"No linear relationship" does not mean "no relationship"

There's a dangerous type of argument that I've noticed recently: pundits will argue that a certain relationship is non-linear and use this to justify any claim they want to make about that relationship.

The example of the hour is the Laffer curve. The basic concept is so simple we expect every high school algebra student to grasp it: you have a function with a global maxima somewhere between zero and one; if you're to the left of that maxima you want to move to the right; if you're to the right you want to the left. Let me draw a picture I could explain it to reasonably attentive elementary schoolers. (Dynamic laffer effects are a different story that I'll leave to Noah Smith.)

We can argue where the peak is (or where it was in 1960 or 1980), but once you've accepted the basic concept, you have to accept the move-toward-the-peak implication. Despite this, you will routinely see supposedly knowledgeable people on television, in print and online using the Laffer Curve to justify the blanket statement that cutting taxes raises revenue.

We see something analogous with health and fitness journalism. The relationship between calories and weight loss is not linear. Neither is the relationship between aerobic exercise and weight loss. In both cases, it's a strong relationship and you generally won't get in trouble assuming that it's strictly monotonic (within reasonable ranges, of course).

Unless you're an athlete in training or a model getting ready for a swimsuit shoot, you can probably assume that eating less and exercising more will cause you to lose weight, but we still get endless experts citing phenomena like metabolism responding to diet and then concluding that there's no point in going to the gym and passing up that pound o' fries.

p.s. Joseph has a great example of how calorie consumption tends to dominate factors like diet make-up. If he'll answer his damned phone I'll see if we can get a post out of him.

US Credit Rating

From Talking Points Memo:

From the S&P release ...

Compared with previous projections, our revised base case scenario now assumes that the 2001 and 2003 tax cuts, due to expire by the end of 2012, remain in place. We have changed our assumption on this because the majority of Republicans in Congress continue to resist any measure that would raise revenues, a position we believe Congress reinforced by passing the act.

I am skeptical, as I said to Mark, that this measure will influence other countries all that much. Japan switched to AA+ and that did not hurt the US, rather it helped. What it really does it mean about 55% of the AAA sovereign debt in the world just vanished. The UK, Canada, Sweden . . . all of these countries are about to pay a lot less for their debt. That actually makes them more creditworthy and not less so so.

By the way, what do all of these countries have in common? They are willing to raise taxes to pay for debt. I remember when Canada began paying down its debt via a national sales tax. Unpopular as the move was, it moved the country firmly into surplus and prevented a ratings cut.

It is quite possible for a country to pay down their debt via internal revenue generation. The survivors on the AAA list are the countries that have been willing to make hard decisions to raise revenue rather than appeal for help.

Question for economic modelers

Has anyone out there run a simulation of what the economy would look like today if two of the big three auto makers had gone under in 2009?

If America's not AAA, is anybody?

I don't mean that in a jingoistic way; I'm simply wondering where the safe harbors are in the aftermath of a US default. The people at Marketplace (which has been doing some great work lately) have been thinking along the same lines:

Heidi Moore: They downgraded the U.S. credit rating. It's like cutting our credit score. We went from a AAA to a AA+ -- which is more than people expected; people thought we'd just be a AA. The importance of this is largely psychological -- we've always been a AAA country. But now that we are a AA+, that's what everyone else will be too. I think everyone else will follow us.

Carney agreed that other countries would be downgraded as well:

John Carney: Remember, we're the country that supports people when they get in trouble. If our credit rating is lower, so is everybody else's.

Grade Inflation

An early stage professor posted this view on grade inflation:

I have to agree with the article that students do tend to expect A's. But mainly because they work hard, and the expectation is that if you work hard and learn the material, you should get an A. I don't really see this grade inflation as a problem. To me, an A grade means you learned the material and showed proficiency in it, not that you performed better than XX% of your classmates. Grades are not a ranking tool, but an indication of proficiency. I think that having a clear expectation of what you need to do to get an A makes it more likely that students will work harder to meet these requirements and learn the material better.

