Deinonychus antirrhopus

Mark Chu-Carroll runs a blog called Good Math, Bad Math and generally he exposes instances of bad math. However, in regards to use statistics Mark gives example of some bad math in two posts. It all started with a post about the Duke rape case and how on another blog a commenter was using some crime data that was dubious in nature to argue that there was a good chance the accuser is lying. Mark persuasively argued why there are problems with that data (see the first post linked above). The problem is that Mark then went on to make some inaccurate statements about how we can use statistics. Namely,

Now, the issue that came up in comments is: can we use statistics to reason about a specific member of a population? The answer is always no. Because a specific, individual member of a population can never be a representative sample. And you can only reason to and from representative samples of the population.

Looks pretty reasonable to most people, which is why I'm writing this post. The above is simply false at least if we take a Bayesian view of statistics. Consider the follwing information on breast cancer and mamograms and a question.

1. Percentage of women over 40 who have breast cancer: 1%
2. 80% of women age forty with breast cancer who get a mamogram will get a positive result.
3. 9.6% of the women (age forty) who get a mamogram without breast cancer will also get a positive test.
4. You (or your wife and who just so happens to be 40) have (has) gotten a positive mamogram test for breast cancer; what is the probability your wife has breast cancer?

The answer is 7.8% The result follows from an application of Bayes theorem, which Bayesian statisiticians view as an important way of evaluating data and making inferences. Mark's position is that we can't apply the population number (1%) to an individual and come up with the new answer of 7.8%.

In comments Mark has argued about that we can only make probability statements like the above is we have a measure of uncertainty. Frankly, I'm not even sure what that is. The probabilities above are statements of uncertainty, and we don't need some extraneous measure hanging around gumming up the works.

Here is another way of looking at this. Suppose Mark and I are out for a walk in New York city and come across a couple of games of chance. Suppose further, that we know that such games are almost always unfair. We have plenty of experience with this to set an initial probability that the game is unfair at 80%. Then we observe the following sequence of outcomes of the game (W = win, L = Loss) for the supposed "Mark":

Based on this, and our population statistics, (with the additional assumption that if the game is rigged the "Mark" will only win 25% of the time), then we can conclude with a probability of 97.9% that the game is actually fair. Even if that initial probability is wildly innaccurate it isn't nearly as devastating for the Bayesian as enough data will swamp that initial probability assessment. For example, if we take the same situation, but this time with the initial probability that only 10% of such games are rigged and a sequence of events,

Our final probability assessment would be 97.2% that the game is actually rigged. So even though I might have a wildly optimistic (and wrong) initial probability assessment that such games are fair enough (accurate) data can overcome this initial "bias" and lead us to a much more accurate estimate.

One commenter put it in a much more amusing manner. Suppose we want to know the probability that a randomly selected individual has a penis. A probability of 50% would be a good starting point. If we then find out that the randomly selected person is a male, we'd revise our initial probability assessment to 100% (of course, using Bayes theorem for this is like driving a thumb tack with a sledge hammer).

So the bottom line is yes, we can use statistics to make probability statements about individuals of that population. The more data we get about the individual we are interested in, the better our statements can be. And since probability statements about individuals are a form of reasoning, Mark Chu-Carroll is simply wrong in his view point, at least from the Bayesian viewpoint. Since his blog is about good math and bad math, he should ideally point this out.

Charles Wheelan (PhD and all), has written article debunking one of the most outlandish ideas in economics. No, he hasn't gone after somebody like Karl Marx and the labor theory of value. No, he hasn't gone after the idea of anarcho-communism. Instead he has decided to go after the Laffer curve. Boy what a laffer...I hate that joke.

What I find absolutely amazing is all that is wrong with Wheelan's article. Right off the bat Wheelan is wrong,

Economist Arthur Laffer made a very interesting supposition: If tax rates are high enough, then cutting taxes might actually generate more revenue for the government, or at least pay for themselves.

In a word, no. The reason that the Laffer curve is called the Laffer curve is that Arthur Laffer, according the the "legend" expressed the idea at a lunch (or dinner) on a napkin. Those present, I believe Jude Wanniski was one of people in attendance, were struck by the description and started calling it the "Laffer" curve. The name stuck.

