Hoisted from comments -- still more on Mankiw's assumptions

Following this and this, here's the latest in my ongoing debate with David over Mankiw's use of assumptions.

Drawn from a longer comment, here's David:

Assumptions may be very sensitive in a model such that if they deviate even slightly, then the results change substantially. And, of course, some assumptions are robust to substantial changes. It would seem that this is the language that Mankiw is speaking in, according to the few short quotes in the past post.

This seems to me to be a different question when evaluating the policy conclusion. For example, I don't believe that all workers earn their Marginal Product (and in some sense there's no way that we could ever tell). In this sense, Mankiw is mostly likely wrong. However, I do strongly believe that there is an important relationship between productivity and wages. The more productive a worker is, the more he or she will likely be paid. This latter formation is much less precise than the former, but I would submit that they carry very similar policy conclusions. Importantly, the assumptions necessary to make the latter statement are much more robust than the former.

Here's my reply (adapted from a previous comment):

David,

Everything you've said is correct but here's the problem: at the level of generality you're talking about, everyone from Mankiw to Paul Krugman to Dan Ariely is in agreement, but many of Mankiw's arguments seem to require much more specific definitions. Rather than being robust, they are so sensitive that making small, common-sense changes can do great damage.

Keep in mind I'm a statistician, not an economist, so I may be getting some of this wrong but let's assume (except for workers on commission -- I'll grant you linearity for that one) the relationship between a worker's productivity and wages is generally monotonic but with plateaus and possibly even the occasional local optimum. I'm not saying this is the case but I suspect it's a pretty good description of what's going on. More importantly, I wouldn't be comfortable assuming this isn't the case.

I'm pretty sure some of Mankiw's arguments break down if you make this assumption. There's a luck factor now as to whether a change in productivity will result in an increase in wages. You also have an asymmetry problem -- the employer has a better idea where the plateaus are.

Or look at his statements about the inheritance tax. He assumes that one component of money's value to a worker is the pleasure of leaving money to an heir (so far, so good) and that the value of that component holds its value even as the inheritance gets well into the millions. If parents start to worry progressively less about each dollar after, say, the first million then the other value components (such as spending, bragging, charitable giving) will swamp the inheritance component long before the inheritance taxes kick in. If this is true, Mankiw's policy arguments simply collapse.

In other words, if pundits' arguments are sufficiently robust or their assumptions are obviously true, they can do what Mankiw does. Unfortunately, neither case applies here.

Contractually obligated to mention Canada again

I'm as tired of it as you are, but as long reform movement advocates* keep bringing up Singapore, I feel someone has to point out that Canada is neck-and-neck with countries like Singapore (except in post-secondary education where it pretty much blows them away) and that Canada, which is a far better match for the U.S. culturally, historically and demographically, has achieved this by taking most of the steps the movement suggests and doing the exact opposite.

If we had a properly functioning debate on education reform in this country, movement advocates would expect to be presented with counter-arguments; they would even anticipate them. New examples would be sought out, positions would be refined and the intellectual framework of the reform movement would be stronger for it.

But we don't have a properly functioning debate. Hell, we don't really have a debate at all. Instead, we have a situation where advocates can talk about Singapore without anyone bringing up Canada, or about PISA without anyone bringing up TIMSS, or about lottery-based analyses without anyone bringing up peer effects (or placebo effects or volunteer effects or treatment/selection interaction or...). Instead of being challenged and having to prove themselves, these claims go directly into the conventional wisdom pile where they are accepted by smart, otherwise well-informed people like Seyward Darby, Ray Fisman and Jonathan Chait.

This is not likely to end well.

* For the distinction between advocating for reform and advocating for the reform movement, see here.

In good company

Joseph,

Have you ever been called 'fascinating' before? It sort of turns a fellow's head.

Mark

p.s. This would still be a cool list even if we weren't on it.

Achilles and the Tortoise, the CBO and the GOP

Perhaps it's just the lateness of the hour but this post by Brad DeLong on the Republicans' refusal to accept CBO numbers reminded me just a bit of the Tortoise's refusal to accept a simple argument in Lewis Carroll's follow-up to Zeno's best-known paradox.

I really need to get to bed.

