Yet another Sheep

Saharon Shelah is the most productive logician of our time. Shelah has authored and co-authored more than nine-hundred papers in mathematical logic and related areas. Many of these were extremely influential, such as his work on cardinal arithmetic. His first major contribution to economics was of a rather indirect nature: He was one of the reasons why Ariel Rubinstein entered economics. As Rubinstein writes:

"And, more than anything, the subjective nature of the things I will say is exemplified by the person I believe to be most responsible for the fact that I found myself involved in microeconomic theory. Indeed, from the gallery of esteemed teachers I mentioned, he is completely unknown in the field of economics. I doubt he will ever be appointed as an economic advisor to the finance minister and, as far as I know, he is not trained in the field of law. He has not even written articles on mathematical economics and I doubt he intended to lead me to choose the path I did (though he certainly thought I was not talented enough to become involved in his line of work). The man I’m referring to is the mathematical logician Saharon Shelah.

I would sit with my friends at the cafeteria of the National Library in the middle of the day, with our notebooks full of the puzzling things that Saharon Shelah (like other teachers in the Mathematics Department in Jerusalem) wrote on the board. We were in great awe from this encounter with intellectual perfection, but we also had a vague feeling that these things, despite - or perhaps because of - their great abstractness, had some connection to life. We were witness to a strict adherence to norms of definition and proof, and unwillingness to compromise on a single detail. We became acquainted with the beauty and splendor of a model, a statement and a proof, and with the purity of things emanating from the mind.

But these things spoke to us because of our interest in the world around us. We tried to give mathematical concepts some realistic meaning derived from the concepts of our daily world. And we tried to explain these wonderful mathematical statements not only as links between concepts in the mathematic world, but as links in a world of concepts that so fascinated us as young students after the army: the world of human interaction."

What changed Rubstein's fate was being introduced to Amartya Sen's wonderful book Collective choice and social welfare. which brings us back to social choice theory. Gil Kalai, an expert in combinatorics with a blog of his own, introduced Shelah to the problem of generalizing Arrows theorem to arbitrary choice functions (that do not have to come from some rational preference ordering), that satisfy symmetries like neutrality. The result is On the Arrow Property. A paper with one central result and a really, really, really long and complicated proof. The paper is written in the most ideosyncratic style I have ever seen. Just see for yourself. Do it.

Now if anyone asks for nontrivial mathematics in economic theory, here it is.

Sometimes I feel like ranting. This is such a time and I want to rant on an article by Guy Sorman, Economics Does Not Lie. The article is supposed to tell us what is the state of the art in economics concerning policy related ideas.

If economics is finally a science, what, exactly, does it teach? With the help of Columbia University economist Pierre-André Chiappori, I have synthesized its findings into ten propositions. Almost all top economists—those who are recognized as such by their peers and who publish in the leading scientific journals—would endorse them (the exceptions are those like Joseph Stiglitz and Jeffrey Sachs, whose public pronouncements are more political than scientific). The more the public understands and embraces these propositions, the more prosperous the world will become.

This is a good deal of megalomania. Given that the author later reveals to know absolutely nothing about economics and economic research, maybe shutting the fuck up would have been preferable to insulting Sachs and Stiglitz. Let´s go through the list:

1. The market economy is the most efficient of all economic systems.

Mhmmm. A bold claim, but maybe he is right. Let´s look at how this entry starts:

Adam Smith’s eighteenth-century take on market efficiency was metaphorical, nearly metaphysical: he said that it seemed to be guided by an “invisible hand” that produced outcomes beneficial to society. In the mid-twentieth century, Friedrich Hayek observed that no central-planning institution could possibly manage the huge quantity of information that the market organized automatically and spontaneously by pricing resources. More recently, Berkeley economist Gérard Debreu has used computers to demonstrate that the spontaneous order that Hayek postulated does indeed exist in a mathematical world.

I don't know what the exact relationship between the work of Hayek and Debreu is supposed to be, but Hayek would have certainly disagreed with the view that Debreu showed something to that effect. Debreu certainly didn't use computers (how did Sorman come up with that nonsense?) and wisely stayed away from trying to look at the actual market process, i.e. it´s dynamics. He actually had the (pretty much confirmed) view that such an approach would fail (see Hildenbrands foreword of this book). Debreu looked at equilibria and didn't ask how they ome to be.

