John Cochrane of Chicago has an exceptionally sensible op-ed in the WSJ on who should be buying stocks now and who shouldn’t.

Categories: Economics Tags:

## A Contraction for "Here are"

I was just writing an email and wrote “Here’s my notes.” Since “notes” is plural, that’s incorrect, and I should say “Here are my notes.” A contraction fit the spirit of the email better, though. In speech, I say, “Here’re my notes.” I wonder if other people do? If they do, then “Here’re” is a legitimate contraction.

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## When Does Human Life Begin?

A hard puzzle in abortion policy is when “human life begins”. Is a one-celled embryo a human? Is an 8-month fetus a human? Is a 2-year-old a human?

How about if we approach the question from the other end. When does human life end? When is someone dead? It could be when his heart stops, but people do get revived often from that state and we don’t call it resurrection. It could be when his brain activity stops, and I think that is the common criterion.

If the criterion for lack of life is lack of brain activity, then the one-celled embryo is not alive. Rather, we need to ask when a brain begins, and when it becomes active. A pro-abortion blog that discusses the brain criterion says that brain activity starts much later than the brain itself is formed, at 21 weeks, which is 5 months. The same blog says anti-abortion people claim the time is 10 weeks (which sounds more plausible to me, and even rather late).

November 18. Another approach would be to ask when an embryo has blood. Blood has special significance in the Bible. This webpage doesn’t mention blood specifically, but it implies the embryo has blood somewhere in the 8 to 21 day range. There is a brain at 29-35 days, and brain waves at 40 days. In Arizona, at least, in 2007 of 10,486 abortions, 3,032 were at 6 weeks (42 days) or less. 102 were at 21 weeks or more.

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## Shaggy Mane Mushrooms

On Sunday we finally stopped to look at the coprinus mushrooms that we’ve seen growing at the intersection of Route 45 and the road to church. I jumped out and picked some. They are shaggy mane mushrooms, which apparently do not poison you if you drink alcohol, though they are closely related to those inky caps

Today we at some of them. They had all opened up, and some had deliquesced completely. Fried in oil (after being cut up, each into 3 or so pieces) they were okay. Amelia, Ben, and Lillie tried them with me. Faith said “Like it!” which means “I don’t like it!” The black ones are a bit bitter and too tasty. I think the books are correct that they are best while still white. They turn pink before turning to ink.

November 14. More had come up by now. Benjamin and I picked the young ones, and I made soup with them chopped up with milk, pepper, salt, butter, milk, and dried onion flakes. They are better in soup than fried. The soup was an interesting gray-black color.

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## C0, C1, and C2 functions

From Wikipedia’s Smooth Functions:

“The class C0 consists of all continuous functions. The class C1 consists of all differentiable functions whose derivative is continuous; such functions are called continuously differentiable.”

A differentiable function might not be C1.
The function f(x) = x^2*sin(1/x) for x \neq 0 and f(x) =0 for x=0 is everywhere continuous and differentiablem, but its derivative is f'(x) = -cos(1/x) + 2x*sin(1/x) for x \neq 0 and f'(x) =0 for x=0, which is discontinuous at x=0, so it is not C1.

Categories: math Tags:

## The Chronology of the Crucifixion

November 9th, 2008 1 comment

Pastor Bayly preached a good sermon on Matthew 26 today, the chapter were Jesus tells the disciples at the Last Supper that one of them will betray him. Some ideas:

1. Judas must have been particularly trusted, since he was in charge of the money. He must have thought that he had no time to spare in betraying Jesus, once Jesus had said one of the disciples was to betray him.

2. The Last Supper was not the Passover meal. Passover was to start the next evening, when the Passover meal would be served. The Last Supper was during the Day of Preparation, when the lamb is killed. Jesus was to be killed that day, and there would be no more Passover meals. The Last Supper instituted a substitute.

3. When the Gospels speak of “the Sabbath”, they don’t necessarily mean a Saturday. Instead, they might mean a special day of rest, such as Passover or Yom Kippur. That was the case here.

Categories: religion Tags:

## Where McCain Did Better than Bush

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## A Good Photo from Mr. Lileks

Categories: art Tags:

## The Weirstrass Function

 The Weierstrass Function

From Wikipedia’s Weirstrass Function comes this good graphic of an everywhere continuous but nowhere differentiable function.

Nov. 9. I wondered about the following questions:

Do there exist monotonic functions that are everywhere continuous but
nowhere differentiable?