The Self-esteem gap

Michelle Rhee was on Marketplace yesterday. She's worried about all the coddling and empty praise we've been heaping on our children.

We've lost our competitive spirit. We've become so obsessed with making kids feel good about themselves that we've lost sight of building the skills they need to actually be good at things.

I can see it in my own household. I have two girls, 8 and 12, and they play soccer. And I can tell you that they suck at soccer! They take after their mother in athletic ability. But if you were to see their rooms, they're adorned with ribbons, medals and trophies. You'd think I was raising the next Mia Hamm.

I routinely try to tell my kids that their soccer skills are lacking and that if they want to be better, they have to practice hard. I also communicate to them that all the practice in the world won't guarantee that they'll ever be great at soccer. It's tough to square this though, with the trophies. And that's part of the issue. We've managed to build a sense of complacency with our children.

Take as a counterpoint South Korea, where my family is originally from. In Korea, they have this culture that focuses on always becoming better. Students are ranked one through 40 in their class and everyone knows where they stand. The adults are honest with kids about what they're not good at and how far they have to go until they are number one. Can you imagine if we suggested anything close to that here? There would be anarchy.

This is an old and much loved refrain in the reform movement, but when you look closely and take the time to disaggregate the data the argument completely collapses. The problem is that the culture of esteem-building Rhee describes is essentially a suburban phenomena. In poor neighborhoods, the situation is exactly the opposite:

Hart and Risley also found that, in the first four years after birth, the average child from a professional family receives 560,000 more instances of encouraging feedback than discouraging feedback; a working- class child receives merely 100,000 more encouragements than discouragements; a welfare child receives 125,000 more discouragements than encouragements.

Other words, our best performing schools are filled with kids who, according to Rhee, should be complacent and lacking competitive spirit while most of the kids in our worst performing schools have received little of the empty praise that so concerns her.

Perhaps we should worry less about the exaggerated self opinions of students and more about that of our pundits and commentators.

Department of better late than never

I just came across this excellent piece on President Obama's education speech at FactCheck.org. It is essential reading for anyone who wants to keep up with the education debate, but if you just want the punchline, here it is:

Most of the major claims in the president's speech were either based on highly selective reading of the data or were simply wrong.

This brings us to one of the strangest aspects of the education debate: the way it makes smart, conscientious people act grossly out of character. Consider this representative example from FactCheck:

But the claim that "our high school dropout rate has tripled in the past thirty years"? That’s not even in the ballpark. According to the Department of Education’s National Center for Education Statistics, the "status dropout rate" – defined as the percentage of people between ages 16 and 24 who are not in school and do not have high school diplomas or GEDs – was 9.3 percent in 2006. In 1976, 30 years before that, it was 14.1. That’s actually a 34 percent decrease in the high school dropout rate.

Of course, dropout rates are notoriously hard to measure and compare. For instance, while NCES shows a status dropout rate of 9.3 in 2006, the high school completion rate for that year was only 74.8 percent. Why the discrepancy? Instead of counting people of a certain age with a diploma or equivalency certificate, this figure compares the number of high school freshman in a certain year to the number receiving a high school diploma four years later. Those who take more than four years to finish aren’t counted, nor are students who get GEDs instead of diplomas. But using this calculation still doesn’t back up Obama’s claim. The dropout rate – that is, the discrepancy between incoming freshmen and graduates – would have been 25.2 percent in the 2006-2007 school year. The rate in 1976-1977 was 25.6 percent.

Even pessimistic accounts don’t show a tripled dropout rate. According to a report by the Educational Testing Service, titled "One Third of a Nation" after the number of students they say are high school dropouts, high school completion rates peaked at 77.1 percent in 1969 and dropped to 69.9 percent in 2000. (NCES shows higher numbers in both years.);That would put dropout rates at 22.9 and 30.1 percent respectively – a 30 percent increase over 31 years. As many sixth-graders could tell you, tripling would mean a 200 percent increase.

