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10.30.2006
OMG...
...something horrible has happened to me. I read these comments from the inside looking out.

10.27.2006
Bounded rationality
I'm discovering I'm a bad mathematician. That's a lie. I knew I was a bad mathematician. Nonetheless, I love theory. This is a problem.

Choices that decision makers make are boundedly rational if a) he would make the same choices when he has fewer options to choose from than when he has more options and b) he doesn't choose something between two options that he wouldn't have chosen when those two options are available plus more. The first one says that if the decision maker chooses chocolate when he gets to choose between broccoli, chocolate and yogurt then he'll choose chocolate when he only has chocolate and yogurt to choose from. The second one says that he won't choose broccoli over chocolate and he won't choose broccoli over yogurt if he doesn't choose broccoli over all three.

He's bounded rational because his choices may not be transitive. He may like chocolate over yogurt and yogurt over broccoli, but he's never compared chocolate to broccoli so its not given that he prefers the former to the later.

10.26.2006
Rhetoric of tyranny
As per usual, I put my students in small groups of 4 or 5 today in class. I find this method helps the more shy students participate, while allowing the know-it-alls to be big fish in smaller ponds. In any case, I have the students introduce themselves and each week I have them tell something about themselves. In the past couple of weeks the something else has been trivial like their favorite color or their favorite movie. This week I upped the ante and asked the students to tell their group mates what problem they think is the biggest the world faces.

I was sitting with one group where a student told the group the world biggest problem was that there was enough selection in foods. He wanted more variety. When it was my turn to share I said something like 'abject poverty like in Africa'. The 'not enough food' guy told me that my answer was trite. I think it was an 'I don't think that word means what you think it means' moment.

Anyway, another group had a student that said the President was the biggest problem the world faced. To prove her point, she said she had an article she'd send me after class. Here it is:
http://www.progressive.org/mag_mc100406?cheney

Absolute power corrupts absolutely. This can't be happening in the US.
But it is.

We are our own biggest enemy. We cannot allow this to continue.
Personal freedoms are more important that "security". Especially when
the security is false. To really understand what's going on you must go
is all about. If our soldiers are dying in Iraq to try to build a
democracy out of a land run by a tyrant that: 1) would arrest people
just because he didn't like what they stood for, 2) jail them without
reason or explanation, 3) not allow fair trail by jury, 4) torture them
until they died. That's why our soldiers are dying. And what will they
come home to? A country where people can be declared an "enemy
combatant" just because the President says so. People can be jailed
without reason or explanation. Not allowed a trial where they can be
presented with evidence against them. And be tortured until near death.
In fact, I could be arrested for this email because it might be viewed as
fomenting terrorism against the US. I could be tortured and locked away.
And as of Tuesday the 17th, it would all be legal. I'm sick that our
leaders are so corrupted by power that they even tried to pull this off.
I'm sick that the Congress rolled over an played dead and sacrificed my
personal freedoms for a false threat. I'm sick that the news wasn't
reported widely (perhaps out of fear of reprisals). Just google habeas
corpus and see how few stories pop up. I'm appalled. Al Queda's power is
an insignificant speck compared to the disastrous leadership of this

The comments are from the person who sent me this.

Hi xxx-

Thanks for sending this along. Let me respond first by saying that I'm very sympathetic to the issues raised by your friend. Personal liberty is a standard I often bear. I'm very suspect of government because I realize it is made up of people. People for better (e.g. market outcomes for the most part) or worse (e.g. greed) are self interested. Government provides the few people that run it with a significant amount of power and the means to subjugate others to their will.

I'll also say I'm a card carrying member of the ACLU and I donate to Amnesty International.

With that qualification, I'll respond to your friends points, point by point.

"1) would arrest people just because he didn't like what they stood for, 2) jail them without reason or explanation"

I assume she is referring to the detainees in places like Guantanamo and Abu Garab. The government tells us these people were detained not because of what they stand for but for their actions. These people were taken not because we didn't like them and there ideas, but because they were actively involved in aggression towards the U.S. Granted you have to believe the government claims to believe the people detained are justly detained.

"3) not allow fair trail by jury"
However, given recent Supreme Court decisions we won't have to take the governments word for it. Those rulings basically say that all the detainees must be given due process. Now, you can be uneased about what that process looks like (their cases won't be reviewed as per usual American legal processes, for example), but its very hard to say they won't be given fair trails.