Do there exist monotonic functions that are nowhere continuous?

No in either case, it seems. Here is an answer:

First, monotone functions only can have a countable number of discontinuities (since these must be jump discontinuities where the function makes progress upward/downward and all uncountable positive sums are infinite).

Moreover, for a more involved reason, the set of points where a monotone function is not differentiable must have lebesgue measure 0. (I.e. they are differentiable almost everywhere.)

One way to see this is from the fact that for an increasing function the limit of the slope of the secant line between (x,f(x)) and (x+h,f(x+h)) for each fixed x as h varies must always exist (and be nonnegative), provided we allow it to also take on the value +infinity. Then one can show this cannot be infinity except on a measure 0 set…again, the function would make too much progress.

On the other hand, the derivative can not exits on an uncountable set (e.g. the Cantor staircase function). Moreover, there is a slightly more sophisticated example of a strictly increasing continuous function that goes from f(0)=0 to f(1)=1 which has a derivative equal to 0 almost everywhere, in fact whenever the derivative exists.

Since they are differentiable almost everywhere, the derivatives of monotone functions are Lebesgue integrable functions (extend to the nondifferentiable points however you want, it won’t affect the integral). So the previous example shows that the Fundamental Theorem of Calculus cannot be extended to even the class of derivatives of continuous monotone functions (even when the resulting derivative function is the constant function), since then we would have 0=\int_01 f'(x)dx=f(1)-f(0)=1. (The FTC does work, however, if f is continuous and the derivative exists except at a countable set).

From PlanetMathm here is Cantor’s Staircase (in a 20-iteration figure, instead of infinite iterations), which uses a Cantor Set to build a function which is continuous and monotonic (strictly?) but with f'(x) =0 almost everywhere.

 Graph of the cantor function using 20 iterations
Categories: math Tags:

## Voter Turnout Same in 2004 and 2008

Via Drudge, this CNN news account of a serious academic analysis says that voter turnout nationwide was about the same in 2008 as in 2004. More Democrats turned out, but fewer Republicans. That’s interesting. It makes sense. Obama had lots of money for turning out voters, and lots of special enthusiasm perhaps from blacks who would not otherwise vote. McCain was not inspiring.

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## Nikkei 1989, Dow 1929, Dow 2008

Key Trends in Globalization looks like a good weblog. It has a very nice post comparing te current stock price decline to 1929-33 in the US and the 90s decline in Japan. During the Depression, the Dow dropped about 90%. The Nikkei has dropped about 80%. Both declines took place over a long period of time.

Categories: Economics Tags:

## The Optimal Savings Rate

Some people think that although people make efficient decisions about how much to save personally, the social discount rate we use is too low. The market gets it right, but government does not. I think the opposite is true.

Individuals are too eager to consume in the present instead of the future. Think of a person as a sequence of selves over time. Most people are selfish and favor the present self over the future self. They save too little.

On the other hand, when it comes to decisions across generations, we have to remember that future generations will be richer than we are. Thus, we should not incur too much cost now in exchange for benefits for them later.

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## Taxing the Rich and National Savings

Now that Obama has won, it is time to start thinking about raising taxes on the rich. I wonder what that will do to the saving rate?

This is trickier than I thought. It might be that net saving by the rich is more than 100% of net national saving, if government and the poor are net borrowers. In that case, our national savings rate could actually go negative as the result of even a 5% increase in the marginal tax rate on the rich.

Categories: Economics Tags:

## Policy Predictions for After an Obama Victory

JD emailed me this good list of policy predictions for after an Obama victory.



I predict we will see activity along the following lines, although I
don't expect Obama to get all of it (and this is hardly a
comprehensive list):

1.      Reinstate the "fairness doctrine" to shut down conservative
2.      Enact pro-union legislation, like card check, forced
mediation, anti-right to work laws.
3.      Higher capital gains tax, no extension of Bush tax cuts,
increased social security taxes by lifting or removing limit on
taxable income, no decrease in corporate income tax, reinstatement of
the estate tax, higher marginal tax rates

4.      Huge (and ineffective) subsidies for users and consumers of
alternative energy; no meaningful relaxation of restrictions on
drilling for oil and gas; no meaningful promotion of nuclear power;
increasingly severe restrictions on coal-fired power plants; cap and

5.      Use of tax money from top 5% to make welfare payments (will be
labeled tax credits) to non-income tax payers.
6.      Appointment of very liberal judges.  The Democrats have been
much worse than Republicans in stalling nominations. The floodgates
will be opened.

