WalMart does not issue `loyalty’ cards. Why not? Other retailers, like Safeway, do. They are not literally loyalty cards since they do not induce holders to concentrate their purchases with a particular retailer. They do allow the retailer to track purchases by household. Why would WalMart choose to forgo that information?

Racial and ethnic profiling of airline passengers is back in the news again. The argument in favor  is that it would be costly to mount a careful examination of all airline passengers. Assuming that such profiling is effective, it means that the costs of the acquired safety benefits are borne by a subset of the population. There is a way to redress this inequity. A profiling tax charged to all passengers. Proceeds from such a tax are paid to those who are profiled. Clearly, there are implementation issues but………..

I take it as self-evident and undisputed that when a group of eminent economists sign a letter endorsing the health care bill, the subtext of their message is that the issue is part of their scientific expertise and that they have studied the details sufficiently to deliver their professional opinion: This is the only way to interpret the fact that the undersigned are all economists, and that their academic position is mentioned in the letter. This is why their advice should carry more weight than the advice of an unknown blogger. If this advice is followed and the bill passes, then some of their professional reputation is tied with its success.

What is perhaps more disputable, but still true in my view, is that even this group of most distinguished economists don’t have individual reputations, and that they are drawing from and contributing to a collective reputation pool of the entire profession. The people of this (or any other) country, who are the audience of this letter, don’t distinguish between different scholars of the same discipline. Public trust in the entire profession is determined by the success of the predictions and policy advices of its members.

Following the death of Paul Samuelson, I looked at his seminal paper `Proof that properly anticipated prices fluctuate randomly’. I found it intriguingly related to my beloved puzzlement about the meaning of probability, and I have something to say about it. Since I didn’t look at the forty-five years of literature that followed this paper I am probably going to flaunt my ignorance in public, but this is just a blog so what harm can it do.

The purpose of Samuelson’s paper is to formalize the intuition that competitive prices must, in some sense, look like random walk: Let be a stochastic process that represents the spot price of some product, say wheat: is the price in which you can buy wheat at day . Fix a day and let , for , be the price at day of a contract that requires the delivery of wheat at day . Samuelson proves the following theorem:

Theorem Assume that

Then the sequence is a martingale

So, in day , the properly anticipated price of wheat in day is given by the conditional expectation of the currently unknown spot price of wheat in day . Note that agents are assumed to be risk neutral and the interest rate is zero (Samuelson later dispenses with these assumptions). It’s a tribute to Samuelson that what he wrote and proved fifty years ago is now probably the first example of a martingale in your favorite probability textbook. Samuelson proves this theorem under some stationary assumptions about the distribution of the -s. Today we know that the theorem is true for every process and the proof is immediate from the properties of conditional expectation. (Please remember that Samuelson’s paper is from 1965).

But anyway, the math is not my subject matter. For me, the main problem with Samuelson’s argument is its starting point: the stochastic process over spot prices.

I have not here discussed where the basic probability distributions are supposed to come from. In whose minds are they ex ante ? Is there any ex post validation of them ? Are they supposed to belong to the market as a whole? And what does that mean ? Are they supposed to belong to the “representative individual” and who is he ? Are they some defensible or necessitous compromise of divergent expectation patterns ? Do price quotations somehow produce a Pareto-optimal configuration of ex ante subjective probabilities ?

So, Samuelson views the probabilities as subjective. What I understand from this paragraph is that he is troubled by the identity of the agent whose mind these probabilities occupy. There is a good reason to be troubled: the assumption in the theorem about the quoted price makes sense if the traders have the same beliefs. Otherwise you have to formalize some way in which the market creates a“representative individual” from the beliefs of the traders.

But I see a more disturbing problem here: Even if we assume for a moment that all the traders actually agree on the distribution of the process , the only sense in which is a martingale is with respect to this distribution. So shouldn’t we view the theorem as proving that properly anticipated prices are a subjective martingale, that is a martingale according to the subjective belief of the traders ? But then, does the theorem says anything about the anticipated prices of wheat in the world should this subjective probability turns out to be incorrect? Admittedly, I don’t know what correct probability means (more on that in another post), but clearly if all probabilities in the model are interpreted as subjective probabilities then there is no reason for us to expect — even as a theoretical conclusion of the model — that the quoted prices will look random; it only means that the traders expect them to look random. But we, the outside observers, might see something entirely different.

Paul Krugman breaks down his hate-mail box

Nothing gets me as many crazed emails and comments as any reference to climate change. The anti-global-warming people are just filled with hate for anyone who suggests that maybe, just maybe, the vast majority of scientists are right.

Since Krugman doesn’t read this blog I can safely offer him a challenge — Give me one example in which your writing about global warming suggested that `maybe, just maybe’ the vast majority of scientists are right.
More likely whatever you have ever written about this issue suggests that for certainty, real certainty, the vast majority of scientists are right about human-made global warming and its long-run consequences and that everybody who says differently  is a flat-earther idiot.