However, the idea of the Laffer curve is far older than Laffer. I recall in an economics course somewhere one of my professors mentioning that John Maynard Keynes was aware of the concept. President John F. Kennedy basically described the concept when he proposed his tax cuts.

In short, it is a paradoxical truth that tax rates are too high today and tax revenues are too low and the soundest way to raise the revenues in the long run is to cut the rates now. The experience of a number of European countries and Japan have borne this out. This country's own experience with tax reduction in 1954 has borne this out. And the reason is that only full employment can balance the budget, and tax reduction can pave the way to that employment. The purpose of cutting taxes now is not to incur a budget deficit, but to achieve the more prosperous, expanding economy which can bring a budget surplus.

According to Wikipedia, the Laffer curve was discussed in some form by,

1. John Maynard Keynes,
2. Frédéric Bastiat,
3. Ibn Khaldun,
4. Alexander Hamilton,
5. The 19th century constitution of the Confederate States of America

The basic idea is quite sound. Here is a pictue of an idealized Laffer curve. When the tax rate is 0%, it is axiomatic that the tax revenues will also be 0. Further, when the tax rate is 100% it can easily be derived from the axioms of neo-classical economics that tax revenue will also be 0. We also know that tax rates are bounded between 0 and 100% (or 1). Hence it follows that tax revenues will reach at least on peak inside the range of 0 and 1.

The idea is that chances are we are not going to be at the peak. Further, if we are to the "right" of the peak, then we can raise tax revenues by decreasing taxes. In fact, if we are to the right of the peak, then there exists another tax rate t* that is less than the current tax rate that will raise exactly the same amount of revenue.

Now, there are issues with the Laffer curve when formulating policy. The big problem is that we don't know the shape of the curve, nor do we know what the maximum is. Hence it really isn't much help in setting some sort of "optimal" tax rate in the sense of maximizing tax revenues. Further, if it happens that we are in fact to the "left" of the maximum then lowering the tax rate will only lower tax revenues.

And from here things just get worse for Dr. Wheelan,

But here's the problem when we take Laffer's theory and try to apply it in the U.S.: We don't have a 99 percent marginal tax rate. Or 70 percent. Or even 50 percent. We start with low marginal tax rates relative to the rest of the developed world. (Yes, I understand that it may not feel that way after the check you wrote last month.)

Actually there have been periods when the marginal tax rate has been very high (link--pdf). Dr. Wheelan notes that cutting the top marginal tax rate from 36% to 33% isn't a big deal. While he is likely correct, this isn't a flaw with the idea of the Laffer curve. In fact, the good Dr. has already conceded that the theory is correct. Frankly, at that point how he can go on and try to make the case that this idea is hair-brained is indicative that perhaps the one who actually hair-brained is Dr. Wheelan.

Here is the nut of Dr. Wheelan's argument,

So why does Laffer's sketch on Dick Cheney's cocktail napkin rank near the top of my list of bad economic ideas? Because, when applied to the U.S., it's intellectually dishonest. The Laffer Curve offers the false promise that we can cut taxes without making any sacrifice on the spending side, and that's simply not true. It's the economic equivalent of arguing that you can lose weight by eating more.

No Dr. Wheelan, the idea isn't dishonest just like the idea that demand falls as prices increase isn't dishonest. What is dishonest is how the idea is used or more accurately misused by some. To Dr. Wheelan the idea itself is bad, how it is used is irrelevant. I find this view to be anti-intellectual and something I'd expect from a primitive savage, not somebody with a PhD.

Cross posted from Outside the Beltway.

Again, most of this comes from the Oil Drum. First is the picture of where the price of gasoline comes from,

Source: EIA

As can be seen the biggest component to gasoline prices is the price of oil. One thing that I'd like to know is, for every $1 increase in the price of oil, what is the increase in the price of gasoline (all else held constant).

The other two pictures deal with gasoline stocks and production (respectively).

So what do we see, both gasoline stocks are low, and production are low. Why are these things low? In part because of the switch over to ethanol from MTBE.

