Yet another Sheep

Gabriel reminds us that core theory is useful in economics and can actually be used in an undergraduate economic education. Personally, I dream about something a lot more radical: A principles textbook based on general equilibrium theory. I think partial equilibrium thinking very misleading. Here are some advantages that a general quilibrum based principles textbook would have:

1. Gains from trade can be discussed correctly.

2. One can introduce incentive problems with nice examples of burning goods.

3. Externalities and efficiency can be treated by Lindahl prices.

4. One can discuss the difference between pairwise trades and market trades.

5. One can talk about the real problem of the firm incompetitive markets.

6. One can discuss nonconvexities.

All these issue are usually treated miserably in principles textbooks. And they aren't harder to understand than all the usual stuff about short-run/lon-run cost crves, elasticities and all that. I think the two welfare theorems are actually very tools that can be used to analyze many economic problems that have little relation with each other i a principles textbook. One can do with few basic principles and give a much deeper understanding.

Kenny Easwaran from Antimeta has a post in which he gives an economic argument for the convergence of a geometric series:

Then we can calculate mathematically that the present value of an income stream of $1000 a year in perpetuity is given by the sum

\frac{1000}{1.01}+\frac{1000}{1.01^2}+\frac{1000}{1.01^3}\dots.

Going through the work of summing this geometric series, we find that the present value is

\frac{1000/1.01}{1-1/1.01}=\frac{1000}{1.01-1}=100,000.

However, there is an easier way to calculate this present value that is purely economic. The argument is not mathematically rigorous, but there are probably economic assumptions that could be used to make it so. We know that physical intuition can often suggest mathematical calculations that can later be worked out in full rigor (consider things like the Kepler conjecture on sphere packing, or the work that led to Witten’s Fields Medal) but I’m suggesting here that the same can be true for economic intuition (though of course the mathematical calculation I’m after is much simpler).

The economic argument goes as follows. If money in any year is worth 1.01 times money in the next year, then in an efficient market, there would be investments one could make that pay an interest of 1% in each year. Investing $100,000 permanently in this and taking out the interest each year gives rise to this income stream, and thus one can fairly trade $100,000 to receive this perpetual income stream, so they must be equal in value. We don’t need to sum the series at all.

Now perhaps there is a sense in which the mathematical argument given above and the economic argument given below can be translated into one another, but it’s far from clear to me. Thus, it looks like at least sometimes, economic intuition can solve mathematical problems.

There is a very simple pseudoproof that

\sum_{n=0}^\infty \delta^n=1/(1-\delta).

It goes like this:

S=1+\delta+\delta^2+\delta^3+\ldots\\
S=1+\delta S\\
S=1/(1-\delta)

It is only a pseudoproof because for this to work we have to show first that the sum converges. Given this formula, it is easy to arrive at Kennys result. In his argument Kenny uses the fact that a present value exists, so there is a price for the income stream. But that can only be true if the sum converges, the hard part is left out. So economics isn't really of much use here.

Often, one can read in macroeconomic papers that there is a continuum of agents each facing the same independent risk. It is further stated that in the aggregate, there is no risk any more by the "law of large numbers".

Now there is a problem. The standard integral, the Lebesgue integral, satisfies three well known properties, called Littlewood's principles. One is that a integrable function is nearly continuous. Formally a Lebesgue integrable function is equal to a continuous function almost everywhere by Lusin's theorem. So if we can build an integral, it doesn't look like the draw of an iid process. While one can define an iid process on the unit intervall, the outcomes cannot be integrated. This poses a problem for models working with the distribution of the aggregate. The first way out is due to Kenneth Judd who solved it in 1985 in a slighlty ad hoc manner: Extend the measure so that the "law of large numbers" holds. This is ad hoc because many other extensions exist, so Judd basically assumes the law of large numbers to hold and proves this to be consistent.

Others have tried other ways: Mark Feldman and Christian Gilles worked with finitely additive measures (or charges), Nabil Al-Najjar does the same by working with finite approximations, Carlos Alos-Ferrer drops the iid assumption and asks under what conditions can we get aggregate certainty, Harald Uhlig doesn't integrate the sample outcomes but the random variables by the Pettis integral. A nice survey can be found here. The best way to do it is IMO to use non-standard analysis and work with processe on a hyperfinite Loeb spaces. Intuitively that's a infinite measure space that looks a lot like a finite set. A nintroduction to the law of large numbers for such a space can be found in an article in the Bulletin of Symbolic Logic: Yeneng Sun, Hyperfinite Law of Large Numbers (subscription required). The mathematics of nonstandard analysis are however unfamiliar to most economists (including mathematical ones).