I think that this really is where the grade inflation is coming from. When I was a wee one, back in my home country, the decoding scheme for grades was:

A: Exceptional Work above and beyond expectations
B: Clear Mastery of material and met all expectations
C: Deficiency in one or more aspects of the course
D: Don't take any more courses in this area
F: Fail (with attendant consequences)

I think that the shift to A's being regarded as showing proficiency has been part of the general creep in academic culture. After all, an A average is starting to look like a requirement for entry to graduate school. I remember when a straight B average was solid evidence that a student was ready for graduate level work.

On the other hand, viewed in this light there isn't any real inflation. We have just changed the definitions of performance and introduced right truncation to make it impossible to pick out the really exceptional students by transcripts alone. I, of course, hate this approach but I can see why it might be popular if the focus is "did they get it or not" and reducing the arms race to demonstrate exceptional performance.

Question for Jonathan Chait

From today's post trying to rebut a movie star's comments (not Chait's proudest moment):

The old liberal slogan always demanded that we "treat teachers like professionals." That entails some measure of accountability -- we can debate the metrics -- which allows both that very bad teachers be fired and that very good ones can obtain greater pay and recognition. That's the definition of a professional career track, and the current absence of it is what drives most of the best college graduates into other professions.

Putting aside the compensation question for the moment, Chait is listing being easy to fire as part of the definition of being a professional. Does anyone else find that a bit odd?

Krugman backslides

Just when it looked like the worst of the punning was over, we get this (which is worth reading, despite the title).

(Still better than "Screw your core-age to the sticking place.")

Excuses, excuses, excuses

Just moved so I'm still threading my way around a maze of boxes and I'm getting my wi-fi from the Starbucks around the corner (which wouldn't be so bad if I didn't hate their coffee), so this won't be much of a post but the Matt Yglesias argument Joseph alludes to just doesn't hold up.

There is plenty of support for merit pay among center and right segments, people who are taking Yglesias's exact position here, so his statement is wrong when applied to the general population. Of course, Yglesias is taking about fighting among progressives so the anti-tax line makes even less sense.

Put bluntly (because my laptop's almost out of power), Yglesias is trying to explain why so many progressives are offended by his movement reformer stand without admitting that he might be the one contradicting progressive principles.

A return to education as a topic

This is an interesting perspective from Matt Yglesias about the tensions in the education reform movement:

The ambiguous policy upshot of this is precisely what makes intra-progressive fights over education policy so fraught. The exact same evidence which suggests that we should offer higher salaries to teachers also suggests that many of our current teachers are sub-par. It’s easy to assemble a “let’s spend less money on teachers” coalition, which is just conventional anti-tax politics. And it’s easy to assemble a “let’s give more money to the teachers we have” coalition, which is conventional service provider politics. What’s tricky is a “let’s spend more money precisely in order to get different people in this field” coalition.

I think that there is another angle to all of this discussion that is often forgotten. Current teachers include people who sacrificed earning potential for long-term job security (and did so in an environment where this was a part of their explicit employment contracts). The modern vogue for reneging on promises that are not inconvenient is not helpful to the debate. There may be cases where this is necessary, but it should be a painful last resort and not a routine talking point (see state pensions and the rhetoric about them).

EDIT: Also worth reading is Dana Goldstein's column

Are we entering the Post-coalition age of American politics?

Probably not, but...

Of the many bizarre turns of the past few weeks, the one that really shocked me was the Republicans agreeing to a deal that will very probably end up gutting the Pentagon's budget. Over less that a year, the GOP has alienated seniors by threatening Medicare, scared the hell out of the financial sector with a threatened shut down, and pissed off the military and related industries by disproportionately targeting defense for deficit reduction.

Perhaps this simply fear of Tea Party retaliation or perhaps the party's stated concern for the deficit was more sincere than most of us realized, but either way this pushes the current political situation even further out of the range of data.

Check out Jonathan Chait's sharp summary here.

Is health care choice important?

Aaron Carroll has a nice overview of the situation in Florida where people who campaigned on health care choice seem to be removing for state employees. He quotes this news story:

Florida is changing part of its state-employee health insurance program to offer only one HMO in each county. The state Department of Management Services, which oversees employee insurance, said changes in the program would save an estimated $400 million over two years. The changes also would require thousands of state employees to switch to different HMOs, a process that would begin in late September.