7.      Reversal of tort reform measures enacted nationally and in
states over the past 10 years.  Expect class action lawsuits seeking
to bankrupt new industries -- guns, fast food.

8.      Reduced defense spending.  Halt to development of anti-
satellite weapons and defensive missile shield, no development of new
bunker buster, no movement to test old weapons, no increase in the
size of the navy.

9.      More race-based entitlements, including reparations (pushed by
his supporters more than by him - but won't pass); changing of
criminal laws deemed to disproportionately affect minorities; more
race-based hiring and contracting decisions at the government level
and more effort to impose affirmative action in the private sector.

10.     Witch-hunt investigations by Congress of the previous
administration to settle old scores and of businessmen as part of the

11.     More campaign restrictions against fund-raising avenues deemed
most favorable to Republicans.  Shakedown of businesses for money to
fuel Democratic coffers.

12.     Continuation of policy of increased involvement in
Afghanistan, but will choose ineffective tactics and won't get allies
to help. "Chickenhawk" approach.

13.     Continuation of Bush appeasement policy of Iran and North
Korea.  Iran will get nuclear weapons under Obama.  North Korea will
continue to be a threat and may implode.

14.     Shift away from Israel to Arab nations.  Increased tolerance
for terrorist activity and for domestic organizations with a history
of supporting terrorists (e.g. CAIR).  No material improvement in
homeland security. Weakening of the Patriot Act (or reduced usage of
its provisions).  More rights granted to terrorists.

15.     Amnesty for illegal aliens.  Reduced enforcement of
immigration laws.  More benefits to illegal aliens.  Work stopped on
fence with Mexico.

16.     No new trade agreements.  Don't know if he will seek to reopen
Nafta -- huge step, may not be that bold.  Increased hostility to
Colombia and other allies.

17.     Socialized medicine -- less drug innovation, long waits for
medical care, weeding out of people too expensive to treat, limited
option to opt out in favor of private medicine, fewer improvements in
technology and slowing in the spread of technology, less incentive for
qualified people to become doctors

18.     No reform of medicare or social security (except for higher
taxes on "wealthy")
19.     Continued assaults on Wall Street, drug companies, oil
companies.  Do not expect any major new drugs for many years to come.

20      Continued bailouts of politically popular industries, such as
auto.
21.     Taxpayer bailout of homeowners who won't pay their mortgages.
Lenders forced to rewrite contracts.
22.     No strategy to deal with resurgent Russia and strengthening
China.
23.     National promotion of gay marriage.
24.     Reduction in limits on harvesting eggs and cloning for medical
research.
25.     Increased financial and regulatory burdens on setting up
charter schools.
26.     No rush to reduce government equity stakes in financial
companies.  Use of this control to make capital allocation decisions
based on politics, not economics.


Categories: obama Tags:

## Redistribution and Forced Saving

I was just thinking about Obama’s plan to increase taxes on the rich, and the recession. Contrary to what some people say, the tax increase won’t worsen the recession. Rich people save a lot, so taxing them during a recession is not especially bad. It will reduce longterm growth, though, by reducing national saving.

If you think that people–rich and poor– do not save enough, then maybe you should oppose this tax cut. It would be better to redistribute towards the rich, so saving will go up.

Categories: Economics Tags:

## Punctuation: The Possessive of Lists

November 3rd, 2008 1 comment

The rule for punctuation of the possessive of items in a list is that you put the “‘s” only after the last item (source, e.g.
this site). Thus:

“I went to John and Mary’s house.”

“I went to John, Mary, Joe, Andrew, and Matilda’s house.”

That sounds right too.

Categories: writing Tags:

## Surviving versus Living

…Medical care is usually about maximizing time itself, about keeping the patient’s heart beating as long as possible. But time isn’t what I want to maximize. Longevity is fine, but life is what matters. And those two words are definitely not synonyms.

Which leads to a crucial characteristic of chemotherapy, at least as I’ve experienced it. Chemo is a strange beast: it restores life by first killing it….

“Killing” is the right word. Forget the many side effects that are too gross to describe. Chemo drains the life from its recipients. …

… I’ve read and heard a good many stories of stage 4 cancers over the past few months, and in more than a few of them, the patient spends his or her last years—the number of years can be considerable—oscillating between yet another surgery to remove the latest tumor, and more months of chemo to slow the cancer’s spread. They call it “extending life,” and sometimes, that’s what the treatment does—but other times the label misleads; patients survive but don’t really live. Which is why this week’s news seemed so joyous: my oncologist told me that, when I resume chemo after this summer’s thoracic surgery, the dosages of the drugs can be dialed back, and if I so choose, dialed back a lot. Thanks be to God: I can do more than survive; I still have some living to do. Before I heard that news, I was starting to wonder.

… Doctors see their job as fixing the broken places in our ailing bodies. When it comes to the kinds of brokenness that can be repaired, that is as it should be. But there is another set of medical problems that cannot be fixed: cancers that won’t disappear, pains that will last as long as life does. When it comes to those problems, repair is not the proper goal. A better word is redemption: the enterprise of carving out some space, however small, for life—not mere survival—in the midst of diseases that seek to squelch it.

Oncologists are better on this score than most doctors, probably because they see the destructive character of the treatments they administer up close. Even so, the tendency to equate success with survival is strong. Too much so, I think: that tendency needs resisting. I suspect I’m far from alone in saying that survival holds little appeal for me. I want to live—for as much time, or as little, as I have left.

That mind-set follows naturally from my faith, I believe—but a good many of my fellow believers seem to disagree. One of the more surprising aspects of Christian culture in our time and place is the widespread embrace of longevity and survival not just as moral goods, but as moral imperatives. That embrace seemed all too evident in the Terri Schiavo controversy of a few years back, and in the long-running conversation about medical treatment of dying patients. I’m no fan of euthanasia, but I’m also no fan of the idea that physical longevity is a morally proper goal in circumstances like Schiavo’s—or in circumstances like mine. Just because medicine can sustain the body for awhile longer, that doesn’t mean it should always do so. Life is more than a beating heart. And life is what we should be seeking. The good news is, if you look in the right places, it’s usually there to be found.

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## A prettty picture

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## Live Birth Abortion

Cranmer has a post on live-birth abortion, the kind Obama is notorious for supporting while an Illinois legislator.

It is a termination process which involves the birth of a live baby, the issuing of a birth certificate, the purposeful abandoning of the baby to a slow and tortuous death, and the callous issuing of a death certificate….

By law, if an aborted baby is born alive, both birth and death certificates must be issued. Ironically, the cause of death often listed for live aborted babies is ‘extreme prematurity’, which amount to a confession by doctors that they have caused this death. It is not uncommon for a live aborted baby to linger for an hour or two or even longer. One baby is reported to have lived for almost an entire eight-hour shift. Many of these babies are born completely healthy, for they are terminated at 40 weeks for the ‘health’ of the mother, and also in cases of rape or incest. Ever since Doe v Bolton (the companion case to Roe v Wade) the United States Supreme Court has adopted the definition of the World Health Organisation for ‘health’, defined as ‘any condition that might impact her physical, emotional, psychological or financial well being’.

So live birth abortion is permitted in many US states up to nine months for emotional (can’t cope), psychological (don’t want to cope) or financial (can’t afford it) reasons, effectively extending abortion to on demand.

Nov. 2. H.U. referred me to Robert George’s Obama’s Abortion Extremism. It’s a good summary of Obama’s positions, and also a good summary of various laws pertaining to abortion and embryonic research about which people disagree.

Categories: obama Tags:

## Persimmons

Yesterday I went jogging with L. and F. in the stroller and B. on his bike. We went to the persimmon tree on Sare Road. All the leaves but only a few fruit had fallen, and they were ripe and delicious. Persimmonpudding.com is a website devoted to persimmons.

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## Subsidiarity and Hierarchies

The idea of “subsidiarity” came up today at a church meeting. The idea is that affairs ought to be handled at the lowest, most decentralized level. An individual congregation, for example, and not the denomination ought to discipline church members. The term is a Roman Catholic one.

The discussion made me think of the following problem. Suppose we have a worker who is misbehaving. It makes sense for his immediate boss to discipline him, since the boss knows the situation best. His immediate boss, however, likes his employees and is reluctant to bear the emotional cost of intervening. Thus, it may actually work out better to have the top boss– or some central committee– begin the discipline process. Perhaps the immediate boss can then handle details, having been positioned as the friend of the worker rather than as the “tough guy”.

This reminds me of the style of hierarchy models in economics. I’m not sure whether modelling is useful here or not.