The great thing with the Cowles Foundation is that they make evrything available. So if you want to read the classics of economics, you can do so for free in many cases:

SILVER MONEY by Dickson H. Leavens


THE VARIATE DIFFERENCE METHOD by Gerhard Tintner


THE ANALYSIS OF ECONOMIC TIME SERIES by Harold T. Davis


GENERAL-EQUILIBRIUM THEORY
IN INTERNATIONAL TRADE by Jacob Mosak


PRICE FLEXIBILITY AND EMPLOYMENT
by Oscar Lange


STATISTICAL INFERENCE
IN DYNAMIC ECONOMIC MODELS by Tjalling Koopmans (Ed.)


ECONOMIC FLUCTUATIONS
IN THE UNITED STATES
1921–1941
by
Lawrence R. Klein


SOCIAL CHOICE
AND INDIVIDUAL VALUES 2nd ED by Kenneth J. Arrow


SOCIAL CHOICE
AND INDIVIDUAL VALUES by kenneth J. Arrow


ACTIVITY ANALYSIS OF
PRODUCTION AND ALLOCATION by Tjalling C. Koopmans (Ed.)


STUDIES IN
ECONOMETRIC METHOD by Tjalling C. Koopmans and William C. Hood (Eds.)


PORTFOLIO SELECTION
EFFICIENT DIVERSIFICATION OF INVESTMENTS by Harry M. Markowitz


THEORY OF VALUE by Gerard Debreu


RISK AVERSION AND PORTFOLIO CHOICE by Donald D. Hester and James Tobin (Eds.)


STUDIES OF PORTFOLIO BEHAVIOR by Donald D. Hester and James Tobin (Eds.)


FINANCIAL MARKETS AND
ECONOMIC ACTIVITY by Donald D. Hester and James Tobin (Eds.)

ECONOMIC THEORY OF TEAMS by Jacob Marschak and Roy Radner

EFFICIENT ESTIMATION
WITH A PRIORI INFORMATION by Thomas J. Rothenberg

THE COMPUTATION OF
ECONOMIC EQUILIBRIA by Herbert Scarf

BANK MANAGEMENT
AND PORTFOLIO BEHAVIOR by Donald D. Hester and James L. Pierce

THE EFFICIENT USE
OF ENERGY RESOURCES by William D. Nordhaus

DISEQUILIBRIUM DYNAMICS by Katsuhito Iwai

Enjoy!

Faruk Gul and Wolfgang Pesendorfer have an excellent workingpaper criticising the methodology of neuroeconomics: The Case for Mindless Economics It´s quite long, but I think it is a must read piece for those who want to come to grips with this movement. I was surprised just how weird the neuroeconomics people are:

"Addiction is an important topic for economics because it seems to resist rational explanation. .... It is relevant to rational models of addiction that every substance to which humans may become biologically addicted is also potentially addictive for rats." - Camerer, Loewenstein and Prelec

I like the commonsensical answer of Gul and Pesendorfer:

"That substances addictive for rats are also addictive in humans is not relevant for economics because (standard) economics does not study rats."

and in a footnote:

"Presumably, psychologists interested in human physiology find it worthwhile to study rats because of the similarities in the neurological make-up of the two species. Apparently, the similarities between the economic institutions of the two species are not sufficient to generate interests in rats among economists."

:-)

Robert Viennau has a post on the logician Barkley Rosser. Rosser himself showed up and commented. He told a nice story:

Another figure of some interest is M.M. Flood, who with Dresher at RAND actually invented the concept of the prisoner's dilemma. They did one of the earliest of economic experiments, a 100-round repeated prisoner's dilemma game in which Armen Alchian and a mathematician whose name I forget now eventually learned to cooperate (the mathematician kept saying "what is the matter with Alchian? Can't he figure this out?"), although they would defect in the final rounds as predicted. This result reportedly upset Nash greatly, who was visiting at RAND at the time, and would lead him to abandon game theory eventually, supposedly, at least for awhile. He could not accept that people would behave so "irrationally" as to cooperate in violation of his equilibrium (which predicts that people defect in a P.D. game).

:-)

Tyler Cowen has a post about a slate article on the relative scarcity of good male catches in early cohorts:

The problem of the eligible bachelor is one of the great riddles of social life. Shouldn't there be about as many highly eligible and appealing men as there are attractive, eligible women?

Actually, no—and here's why. Consider the classic version of the marriage proposal: A woman makes it known that she is open to a proposal, the man proposes, and the woman chooses to say yes or no. The structure of the proposal is not, "I choose you." It is, "Will you choose me?" A woman chooses to receive the question and chooses again once the question is asked.

[...]

You can think of this traditional concept of the search for marriage partners as a kind of an auction. In this auction, some women will be more confident of their prospects, others less so. In game-theory terms, you would call the first group "strong bidders" and the second "weak bidders." Your first thought might be that the "strong bidders"—women who (whether because of looks, social ability, or any other reason) are conventionally deemed more of a catch—would consistently win this kind of auction.

But this is not true. In fact, game theory predicts, and empirical studies of auctions bear out, that auctions will often be won by "weak" bidders, who know that they can be outbid and so bid more aggressively, while the "strong" bidders will hold out for a really great deal. You can find a technical discussion of this here. (Be warned: "Bidding Behavior in Asymmetric Auctions" is not for everyone, and I certainly won't claim to have a handle on all the math.) But you can also see how this works intuitively if you just consider that with a lot at stake in getting it right in one shot, it's the women who are confident that they are holding a strong hand who are likely to hold out and wait for the perfect prospect.

The argument has a very simply flaw: The (relative) value of a bachelor depends on the value of the option to search: But this option changes with the distribution of singles, which changes over time. There are ther things changing too: Young women are empirically more in demand and expected "living ever happily after" depends on life expectancy.

No, according to a working paper by Andreas Hornstein, Per Krusell and Giovanni L. Violante: Frictional Wage Dispersion in Search Models:
A Quantitative Assessment. They show that the ratio between the mean of the distribution of wage offers and the reservation wage, the mean/min-ratio, is independent of the exact form of the distribution of wage offers and use it to test the model. The diffeence between observed and predicted wage dispersion is of order 20, standard extensions don't change much.

What should one learn in a principles course? Here´s what I think is really essential:

• Many social phenomena can be explained by preferences, beliefs and constraints.


• There´s a difference between causality and correlation.


• What is individually rational may be bad in the aggregate.


• Aggregate behavior can differ much from individual behavior.


• Wether a threat is credible depends on wether one would want to enforce the threat.


• A social situation with large unexhausted profit possibilities is not likely to persist.


• Cooperation is often hard to sustain and requires clever incentive schemes.

Actually, this stuff should be thaught in highscool.

At Wikipedia, a transaction cost is defined as "a cost incurred in making an economic exchange." That (and some equivalents) are pretty much the only definition I found that is not simply a list of things that should be counted as costs. So let´s take the Wiki definition as a starting point.

The problem is that people speak even about transaction costs in cases where there is no transaction: "The agents didn't make the transaction, because transaction costs were too high." This is basically reasoning involving what is known as a counterfactual in philosophy:

If they would have made the exchange, they would have incurred a certain cost and that cost was higher than what they expected to get from the transaction which resulted in them not making the transaction.

So transaction costs are often costs not incurred by anyone actually. This is no problem in science, almost everything in science is about counterfactuals: "X is ealastic." means that if I would deform X, it would go into its original form afterwards. What we need is to have a concept about what would happen. So if a transaction wasn't made "because transaction costs would have been too high.", we should be able to say what would have been if the transaction was actually made. Often, this poses no problem: "I don't buy X, because I would have to drive at least an hour to get to the store".

But sometimes it is not so clear what is the issue. Let´s take a classical problem of adverse selection:

"I didn't buy the used car, because it is probably a lemon. I mean, who would have given a good car at that price?"

There is no transaction here. Proponents of "transaction cost economics" would say there was no transaction here because the cost was too high. But the cost of the car is simply its price plus some inconveniences like paperwork. What is unknown is wether the good is good enough, the transaction cost is well known. Now a clever transaction cost economist might say: What you want to buy is a good car for sure; good in every state. Buying a good car for sure from a used car seller would require expensive checkups, the transaction costs here. And they are too high.". That might well be true but, it does miss the point of adverse selection. If the seller were clueless about the quality of the car, adverse selection would be no problem and both could exchange a lottery over quality. If this would be acceptable, the problem was not an issue of transaction costs.

So why should we view problems of asymmetric information as transaction costs being too high?