2. Free trade helps economic development.

Maybe. I don't know. But I actually do know that the argument given is complete nonsense:

In fact, economists have long understood the law of comparative advantage: whenever differences in the cost of producing goods exist between two countries, both will benefit from free trade, a mechanism that allocates their resources most effectively.

Free trade not only generates the greatest possible growth; it tends to distribute it widely, both within nations and among them.

Comparative advantaes may lead to countries becoming richer after opening borders- but it is certainly not leading to sustained growth. Growth is something else.

3. Good institutions help development.

I think so.

4. The best measure of a good economy is its growth.

How did he came up with this insight?

Unlike other proposed measures (happiness, for example), economic growth can be determined objectively: it is the rate of increase in a country’s gross domestic product (GDP) over a given period.

In a one good world, this is certainly true. Defining real income in a multi-good world is really challenging (here´s a brave attempt). Much less subtle, it is good to be in a rich country. Real income is more important than growth of real income (otherwise one could promote growth with a few bombs).

5. Creative destruction is the engine of economic growth.

Ok.

6. Monetary stability, too, is necessary for growth; inflation is always harmful.

No reputable economist today would deny that a stable money supply encourages investment and bolsters social cohesion, since it helps people save for the future. Inflation, on the other hand—always caused by governments’ spending more money than they have, and then printing extra money or borrowing to finance the expenditure—destroys entrepreneurship, slows growth, and generates social inequality. It is an incentive not for investment but for speculation: those who can afford to will buy goods, wait, and then resell them at higher prices, a process that creates

nothing at home—least of all, new jobs. Those with less money fall victim as wages and pensions lag behind prices. It’s no surprise that hyperinflation often leads to revolution. Milton Friedman’s advocacy of monetary stability, “monetarism,” considered revolutionary when first proposed in the sixties, is now common wisdom.

So the price of, say, imports has no effect on inflation. And people are too dumb to calculate with constant inflation. Of course central banks are today more interested in keeping inflation constant (and above zero!!!) and are not interested in constant growth of money.

The list goes on, but I´m to tired to work through this muddle. Long live economics!

I read through Donald Saaris new book during the holidays and here are my thoughts. Let´s start with the target audience. Who should read this book? Well, anyone interested in voting theory. But one should know some voting theory beforehand. Saari uses some terms like "strategy-proofness" without explaining them. If, however, you know the basic theory, the book makes for an easy pleasurable read.

The content is basically an overview over Saaris work on voting for the very educated layhuman. Those who have read his papers or even just some other book of him will recognize a lot of themes: How independence of irrelevant alternatives forces a voting rule to ignore the transitivity of preferences, the proccedure line, how one can use linear algebra to decompose profiles, why the axiomatic method is flawed and similar themes running to most of his work on voting theory. Some of the material included cannot be found in any of his other books, in particular his discussion of topological social choice theory, voting dictionaries, and of voting with Euclidean preferences and its extensions. If you don't know this stuff but have some basic background knowledge, this book makes for a great introduction. But even those who have read Saaris papers will learn a lot of new things and get very insightful discussions. He actually presents a new way of decomposing profiles, so researches will get some new ideas. Personally, I have most benefitted from his discussions. Here´s Saari on what´s wrong with "axiomatic charaterizations":

Rather than axioms, this field usually uses assumtions, or properties, or hypotheses. Often these conditions just uniquely identify a particular voting rule. "Uniquely identifying" is very different from "characterizing" or "creating the building blocks for a theory." For instance, the two properties of being of Finnish-American background and receiving my Ph.D. in mathematics from Purdue University in a certain year uniquely identify me, but they most surely do not characterize me.

The book is full of gems like this and warmely recommended.

By googling a related topic, I stumbled over this old post of Bryan Caplan.

After giving an old school form of Arrows theorem, he writes the following:

So how can I furrow my brow in annoyance at this whole field? Simple: Social choice theorists want to morally rank choices without mentioning what the choices are. For example, suppose a group can do A, B, or C, and A is everyone's first choice. Surely they should do A, right?

Wrong! Suppose:

A="Murder everyone who isn't in our group"

B="Murder everyone over 6 feet tall who isn't in our group"

C="Don't murder anyone.

Then it's morally obvious that the group should choose C, and any rule that gives a different result is wrong. For Arrow's Theorem buffs, my claim is that the non-imposition axiom is not only not obviously right; it is obviouslyouldo wrong.

Well, there´s an obvious counter. If people decide about people outside the group, maybe we should simply enlarge the group of voters. Problem solved. Otherwise every rule could be dictatorial (just reduce the group to one person). But that´s beside, because with two alternatives, Arrows conditions are of course satisfied for plurality rule, but we don't want 51% of the people exploit the rest. Maybe one really should introduce things like rights, welfare comparisons and similar things into social choice theory? Duh. It´s been done of course. Just take a look at an elementary social choice textbook like, the one of Wulf Gaertner (recommended). You can find all these issues there.

I think I´m going to make a post in which I explain that all of microeconomics is flawed because imperfect competition is completely ignored. Or that labor economists should start using search theory...

"all the women are strong, all the men are good looking, and all the children are above average," - Garrison Keillor on Lake Wobegon

One of the most touted results in behavioral economics is that people are overconfident. Most people see themselves as better than average or even better than the median. Now there's a working paper by Jean-Pierre Benoit and Juan Dubra, Overconfidence? that shows much of the evidence to the effect that people are irrationally overconfident actually isn't. Here's a beautiful example they give:

consider a large population with three types of drivers, low skilled, medium skilled, and high skilled, and suppose that the probabilities
of any one of them causing an accident in any single period are pL = 4/5, pM = 2/5 and pH = 0, respectively. In period 0, nature chooses a skill level for each person with equal probability. Initially no driver knows his or her own skill level, and so each person (rationally) evaluates himself as no better or worse than average. In period 1, everyone drives and learns something about his skill, based upon whether or not he has caused an accident. Each person is then asked how his driving skill compares to the rest of the population. How does a driver who has not caused an accident reply?

The answer is a straightforward exercise in applying Bayes law. And one can expect most drivers do think they are most likely in the top third of drivers- provided they are good Bayesians.

After receiving an impressive amount of ad hominem attacks for writing on my views on the Austrian sect of economics, I#'e decided to go against my own advise and explain just why this school is nonsense. I focus on the Rothbard nonsense that seems to be "popular" in the US. And no, I have nothing against good old Menger (although I prefer Karl to Carl). And while I´m not impressed with Hayek, he has at least not dabbled in anti-empiricist praxeology.

Rothbard writes stupid nonsense and has problems arguing logical. Let´s take a look at his book Man, Economy and State. And no, I haven't read the book. I read the first chapters and realized I cannot stand more nonsense. So my criticism will be restricted to stuff from the beginning of the book:

Supposedly, one can derive all of economics from one axiom. Why this has to be nonsense should be clear from reading any book from any major philosopher of science of the last 100 years or so. But being sympathetic to mathematical economics, I can happily live with axiomatic approaches. Let´s look what the axiom is and what follows. The "axiom" is:

The distinctive and crucial feature in the study of man is the concept of action. Human action is defined simply as purposeful behavior. It is therefore sharply distinguishable from those observed movements which, from the point of view of man, are not purposeful. These include all the observed movements of inorganic matter and those types of human behavior that are purely reflex, that are simply involuntary responses to certain stimuli. Human action, on the other hand, can be meaningfully interpreted by other men, for it is governed by a certain purpose that the actor has in view.[2] The purpose of a man’s act is his end; the desire to achieve this end is the man’s motive for instituting the action.

All human beings act by virtue of their existence and their nature as human beings.[3]We could not conceive of human beings who do not act purposefully, who have no ends in view that they desire and attempt to attain. Things that did not act, that did not behave purposefully, would no longer be classified as human.

It is this fundamental truth—this axiom of human action—that forms the key to our study. The entire realm of praxeology and its best developed subdivision, economics, is based on an analysis of the necessary logical implications of this concept.

So "man" (and maybe the other half of humanity) act purposeful. Granting that, let´s look at what supposedly follows:

Another fundamental implication derived from the existence of human action is the uncertainty of the future. This must be true because the contrary would completely negate the possibility of action. If man knew future events completely, he would never act, since no act of his could change the situation. Thus, the fact of action signifies that the future is uncertain to the actors.

Let´s look at the last wo sentences once more:

If man knew future events completely, he would never act, since no act of his could change the situation. Thus, the fact of action signifies that the future is uncertain to the actors.

This is of course an obvious confusion. The first sentence refers to uncertainty generated by uncertainty about how "man" chooses, the second refers to the uncertainty "man" faces. Suppose our "man" has a choice set {a,b} and is indifferent between a and b. We are uncertain about the actors choice, but she isn't. Replace "she" by "he" and you get a counterexample to Rothbarts claim.

In chapter 2 Rothbard manages to "derive" a structure of time preferences from his "axiom":

A fundamental and constant truth about human action is that man prefers his end to be achieved in the shortest possible time. Given the specific satisfaction, the sooner it arrives, the better. This results from the fact that time is always scarce, and a means to be economized. The sooner any end is attained, the better. Thus, with any given end to be attained, the shorter the period of action, i.e., production, the more preferable for the actor. This is the universal fact of time preference. At any point of time, and for any action, the actor most prefers to have his end attained in the immediate present. Next best for him is the immediate future, and the further in the future the attainment of the end appears to be, the less preferable it is. The less waiting time, the more preferable it is for him.[15]

Exercise: Write down a two-period model without discounting in which "man" acts purposefully. But Rothbart is not that stupid- so he contradicts himself in footnote 15:

Thus, a common type of objection to the assertion of universal time preference is that, in the wintertime, a man will prefer the delivery of ice the next summer (future) to delivery of ice in the present. This, however, confuses the concept “good” with the material properties of a thing, whereas it actually refers to subjective satisfactions. Since ice-in-the-summer provides different (and greater) satisfactions than ice-in-the-winter, they are not the same, but different goods. In this case, it is different satisfactions that are being compared, despite the fact that the physical property of the thing may be the same.

With time-dependent consumption, we are after all all fans of Arrow and Debreu, of course all goods at different times are different goods- so Rothbarts claim is vacously fulfilled.

Those who think non-convex preferences are at least logically compatible with purposeful action are in for a shock at 2b. Rothbard derives the "law of marginal utility" from his "axiom".

The important consideration is the relation between the unit to be acquired or given up and the quantity of supply (stock) already available to the actor. Thus, if no units of a good (whatever the good may be) are available, the first unit will satisfy the most urgent wants that such a good is capable of satisfying. If to this supply of one unit is added a second unit, the latter will fulfill the most urgent wants remaining, but these will be less urgent than the ones the first fulfilled. Therefore, the value of the second unit to the actor will be less than the value of the first unit. Simi­larly, the value of the third unit of the supply (added to a stock of two units) will be less than the value of the second unit. It may not matter to the individual which horse is chosen first and which second, or which pounds of butter he consumes, but those units which he does use first will be the ones that he values more highly. Thus, for all human actions, as the quantity of the supply (stock) of a good increases, the utility (value) of each additional unit decreases.

Exercise: Write down a utility function on the positve orthant of R² that violates the "law of marginal utility".



Enough. Time is scarcy and I don't want to waste my young life on reading pornography for libertarians. I already became dumber from browsing through this stuff. It should be obvious by now that one cannot get more out of axioms than one puts in there. And for doing economics, one has to put a lot more into it.

Leonid Teytelman, a Berkley grad student who has created www.obamaforeconomy.com. (check what Heckman wrote) claims to have had a rather remarkable email conversation with Ed Prescott. Read the whole thing at Pandagon. DeLong comments too. Here are some excerpts of what prescott supposedly wrote (wirting mistaks are original):

All respectable students of public finance agree the taxing of capital income is bad policy.

Our health systemn was great until the federal government got involved.

In economics there is almost always one theory or no theory.

Society needs religion to get around the time inconsistency problem. Your religion of Statism is a not a good religion. It is detrimental to the welfare of the people. A basic tenet of my religion is free to choose and to enter into mutually beneficial contracts.

I have left out the many insults. I fear it is really Prescott.

In this (HT to Gabriel) strangely fascinating piece, Walter Block makes a very valid point.And no, it´s not about fractional reserve banking:

[Bryan Caplan] is, however, a bitter critic of all things concerning Austrian economics ([...]). On the other hand, in my view, Caplan is fast becoming a rising star among the neo-classicals; he writes voluminously and negatively about Austrian economics. But he always spells that name correctly, and, thus, garners far more publicity for us than would otherwise be the case. I would vastly prefer that mainstream economists attack praxeologists rather than ignore us. In that way, they set up targets for us, and better enable us to break out into the society at large.

Which is exactly why one shouldn't debate them that much. And by the way: "Austrian" refers to things coming out of Austria and "Economics" stands for a science, "Austrian Economics" is neither of them, which is why I used "Austrian school of economics". The wisest words on this have been said by Robert Solow when Interviewed by Arjo Klamer when attacking a far less deserving target:

Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the Battle of Austerlitz. If I do that, I'm getting tacitly drawn into the game that he is Napoleon Bonaparte.

Similarly, I certainly don't want to get tacitly drawn into the view that this school is a serious alternative to anything. I don't think one should feed delusions. Let´s read some Block:

Reading from here, I see the following:

"Yesterday at the FEE seminar, I got to hear the excellent Jeff Hummel thoroughly debunk the crazy Rothbardian view that fractional reserve banking is "fraudulent." It was fun (and funny) lecture, but the target was too easy."

I infer, then, that you guys, both of you, have published attacks on the "crazy Rothbardian view." I'm trying to put together a bibliography on both sides of this "easy" target, see below. Yet, I don't have anything from either of you on this list. Please send me the cites of your pubs debunking the Rothbard-Hoppe view that frb amounts to fraud, counterfeiting and theft.

WTF? One publishes criticism of important but misguided views, not on a target that is too easy. This reminds me of a book I heard about a long time ago (can someone help me out?). A guy published his correspondences with prominent figures such as Einstein or the pope. Which does of course notimply that they actually wrote back. I think that´s a natural evolution for the discourse on the Austrian school of economics.

P.S.: Those guys are really against fractional reserve banking? I really didn't expect that these guys want to destroy capitalism.

Arnold Kling thinks that we know way to little about the economics behind the crisis. He seems to be a little bit angry:

My main beef with economists is that standard macroeconomics does such a poor job of describing what is going on. The textbooks models are pretty much useless. Where in the textbooks is "liquidity preference" a demand for Treasury securities? Where in the textbooks does it say that injecting capital into banks is a policy tool?

Graduate macro is even worse. Have the courses that use representative-agent models solving Euler equations been abolished? Have the professors teaching those courses been fired? Why not?

I have always thought that the issue of the relationship between financial markets and the "real economy" was really deep. I thought that it was a critical part of macroeconomic theory that was poorly developed. But the economics profession for the past thirty years instead focused on producing stochastic calculus porn to satisfy young men's urge for mathematical masturbation.

Economists ought to admit that we do not know much about what is going on today. Neither do the Fed Chairman and the Treasury Secretary. Of course, the market demand is for "strong" leaders and for "strong" economists, who can fool the public into believing that they have great knowledge. The ones who do this best are those who have fooled themselves.

I don't really understand why he wants professors fired for teaching things not applicable to the crisis, but that´s kind of besides the point. We do actually know a great deal about the crisis. There´s an excellent survey by Markus Brunnermeier, Deciphering the 2007-08 Liquidity and Credit Crunch, to appear in the Journal of Economic Perspectives. The survey cites lots of theoretical literature relevant to the crisis. But Markus Brunnermeier is not a macroeconomist. He´s a finance theorist. And the literature he cites doesn't really come from macroeconomics either. What matters for understanding these things are knowledge and assymmetric information and a solid knowledge of institutional details. One can understand liquidity from the microeconomic perspective. Here is a nice paper from Hyun Song Shin on the topic, and here is a relevant working paper.

There are actually textbooks on financial crisis. See here and here.

But don't expect DSGEs to be of much use in understanding the crisis...

It´s polpular to bash Nobel memorial medalist Gunnar Myrdal. As yet another sheep I internalized this view without really knowing much about Myrdals work. I started to doubt the received view when I heard Larry Blume praising Myrdals "Monetary Equilibrium" of 1939. Gunnar Myrdal was a really clever economist and one of the first to have a modern concept of dynamic, intertemporal equilibrium as opposed to the steady state view of Hicks and company that was popular back then. Read the first part of this to get some idea of how brilliant his thinking was.