Monday, January 18, 2016

Assuming answers to complex integrals


The basic problem with a lot of discussion of economic methodology is that many people (e.g. [1], [2]) assume they know the answer to this:

$$
\text{(1)}\;\;\; \int dE \;\;\;  \left( \hat{O} | H. \;\; economicus \right) \stackrel{?}{=} \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right)
$$

where $E$ is an economy and $\hat{O}$ is some observable operator. The integral is just a notational way of representing an aggregation problem using a given agent model. But we don't know the answer. No one does. Anyone who claims an answer is probably just assuming an answer.

On this blog, I make a case that most of the time

$$ \text{(2)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \simeq \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right) $$

where $H. \;\; atomicus$ is an even simpler creature that has no brain whatsoever and simply randomly walks into an office, receives money, and then bumps into products and buys them.

And whenever

$$ \text{(3)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \neq \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right) $$
it is generally bad news.

I did show that under certain conditions:

$$ \text{(4)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \simeq \int dE \;\;\; \left( \hat{O} | H. \;\; economicus \right) $$

But at the end of the day there is no answer to equation (1).

6 comments:

  1. Where "most of the time" intersects "under certain conditions" it appears that you "make the case" "on this blog" that (1) approximately holds.

    ReplyDelete
    Replies
    1. In (4), I should probably say $d\tilde{E}$ since it isn't an integral over a real economy.

      Delete
    2. On both sides of the equation?

      Delete
  2. I think this is the best paragraph-long introduction to economics I have ever seen! Bravo, sir!!

    Perhaps OT but have you seen the recent Atlanta Fed inflation forecast? Looks like they are doubling down on the 2.5% inflation forecast going forward.

    Atlanta Fed's Inflation Forecast

    ReplyDelete
    Replies
    1. I had seen that. I might be wrong, but I interpreted it as saying the breakeven wasn't actually falling. Naive interpretation of the breakeven says expected inflation is closer to 1%, but ATL Fed says naive interpretation is wrong and expectations are closer to 2-2.5% and stable.

      Which means that if inflation does come out to be 1%, then either a) the ATL Fed is right and markets are wrong or b) the ATL Fed's method of extracting expectations from the breakeven is wrong (and the status of the market forecast is unknown).

      Delete

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