Just got to Paul Krugman’s criticism of Economics in the Sunday New York Times magazine. Members of the profession are excoriated for being beguiled beyond the bounds of decency by mathematics. Groan! Why do mid-life crisis always lead to proclamations that theory is dead? The militantly middle of the road columnist David Brooks has also joined in while promoting the behavioral cause. I suppose being middle of the road is hard since one has to avoid oncoming traffic in both directions.

These and other criticisms brought to mind Capra’s series of WWII films, `Why We Fight.’ They were conceived to convince an isolationist nation about the need to fight the Nazis. No, I’m not comparing the atheoretical unwashed to the Nazi’s. But it did inspire a desire to take up my puny cudgels in defence of mathematical modeling. Herewith, 3 of the usual objections to quantitative models and responses.

Objection #1: Not everything can be reduced to numbers.

True. But a great deal of importance can.

Objection #2: Workable Quantitative models cannot capture the complexities of real life.

So what? The question is not whether a particular quantitative model accurately represents reality but whether there is an alternative model that is more accurate. How do we know that a decision arrived at by what we are pleased to call instinct, intuition or experience has really acknowledged all the complexities of reality? Indeed, one of the beauties of quantitative models is their explicitness. Like Cromwell’s portrait they appear warts and all.

Simple quantitative models frequently provide profound qualitative insights into the process being modeled. Thus, one may wish to build a model not so much to decide what to do, but to test and refine ones intuition about what is going on.

Objection #3: Quantitative models ignore the context.

Yes. However, there is no law that obliges one to follow the recommendations of a quantitative model that is not appropriate to the context. Second, ignoring the context can be a good thing because the context of the decision is irrelevant. A quantitative model often captures the essence of a decision, say, the choice between a gamble and a sure thing. It does not matter whether the context is the stock market, a medical diagnosis or wildcatting. This allows for the transfer of insight from one setting to another.

One of my favorite game theoretic insights is that rational players should not play chess: The outcome is already determined at the beginning of the game. This is what’s usually called Zermelo’s Theorem, but it is a common rant among game theorists that this is a misattribute. Zamir, Maschler and Solan, for example, in their recent game theory textbook credit the theorem to von-Neumann, citing his minimax paper. Following a conversation with David Schmeidler, who suggested that Zermelo might have used this theorem but didn’t make a fuss over it because it’s so trivial, I decided to look at Zermelo’s paper myself. This is possible thanks to translation from German by Ulrich Schwalbe and Paul Walker.

A game in Zermelo’s setup is given by a finite set of positions. A position in chess includes the configuration of the board, whether White or Black has to move, whether there was castling, etc.. A history (Zermelo called it an endgame) is a sequence of positions that can follow each other in accordance with the rule of the games. An history can be finite, ending with a position which is win or loss to one of the players, but can also be infinite, in which case the outcome of the game is a draw. (In a game like chess there is also the possibility of a finite history that ends with a stalemate. This issue has no independent interest so, as mathematicians will do, we ignore it.)

What is usually called Zermelo’s Theorem in the literature now becomes:

Theorem 1 Let be a position. If there is a number such that the length of every history starting with is smaller than , then one and only one of the following holds:

• White can force a win for White.
• Black can force a win for Black.

I (and Zermelo) do not explicitly define strategies, but `force’ means what you think it means: That the player has a strategy such that every history which is consistent with this strategy achieves the desired outcome.

Zermelo’s theorem is true, though I hasten to add that the assumption about the existence of such a number   is unnecessary. However, this theorem is not the subject matter of Zermelo’s paper. The question that Zermelo asks is this:

for some natural number , what properties does a position q has such that White, independently of how the Black plays, can force a win in at most r moves?

(Apparently Zermelo was motivated by the kind of `chess problem’ which bound the number of moves until a checkmate)

So, Zermelo clearly did not set out to prove his eponymous theorem. But was he aware of it ? I guess the answer depends on what you mean by being aware of a mathematical statement (were you aware of the fact that any even number greater than 2 can be written as a sum of a prime number and an even number before you read this sentence ?). But I do believe that some of the logical implications in Zermelo’s paper only make sense if you already assume his theorem. Here is one such implication:

The numbers for which are either infinite or , since the opponent, if he can win at all, must be able to force a win in at most moves

Here are some sets histories of length and Zermelo shows that iff White can hold out until the -th move without losing. The argument makes sense only if you assume that (which, according to what Zermelo when White cannot postpone losing in moves) implies Black can force winning in moves, which is the essence of the theorem.

My conclusion ? I believe that Zermelo and his readers were taking what is now called Zermelo’s Theorem for granted, though they didn’t recognize its significance yet.

To little light and narrow room have I been  consigned, to stamp out ignorance. After 7 weeks of blood, bile and ink, it appears another cohort has been saved from barbarism, prepped and ready to be delivered into the capitalist maw.