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## Hydrogen Bonds

H. was asking me why ice floats in water– that is, why solid water is lighter than liquid water. The answer has to do with hydrogen bonds. When hydrogen and oxygen form a molecule together, the hydrogen’s lone electron is pulled toward the oxygen, so the other side of the hydrogen has a positive charge from its lone proton. This positive charge is attracted to the negative charge of another oxygen atom’s electrons, forming a hydrogen bond. Well, that’s my simple story.

The Edinformatics article on ice is good. It has pictures too. It explains that in ice, the hydrogen bonds hold the water molecules apart in a lattice with lots of space, but in water, the molecules do not have such orderly hydrogen bonds.

Here’s what Edinformatics’s article on hydrogen bonds says:

As the name “hydrogen bond” implies, one part of the bond involves a hydrogen atom. The hydrogen must be attached to a strongly electronegative heteroatom, such as oxygen, nitrogen or fluorine, which is called the hydrogen-bond donor. This electronegative element attracts the electron cloud from around the hydrogen nucleus and, by decentralizing the cloud, leaves the atom with a positive partial charge. Because of the small size of hydrogen relative to other atoms and molecules, the resulting charge, though only partial, nevertheless represents a large charge density. A hydrogen bond results when this strong positive charge density attracts a lone pair of electrons on another heteroatom, which becomes the hydrogen-bond acceptor.

and

In ice, the crystalline lattice is dominated by a regular array of hydrogen bonds which space the water molecules farther apart than they are in liquid water. This accounts for water’s decrease in density upon freezing. In other words, the presence of hydrogen bonds enables ice to float, because this spacing causes ice to be less dense than liquid water.

Someone else says:

The hydrogen bonds that form between water molecules account for some of the essential — and unique — properties of water.

* The attraction created by hydrogen bonds keeps water liquid over a wider range of temperature than is found for any other molecule its size.
* The energy required to break multiple hydrogen bonds causes water to have a high heat of vaporization; that is, a large amount of energy is needed to convert liquid water, where the molecules are attracted through their hydrogen bonds, to water vapor, where they are not.

Two outcomes of this:

* The evaporation of sweat, used by many mammals to cool themselves, achieves this by the large amount of heat needed to break the hydrogen bonds between water molecules.
* Moderating temperature shifts in the ecosystem (which is why the climate is more moderate near large bodies of water like the ocean)

Categories: science Tags:

## The Risk of Common Investments

I’m frustrated by how we economists have failed to incorporate most of wealth into our theory of asset pricing. The CAPM says that a stock needs a higher expected return if its return is more correlated with the return of the stock market as a whole. That’s a good start. It is true, too, that it is possible to hold a diversified portfolio of public stocks, whereas other assets such as private business stock can’t be held by everybody.

I worry about other assets. How about bonds? Surely they should be in the CAPM, since they are public and easily diversified into.

How about housing? That’s the asset most people hold. And it isn’t valued well by economists. It is a hedge against housing consumption risk. If rents rise, then if I own my house, I am insulated. But when I sell my house, I do face risk. Also, if rents rise, maybe I’d like to consume less housing. The optimal house ownership contract isn’t what we normally observe. It would involve some insurance against resale capital gains and losses, and adjustment for desired amount of house consumption.

How about labor income? Labor is our greatest wealth– human capital, and just plain labor endowment. It’s risky, and the risk is correlated with the stock market. I’d like a stock that does well when my salary goes down.

The Consumption CAPM is an advance. It notes that we want to have higher stock returns when we want higher consumption. That’s odd, though, because consumption is endogenous. Really, we ought to look for the correlation between a stock’s return and the return on wealth as a whole, which would be the ratio of GNP to wealth. We should look for the correlation between GNP and stock return, not consumption and stock return. But no, that’s not right. Ideally, we’d want the change in total wealth, including labor wealth, which is not the flow of GNP, but a change in a capitalized value of future GNP. I’d like a stock which is uncorrelated with other stocks, and uncorrelated with changes in the value of my labor.

There’s another problem. THe price of stocks is determined by the kind of people who buy them. Poor people don’t. The only labor wealth that matters to stock prices is that of the people who buy stocks. So what we want to measure is the value of public stocks, bonds, private companies, housing of people who hold stocks, and labor wealth of people who hold stocks.

Categories: Economics Tags:

## Quasiconcavity

Martin Osborne has some good notes on quasiconcavity. I’m still not satisfied, though. It’s a basic enough idea that I wish I had better intuition for it, and lots and lots of pictures of functions that are or are not quasiconcave.