As Heading Out (the author of the Oil Drum post) notes, the current discourse about investigating the oil industry, windfall profit taxes, and so forth are all pretty much nonsense and will do damn little to help the situation. In fact, I'd argue that things like the windfall profits tax would make it worse.

Walter Williams gave an example of the problem here. The example in a nutshell is as follows:

1. There is a disaster in Pittsburgh.
2. Prof. Williams loads up a U-haul with bottled water bought at $2/bottle.
3. He drives to Pittsburgh and sells the water for $20/bottle.

Now politicians who deplore Prof. Williams profitting off of the misery of others invoke a windfall profits law taking $18/bottle from Prof. Williams.

Now suppose there is a disaster in Baltimore the following year. Would Prof. Williams load up his truck with water again? Nope. Would the people in Baltimore get the water they need? Probably not since it would be up to FEMA and local emergency response agencies and we all know what kind of job those guys do. So people go thirsty in Baltimore because Prof. Williams would rationally expect to have profits he earns taken from him by the government.

If we do the same thing with oil, say charging a 100% tax on every barrel for the difference of the price less $40 what would happen? Well oil companies would have no incentive to increase production or perhaps they'd send it overseas and sell it in another market. In short, such a tax would if anything reduce production here in the U.S. or at least prevent it from rising. Higher prices tend to increase the supply. This is why supply curves in economics have an upwards slope with respect to price. The higher the price, the more supplied. Artificial take away some of that price and you get less.

Investigating the oil industry wont likely have a downward impact on prices if the problems really and truly are the reduce oil production here in the U.S., Nigeria, etc. and increased world demand in places like China and India, and transportation/distribution issues stemming from the switch from MTBE to ethanol. Further, it will divert our attention away from the real problems and looking for solutions that might actually help in the longer term. For example, more refineries and competition there might help. Coming up with a uniform nationwide blend for gasoline could also help. Investing in oil pruduction as well could help. Right now we seem to be approaching our limit in terms of producing oil. And of course, looking for alternative fuels. The high price of oil and gasoline make alternatives relatively more attractive. If we think oil prices are going to remain high for the foreseeable future then research and development into such alternatives also becomes more attractive.

Now I disagree with the implication by Heading Out that something other than the market place is needed for alternative sources of energy.

I learned in the last Energy Crisis that to expect energy companies to invest in new ideas when they are getting buried in money using the old ones is not really fruitful.

I agree that ExxonMobil right now has little incentive to look for an alternative to oil/gasoline. However, ExxonMobil is not the begining and end of market. There are other firms out there that can look for alternatives. In fact, the huge profits that the oil industry are currently enjoying are the incentive. Come up with something that is at least as costly as gasoline is now with the potential to be cheaper (or even hold costs at a constant level) in the future and you could find yourself taking away some of those profits from ExxonMobil.

The bottom line, in my view, is that many in this country are heading in the wrong direction about who is to blame for high gasoline prices and what to do about it.

Cross posted from Outside the Beltway.

Michelle Malkin seems to be all a twitter over the notion of Reconquista, that is that the U.S. or at least a big chunk of it (i.e., the Southwest) will be re-absorbed by Mexico. Apparently this Grand Master Plan is going to be executed by having illegals sneak into this country, then they will agitate for amnesty, get it, then vote for politicians that will return parts (or even all of) the U.S. to Mexico. That is, these wily illegal immigrants, who at other times Michelle Malkin bemoans as illiterate and uneducated but nevermind that, want to take the land of opportunity and turn it into Mexico Del Norte or something. Say, maybe these wily immigrants aren't that smart...I don't know I have a hard time following Michelle Malkin's torturous logic.

First of, as I've already noted, Malkin wants to have her cake and eat it too when it comes to immigrants and their Grand Master Plan. On the one hand she hosts an article about how uneducated the illegal immigrants are, but at the same time there is this cunning plan in place to steal elections. And yes, it is true that illegal immigrants are less educated than the average American, the idea that there is this cunning plan is well...unhinged.

As for Malkin's article about the Reconquista she starts out great. Great in the sense that she effectively silences any and all criticism.