"4) torture them until they died."
This is a red herring. We have no idea the extent of problems like Abu Graib. Is it an isolated incident? Was torture wide spread and sanctioned? Nobody knows. All we can do is denounce it and hold our leaders accountable (by voting against incumbents for example) for any exposed malfeasance. Torture is unacceptable. End of story. That said, Congress recently passed a law to specifically outlaw torture and to give it better definition. The law, by the way, was authored by John McCain a man who endured torture while a captive of the North Vietnamese.

"A country where people can be declared an "enemy combatant" just because the President says so"
The President has this right because it was given to him by an act of Congress. Congress, in essence, declared a state of war after 9/11 (this law is called AUMF). An "enemy combatant" is an old term to refer to people that are fighting against your country in a War. The President issued an order that explicitly defined them as "an individual who was part of or supporting the Taliban or al Qaida forces, or associated forces that are engaged in hostilities against the United States or its coalition partners. This includes any person who committed a belligerent act or has directly supported hostilities in aid of enemy armed forces." (See this wikipedia article).

The point of citing all of these laws is just my attempt to show that we're still being ruled by laws. The Congress can change the law (i.e. say we're no longer at war) and because the definition is pretty clear, the President can be shown to be in violation of the law. For example, its clear that your friend, by sending this email, would NOT fall under the definition of enemy combatant. Furthermore, all these laws can, and some of them have been, reviewed by the Supreme Court. In more than one instance, the President's interpretation of AUMF (i.e. the status of Guantanamo detainees) has been overruled by the Supreme Courts constitutional interpretation. There's a case in the lower courts right now that is contesting the President's wire tapping program.

Finally, your friend calls al Qaida a "... false threat."
I hope its obvious that this is just an incorrect statement. Al Qaida has shown itself to be a dire threat. The 3000 dead on 9/11 can attest to that. Its not unthinkable to think they're looking to get a nuclear weapon, for example. You don't have to stretch your imagination far to see that the impact of their successful use of one such weapon would be catastrophic in terms of lives and to our system of government. Al Qauida is a threat whether or not Bush is President.

In any case, while your friend seems to be in poor spirits about our system of government in this post-9/11 era, all that has transpired has actually lifted my confidence in our system. If you can believe it! Yes, the President did try to overreach his authority, but the President doesn't act in isolation. Our Courts, Congress and non-governmental institutions like the Press, Amnesty International and the ACLU have been there to check his power. In some sense, we've had to endure the pain of a Bush presidency so that we can get this right. We must create a system that can endure terrorist threats while balancing individual freedom.

I think you'd agree its important for us to get this right.

Thanks again for sending this too me.

Have hope,
Will

UPDATE: The guest on the Keith Olbermann video linked to above implies the McCain torture law, alluded to above, would allow the President to detain Americans. This seems false according to this wiki article. The stated purpose of the law is to apply to alien combatants. There is a troubling section in the definition of the combatant, though: "a person who, before, on, or after the date of the enactment of the Military Commissions Act of 2006, has been determined to be an unlawful enemy combatant by a Combatant Status Review Tribunal or another competent tribunal established under the authority of the President or the Secretary of Defense." Do these tribunals have jurisdiction over American citizens?

Gun control
127 kids died of a firearm accident in 2003. 910 died in drowning accidents.

Preventing accidental gun deaths is NOT a reason for gun control. (h/t Darwin Catholic)

10.21.2006
Data mining
I can't remember who I was talking to recently, but we were discussing data mining. Data mining is bad. Real bad. Everyone knows this, but why is it so bad?

Researchers in any discipline are suppose to check their biases at the lab door. They are to be objective observers of reality. The facts are the facts and the researcher's job is to uncover them.

In the physical sciences, I imagine this part of the job is a little bit easier than in social sciences. Its easy to separate your personal opinions from empirical observation when the thing being observed is inanimate. There are vested interests, of course. The scientist may feel very strongly about which way the data should come out. He would find it strange to have a result that refuted a law of thermodynamics or violated the speed of light. Not that physicists and chemists can't be passionate about their work, it just seems more likely for them to be able to separate their feelings from their observations. The picture gets a little more clouded if the scientist realizes if his experiments come out the 'wrong' way he may lose his funding. Someone who spent his whole career experimenting on ether, may be less than excited with experiments that show the atomic theory to be correct.