October 25: Here are some key features of a quasiconcave function f(x).

• It has convex upper level sets. The set of points x such that f(x) >= a is convex for any number a.
• It has convex indifference curves if it is a utility function. If f(x) is strictly monotonically increasing, the function g(x) such that f(x)=a is a convex function.

Every concave function is quasiconcave, but some quasiconcave functions are not concave. A key feature of quasiconcavity that concavity doesn’t have is that if you do an increasing transformation of a qc function, it is still qc. I wonder if the following is true:

Conjecture: Iff function f(.) is quasiconcave, there exists an increasing transformation g(.) such that g(f(.)) is concave.

I’d start to prove the conjecture this way. Let x and y be points in the upper level set of f(.), which means f(x)>=a and f(y)>=a. Since f(.) is quasiconcave, the upper level set is convex, which means that f(mx+ (1-m)y) >=a too. What we need to show first is that there exists some increasing function g() such that
g(f(mx+ (1-m)y)) >= mg(f(x)) + (1-m)g(f(y)). I think we need to start by assuming that f(x) \neq f(y), and that they are both on the boundary of that convex upper level set. Then we can see how g has to affect those two levels of f differently.

If the conjecture is true, then maybe we can think of quasiconcavity as being the equivalent of concavity for functions that are just defined on ordinal, not cardinal spaces.

October 26. Why, though, do we worry about quasi-concavity at all in economics? Why not just assume that utility functions are concave? The conventional answer would be that utility is ordinal, not cardinal. That is a bad answer for three reasons. First, even if it is ordinal, we could say, “It’s only the ordinal properties of a utility function that affect decisions. Therefore, for convenience, let’s say that whatever function you start with, you have to use a monotonic transformation to make it concave before we start working with it.” Second, we might say, “Since only ordinal properties matter, let’s assume utility is concave for convenience.” Third, we might accept cardinality. Everybody uses von-Neumann Morgenstern cardinal utility in their models anyway, making only a brief nod, if any, to ordinality. But a risk-averse agent has concave utility. For these reasons, I wonder why it’s worth making our graduate students learn about quasi-concavity. The opportunity cost is that they’re not learning about something more useful such as the CAPM or the Coase Theorem.

Maybe quasi-concavity comes up in enough other contexts to be important. I know Rick Harbaugh has a paper on comparative cheap talk where it comes up. In Varian, it comes up first in production functions, where it allows you to have convex input sets for a given output without requiring diminishing returns to scale, as true concavity would.

October 27. Yet another thought. Margherita Cigola has done work on defining quasiconcavity in ordinal spaces, on lattices. Convexity has to be defined specially there. She uses a different (equivalent in R space) definition of quasiconcavity:
f(mx + (1-m)y) >= mf(x) + (1-m)f(y)

I like that because it is closer to the definition of concavity.

Or another, suitable when the function is differentiable: f is quasiconcave if whenever there is a maximum (i.e., the first derivatives are zero), the matrix of second derivatives is negative definite. MR suggested that, for the single-dimensional x case. I’m not sure it does generalize that way.

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## Significant Figures

I haven’t used this idea since high school, really, but it comes up now and then, so I looked it up in Wikipedia. 100 has one significant figure, as do 20 and 23 and .0001, the article says. The number .00200, however, has three significant figures. The number 1.234 has 4 significant figures. Digits beyond accurate measurement don’t count as significant. There is ambiguity, however, in whether 100 feet really has just one significant figure. It may be that you have measured it to the nearest foot, in which case it really has three significant figures.

The real importance of significant figures comes in doing arithmetic. If you run 100 yards in 11.71 seconds, and the 100 has three significant figures, then the speed should be written with three significant figures as 8.54 yards per second, not as 8.53970965 yards per second.

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## Optical Illusions

U. of Washington has a good optical illusion-experiment site. It has the Muller-Lyon illusion below and lots more that[‘s harder to post in this blog.

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## Risky Borrowing

When you save, you have a choice between investing in a risky asset like a stock or a safe asset like a bank account. When you borrow, there is much less choice. Usually, you just borrow at a nominal interest rate, paying back 10% regardless of the return on the stock market or the level of inflation. The only exception I can think of is the variable-rate mortgage, which at least varies with the nominal interest rate.

