from Russia to China, India, Pakistan, Iran, Iraq. Classics has been on the endangered species list for decades. As for theater, the first thing to go in a regime of bottom-line efficiency are the plays.

And indeed, if your criteria are productivity, efficiency and consumer satisfaction, it makes perfect sense to withdraw funds and material support from the humanities — which do not earn their keep and often draw the ire of a public suspicious of what humanities teachers do in the classroom — and leave standing programs that have a more obvious relationship to a state’s economic prosperity and produce results the man or woman in the street can recognize and appreciate. (What can you say to the tax-payer who asks, “What good does a program in Byzantine art do me?” Nothing.)

President Philip cites as one justification for his action the fact “that there are comparatively fewer students enrolled in these degree programs.” Of course, in a bygone time seats in those programs’ classes would have been filled by students who were meeting quite specific distribution requirements; you remember, two advanced language courses, one course in American lit and another in British lit, and so on.

Those requirements have largely gone away. SUNY Albany does have general education requirements, but so many courses fulfill them — any one of dozens will meet your humanities requirement — that they are hardly a constraint at all, something the Web site acknowledges and even underlines with pride. This has happened in part because progressive academics have argued that traditional disciplinary departments were relics from the past kept artificially alive by outmoded requirements.

Perhaps this is being unfair to MBAs (God knows there are plenty of examples elsewhere), but there's a certain misguided kind of thinking that's common in business school graduates, an approach to complex problems that fetishizes metrics yet takes a dangerously naive approach to numbers. Factors that are difficult to quantify are casually dismissed. Synergy is a heavy-rotation buzzword but simplistic reductionism is the actual default.

New Coke was a notorious example of metric-driven thinking. The metric here was a taste-test score, a well-defined scalar that seemed to measure the nebulous concept of appeal. The executives were so pleased to have an actual number that they put one of the world's most popular and profitable brands at risk in an effort to optimize that metric.

What they overlooked was the need to look at every successful product, institution or organization as a gestalt where the success is a function of the whole.

I am certain president Philip can point to extensive cost benefit analyses justifying the school's decision. I am also certain that these analyses rely almost entirely on easy-to-measure quantities and short-term projections and largely (if not completely) ignore important factors that are more difficult to deal with.

The American university system has been a tremendous success over the past century or so and a major part of that success has been the rich and diverse intellectual gene pool that universities offered. It would be next to impossible to quantify the value of that gene pool but it's safe to say that narrowing it will come with hidden costs.

Wolfmeat

It's time to face the ugly truth: the readership of Observational Epidemiology tends to run more than a little nerd-heavy. That's okay. With the success of the Big Bang Theory, geek chic has never been less uncool.

So there's no reason not to check out this list of math-based games I put together for beginning teachers. You can even go here and find still more.

Of course, I still wouldn't mention it around the cool kids.

Greg Mankiw's reply -- dishonesty or just bad prose?

From Mankiw's follow-up to his NYT editorial:

Aren't you motivated by more than money? Of course. I have never suggested that money is my, or anyone's, sole motivation in choosing a lifestyle.

The phrase "sole motivation in choosing a lifestyle" is going to cause us some problems; it's difficult to rebut this kind of practiced vagueness, but we were talking about the choice to do certain work. If we read choice of lifestyle to mean choice of work, then yes, he did suggest exactly that.

Let's roll the tape:

By contrast, without the tax increases advocated by the Obama administration, the numbers would look quite different. I would face a lower income tax rate, a lower Medicare tax rate, and no deduction phaseout or estate tax. Taking that writing assignment would yield my kids about $2,000. I would have twice the incentive to keep working.

If doubling the money you're paid doubles your incentive, doesn't that suggest that your incentive is solely pecuniary?

Make sure to thank the senator

I forgot to mention in my last post that Senator Richard Shelby (also known for his work as a character actor in shows such as Dark Shadows and Nero Wolfe) was the one who pointed out the nominee's lack of qualifications.

So thanks, senator. We certainly appreciate everything you and your party has done to uphold the quality of the Fed.

If the President wants to get his nominees approved...

Maybe he should stop nominating boobs who can't even stay awake through a seminar.

The indispensable Professor Thoma

Having spent a lot of time recently on the issue of compensation, this post by Mark Thoma caught my eye:

Greg Mankiw complains that if taxes go up for people with incomes as high as his, he won't work as hard and that means he won't be able to leave as much for his kids. Incentives matter he says. If that's the case, I wonder why someone who is trying to take away the incentive for his kids to work hard and be successful on their own doesn't leave academia and become a high paid consultant.

I'm sure Greg Mankiw could clean up as a consultant. The same effort he puts into academics would be much more highly compensated somewhere else. The fact that he decided to become an academic in the first place indicates that it's not all about the money.

As Greg Mankiw makes clear every chance he gets, he's at Harvard. That tells me that the return to his ego is every bit as important as the financial return. I'd further guess that even if the New York Times stopped paying him for his column, he'd write it anyway. It's a boost to his ego and reputation that he'd want even without whatever small payment he gets for each column (he could make more by using the time to prepare a talk "to a business group, consulting on a legal case, [or] giving a guest lecture," so the opportunity cost of the column is quite high).

I have only anecdotal evidence for the following statement (but it is pretty damned extensive anecdotal evidence so here goes):

When it comes to assumptions, statisticians and economists (particularly freshwater economists) tend to take opposite approaches. Statisticians generally insist on running through more assumptions than the listener has any interest in hearing about, often including those of no relevance to the situation you're in. (A former manager of mine once joked that it was easy being a statistician -- whatever the question, you just answered "it depends.") Economists tend to leave assumptions unsaid, even the really important ones that probably aren't being met.

I can give you plenty of examples of these buried assumptions (if you can make it through a chapter of Freakonomics without finding a few you're not paying attention), but there are also economists who do their best to unearth these assumptions, to bring them back into the debate where they belong. One of the best and most diligent of those diggers is Mark Thoma.

Which brings us back to Greg Mankiw's recent column. On one level, Mankiw's argument is sound. Every product that reaches the marketplace did start with the producer asking "Is this worth my while?" Tax rates do factor into that calculation, so, yes, there can a situation where dropping the Bush tax cuts would cause someone to decide not to make a product.

But there are a couple of big assumptions here. First, since we're talking about a return to Clinton (not Eisenhower) era tax rates here, a product would have to be just barely worth doing now -- the drop in returns under the proposed change is very small. Since this is known economic territory, we know that Clinton's tax increase caused at most a trivial number of products and services to be dropped for the reason Mankaw suggests and the Clinton rates were as high or higher than anything proposed by Obama. (Mankiw gets around this by starting out talking about the income tax increases for people making over 250K then slipping in the estate tax about half a page down, leaving most readers with the impression that making the income tax slightly more progressive will cut his take home pay in half but that's more a case of lying through misdirection than of burying the assumption).

The second, and more important assumption is where Thoma really shines. The idea that a producer will stop making a product if the tax rate passes a certain point assumes that primary return on that product is taxable, an assumption that is in no way justified here. As Thoma points out, the compensation Mankiw receives in the form of ego-stroking and reputation-building far exceed the $650 he gets for each column. I would add to that the satisfaction of influencing the debate. Conservative groups spend millions of dollars getting anti-tax arguments in the papers. When Mankiw does it, the papers send him the check.

When the compensation for a product or service is overwhelmingly non-taxable, an increase in tax rates will almost never cause a provider to drop that product or service. Mankiw is smart enough to be aware of this (he is at Harvard, after all); he just doesn't want the rest of us to realize it.