So where did Obama’s figure come from? A White House spokesman pointed us to a report by the College Board, which said: "The rate at which American students disappear from school between grades nine and 12 has tripled in the last 30 years." But the College Board’s report included a mistake, which it later corrected: The rate really refers to what happened between grades nine and 10. More important, however, it is not really a "dropout rate." The College Board report in turn cites a 2004 study by the National Board on Educational Testing and Public Policy, which actually shows a tripling of the attrition rate between grades nine and 10, not the dropout rate. In other words, the difference between the number of students enrolled in grade nine in one year and the number enrolled in grade 10 the next year has increased threefold. At the same time, there has been a corresponding threefold increase in grade nine enrollments relative to grade eight. The report shows more ninth-graders failing that grade, not dropping out.

Given that the reform movement has been railing against social promotion for years, it's hard to argue that an increase in students held back is a cause for alarm.

The spam filter on Blogger... what's the word?...

Oh, I remember, sucks.

It seems to have a problem with long comments so if you write a comment and it doesn't appear, please follow up with a short note and Joseph or I will check the filter.

Sorry for the inconvenience.

Jonathan Chait disapproves of a liberal journalist's flip-flop on unions

In today's TNR:

New York has a mordantly funny piece about the effort by staffers at Harper's to unionize. The saga begins with gross mismanagement by owner Rick MacArthur, spurring the staff to organize. Then the left-wing MacArthur started to act a lot like a union-crushing boss.

I have a bit more sympathy for MacArthur. He's in a difficult situation trying to save a tremendously worthwhile institution. I tend to be very union-friendly but the situation can get murky when the business in question really is struggling to survive, not just making a play for sympathy. Given that my only source of information is the gossipy and badly written New York piece, it's difficult to assign much blame.

Besides, it's not like he attacked a fundamental role of unions like the right to protect their employees from unfair termination.

Mortgage Questions

This post had a very perceptive take on a question from Megan McArdle:

McArdle: “Let’s turn it around,” I asked. “What if the bank decided that it wanted to exercise the same sort of option?…What if the bank foreclosed on your house, even though you made the payments, because it figured it could make more money taking the house and selling it?” (Not a likely scenario, I know, but a useful thought experiment.).

Response:

Banks exercise the same sort of option all the time when they resell mortgages (and hopefully notes!) from one entity to another entity. That’s the problem we have right now, that this reselling option banks use was so sloppy it’s tearing up the economy.

This is why if you are the type of person who thinks markets self-regulate through consumer demand and reputation there’s a major problem, as consumers have no choice over their mortgage servicer. If you don’t like your servicer, and refinance your mortgage with another bank, that bank can still sell off your mortgage and you can still end up serviced by the same institution.

I never quite thought of the decision to resell mortgages in this light, but this is a remarkably good point. It's not quite the same scenario as "seize the house" (which I think was the actual tactic that McArdle had in mind) but it certainly does put the decision to resell mortgages in perspective.

In a more pragmatic light, the decision to try and do regulation by reputation (long a bad idea) has even less relevance in the modern world. First of all, job tenures at banks may be quite short so the people making decisions that undermine a firms reputation may be elsewhere at the end of this period. Second, firms themselves often vanish or are absorbed by other firms (consider Washington Mutual as an example). These features of the modern corporate environment make it difficult to use a reputation based system as the primary check on the system.

This is not to say that homeowners who are in default should be given free houses (I'd think that was obviously an incorrect conclusion) but rather that we should give the regulatory structure of banks some serious thought.

The Golden Globes as a collective action problem

Even by the standards of Hollywood awards, the Golden Globes was a largely pointless exercise, selected by small and lightly credentialed group of no particular standing. For awhile, it represented a small net positive for the industry -- it did generate publicity and the large number of categories meant that a lot of shows could add "winner of..." to their promotional material -- but eventually the meaninglessness, the poor choices and the suspicion that nominations were made based on who might attend the ceremony all pushed the Golden Globes into the liability category. This came to a head this year with multiple nominations for the Tourist, one of the worst-reviewed pictures of the season, and with a payola scandal.

I suspect that most of the industry would like to see the Golden Globes go away but here's where the collective action problem comes in. If everyone who disapproved would stop covering or attending the event, they could probably kill it in a year or two (I'm counting being bumped to E! as virtual death), but even the Globes' harshest critics haven't been able to go cold turkey. As long as the show is there, all the incentives on the individual level are lined up to keep the show going. The journalist who refuses to write about the nominations or the ceremony loses ground to competitors. The nominated star who boycotts the awards passes up publicity and may be seen as difficult to work with (a label that can devastate an actor's career).