Why is that? We can imagine a person being able to borrow at a lower interest rate if he agrees to bear risk. His interest rate could be 20% minus the return on the stock market, for example. If the average stock market return is 6%, his average interest rate would be 14% then. Someone who wanted a safe interest rate could borrow at 16% instead.

Our borrower would be hedging someone else against stock market risk. This would be useful if the borrower were less risk averse than some saver.

Yet we don’t see that. Is it because borrowers are usually more risk averse than savers? Is it because borrowers are too likely to default if they have a risky payment to make?

October 21. At lunch I figured out a new twist. Suppose I want to borrow $100 for consumption, and I am risk-loving. I could borrow an extra$50, and invest it in the stock market. That way, I have to pay back $150 in cash, but my later wealth will be$(150-value of stocks I bought) lower as a result. Thus, even a poor person could take on risk if it weren’t for the possibility of going bankrupt.

Categories: Economics Tags:

## Cygnus

From the Wikipedia entry on the constellation Cygnus, the Northern Cross, one of the easiest to find this time of year:

The constellation also contains the X-ray source Cygnus X-1, which is now known to be caused by a black hole accreting matter in a binary star system. The system is located close to the star Eta Cygni on star charts.

Eta Cygni is in the long part of the neck of Cygnus, about halfway from the wings to the head. Cygnus X1 isn’t visible to the naked eye, though, and Eta Cygni is very faint.

Beta Cygni is Albireo, a double star, at the swan’s head. Alpha Cygni, the tail, is the brightest star, named Deneb.

Cygnus contains several variable stars too, as this website describes.

Categories: science Tags:

## Wald, LR, and Score Tests

From Cornell, “Econ 620: Three Classical Tests; Wald, LM(Score), and LR tests” is a good description of the Wald, likelihood ratio, and score tests. The Hausman test seems more like an LR test, since it estimates both the restricted and unrestricted equations. I found the statalist post below on the Wald test for exogeneity of regressors:

This test is mentioned along with the theory behind -ivprobit- in Wooldridge’s “Econometric Analysis of Cross Section and Panel Data” (2002, pp. 472-477).

For the maximum likelihood variant with a single endogenous variable, the test is simply a Wald test that the correlation parameter rho is equal to zero. That is, the test simply asks whether the error terms in the structural equation and the reduced-form equation for the endogenous variable are correlated. If there are multiple endogenous variables, then it is a joint test of the covariances between the k reduced form equations’ errors and the structural equation’s error.

In the two-step estimator, in the second stage we include the residuals from the first-stage OLS regression(s) as regressors. The Wald test is a test of significance on those residuals’ coefficients.

Categories: statistics Tags:

## Learning Hebrew

John Parsons has a good Biblical Hebrew site, Hebrew for Christians. The page I’ve linked has the ABCD song with Hebrew letters, nicely done, and if you click on the letters on that page, you get interesting tidbits of information

The Scriptures begin with the book of Genesis, but in Hebrew this book is named after its first word: [Hebrew omitted] (bereshit). The first letter of revelation from the LORD, then, was the Bet found in this word….

Note: The sole difference between the letter Bet and the letter Vet is the presence or absence of the dot in the middle of the letter (called a dagesh mark). When you see the dot in the middle of this letter, pronounce it as a “b”; otherwise, pronounce it as a “v.”

Categories: religion Tags:
October 13th, 2008 1 comment

M.R. sent me a link to a page describing a \$125,000 bicycle. It looks like it lacks fenders or kickstand, so I’m not enthusiastic. My other question is this:

What kind of lock does it come with?

Categories: art Tags:

## Conditional Logit

October 11th, 2008 1 comment

I was trying to understand how conditional logit and fixed effects in multinomial logit worked, to explain to someone who asked, and I failed. Greene’s text was not very helpful. The best thing I found was some notes from Penn: “Conditional Logistic Regression (CLR) for Matched or Stratified Data”. The bottom line seems to be that conditional logit (clogit in Stata) chooses its parameter estimates to maximize the likelihood of the variation we see within the strata, while ignoring variation across strata. Thus, if we have data on 30 people choosing to travel by either car or bus over 200 days, we could use 30 dummies for the people, but in conditional logit we don’t. Also, in conditional logit, unlike logit with dummies, if someone always travels by car instead of varying, that person is useless to the estimation.

Categories: statistics Tags:

## Reuleaux Triangle

This Reuleaux Triangle from Wolfram/Mathematica is a nice idea for a shape. It is the shape a Wankel engine takes, perhaps because you can rotate this triangle inside a square as shown at the Wolfram site.