In softer sciences the object of study isn't inanimate. Worse, the lab rats for economics, sociology and political science are living breathing people with feelings and such. People, even the most autistic-like math-nerd theoretical economist types, tend to have strong feelings about how people act and should act as individuals and how they act and should act collectively.

Worse still, the motivation for most social scientists to enter their field is most likely tied up with their biases. The public economics researcher went into that field because he felt strongly about the role of the government in improving peoples lives. Certainly, the research he decides to do, the decision to study the impact of education on life outcomes or the effects of immigration on the working poor, stemmed from his particular opinions and experiences, his biases.

Checking your biases at the door becomes a lot harder when your so emotionally invested in the outcome. This is why social scientists have to be especially cautious about researcher bias.

Unlike in the physical sciences, most of the data in social science isn't acquired experimentally. In experiments, researchers control in the environment to very high degree. When a variable is tweaked, the experiment is set up such that it is known exactly the impact of the tweak. Thus, experimental data is context free and so repeatable. Additionally, experiments are generally engineered to reduce the noise to signal ratio. Very precise instruments measure to a very precise degree.

Most data in the social sciences is historical, entangled and dirty. They are path dependent, mired in context and contain a lot of noise. On the plus side, there's a lot more data essentially because everything is data. The government collects data. Business' collect data. Everyone collects data. And even where there was no data before (wages in 15th century Cairo), the clever researcher can discover it (http://gpih.ucdavis.edu/Datafilelist.htm#Africa ). The social scientist's job is to find the data, clean them, and disentangle them to find patterns and relationships. How does he do this?

First, before even looking for data or looking at it after found, he should have a theory of the data. What relationships should be found? What patterns are expected? How might one find such patterns? Next, he should delineate a research strategy, identify the data he will need and outline the methods that will be used to test the theory. Then, and only then, he should go to the data.

Data mining reverses this method. One starts with the data set and precedes to find relationships and patterns. This sounds innocuous at first. If the patterns are there, then why should this matter? Well, because of the sheer volume of data, the researcher will no doubt 'find' the relationships that correspond to his biases. Significant results (those that we have a 95% confidence in) are more likely to be insignificant if one is looking through piles of data to find the pattern he wants to find. If 1 out of 20 times, perceived patterns are just the result of randomness, then the more one 'mines' for patterns the more likely they'll be fooled. If you find 10 patterns that have 5% chance of being caused by chance, you're almost 40% likely to find at least one of them is random. If you dig for more and more patterns, you're more and more likely to find what you're looking for whether or not its is caused by randomness.

So, don't data mine is the mantra. Just don't do it.

However, on the off chance that a significant pattern is hiding in the data, it seems odd to dismiss data mining out of hand. The problem with data mining isn't data mining itself, its the bias the data miner brings to the job.

Its a wonder why data mining rates as such a sin in economics as to be on par with a certain Victorian era sin that caused hair to grow on the palm of the hands. Both sins are much committed but never discussed except to say they're bad. Is this sin always bad? Are there healthy ways to commit this sin?

This paper asks us to consider the difference between classical statistics (the kind of statistics that is more concerned with summarizing data) and econometrics (the kind of statistics that is more concerned with cleaning and disentangling data). Admitting those differences means that we must admit the researcher brings bias to his or her work. As such, we should have standard tests/corrections for researcher bias.

Here are some points that stuck out at me:

Point # 1: Researchers will always respond to incentives and will be more skeptical than standard statistical techniques suggest.

The most well-studied example of researcher initiative bias is data-mining (Leamer, 1978, Lovell, 1983). In this case, consider a researcher presenting a univariate regression explaining an outcome, which might be workers' wages or national income growth. That researcher has a data set with k additional variables other than the dependent variable. The researcher is selecting an independent variable to maximize the correlation coefficient (r) or r-squared or the t-statistic of the independent variable all of which are identical objective functions... If the true correlation between every one of the k independent variables and the dependent variable is zero, and if all of the independent variables are independent, then the probability that the researcher will able to produce a variable which is significant at the ninety-five percent level is 1－ .95k . If the researcher has ten potential independent variables, then the probability that he can come up with a false positive is 40 percent... Lovell (1983) provides a rule of thumb "when a search has been conducted for the best k
out of c candidate explanatory variables, a regression coefficient that appears to be significant at the level alpha_hat should be regarded as significant at only the level alpha = 1－ (1－alpha_hat)^(c/k)."