There's something refreshingly trivial about Hollywood versus the Golden Globes, but it does raise an interesting point: just how embarrassing does a situation have to be for an industry to find a solution to a collective action problem? Apparently it need to be worse than having the host of a prime-time network awards show opening with jokes about the fact that the nominations are fixed.

School segregation

From Dana Goldstein:

American schools are more segregated by race and class today than they were on the day Martin Luther King, Jr. was killed, 43 years ago. The average white child in America attends a school that is 77 percent white, and where just 32 percent of the student body lives in poverty. The average black child attends a school that is 59 percent poor but only 29 percent white. The typical Latino kid is similarly segregated; his school is 57 percent poor and 27 percent white.

There are clearly some places that our current educational system could stand to be reformed. I would rather focus on issues like segregation and access rather than whether removing tenure would be a panacea.

h/t Tyler Cowen of Marginal Revolution

What can I say, I'm a sucker for a good Procrustes joke

Click for the full strip.

Academics

Female Science Professor has an absolutely delightful take down of a Andrew Hacker and his book:

My vote for the strangest part of the book is the paragraph in which the authors describe a "workingman" who "jumped on a subway track to rescue a child who tripped and fell." The workingman didn't think; he just did it. The authors posit that professors on that same platform would not have jumped on the track to save the child:

"We wonder if, had some professors been on the platform, would they have paused to ponder how John Stuart Mill might have parsed the choices?"

I wonder if that is a sane thing to wonder. Of course the professors would save the child. What better way to combine broader impacts, a synergistic activity, and outreach?

and

Similarly, what is your evidence for your contention that professors don't work as much as they say they do? This seems to be it: "A story is told of a classroom where all the students were busy scribbling as the professor droned on. All, that is, but one, a young woman in the back row, who wrote down nary a word. How so? She had with her the notes that her mother had taken for that class during her own student days." That's the evidence? A possibly apocryphal story?

and

For example, your book starts with the story of a candidate who, in his interview for a faculty position, makes it clear that he is not interested in teaching and is only interested in research. The fact that he was not hired indicates to me that the system worked well, yet you used this anecdote to illustrate your hypothesis that professors don't care about teaching and try to do as little of it as possible.

There are a lot more really good examples in this text, these were just my favorites. It is definitely worth an afternoon read.

Joe Gores wrote the best chimpanzee sex scene you'll ever read

That sounds like a joke (and a rather tasteless one given that Gores died this week). It's not. The scene occurs in the book Menaced Assassin and in the most unlikely of settings it goes from wrenching despair to a moment of extraordinary sympathy. It was, like much of Gores' writing sentimental, but it was always honest and hard-earned sentiment.

And damn, the man could write.

Continued (battery issues)

My first exposure to Gores was the short story "The Second Coming" about two hipsters who volunteer as witnesses to an execution, just for kicks. It was published in 1966 in a now forgotten men's magazine and was, in its way, as unlikely as that chapter in Menaced Assassin. There was no mystery -- the accused was guilty -- and no violence except for that mandated by the state, but like the chapter in Menaced Assassin, it will stay with you.

When relative rates are misleading

Mark points me to this article.

To me these effects are hard to interpret in terms of relative growth rates given that rich areas of the country remained richer (on average) than the poor areas of the country. Let us consider a thought experiment to see what I mean by the problem of relative rates.

One region, call it sunbelt, has income of $1,000 per capita and this income increases by $20 (2% growth per year).

Another region, call it rustbelt, has an income of $500 per capita which increases by $15 (3% growth per year).

Clearly the rustbelt region has better growth (in % terms) but has a lower growth in absolute wealth. Now let us presume that the absolute growth rates remained constant over a decade.

At the end, despite always having lower growth, sunbelt has $1,200 in income while rustbelt has $650 per capita. The relative difference is smaller (as 650 > 50% of 1200) but, in absolute terms, the people in sunbelt now make $550 per year more than the people in the rustbelt.

Are we sure that % growth rates are always the best metric of economic progress?