28 Jun 2011

On Using Models

Economics, Federal Reserve, Financial Economics 5 Comments

From Mises’ Theory of Money and Credit (though it is from the later material, which was written much later than the original 1912 edition):

“There are problems of theory full comprehension of which can be attained only with the aid of the theory of indirect exchange. To seek a solution of these problems, among which, for example, is the problem of crises, with no instruments but those of the theory of direct exchange, is inevitably to go astray.” (p. 462)

I’m not as knee-jerk opposed to “mathematical models” in economics as many Austrians claim to be. I think when we talk about Robinson Crusoe, or a two-country international trade problem, or use a Hayekian triangle, we’re basically doing the same type of thing.

However, Mises’ quote above really struck me, because I had had similar misgivings in our upper-level macro courses at NYU. In the world of the model, people (or should I say, the Representative Agent) had rational expectations, knew all the production functions, demand functions, and vector of equilibrium prices.

In that world, there was no role for money as a medium of exchange. We could arbitrarily pick one of the commodities as the numeraire, define its price as 1, and then price everything else relative to it. But ultimately this was a world of direct exchange, because there was no issue of goods having different degrees of liquidity (which is what drives the demand for money in the Austrian story).

Now of course, the mainstream macro guys want to be able to have a central bank in the model, and to put different monetary policy rules through a windtunnel. So there has to be “money” in the model, and there has to be a reason for people to hold it. So (at least in the standard models we were learning) they would just throw real cash balances directly in the utility function, so that the Representative Agent got utility from holding purchasing power the same way he would get utility from holding a Picasso.

It always seemed fishy to me that we were deriving “optimal” monetary policy in a model in which money really served no purpose, and where we had to make ad hoc tweaks to force people to even want to hold money.

5 Responses to “On Using Models”

  1. Jonathan M. F. Catalán says:

    Well, in regards to the Hayekian triangle, that’s pretty much what Hayek had in mind. The difference is that Hayek is clear in Prices & Production that he is going for simplicity versus absolute accuracy in his models. His intentions in Pure Theory of Capital, on the other hand, are accuracy over simplicity, which is why his models in this book are much more difficult to understand. I don’t think Hayek opposed mathematical modelling on the grounds of accuracy at all, at least not to the same degree as Mises and Rothbard.

  2. Mattheus von Guttenberg says:

    I had the exact same problems when taking my upper level macro course. My professor was explaining this model to us (it was a short run household budget constraint model in equilibrium) where C+S=Y.

    He modeled the equation as PvofConsumption + Bond holdings/Capital holdings = labor income, rent income, interest income, profit income, etc.

    And I asked him – since we weren’t using money, but a product “X” that everyone was paid wages in – how anyone could possibly earn profit income if there’s 1 good in society and we’re already in equilibrium???

    He thought for a minute.. and just erased that part of the function from the chalkboard. We never talked about it for the next 3 weeks.

    • Tel says:

      Egats! You have discovered a question that can be usefully answered by Krugman. Of course, I’m talking about the now famous babysitters, who only had one commodity (hours of babysitting) and yet it still turns out to be worth trading because some days people want to go out for the night (but those same people might be happy to stay home some other night).

      • Subhi Andrews says:

        I didn’t quite understand the point matthew was making, but I thinkin your babysitter coop that Krugman talks about, they had two goods/services of value – going out & baby sitting. Baby sitting coupons was the medium of exchange.

        BTW, after class, I asked my Macro Econ professor about whether demand creates supply or supply creates demand ( of course professor is a keynesian), she said companies will not produce unless there is demand ( which is true in the sense that they atleast believe there is a certain amount of demand) but in a more aggregate sense supply has to precede demand (I didn’t make that point at that time). I went to make a Robinson Crusoe Island analogy – professor told me that island analogies are crazy, asked me to look at the real world.

  3. Major_Freedom says:

    This reminds me of a time in one of my economics classes I took a while back.

    The prof was talking about indifference curves between two goods, X1 and X2, with the presence of a risk free bond. I can’t remember the details but I remember him assuming away that the risk free asset had a positive demand, in order to assume away money as a medium of exchange, so that he can explain why X1 and X2 traded at the ratio they did. I then stuck up my hand and said this implies the risk free bond would have an infinite return, because without a demand for the risk free asset, the price would be zero, and with a zero price, any payback of the risk free bond means infinite return. He said “you got me kiddo”, then the next week he came back with an explanation, saying “the investor would still behave as if” so many times that I lost interest.

    Could it really be the case that the nation’s foremost experts on money have absolutely no idea how money works? That their models which display direct exchange of money as opposed to indirect exchange of money really reflects a misunderstanding of money and the market process?