ObamaCare's invidual mandate upheld by the Supreme Court

From the dissent:

That clear principle carries the day here. The striking case of Wickard v. Filburn, 317 U. S. 111 (1942), which held that the economic activity of growing wheat, even for one's own consumption, affected commerce sufficiently that it could be regulated, always has been regarded as the ne plus ultra of expansive Commerce Clause jurisprudence. To go beyond that, and to say the failure to grow wheat (which is not an economic activity, or any activity at all) nonetheless affects commerce and therefore can be federally regulated, is to make mere breathing in and out the basis for federal prescription and to extend federal power to virtually all human activity.

From now on, everything you do, or do not do, can be regulated by the Federal Government.

The Government was invited, at oral argument, to suggest what federal controls over private conduct (other than those explicitly prohibited by the Bill of Rights or other constitutional controls) could not be justified as necessary and proper for the carrying out of a general regulatory scheme. … It was unable to name any.

If the concern is that the uninsured impose costs on the rest of the country, the solution is for them to bear the cost of their decisions while opening up the health insurance market for competition.

Do you ride a bicycle? That increases your risk of injury. Since everyone else pays for your injuries, the Federal Government now has the power to regulate whether, when, and how, and which bicycles you may ride, anywhere, even on your own property.

In fact, the Federal Government's bureaucrats now have the power to decide whether your life is worth enough to keep you living for an extra few days, or be able to walk for an extra few years.

You may think the current political authority will always decide according to your wishes, but don't depend on it:

The critics of the capitalistic order always seem to believe that the socialistic system of their dreams will do precisely what they think correct. While they may not always count on becoming dictators themselves, they are hoping that the dictator will not act without first seeking their advice.

…

They forget that a dictator, too, may act differently from their wishes, and that there is no assurance that he will really try for the "best," and, even if he should seek it, that he should find the way to the "best."

A Critique of Interventionism by Ludwig von Mises

This decision serves no other purpose than to strengthen the argument that everyone who supports it must be replaced in the next election so that there is a fighting chance to implement solutions in health care financing that do not depend on intricate central planning bureaucracies.

… the Framers considered structural protections of freedom the most important ones, for which reason they alone were embodied in the original Constitution and not left to later amendment. The fragmentation of power produced by the structure of our Government is central to liberty, and when we destroy it, we place liberty at peril. Today's decision should have vindicated, should have taught, this truth; instead, our judgment today has disregarded it. (emphasis mine)

What constitutes major airline crash?

Bloomberg has a Crazy Story which I found out via Best of the Web.

The title of the story, and I am not joking here, is Airline Crash Deaths Too Few to Make New Safety Rules Pay.

See, not enough people are dying in crashes to be able to justify new safety rules in terms of simple cost-benefit analysis where benefits of a regulation in terms of statistical lives saved. A rational regulatory body ought to target maximizing statistical lives saved per dollar spent, or minimize dollars spent per statistical life saved.

It makes no sense making people spend, say $100 million, so, on average, one fewer person might die every ten years of a specific cause, when there are other ways people can die or get hurt.

If regulations in one particular area are very effective, additional regulations may not provide large enough increases in lives saved to justify the cost.

So, that's what's got Bloomberg reporters worried: We may not get additional, costly regulations that provide no benefit larger than their costs.

But, the report opens with a sentence that is interesting on its own:

More than a decade has passed since the last major-airline accident on U.S. soil. That's great news for aviation companies and their passengers — and a complication for rule makers trying to improve flight safety.

The Colgan Air Flight 3407 crash that took the lives of 50 people is not considered major enough by the reporter (although it is mentioned).

I am not sure how a passenger plane falling out of the sky on top of a bunch of houses and killing 50 people is not major. Is it because it happened far away from where Andrew Zajac lives? Would he have thought differently about this crash had he or someone he loved been in one of those houses?

Also, I don't know about you, but I do consider the Miracle on the Hudson to be a major accident as well.

No, it's not that major events are not occurring that upsets these guys.

They are seriously disappointed that too few people are dying in them, which makes it harder for them to justify imposing more costs on airline passengers.