I wonder if these positions are more harmonious than they appear on first glance. If the goal is to make government service less appealing, reducing health care choice (and thus competition) makes these positions less desirable.

Math issues

Felix Salmon's last two posts are brilliant. I strongly recommend reading both of these posts. Seriously!

Heck, I am likely to come back and post on them later today if I have enough time. Paul Krugman and Mark Thoma might be representing the outrage of progressives, but Felix is documenting the damage coldly and dispassionately.

However, this is a statistics blog. So I wanted to visit a comment on one of Felix Salmon's posts:

The top 10% of Americans pays 45% of all taxes, a higher proportion by far than any other country, while the American top 10% earns only 33% of total income.

By comparison, the 10% of the UK earns 32% of total income and pays only 38% of all taxes. And the UK is one of the more progressively taxed countries. The taxes paid by the top 10% of other European countries are on average around 30% of total taxes.

As an epidemiologist (a field that is in love with proportions), I realize how misleading they can be. In the example above, the rich earn roughly the same amount of income. But they pay a higher proportion of taxes. However, is it the proportion of taxes that matters or the absolute tax burden?

Consider a simple example. In two countries there are 10 people. Of these people, nine make 10 units of income per year and one makes 50 unites of income. This is pretty close to the income distribution of the US and UK cited above.

In country A, the nine people pay 2 units of tax per year and the rich person pays 16 units of tax. Total tax revenues are 34 units (or 24% of GDP). The rich definitely pay more as a proportion of taxes but pay 47% of the taxes overall.

In country B, they pay something more like the OECD average (35%). So the nine people pay 3.5 units of tax (31.5) and the rich pay 17.5 units of tax. That is 49 units of tax collected (exactly 35%). The rich pay 36% of the tax burden.

Which country is a low tax country for rich people to live in? One where they pay an effective tax rate of 32% versus 35%? Or one where they pay a higher proportion of total taxes collected?

The trick here is that the US total tax burden is so light that the top 10% can both pay a higher proportion of taxes than in other countries and, at the same time, still pay less absolute tax. That can make proportional analysis potentially misleading.

Apologies to Mr. Raz

I've never been a big fan of NPR's Guy Raz but his handling of the coverage of the debt crisis was very good today, peaking with this interview with Felix Salmon.

Overly-trusting Straussians

There is a strong strain of Straussianism in the conservative movement. Of course, not all prominent conservative intellectuals believe that you have to lie and oversimplify to move the masses in the best direction for society, but pretty much all have accepted and, more importantly, internalized the fact that many of their colleagues do believe in the need for these noble lies.

Once you've internalized the idea that people in your circle are smart and sane but occasionally make ludicrous statements for the benefit of the crowds (call it the Elsinore strategy -- feigning madness), it becomes easy to ignore craziness in your own party, particularly when there's a penalty for suggesting the alternative (see Bartlett and Frum).

In other words, we have something like conservation of cynicism. The Straussian assumes the worst about the masses, but has an excuse to assume the best about allies, even when they give every indication of being crazy and/or stupid. The result is that it has taken smart, sane conservatives far too long to acknowledge what's going on with House Republicans.

The consequences of this lack of cynicism is spelled out in detail in excellent posts by Jon Chait and Paul Krugman.

A view into the queue

Still in the middle of a move but here are some of the posts I'm trying to find time for. Given the speed at which events are moving, I thought I should at least get something out in preview form.

-- The worst thing about the Tea Party from a Republican perspective is not the movement's extremism. If a (slightly modified) modified stag hunt is an appropriate analogy, players who decrease the chances of a successful hunt (by demanding you take unpopular positions) and who are disloyal (bolting to third party candidates when offended) are the worst possible allies.

-- When Straussianism makes people insufficiently cynical. Conservative thinkers may have underestimated the danger of a default crisis because they assumed the rhetoric coming out of the Republicans in the house was fodder for the masses rather than sincere statements.

-- Fox News and flawed control systems.

-- Political science models may tell us that spouses don't effect candidates' chances, but how far out of the range of data is Michelle Bachmann's husband?