Robert's Stochastic thoughts

Friday, September 18, 2009

What would it take for Say's law to hold

Say thought that aggregate demand had to equal aggregate supply. This is true in the simplest model in which people trade non durable consumption goods (always called apples and oranges). Add up individual budget constraints and you get that planned spending can't be higher than planned sales unless someone made an arithmetic mistake.

John Cochrane appears to believe in Say's law. Many people have pointed out that he forgot about the existence of money. If people want to increase their money holdings then planned spending can be less than income.

It's not just about money II

Cochrane's error is not just that he forgot about money. For one thing, less liquid financial instruments invalidate Say's law too.
Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.

Let's say we all plan to sell our shares (commmon stock) to buy goods and services. That way planned consumption plus taxes plus investment plus net exports can be greater than GNP. The distinction between money and other financial assets is very important in many ways, but it is not relevant to Say's law which would be invalid even if we bought and sold stock with non-durable consumption goods (apples) and not with money.

But it isn't enought to assume no financial instruments (which is odd for a finance professor but hey ...). The demand for currently produced goods can be greater (or less) than production of goods, because people can trade durable goods made long ago for currently produced goods and services.

Cochrane is right in a Walrasian model with one period or in a Walrasian model in which nothing nothing at all lasts from period to period. So a model where we trade apples for oranges is a model in which my yearly planned consumption must be roughtly equal to my yearly income. However, if the model also includes apple trees and orange trees, then this is no longer true.

If I own apple trees then my demand can be greater than my income. I have wealth (the trees). I can buy apples and oranges by selling my trees. If everyone wan't to sell trees (not made this period) to buy fruit (made this period) then planned consumption of goods produced this period will be greater than production of goods produced this period.

The value of trees does not appear in GNP unless they just matured (the value of pruning trees does). The budget constraint includes, at least, current income plus wealth (with perfect financial markets it also includes the expected present value of future labor income).

Cochrane is assuming that income = wealth. This is a much stronger assumption than that there is no money or no financial instruments.

6 comments:

Anonymous said...: "This is true in the simplest model in which people trade non durable consumption goods (always called apples and oranges)."

Not so. In some places, the preferred consumptions goods are beer and pretzels; of course, these are complements rather than substitutes, so complicate the analysis in interesting ways.; 4:48 PM
Unknown said...: "Cochrane's error is not just that he forgot about money."

Cochrane may or may not have forgotten about money, but you forgot about prices. In perfect markets, prices adjust so that the PV of discounted future expected spending equals the PV of discounted future expected income.

You would be better served to explain why prices don't adjust than waste time on some amorphous "law" about aggregation. There are many markets in which prices don't adjust quickly (e.g., labor), and you could have a reasonable discussion with the likes of Cochrane if you focused on the market failures rather than yelling about what you think he said about Say's "law".; 9:42 PM
Robert said...: I consider it odd to suggest that a post on "What would it take for Say's law to be true" is criticized for discussing Say's law.

I also find it odd, that your criticism of my post does not consider the definition of Say's law. How about checking the Wikipedia

http://en.wikipedia.org/wiki/Say%27s_law

Say was not talking about equilibrium with market clearing prices. He claimed that the law had to hold even if prices weren't market clearing prices.

Say definitely claimed that there could not be a general glut for any prices. When discussing his claim, I correctly, found a counter example based on prices other than market clearing prices, since he asserted that his claim was valid for all prices.

the point of my post was that, as far as Say's law is concerned, there is nothing special about money.

Your criticism, basically, is that I should have written on another topic, not that I wrote something incorrect on my chosen topic.

The; 8:49 PM
Unknown said...: Cochrane also thinks externalities, asymmetric information and bounded rationality don't exist because they don't appear in his models.; 2:26 PM
Don Coffin said...: I recall concluding that the real function of Say's Law (in his *A Treatist on Political Economy*) was to guarantee that deficient demand was not an impediment to growth.

In (roughly) the first half of the book, he presents a static version of the Law. But where he's going (which is where a lot of the classical economists ultimately were going) was to discuss growth. There were in fact stagnationists--or, perhaps, it's better to call them believers in satiation--who thought that demand for goods and services would lag behind our ability to produce (call it potential GDP). Say used his law of markets to argue that satiation would not (necessarily) lead to stagnation.

In making the argument in the way he did, he used the law of markets in a dynamic framework. Unfortunately, almost everyone who later refered to Say's Law apparently quit half-way through his book...or at least that's how it seemed to me when I was in grad school...and I've never found a reason to change my mind.; 12:18 PM
Bruce Wilder said...: I doubt very much that Cochrane really "forgot" that Say's Law is a fallacy, or that money and credit and durable goods makes it a fallacy.

In the paragraph following, in Cochrane's rant, Cochrane took up Barro's Ricardian Equivalence. He mis-stated that as well, but also explained a bit more about how he saw the requirements of careful thinking and analysis in economics.

My interpretation is very generous, given Cochrane's intemperate rage, but I think what Cochrane is trying to say is that economics needs Laws of Conservation.

To analyze the aerodynamics of an airflow moving through a fluid, air, we could analyze the sitution in terms of energy, momentum or mass, relying on the principles of conservation of energy, momentum, or mass. The whole shebang, save viscosity, is laid out in "Euler's Equations".

Say's Law is a kind of primitive Law of Conservation, and so is Barro's Ricardian Equivalence.

Cochrane is saying good economic analysis ought to respect some principle of conservation -- an adding-up constraint that forces us to fully account for effects.

If money is, variously, unit-of-account, medium-of-exchange, and store-of-value, then each of those functions might be thought of, as subject to its own law of conservation, and the three together constituting a system.; 7:58 PM