Please, we are still having to deal with flights canceled at the slightest sign of trouble because the regulatory cost of delayed flights is too high. If air travel in the U.S. has become so safe (i.e. if the current regulations are working), please leave them alone so we can get where we want to go.

Thank you!

Is there reason for a "Housing Exuberance"?

Apparently, every day brings us more reasons to believe that everything is getting better. A recent example is summarized in Bloomberg's report titled Housing Exuberance Led by Shiller's U.S. Glamorous Cities.

Given that the index is available online, there is no reason not to look at it ourselves and see where this exuberance is coming from.

The Composite-10 measure is at a not seasonally adjusted value of 148.40 for April 2012 which is actually about 2.3% lower than its April 2011 value of 151.78. The Composite-20 measure is at a not seasonally adjusted value of 135.80 for April 2012 which is actually about 1.9% lower than its April 2011 value of 138.43.

We can also look at all included cities:

If that's too crowded for you, here are just the composites:

Of course, prices without a measure of volume don't mean much. Below, I normalized the two composites so that their January 2007 values are set to 100:

Conclusion: Home prices and sales fell. There are occasional upticks and downticks, mostly related to the seasonal nature of home sales, but if these data can make you exuberant, you must have very low expectations to being with.

And, just in case you might be thinking the seasonally adjusted data show something different, here are the adjusted composites:

There will always be variations across regions. What matters is where things are going overall. The answers seems to be nowhere in particular.

The Bloomberg report singles out certain areas. Let's look at them in turn.

AZ-Phoenix (PHXR)

The April 2012 value of the price index is 8.62% higher than April 2011, but volume is 19.32% lower.

WA-Seattle (SEXR)

April 2012 price index is 0.96% lower and the volume index is 8.51% higher than the April 2011 values.

FL-Tampa (TPXR)

Price index rose by 0.81% from April 2011 to April 2012 whereas volume fell by 11.03%

FL-Miami (MIXR)

April 2012 price index is 3.17% higher than April 2011. Volume index fell by 3.62% compared to a year before.

CA-San Francisco (SFXR)

In April 2012, the price index fell by -1.36% from a year before and volume fell by 4.93%.

GA-Atlanta (ATXR)

Atlanta was not mentioned in the story. The price index fell by 17% in April compared to April 2011, but volume was up 149.33%.

Composites

Composite-10 price index was 2.23% lower in April 2012 than in April 2011 and volume was 6.09% lower.

Composite-20 price index was 1.9% lower in April 2012 than in April 2011 and volume was 0.45% lower.

Active Markets

Boston, Denver, and Dallas saw both higher prices and higher volume in April 2012 than in April 2011.

Polls me ... polls me not

Best of the Web mentions a biased poll question:

I'm going to read two statements. Which of the following approaches do you think makes the most sense for New York in deciding whether or not to open up the state to fracking for shale/natural gas? Here’s the first statement: New York should wait for all the necessary health and environmental studies to be completed first before opening the state to fracking. Here’s the second statement: New York should move ahead now before the studies are completed to allow fracking in all or some of the state.

For this to be a valid question, the first statement should have read: New York should wait for all the health and environmental studies requested by the opponents of fracking before allowing it anywhere in the state.

By definition, all unnecessary studies should not have been initiated in the first place.

In the grand scheme of things, this might sound like a trivial excuse for a blog post, but it is very important to pay attention to what's in a poll, especially with what we are going to be subjected to until election day.

This question, extremely biased to produce a result against fracking, is good reminder that how poll questions are formulated matters just as much as who's asked.

Are you a stupid immigrant?

You might be a stupid immigrant, if you try to comply with every single rule you have to deal with while remaining in the U.S. legally.

You might be a stupid immigrant, if your brother really just comes to the U.S. to visit you and returns home like he should after the visit.

You might be a stupid immigrant, if, after countless hours of reading, visits to the lawyer's office, phone calls with the BCIS, browsing through web sites, and asking people who should know, you are still uncertain exactly which form to file, and keep wondering if you've done anything that might jeopardize your status.

You might be a stupid immigrant, if you have to smile patiently when your colleagues think you're taking an extended vacation even though you must leave the country until October 1st to be able to remain in status.

You might be a stupid immigrant, if you ever tried to explain and failed, because nobody listens to you, how come the dude at the coffee shop down the street has no problem taking a job, but, you, with a Ph.D., cannot accept an offer because of your status.

Clearly, you're a smart immigrant if you overstay your visa, take jobs you're not allowed to take, sign mortgages you are not supposed to borrow, send your children to school on the dime of citizens and legal residents, get your children college loans, or, even, have your children accepted at Ivy League schools on the sob story of them being "illegally" in the United States.

We need real immigration reform now!

Rewarding people (and, yes, giving work permits to children of illegal aliens is rewarding both the children and their parents) for breaking the law only invites more.

If you could claim yourself a primo parking spot on New York City's Fifth Avenue just by illegally parking your car there for a few days, what do you think would happen?

These children can travel back to the countries where their parents are from. Most of them very likely still have either friends or family back home who could take in these "children" while they sent their college applications and waited for responses. Having been raised in the U.S., they would already have several advantages compared to the local population. Some of these are:

1. Fluency in English to help them score higher on tests like the SAT and TOEFL.

2. A high school degree from a U.S. high school.

3. Familiarity with how the system works.

4. Connections with American teachers, business people or others who might write nice recommendation letters.

5. etc

After being accepted at a college, these "children" can apply for an F1 visa and enter the U.S. under the terms of the F1 visa. Following graduation, they can find employment by taking advantage of F1 Practical Training which would provide them with a transition to H1 which allows for immigration intent. They can use their time on H1 as a springboard to resident alien status (i.e. obtain a so-called Green Card). After five years as a law abiding legal resident alien, they can apply for their citizenship.

So, clearly, children of illegal aliens do have a clear path to becoming law abiding U.S. citizens.

They just think that the path is too arduous.

'cause they're smart.

'cause people who follow the rules are stupid immigrants.

To counter this while taking advantage of the human capital of people who want to play by the rules, we need real immigration reform now!

Krugman thinks we're all idiots

In a follow-up post to the one I discussed earlier, Krugman shows another product of his chartmanship:

and goes on to ask:

Since some people insist that Estonia's partial — but only partial — recovery from a severe economic crisis demonstrates the wonders of austerity, would they also agree that the evidence below demonstrates the incredible success of FDR’s New Deal policies of promoting unions, raising wages, and increasing government employment?

Nice trick! If you buy that one, I have some bridges in İstanbul that I'd like you to consider adding to your real estate portfolio.

First, note the graph above spans eight years, and it took 7 years for output to reach its 1929 level. But, more importantly, his graph for Estonia was using per capita real GDP.

So, I went and got the GDP numbers from BEA and the population estimates from the Census Bureau, and looked at per capita real GDP for years 1929-1937, setting the 1929 value to 100 as he had done in his Estonia post. In addition, I superimposed the 3rd quarter values for Estonia (again setting the peak, 2007Q3 value to 100) between 2007Q3 to 2011Q3. The chart indicates that Estonia's policies and economic freedom really might have resulted in a faster recovery than the New Deal.

Of course, the future is yet to be written, so we have no idea where Estonia's curve will go next. However, barring huge calamities, the future looks bright for Estonians who have weathered a huge storm less than 20 years after breaking the chains of Russian oppression, and less than a decade after joining the E.U.

Watch out when Krugman shows you a chart

Krugman shows the following graph in his post yesterday:

He then says:

So, a terrible — Depression-level — slump, followed by a significant but still incomplete recovery. Better than no recovery at all, obviously — but this is what passes for economic triumph?

As usual, when Krugman shows you a graph, it pays to look more closely. So, I head over to the Eurostat site he mentions (which, BTW, has the most terrible interface for extracting data) and look up the real GDP per capita index I think he used. I cannot be sure because his graph shows a 2012Q1 value whereas the data I got did not have one for Estonia. However, eyeballing his chart and the numbers I had, I am reasonably convinced I got the same series. While there, I also picked up the one for Greece.

For comparison, I wanted to also show the quarterly real GDP per capita in the U.S. as well. However, BEA or any other place did not seem to have it, so I put together one myself by using the quarterly real GDP series from the BEA and population estimates from the Census Bureau. In doing so, I committed some cardinal sins such as using the April 1st population for first quarter population, and resorting to using projections for 2011. I don't think they affect anything much. After all, the quarterly GDP figures are in billions and it matters little if you divide 13429 by 0.312602730 or 0.312615324.

I wanted to see greater context than Krugman was willing to show, so I went back to the first quarter of 2000. Just like Krugman, I first re-based all three series so that the 2007Q3 value was 100. The third quarter of 2007 is when the quarterly real per capita GDP of Estonia peaked.

Without further ado, here's the picture:

What is interesting, however, is the meteoric rise of per capita GDP in Estonia and the severe fall. Just as interesting, however, is the magnitude of their recovery.

To look at the series in a different light, I put together a chart where I reverted to the 2000-based series provided by Eurostat. For the U.S., I took 2000Q1 to be 100, even though, strictly speaking, that's not correct.

Here, you can clearly see that the per capita purchasing power of Estonians increased by almost 70% in 7 years. In comparison, the total real GDP of the U.S. increased by about about 18% from 2000Q3 to 2007Q3.

Further, the lowest point in Estonia's crash came in 2009Q3. By 2011Q3, per capita real GDP had grown by 13.4%. In contrast, 2011Q3 per capita real U.S. GDP was only 5% higher than its 2009Q3 value, and the 2012Q1 value was 6.5% higher than the 2009Q1 value.

If the quarterly per capita GDP figures I calculated for the U.S. are to be believed, the value in 2011Q3 was only 3.7% higher than the 2009Q3 value.

That is a 0.4% quarterly growth rate in per capita real GDP in the U.S. compared to about a 1.5% quarterly growth rate in Estonia.

So, if Krugman calls Estonia's experience a a … slump, followed by a significant but still incomplete recovery, what does he call the U.S. experience?

P.S. It is important to note that the last Russian troops left Estonia in 1994. When thinking about the incredible increase in real GDP of Estonia, it is useful to keep in mind that it was one of the first countries in the world to adopt a flat income tax which is currently 21%.

A primer on polls for those comfortable with a little algebra

I used to begin my lectures on probability in Intro Stats with the following slide:

Probability is a normalized denumerably additive measure defined over a sigma algebra of subsets of an abstract space.

If I remember correctly, that's a direct quotation from Kolmogorov, but I can't find the chapter and verse right now.

Following it was a flurry of note-taking activity despite the fact that my slides were available on the course web site (and apparently widely disseminated through a bunch of sites in complete violation of my copyrights). Why do people start writing stuff down if they don't understand it? Every time I put that slide up, I hoped someone would yell Well, what on earth does that mean? instead of writing it down, but I was regularly disappointed.

In a nutshell, it means that the concept of probability is a figment of our imagination.

Normalized means it takes on values between 0 and 1. Denumerably additive measure means you can add up the probabilities of a bunch of events in a finite or countable infinite set if those events are mutually exclusive, and I am not even going to begin to try to explain in an intuitive manner what a σ-algebra of subsets of an abstract space means, but you can look it up on Wikipedia, which, if you didn't know what they were to begin with, may not help at all.

The point is, yes, all that sounds like gobbledygook, but when you come down to it, what you need to know to understand what a poll is, and how to interpret its results is actually rather straightforward. It is therefore very disappointing that practically no one does it properly.

Let's take the simplest type of poll question: If the election were held today, would you vote for President Obama?. We'll assume there are only two possible responses to this question: Yes and No.

Note that we are only interested in the answers of people who would indeed vote. We're not interested in the opinions of those who cannot or will not vote. Keep that in mind for later.

We want to say something about the true proportion of voters who would indeed vote for President Obama if the election were held today. Let's call that value p. The only way to know that is to hold an election today. But, the election is in November. So, instead, we do the next best thing, like a cook tasting a small amount of a well-mixed soup to figure out how salty it is, and ask a small number of people.

The key to the validity of any poll is the random selection of its respondents. If you just ask a bunch of people in the neighborhood, or look at the responses to an online poll taken during your favorite talk show host's program, you will bias your poll to reflect the preferences of people whose preferences do not reflect the true proportion of voters who'd vote for President Obama.

If you randomly and independently pick respondents for your poll, each response is what is called a random variable which takes the value Yes with probability p and the value No with probability (1 - p). That's because we assumed those are the only two responses.

You can't do arithmetic with Yes and No, so let's represent a Yes with the number 1, and represent a No with the number 0.

If you ask just one person at random, there are only two possible samples: {1} or {0}, whose probabilities are, respectively, p and (1 - p). If ask two people picked randomly, there are four possible samples: S₁={0,0} (neither person would vote for the president, S₂={0,1} and S₃={1,0} (one out of the two would vote for the president), and S₄={1,1} (both people would vote for the president.

If these two respondents were picked independently, then we can multiply the probabilities of respondents declaring a preference for the president to get the probabilities of obtaining each sample.

If you get S₁, the poll result is 0% support for the president, if you get S₂ or S₃, the poll result is 50% support for the president, and if you get S₄, the poll result is 100% support for the president.

If respondents are picked independently, then the probability of getting two people who would not vote for the president is simply P(S₁) = (1-p)×(1-p). The probability of getting S₂ and S₃ are the same: P(S₂) = P(S₃) = p×(1-p), and the probability that both people would vote for the president is P(S₄) = p×p.

The key point to understand here is that there are two mutually exclusive ways our poll with only two people can indicate 50% support for the president, and therefore the probability that the poll indicates 50% support for the president is P(S₂) + P(S₃) = 2p(1-p).

Just for illustration, let's suppose the president has 80% support. That is, p = 0.8

. Then, we have:

• P(poll shows 0% support) = 0.2×0.2 = 0.04 = 4%
• P(poll shows 50% support) = 2×0.8×0.2 = 0.32 = 32%
• P(poll shows 100% support) = 0.8×0.8 = 0.64 = 64%

Note that the probability that poll will indicate at least 50% support for the president, assuming 80% would vote for him is 0.96, i.e. 96%.

Well, OK, so what? How do we figure out the true probability if we don't already know it?

The short answer is, we don't.

Now, most polls involve about a 1,000 respondents (again, keep that in mind for later, there is a reason for it). There is, as before, only one sample with 1,000 respondents that will give us 0% for the president, and there is only one sample that will give us 100% for the president.

But, there are 1,000 ways such a sample can indicate 0.1% (1 out of a 1,000) supporting the president, a whopping 499,500 ways such a sample can indicate 0.2% support, and gargantuan numbers of ways it can indicate 50% support. You can find the formula on Wikipedia and calculate them using the COMBIN function in Excel, but don't try to count them by hand.

What is nice is we can approximate the distribution of samples using the Normal distribution:

suppose one randomly samples n people out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree will of course depend on the sample. If groups of n people were sampled repeatedly and truly randomly, the proportions would follow an approximate normal distribution with mean equal to the true proportion p of agreement in the population and with standard deviation σ = sqrt(p(1 − p)/n).

We refer to the distribution of all possible percentages that can be obtained from taking random samples of a given size n as the sampling distribution. Right smack in the middle of that distribution is the true proportion of the population supporting the president. Again, we will never know this number until and unless there is an election. What we do know is that about 96% percent of all sample proportions will lie within ±1.96σ of the true population proportion.

Therefore, we can say that the true population proportion p will be within ±1.96σ of the sample proportion about 95% of the time.

We know that σ is determined by the sample size n and the true population proportion p. But we don't know p! What do we do?!

The best information we have on the true population proportion p is the sample proportion, which we'll denote using p′.

p′ is the number of people in our sample who'd vote for the president divided by the total number of people. For example, if 532 people declared they'd vote for him, p′ is 532/1,000 = 0.532 = 53.2%

Our estimate of the standard deviation of the sampling distribution, which is called standard error is then sqrt(p′(1 − p′)/n) = sqrt(0.532*0.468/1,000) ≈ 0.016. Multiplying that with 1.96 gives us the so-called 95% margin of error as approximately 0.031.

Thus, the 95% confidence interval for the population proportion of support for the president on the basis of this poll is 53.2% ± 3.1 percentage points.

This does not mean that there is a 95% chance that the true population proportion is between 50.1% and 56.3%.

The population proportion is either in this interval or it is not. That is, the probability that the population proportion is in this interval is either zero or one. We do not know. We cannot know without holding an actual election today.

What this means is that the confidence interval was constructed using a method such that 95% of confidence intervals so constructed would include the true population proportion.

That's why you do not take the results of a single poll, no matter how properly done, as gospel. If many polls, independently taken, all yield confidence intervals above 50%, your confidence that the true proportion of support is greater than 50% grows. But, a single poll is just that, a single poll.

Now, we can ask interesting questions. For example, what is the probability of getting a poll result of 53.2% support for the president if the true population proportion of support were 49.9%?

In that case, the sampling distribution is approximated using N(0.49, 0.0158). From this distribution, we want the area under the normal curve to the right of 0.532. You can look it up in a table or just use Excel: 1 - NORMDIST(0.532, 0.49, 0.015808, 1) which gives you approximately 0.4%.

What if you had sampled only 250 people as I see on some TV shows, and 133 people (53.2%) had said they'd vote for the president. What is the probability of obtaining such a sample proportion assuming the true population support is 49.9%. The standard deviation of the sampling distribution in this case is sqrt(0.49×0.51/250) = 0.032. Therefore, the probability of obtaining a sample proportion greater than or equal to 53.2% is 1 - NORMDIST(0.532, 0.49, 0.031616451) which gives you approximately 9.2%.

What is the standard error (i.e. our estimate of the standard deviation of the sampling distribution) if the sample proportion is 53.2% with a sample size of 250? That's simply sqrt(0.532*0.468/250) ≈ 0.032. That gives us a 95% margin of error of approximately 6.2 percentage points. Therefore, the 95% confidence interval for this poll would be approximately [0.48, 0.59].

What sample size would have given us a margin of error of only 1 percentage point? That's easy: You'd need about 9,565 observations to give you a margin of error of one percentage point.

Now, you usually do not know what sample proportion you'll get before you take a sample, so usual rule of thumb is to calculate the required sample size using the assumption that p = 0.5. For example, this sample size calculator does it that way. This is conservative because p×(1-p) is maximized at p = 0.5 for p in [0, 1].

Conclusions

1. None of this means anything if the sample was not random and respondents were not independently selected.

2. Also, none of this means much if the correct population was not sampled. The key here is that 1) some people in the U.S. are not allowed to vote (for example, children, non-citizens etc), and 2) some people choose not to vote. Using their responses to judge what voters would do is inappropriate.

3. A 95% confidence interval does not mean there is a 95% chance the true population proportion lies within the interval. It means 95% of all samples will give confidence intervals that contain the population proportion.

4. A national poll does not say much about the outcome of the presidential election given the electoral college system. Individual state polls are much more informative.

5. The poll-taker can do everything right, but if there is an unknown reason that systematically leads some people not to respond to a poll and that factor is related to their political preferences, the poll result does not reflect the preferences of the general voting population.

6. In light of that, exit polls, conducted as voters are leaving polling places, are likely to be the most susceptible to sample selection bias.

That was almost 3/4 of an Intro Stats class all condensed into one blog post.

President Obama wins in Wisconsin

I did not follow the Wisconsin recall election very closely. Thanks to charliespiering, here is a recap of MSNBC's coverage:

Hat tip James Taranto.

President Obama connects with the average American

This is where Obama goes when he's not having a quiet soiree at the White House:

You have to watch that video many, many times until you can fully come to terms with the fact that it is not meant as a joke or spoof.

Employment levels in Massachusetts during Romney's tenure

Mitt Romney's tenure in Massachusetts ran from January 2003 to January 2007. According to BLS series SMU25000000000000001, total employment in Massachusetts' private sector in January 2003 was 3,158,800. The day he month he left office, the employment level stood at 3,198,500.

The following graph shows that employment was falling when Romney was elected and was on the rise when he left: