Pretentious and Unhelpful Symbols

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Economist William Baumol, a professor emeritus at Princeton University, passed away on May 4. I imagine he couldn't bear the thought of witnessing one more silly pseudo holiday where Yankees pretend we care about Mexican history in order to drink tequila. In that case, his timing was perfect.

Baumol is one of the two gentlemen immortalized in the name of the Baumol-Tobin model of the transactions demand for money. (The other, of course, is James Tobin who passed away 15 years ago.) Baumol's paper outlining this theory preceded Tobin's by four years, but the model seems to have languished in obscurity until Tobin's revival.

Baumol did much else, too, but I'd like to write about transactions demand today. Indeed, I'm going to criticize its role in subsequent developments. This may seem a violation of the old rule "speak no ill of the dead." So I should preface it by saying the following: I'm certain Baumol made many other contributions more positive than this one, and I don't blame him for the relative prominence of this one. His passing is merely the catalyst of my invocation of Baumol-Tobin today!

The model is quite straightforward. Developed in a pre-debt card, pre-ATM era, it posits that a given individual has a demand for money (for immediately accessible cash, in the wallet or in a pillow case or the like, or in a no-cost checking account, obtainable without any further transaction with anyone). The demand is subject to a trade-off: if my money is ready at hand then it isn't earning interest and, in an inflationary environment, it is losing value. In even simpler terms: one pays a price to have cash at hand.

Given certain simplifying assumptions (which were to be relaxed in more sophisticated versions of the model developed later), Baumol's discussion of this trade-off indicated that "the rational individual will, given the price level, demand cash in proportion to the square root of the value of his transactions."

Notice, though, that this is only transactions demand. It isn't total demand for money. It is what is left when one deletes both speculative and precautionary demand. Transaction demand is the demand that arises because of the expected normal spending that has to be done from one payday to the next. Speculative demand: some good opportunity might arise that one will want to be able to act upon quickly (I may run into a scalper with really desirable tickets). Precautionary demand is that which arises because I fear something awful may happen and 'extra' cash will help deal with it.

So the supply and demand for cash determines the price of cash. One part of the demand is the transactions demand. If we imagine supply kept constant, and both of the other elements of demand kept constant, and only transaction demand changed, then we can predict the outcome for the price.

This is the epitome of the sort of "analysis" that into which too many economists get caught up. It is in principle unfalsifiable, it is useless in a pragmatic and policy-oriented sense, and it is intellectually elegant not as a virtue but as a fault.

Baumol was in essence refuted by none other than John Maynard Keynes, who in his GENERAL THEORY (1936) wrote,

"It is a great fault of symbolic pseudo-mathematical methods of formalizing a system of economic analysis -- that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed: whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols."

I'm afraid that Baumol gave rise (in the name of the elaboration of certain Keynesian theses, as it happens) to precisely this sort of maze of pretentious and unhelpful symbols.

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