There are none so blind as those who will not see. While the mainstream media heaped praise on the "peaceful" May Day protesters and newspapers plastered sympathetic photos of the pro-illegal alien "sea of humanity" all over their front pages, freelance photographers, bloggers, and radio interviewers captured a sea of open-borders militancy nationwide.

Uninformed political observers delude themselves into thinking that these sentiments are relegated to the fringe. But the core concepts of reconquista (the "re-conquest" of the Southwest by Mexico) have spread wide and deep-from San Francisco to Los Angeles to Milwaukee to Arkansas and beyond.

It is a brilliant rhetorical strategy if one can get away with it: cast all critics as blind and uninformed. Disagree with the notion of reconquista and you are blind and uninformed. Now you have to spend time demonstrating that one is informed and not blind.

Further, Malkin argues her point, that the reconquista is strong and broadly supported based on virtually no evidence. Her only evidence is biased pictures from bloggers and such who support her position. Is it any stretch that these people would seek out the most striking examples of banners and signs that support their viewpoints? Seems that is probably a good default assumption vs. the idea that Malkin's confederates are in reality out there taking a random sample of all the signs and banners at various marches and demonstrations.

In Seattle, photojournalist Byron Dazey of CreativeFlashes.com snapped hundreds of pictures of extremist left-wing claptrap. "Open the Borders" screamed a giant banner. "No more blood! No more borders!" echoed another placard. "Stop the War! Stop the Borders!" preaches a sign carried by a "Freedom Socialist Worker." Other protesters displayed a rambling, illiterate message scrawled on a giant blue tarp:

"To the diplomats in Arizona talking of illegal deal, why R U so hipocratics (sic) when we know that almost ½ of what it was Mexico, was bought illegally by the US . Santa Ana was a conquestee from France, he was not the president of Mexico or Mexican. 1845-1847 we were fighting our own independence with their own people and also fighting the French. The US took advantage N offered Santa Ana money for the Mexicans land. Do U call this legal?"

Okay, so there are hundreds of photos...exactly how many supported reconquista and how many didn't. And how many banners and signs were there at the march? I don't know, but is this an example of reconquista claptrap? Or how about this? Now, you may not agree with the sentiment of that picture, but it doesn't strike me as expressing some sort of reconquista viewpoint. Similarly for this picture? And this one, this one, this one, and this one? To be sure there are the kooky element, but the kooky element comes out for just about any march or parade (don't those people who carry the signs about Palestine have real jobs?).

The bottomline is that Malkin has completely failed to demonstrate her point. Many of the pictures either say nothing about the reconquista or they indicate support for becoming Americans. It must be great being a pundit in that you don't have to actually deal with things like facts and evidence.

Update: Many commenters are having a problem with this post (or maybe I just didn't get the point across well). I am not denying that there are whacky fringe elements in the open borders/immigrant crowd. Heck one of the pictures at the Creative Flashes website was about justice for Palestine. Huh? My point is that Michelle Malkin's thesis: That la Reconquista is a widespread belief of many of these immigrants is just not supported by the "facts" that Michelle Malkin has brought forth? What does she have?

Some pictures. Pictures that are selected to show the point she wants to make. Notice she didn't point to any of the pictures that I linked to above.

Other evidence? Some whacky speakers at the rallies. There are whacky speakers are every rally. The Million Man March had Louis Farakhan as a speaker (to name one) and I have to say...that guy is whacky. So are we to conclude that every single black man at the Million Man March is now a member of the Nation of Islam? That is what the MalkinLogic^TM would suggest.

When we get right down to it, Malkin has failed to show that the idea of la Reconquista is actually a widely held belief that she claims. Most commenters engage in speculation, conjecture and outright conspiracy theorizing. The idea that the immigrants are "useful idiots" and that once inside the voting booths (assuming they become citizens) they will vote in lock-step to return California, New Mexico, Arizona and perhaps Nevada to Mexico. Nevermind that many of these illegal immigrants aren't even Mexican! Nope, they will all vote in lockstep.

I find this kind of thing complete nonsense. At least with the "evidence" that Malkin claims to have. Malkin is very good at manufacturing outrage out of things that are not outrageous such as the Ports deal. When all was settled in that fiasco all that the U.S. accomplished was to piss off a long time ally in the Middle East.