Point # 2: The optimal amount of data mining is not zero.

[E]conomic models have an uncountable number of potential parameters, non-linearities, temporal relationship and probability distributions. It would utterly impossible to test everything. Selective testing, and selective presentation of testing, is a natural response to vast number of possible tests.

Point # 5: Increasing methodological complexity will generally increase researcher initiative bias.

[New methodologies] clearly increase the degrees of freedom available to the researcher... A second reason for increased bias is introduced by the existence of particularly complex empirical methodologies. Methodological complexity increases the costs of competitors refuting or confirming results.

Point # 8: The search for causal inference may have increased the scope for researcher initiative bias.

The most worrisome aspect of causal inference is the prevalence of instrumental variables drawn from observational data selected, or even collected by the researcher. In that case, the scope for researcher effort is quite large, although some of this freedom is restricted when the researcher focuses on a clean public policy change that is directly targeted at a particular outcome. The problem will be most severe when the variables are general characteristics that may have only a weak correlation with the endogenous regressor.

10.06.2006
Somebody's trying to tell me something
While my department listserv is a debating the merits of the graduate student union (loss of liberty vs. well the other side hasn't really articulated their POV yet except to say that unions must be good), the following two articles, in succession, show up in my news reader

New Scientist - "Sense of justice discovered in the brain"

A brain region that curbs our natural self interest has been identified. The studies could explain how we control fairness in our society, researchers say... [U]sing a tool called the “ultimatum game”, researchers have identified the part of the brain responsible for punishing unfairness...

"Self interest is one important motive in every human," says Fehr, "but there are also fairness concerns in most people."

"In other words, this is the part of the brain dealing with morality," says Herb Gintis, an economist at the University of Massachusetts in Amherst, US. "[It] is involved in comparing the costs and benefits of the material in terms of its fairness. It represses the basic instincts."

and Tim Hartford - "The Undercover Economist: The great giveaway"

Selfishness is one of those issues where economists seem to see the world differently. It is not that economists are incapable of imagining - or even modelling - altruism. They can, but they usually don’t. And there is a good reason for that: people aren’t selfless... In fact, the closer you look at charitable giving, the less charitable it appears to be. A recent experiment by John List, an economist at the University of Chicago, and a team of colleagues, showed that donations are less than charitable after all. Using controlled trials to compare different methods of door-to-door fundraising, Professor List’s team discovered that it was much more effective to raise funds by selling lottery tickets than by asking for money. This hardly suggests a world populated by altruists seeking to do the maximum good with their charitable cash... Robert Frank, from Cornell, wryly observes that those organising fundraising drives for the vast US charity United Way tend to be disproportionately estate agents, insurance brokers, car dealers and other people with something to sell.

All I know is that *someone* is trying to tell me that justice matters (or maybe it doesn't).

I'd have no idea who to go for a good argument for justice. I find myself moved by arguments for liberty while arguments for justice often come off as whining. For all I know, this is only because those making the arguments for liberty are just better at making arguments than those that argue for justice.

Who is the Hayek or Friedman for justice?

It's all been said before
Some funny economics related quotes. My favorites:
• "Stiglitz's outlook is that markets are imperfect, but he is not. Where Marx offered dictatorship of the proletariat, Stiglitz would give us dictatorship of the Nobel Laureate. Between the two, we might be safer with Marx." - Arnold Kling
• "See, when the Government spends money, it creates jobs; whereas when the money is left in the hands of Taxpayers, God only knows what they do with it. Bake it into pies, probably. Anything to avoid creating jobs." - Dave Barry
• "There are two methods, or means, and only two, whereby man's needs and desires can be satisfied. One is the production and exchange of wealth; this is the economic means. The other is the uncompensated appropriation of wealth produced by others; this is the political means." - Albert Jay Nock
• "The best minds are not in government. If any were, business would steal them away." - Ronald Reagan
• "It's a very sobering feeling to be up in space and realize that one's safety factor was determined by the lowest bidder on a government contract."- Alan Shepherd

10.04.2006
Paper: Bar-Hillel, "Cycles of Intransitive Choice"
Transitivity is a property of preferences where if A is preferred to B (denoted A > B) and B preferred to C (B > C) then A must be preferred to C (A > C). The paper discussions various examples where this property doesn't hold.

The most famous "intransitivity" is in group decision making by majority rule. If person one has preferences A > B > C, person two has preferences B > C > A and person 3 has preferences C > A > B. A majority of people prefer A to B and B to C, but a majority also prefers C to A. Thus, for the group A > B > C > A > B and so on.

Group decision making is analogous to multi-dimensional decision making. If you're buying a new computer, you may think CPU speed, amount of memory and hard drive space are the important attributes. Let's say model A is fastest, B second fastest and C is the slowest. Likewise, B has the most memory, C the second most and A the least and C has the biggest hard drive, A the second biggest and B the smallest. You can see that this situation is very similar to the above and the decision rule "pick the model that has most preferred categories" gets you no where.

The paper also talks about "inherently comparative choice". The idea is that in the case where the satisfaction (or dissatisfaction) derived from a choose is dependent on the thing chosen and the things not chosen (e.g. regret), transitivity can be violated. A good example compares the difference in regard to stock market returns in the case where you bought a share of stock yesterday that doubled today versus the case where you've owned 2 shares of the same stock for a long while and it doubled. You may find yourself more pleased with the first situation because you where able to "time the market" even though the outcomes in the second case is better in a money-in-your-pocket sense. Comparing these situations to the situation where you had 4 shares of the stock yesterday but then sold one share, you may find yourself regretting that choice today when the stock price doubled. Even though you have higher return in this case than in the second case, the feeling of regret may make you to prefer the second case to the third. However, despite the regret in the third case, the money gain is so high that you still prefer the third to the first case. Thus, we have a violation of transitivity... timing the market with a small return is preferred to buy and hold with a medium return is preferred to regretting a sale with a large return is preferred timing the market with a small return, etc.

The paper concludes by remarking that it is implicit in revealed preference that choice is driven by preferences, but that perhaps preferences are "constructed" by choice and thus "choice procedures are geared towards justification and conflict resolution rather than towards optimization."

10.02.2006
Chapter: Kreps, "Notes on the theory of choice," chapter 2
Quick review of binary relations generally and preference relations specifically. The minimum requirement of binary relations to make them preference relations is asymmetry and negative transitivity. These two things imply the 'normal' qualities of preference relations (irreflexivity, transitivity and acyclicity). Phew, I was worried they might not.

It would be tedious to display the whole set of options to agents and have them state their preferences, e.g. "I prefer x to y, y to z and z to x... oops, I mean x to z." Another tact is choice theory or revealed preference theory. A choice function is a function that takes a subset of the total number of items to choose from and picks a subset, i.e. the agents choice(s). The interesting question is when are there correspondences between preference relations and choice functions. The weak axiom is explored via Houthakker's axiom and Sen's alpha and beta properties (pg 13-15).

Paper: Samuelson, "Exact Consumption-Loan Model of Interest"
The model is a one of multiple, identical generations (OLG), with each generation living 3 periods, working in the first 2 and being retired in the last. Total lifetime savings has to equal zero (i.e. grandparents don't go to the grave with their money and they don't leave estates).

In the stationary case, the case where interest rates don't change over time and population doesn't grow, the interest rate must zero. This is the case because everyone is assumed to be the same. There are no "savers", those that don't mind consuming in the future rather than today, who would get positive interest rates from "spenders", those that want to consume today. "Saver" and "spender" are relative, you're only a "saver" in relation to all the "spenders", terms and because everyone is the same there can't be relative differences.

If you let the population grow (exponentially) but keep interest rates constant over time, you find the interest rate must be equal to the population growth rate. Of course, this means that if the population is declining, you'd see a negative interest rate... Hmmmm.

Further, with equal interest rates over time, interest rate equal to the population growth rate is socially optimal.

But will each generation trade with the others. Its easy to see in the 2 period case, generations will not trade. The old won't buy bonds they'll be dead before they mature. Thus, the young consume all of their product and the old, well, consume their product (poor them). Recall, that we had interest rates on bonds equal to the population growth. So, in this case with no trading, why would there be any interest rate (not to mention a sensible one) on bonds?

Samuelson goes on to show that the optimal amount of savings won't be achieved in most settings and comments that this is where there is a role for government. He ends the essay by declaring that money is an asset that can be traded across generations, "as long as the new current generations of workers do not repudiate the old money, this gives workers of one epoch a claim on workers of a later epoch." Money, beyond being a medium of exchange, is the "social compact" that brings the economy into optimality.

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