Flipping Bias

Here's something that should make perfect sense, but most people don't believe. There's no such thing as a biased coin - only a biased toss, if there's a catch. No, not "but there's a catch," literally "if" there's a catch preventing the coin from bouncing or rolling and there is no rotational spin on the flat axis of the coin. The summary of the explanation can be found in Teaching Statisitics by Gelman and Nolan.

"But," you might say, "what if the coin's center of gravity is closer to the head side?" or "what if one edge is heavier?" or "what if it's slightly concave like a frisbee?" Still, the coin is not the source of any bias that results. As long as the coin does not bounce or roll after it lands, it has an equal chance of heads and tails (I've never observed a coin landing vertically on its edge but I won't completely rule it out!). Just think, a coin tossed with only "flipping" momentum spends 50% of it's time heads up, and 50% of it's time heads down. No bounce, no roll, no spin, no bias.

E.T. Jaynes is Professor of Physics (and, as it turns out teaches statistics to physics students) at Washington University in St. Louis. To illustrate, he used a pickle jar (to view this you need GSView for free or some other postscript file, *.ps, viewer), which is top-heavy and concave. Tossing it 100 times without spin, bounce or roll, he got results (p=0.54) that were not statistically different from 0.5 (z = 0.04/sqrt(0.5^2/100) = 0.8 --> P(z>0.8) = 0.424). He also tossed it to favor tails (allowing it to roll) and to favor heads (by appling rotational spin to it). When it was tossed in a way that made it roll, heads came up zero out of 100 trials, and when it was tossed with rotational spin, it came up heads 99 times.

So, the moral of the story is this. I've discussed before the notion of bias in flipping one versus two discs to determine the pull preceding an ultimate game. This tells us that the disc (uneven as it might be) is not biased unless the tosser applies bias. If the bias in the tosses is the same, then even is a dominant choice, even if the direction of the bias is unknown (but it should be known if you see the toss - will it spin or roll?). This can be proven as long as you know that the area of a square is more than the area of a rectangle with equal perimeter, i.e. it can be shown that p^2 + (1-p)^2 >= 2p(1-p), with equality only at p = 0.5. However, that point is now moot. If the tosser is not manipulating the toss, any single flip (heads or tails) and any double flip (odd or even) has "fair odds."

I'm convinced. Hope you are too.

Government's Net Worth?

This got me thinking:


US To Trade Gold Reserves For Cash Through Cash4Gold.com

What exactly is the net worth of the US Government? Yes, the deficit/debt are large, and should be reduced, but how much is the stuff lying around that belongs to the public (land, fighter jets, buildings, etc.) worth? Anyone know of a place to try to get a ballpark for this information?

The Income Distribution Argument

I'd like to propose that the main hubub about health care is about distribution of income, i.e. a shift in the burden of health care from a "benefits received" principle to a "ability to pay" principle. To make any sort of shift like this you have to accept the principle that health care has certain characteristics attributable to a public good (something whose provision is non-excludable and benefits us all) or a merit good (something worth making more universially accessible). These premises are debatable, but I won't deal with them. Let's just suppose that we shift from fully individual, private-paid to fully public-paid (this is, of course not the change that would really be taking place because our current system is not fully private-pay, and no proposal on the table is fully public-pay).

There's not much reason to believe that the financial costs will be too much higher in public-pay as they are in a private-pay system, at least not per-person. But a private, free-market system tells me that if I want 10,000 dollars of benefit, I pay 10,000 (actually, since these contracts are not usually "actuarially fair" it would be more like paying 10000 and getting 8 or 9 thousand). Same goes for everyone else. This is a very "fair" stystem in terms of "benefits received," i.e. what you put in is what you get out.

Unfortunately, there are a lot of people who don't have the dough for 10,000 of health insurance, and there might not be a lower-priced option they can afford. Besides, if there is, it might not cover a lot of things or have a really high deductible (in fact the deductible might be so high that if they ever got so sick that their costs ever required insurance, it might put those same folks into bankruptcy - 68 percent of all individual bankruptcies are heath care related - anyway, so why bother!). This adds to the dimensions of adverse selection and moral hazard typical to the insurance market. Another "fairness" metric is a person's "ability to pay." If a good has "merit" qualities, and some folks cannot afford even a minimal level of it then what you pay is could be indexed to what you earn. Everyone gets 10000 in benefits, but a rich person pays 15000 or more, and a poor person pays a 5-6000. But is it "fair?" Yes, in a manner of speaking, because if we agree that everyone "should" have 10000 in basic coverage, then we wouldn't expect a person earning just 15000 a year to pay 10000 of it to for health insurance. (N.B. At moments like this I almost wish I remembered the game-theory formal notational definitions of "fair" and "envy-free," as well as the proofs for why Walrasian (free-market) equilibria do not generally exhibit this property....almost.)

Here's where I think the income distribution question slips in. Basically, the fight is this: Republicans represent rich folks, and Democrats represent poor folks. Making health care universal will necessitate a higher burden on richer folksto provide a benefit for poorer folks who cannot afford it. The poorest already get medicaid. Median wages have fallen over the last 9 years. Private health care costs are rising. Households view health care as a necessity. Somthing's gotta give. I suspect that if the Bush economic record were more favorable to the middle quintile of the income distribution then the "get costs under control" rhetoric would have been more effective, but rising health costs coupled with falling middle-class incomes means most people are wise enough to know that cutting costs around the edges won't do much. So, let's look at a couple of the proposals:

1. Sort of the two-tiered "keep what you want if you like it" option. People happy with their stuff now get to keep it but you still pay a percentage of your income into the public system. Of course, they will have to help pay for the publicly funded option, so their costs will either go up, or their coverage will change (by moving into the public pool). Poor people could get covered even if they cannot pay for it themselves, or can only afford a small portion of the burden. This would be a little like the education system, which, of course, is not perfect either.
2. Fully public "single-payer" system. This abandons the private option, and everyone receives the same basic plan. However, payment is based on a percentage of your income, thus shifting the payment burden up the income distribution even farther.
3. "Tax Credits." Rich folks love this option. Being able to deduct health care from their taxable income is great for them for two reasons: one, they all purchase health care anyway; and two, they pay a higher marginal tax on the income they get to deduct. This option would actually be MORE regressive than the current system (and if you think the revenues to make up for the "credit" are growing on trees you're crazy!). Good God, if you believed the republicans you'd think that tax cuts are could discover a cure for AIDS and build moon colonies, but guess what? They won't insure more people.
4. Stay with what we have and try to curb costs. Either way cost-efficiency needs to be addressed. Pulling more people into the pool for normal coverage might cut some costs per-person, but might increase costs in the aggregate, so this might not be such a bad thing.

Unless you believe that health care is a merit good, there will probably continue to be 12-15% of the population uninsured, and a growing percentage who are underinsured.

Markets and Health Care

It's not at all clear what the "best" solution to the current health care problem is. Of course, if the market were competitive and well-functioning, the "most efficient" thing to do would be to just price it and let people choose whether or not they want it.

Sounds great, but that's problematic. People choosing whether or not to get health insurance might know somewhat more about their own health histories than the insurer does, and try to game the system. People who think they're healthy might try to go without health insurance, or maybe alternate their decision so that they get it one year and not the next and so on. (In fact, a lot of people do this with the optional vision or dental coverage in their current health plans.) This gaming of the system by "healthy" people would drive up the price of insurance for regular subscribers because the insurer would know that those people are less healthy on average (or have an informed guess to that effect). That's why as a compulsory subscriber to a group plan most folks "pay" (between themselves and the portion that their employers pay) about $10,000 for insurance, whereas the on the individual market prices run about 15,000. Also, when "healthy" non-subscribers get "unlucky" (which some inevitably will) their reliance on urgent care drives the costs up even more for everyone, including subscribers.Thus, since there is incomplete information, adverse selection, etc., markets don't do the job all that well.

The employer-based system we have now is pretty good, in the sense that it resolves most of the adverse-selection problem by pooling subscribers according to something roughly independent of the quality of their health (i.e. subscribing everyone according to where they work rather than whether they voluntarily enter the insurance market). This does reduce costs, but this system is flawed, too. It distorts labor markets (giving some firms an incentive to move operations to Canada, Mexico, or Asia) because health benefits can comprise up to 30% of the labor cost for some lower-skill occupations. Not only that, but if you can only find part-time work or lose your job, you become uninsured, too (or face the higher prices of the private insurance market discussed above). Mandates might resolve this (we do this for auto insurance, by the way), but people are afraid of this option because some folks are likely to not be able to afford the cost.

That sort of brings us to the current debate, which is more about income distribution than anything else. It represents the classic trade-off between equity and efficiency in drawing up economic policy. It also brings the issue of "public goods" and "merit goods" into the debate. While there is little argument that health care is really a "public good," it may be a "merit good." I'll think about the distributional effects of "reform" tomorrow.

Trust the Producer?

Even in well-functioning, reasonably competitive markets, I cannot think of an economist who would simply say "trust the producer to tell you how much should be consumed and at what price." I don't walk into Walmart and say "tell me what I need this week and we'll pay for it," and neither do most people. But that is exactly the argument some people make about health care. With this propaganda coming out, no wonder prices are so high!
Point 1: The market for health care is one that is inherently prone to imperfect information. In some ways, patients know more about their health and their habits, but doctors know more about their diagnosis and treatment. In fact, doctors specialize in knowing more about things that are wrong with you, so we really don't wand to correct the problem by making patients 100% informed (that would be prohibitively costly). There needs to be some sort of external regulator here.
Point 2: Health care is already rationed by bureaucrats, and we wouldn't have it any other way. Private insurance has armies of bureaucrats that determine what types of procedures and what costs will be approved for your care, not your doctor. If they didn't do this, you wouldn't be able to afford health care.
Point 3: Lots of people have public insurance already, and actually prefer it to being thrown out on the market for private insurance. Most people who are eligible for Medicare, VA benefits, or TriCare (and do not have any employer-provided benefits) happily take these benefits. Even the bureaucracy doesn't seem to bother them that much. In fact a lot of the most expensive patients in the system are already paid for using tax dollars.
Point 4: Private insurance is much more costly per person than being part of a group plan because insurees in the private individual market are adversely selected. Mostly sick people choose to be insured in this corner of the market. Healthy people in this part of the market who don't have insurance sometimes get very unlucky all of a sudden, and their urgent-care costs drive up costs for others.
Point 5: Private insurance premiums are not "actuarially fair" in economic terms. In other words, the premium i pay them exceeds the total expected cost of providing care over the entire pool of insurees. In other words, insurance companies make "economic profit," which should be distinguished from "accounting profit," or "proprietors' income."
I'm not sure if single-payer is the way to go, but the total net cost probably won't go up too much. If you think of the labor cost your employer pays in health insurance as wages you're not getting, it's outrageous! Between my employer and myself, I already pay about $10,000 per year! If that money simply shifted from my BC/BS to the government, and I got a comparable level of care, what does it matter? Bottom line: it's not patients and doctors who decide things now. Bureaucrats already decide and will continue to do so regardless.

Uh, Yeah.

Hmmm

Charging your cell out of thin air?

Egg-cellent Hotel Cooking

Speaks for itself.

This Ain't True, Neither!

The other way of saying "a near-doubling of the U.S. price level over the next decade" is "The value of your savings will be cut in half over the next 10 years."

Uh, no. That would only happen if you stuffed your entire savings under a mattress in cash. And his "hyperinflation" of 7% was actually meant to be a scare compared to what he calls an "uncomfortable 5-6%. What a stooge.

Blodget-Flation

OK. I won't mention the fact that Henry Blodget was charged with securities fraud, and settled for $4m. in penalties and a ban from ever trading again. Oops.

Starting over, he's been worried about "hyperinflation," but he doesn't know what hyperinflation is. That, or he can't do math. By "math" I mean the simple arithmetic involved with the finance "rule of seventy." I'm worried about hype. Anyone with an undergrad B-school degree should know the Rule of 70, which approximates an asset's doubling time (here goods prices). Blodget fears high-end estimates of inflation meaning prices doubling in 10 years. Specifically, Years to double = 70/rate of change. Since exponential growth is not linear (hey, it's exponential in fact!) it's only an approximation, but it's a decent one as they go. So, some very elementary algebra tells us that prices doubling in 10 years means 7% inflation annually. Uncomfortable, but not "hyper." By contrast, hyperinflation is usually reserved for situations like Argentina in the mid-80s (about 650%, or doubling every 39 days) or Weimar Germany (3,000,000%, or doubling every 5 days or so).

To say doubling in 10 years is hyperinflation is simply false. Prices in the US more than doubled between 1973 and 1982, and while it was uncomfortable, it was not "hyper."

Trade is Dead. Long Live Trade!

Is free trade passe?

Summer Thoughts

Interesting, but not really answering the more relevant question, which is, "why has a long summer vacation persisted?"

A greener middle class

Like any new thing, green is not something that people are going to care much about until it is economical and practical for the middle class on the demand side (that, in large part is why the industrial revolution took off in UK, some have argued). So, this is a neat little piece.

Water, Property, and Conflict

Since water is the driving force behind Darfur, it's interesting to see how water rights get defined. This is sort of an interesting legal change. Is rainwater a public good that should be regulated or is what falls on your own property your own? How far can you go to keep it for yourself instead of letting it feed streams and riverbeds?

Multiple equilibria

Check this out.
Equilibrium One: No Dancing
Equilibrium Two: (Almost) Everyone Dancing
Purturbation: One person dancing
Result: Cascade

Talk is Cheap

China puffed its chest out with a call for a "new reserve currency." Never minding the fact that China was never forced to buy dollar-denominated assets with its surpluses, and a collapse of the dollar appearing to be most harmful to US creditors, there is some interesting analysis from Free Exchange. Developing countries' actions belie the notion that they are not willing to finance our debt. It's even less clear that our total net external debt is increasing (public debt is increasing but private debt is decreasing). If emerging markets do have "a greater incentive ... to move to a new system," the question I ask is: move to what, and how?

Not In My Back Yard!

I don't want seniors coming to my community, driving up real estate prices, inflating health care costs, and driving 18 miles per hour in a 35 zone (for the love of god, it's the skinny pedal on the right, granny!). Go to India! It's low-rent, good care, and apparently 'In India they really like older people.'

Macroeconomists' dirty secret

The first six or seven paragraphs and the last 2 or 3 are pretty interesting. I don't think I buy the crap in the middle about racism and chauvinism holding together the era of shared prosperity. But, it is the cato institute, so what do you expect them to do? Blame Reago-Bush-onomics? 

Macroeconomists' dirty secret

How bout this. Interesting how Levitt talks about a dearth of macro data for testing current macro models. But here's a dirty little secret: most current macro models cannot be tested empirically because they are founded on Walrasian equilibrium concepts, which, at least as of the time I was in grad school just a few years ago, could not be identified econometrically.

Anyone want to put my name on their AER paper?

Saw this today. If anyone out there has bonuses for getting your papers in top fivers like the ones here, and wants to put my name on their submissions to AER, I'd probably willing to pay the $7,000 shadow price of a deadbeat co-author implied here.