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## Mortgage-backed Securities

October 7th, 2008 1 comment

Via Marginal Revolution, I found Gary Gorton’s The Panic of 2007, a long paper on the institutional details of the financial crisis. It gives particular examples of subprime mortgage bonds, tells how subprime mortgages work in detail, talks about the collateralized debt obligations that buy the bonds and issue their own securities, and so forth. It also talks about why there is a liquidity crisis. Prof. Gorton assigns blame entirely to subprime mortgages, because they are especially sensitive to housing prices (as opposed to interest rates). I only read a little of the article, and it makes difficult reading. The main impression I get is that these mortgage-backed assets are far more complicated than I had thought, and it is no wonder that they are hard to value. I’m also amazed anyone would buy them, for that very reason. It seems that they must just have trusted the rating agencies, which should not have assigned ratings to such complicated securities.

Categories: Economics Tags:

## Fannie Mae and Freddie Mac Regulation

Charles Calomiris has a WSJ op-ed (with someone else) on Fannie Mae and Freddie Mac’s role in the subprime mortgage market and the Republicans’ attempt to stop them. The Democrats are squarely to blame, it seems. The op-ed also points out that deregulation has played no role in this crisis. The problem on Wall Street is that we’ve never regulated investment banks’ capital levels, not that we’ve deregulated them, and that financial innovations have created a need for regulation.

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## Power Law– A New Gabaix Paper

Xavier Gabaix has a new paper, “Power Laws in Economics and Finance” that surveys research on when and why variables such as city size or executive pay follow the power law distribution. One gets a power law distribution if a city’s relative population (its population relative to the average city) grows proportionally to its relative population except for a small absolute increase that gives small cities a bit of an advantage. Even writing that first step is tricky, alas, and I don’t think I’ll be able to understand well enough to do research in the area. The reason the power law is useful seems to be that when it applies, the same laws are at work for big values and little values of variables, so, for example, one wouldn’t need a special theory of stock price plunges– it would just be a chance occurrence from the same distribution as small price declines.

Categories: Economics Tags:

## Longer Sale Times in Depressed Housing Markets

September 15th, 2008 1 comment

Why should it take longer to sell a house in a depressed market? The answer may seem obvious– nobody wants to buy– but it is not. If the price fell enough, somebody would buy. The question is why the weak market is reflected in both lower prices and longer waiting times, rather than just lower prices.

I think there is a 1995 Jeremy Stein article on this where he thinks about the financing of housebuying. Christopher Mayer has some papers too. But I wonder whether the answer may not lie in transaction costs.

Suppose too many houses have been built by mistake. It will take a few years before population growth catches up. We can forecast the house price will recover by that date. We could sell now, though, and somebody now renting could live in the house until demand recovered. If transaction costs were zero, that is what would happen. The person would buy the house, live in it cheaply until demand recovered, and then move out when a house that size became expensive again. But if there is a fixed cost to moving in and out (or to arranging sale or rental) then that won’t happen.

This seems too obvious an explanation, but I haven’t heard it mentioned. It could be modelled by assuming that there are big houses and little houses, with two types of people who prefer each at their construction cost. Everyone prefers a big house, but poor people would prefer a small house if they must pay the cost of building a house. Population grows steadily, but then there is a shock and not enough rich people enter in one year. If there is no transaction cost, then some poor people move into big houses, and some small houses stay empty. If there is a big enough transaction cost, big house prices fall somewhat, but no poor people move into big houses. The best model might have a distribution of moving costs across people, so that there would be some poor people moving into big houses, but some big houses staying empty. Note that the price of small houses would fall too, because of poor people’s demand for them falling as some move into big houses.

Categories: research Tags:

## Semi-elasticities in Regressions

Suppose you have a log-linear regression like this:

log(y) = beta*x

The way to interpret beta is as the percentage change in y that we get from a 1 unit change in x. To see that note that the regression equatino is the same as y = exp(beta*x), in which case dy/dx = beta*exp(beta*x). Thus, the percentage change in y when x changes is (dy/dx)/y = (beta*exp(beta*x))/exp(beta*x) = beta.

This contrasts with the log-log form, log(y) = beta*log(x), in which case beta is the elasticity of y with respect to x, i.e., the percentage change in y that we get from a 1 percent change in x.

Categories: Uncategorized Tags: