Wednesday, September 26, 2012

Math, Complexity, Economy

In his 2010 paper "Some Epistemological Implications of Economic Complexity," Roger Koppl cites Fritz Machlup's (1978)
examples of statements exhibiting economic logic Statement(1): "If, because of an abundant crop, the output of wheat is much increased, the price of wheat will fall." Statement(2): "If, because of increased wage-rates and decreased interest rates, capital becomes relatively cheaper than labor, new labor-saving devices will be invented." Statement(3): "If, because of heavy withdrawals of foreign deposits, the banks are in danger of insolvency, the Central Bank Authorities will extend the necessary credit." (Machlup, 1978, p. 64)
Koppl notes that
The first statement is more reliable than the second and the second is more reliable than the third.
This is because, citing Machlup again,
causal relations such as stated in (2) and (3) are derived from types of human conduct of a lesser generality or anonymity. To make a statement about the actions of bank authorities (such as (3)) calls for reasoning in a stratum of behavior conceptions of much less anonymous types of actors. We have to know or imagine the acting persons much more intimately (Machlup, 1978, p. 68)
Koppl relates this to his "Big Players" thesis. And I think he is right to do so. And he argues that this makes "literary methods" necessary in economics. And I think he is right to do so. But there is also something implied here that is not stated explicitly.

The situation in statement(1) is that of a "pure market." Such a "pure market" is calculable. One could easily use mathematical methods. But too many who use mathematical methods think that they can use these methods to plan or at the very least regulate the economy. But note that the emergence of a Big Player who can in fact use such math to adjust the economy to try to make it perform in this or that fashion creates a situation in which mathematical methods fail.

In other words, modeling pure markets with math gives us the hubris to believe we can use math to control the market, but in creating a position in which someone can control the market, the math is then necessarily going to fail to model the new condition of Market + Big Player. And what about statement(2)? Well, with statement(1), we have a "pure market," or, more accurately, a catallaxy statement. Statement(2) is a statement of Catalaxy + Technological Order. The addition of a second spontaneous order makes the process too complex for math.

And the Catallaxy never stands alone. It is always interacting with the Technology order, the Monetary order, etc. And if the order is mostly dominated by a Big Player (as is the case with the Monetary order), the interactions are even less calculable. Another way of putting this is to turn the statements above into the questions "If . . . will . . . ?" Then we can answer them as such:

(1) Yes

(2) Probably, but the nature of the change will be unknown until developed.

(3) It depends on the Authorities' knowledge, understanding, background, ideology, etc. We cannot know what they will do, even if we know what they did in the past under what we assume to be similar circumstances.

Note that even here the answers increase in complexity. And I greatly truncated (3). We thus have what seems to be a paradoxical situation. So long as we leave the economy alone, we can compute or calculate it; but if we try to use those computations/calculations to intervene in the economy, we can no longer compute or calculate it, meaning the early computations/calculations are no longer valid. Alas, such paradoxes are of the very nature of the world.
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