In the meantime the junior economics job market has lurched into action. It begins with the `great sorting’. Departments with large numbers of students on the market meet to sort their `product’ by quality. There is no sorting hat to do the work. Instead, advisers, who must balance the parental impulse to promote their progeny against professional propriety, execute the task. This demand to constantly judge, weigh and evaluate others is perhaps the most unpleasant duty that those who `seek for truth in the groves of academe’ must perform. It wearies the mind and corrodes the soul.

The second big step of the junior economics job market is the `great herding’. Major institutions must coordinate upon a handful of bright young things bound for greatness. In six years, these new minted pennies will be so much loose change, sic transit gloria mundi.

Who are this years, superstars? Haven’t the faintest. However, one does not need to don tweed and move to the hub of the universe to find out. There is a web site that passes along rumors about the job market in which names are named, cutting remarks made and blood drawn.

A puzzle, to me at least, is why herding does take place (OK, I probably need some way  to distinguish between herding and not herding, a measure of the extent of herding etc. But, this is not the pages of Econometrica). The decision to hire at the untenured assistant professor level is not irrevocable. One can let the person go if things do not work out (see what I mean about the corrosion of the soul). Thus a department should be willing to take on more risk in hiring at the junior level (I’m assuming of course that the department is willing to bite the bullet when the time comes). In particular  a department at rank x looking to make it into rank x-10, should be willing to take on more risk then the department currently at rank x-10. Thus, why so much agreement on who they interview?

For someone who doesn’t care much for experimental studies and data analysis, I often come up with experimental tasks or statistical surveys for other people to do. Here is one: Take a bunch of graduate students of nuclear physics and ask them about the role of falsifiability in science. Then take a bunch of graduate students of macro-economics and ask them the same question. My guess is that the physicists will not know what you are talking about, and at any rate  wouldn’t have come accross this issue during their studies, whereas the economists will know all about Popper, logical positivism, demarcation and other latin words I never heard of.

I thought about this comparison when I watched this diavblog. As usual with bloggingheads I lost interest quickly, but it’s  worth watching for a while, if only to keep track of the fluctuations in the frequency of David Levine’s blinks while the other head is talking. Best Levine’s quote from the part I watched — `You will have to fill me on which these three axioms are’, responding to the assertion that `nothing is more true than that the three axioms of rational choice have all been falsified’. I actually replayed this part to retrieve the quote, and I still managed to forget the three axioms.

Anyway, back to my (testable !) prediction. Suppose it turns out to be correct. Then, since I am the one that made the prediction, Popper tells us that the fact that it was verified renders my explanation for it more credible. And the explanation is that physicists are robins and economists are penguins.

Let me elaborate. Richard Feyman famously said that philosophy of science is as useful to scientists as ornithology is to birds. It’s an awesome observation, and I would like to apply it specifically to the part of philosophy of science that deals with the demarcation problem, or the distinction between science and non-science. And I’ll start with the physicists, because our whole idea of science is essentially `the stuff that physicists do’. Popper was trying to pin down what are the special characteristics of the physics enterprise. Thus, the fact that physics is science is almost a tautology. Every child knows it as every child knows that robin is a bird. That’s why Popper’s (or anybody’s) answer the demarcation problem is useless to physicists.

Things are different with penguins. A layman might not recognize them as birds. In order to prove that they qualify, penguins have to appeal to some standards that describe what are the special properties of birds that distinguish them from humanities mammals. That’s why penguins care about ornithology. And that’s why economists care about falsifiability.

Rosenberg is right it’s a bit ironic that economists adopt falsifiability as a litmus test for science, since philosophers of science have generally rejected it. But the irony I think is on the philosophers, not the economists. How would the ornitologists feel if the birds that actually read their papers would only be interested in what was written eighty years ago ?

I confess. Blogging is harder than publishing. Lance Fortnow tells me that I would find Blogging easier if the orifice in my antipodes was not constricted. Perhaps this is true, but it does make one wonder about the source of a bloggers wisdom.

Very well then. I will follow his advice. Where is the milk of magnesia? Jacta alea est.

Drive-by theorizing. Practiced by applied theorists. This is the species that theorizes about phenomena, rather than theory.

Works like this. Read a book from another discipline about some unusual phenomena over the summer. In the fall, write a paper with an economic model about the phenomena. Usually with a title like `An Economic Theory of BLANK.’ A popular choice for BLANK is one of the 7 deadly sins (but these have  been exhausted) or something magesterial like empire, justice, language, family or sex.

The contents of said paper consist of a verbal intuition formalized with a patina of mathematics. Indeed, the best examples, admit no other intuition but the one advanced by the author. Of course, this makes the mathematical exercise utterly pointless. We build mathematical models to sort out competing intuitions not to codify them.

 When completed, move on. It is always best to have the first word, no matter how anemic, than the last.

Of course, one should name names. I won’t. I’ve sipped a laxative not drowned in it.