Mathematical economics is fraying at both ends. Critics of the over-mathematization of economics keep chipping away at the spurious correlations and the theoretical equations that are either too simple or too complicated. At the other end, notable mainstream economists like Paul Romer see fundamental problems in the way economics is done today.
His paper on “Mathiness” was picked up by the Wall Street Journal. “Mathiness” is “the use of mathematics to persuade or mislead rather than to clarify,” and is ubiquitous in the economics profession these days.
Unfortunately, Romer’s conclusion in his paper offers a non-solution:
[back in the good ol’ days] Not universally, but much more so than today, when economic theorists used math to explore abstractions, it was a point of pride to do so with clarity, precision, and rigor. Then too, a faction like Robinson’s [politically motivated] that risked losing a battle might resort to mathiness as a last-ditch defense, but doing so carried a risk. Reputations suffered.
So all the profession needs to do to get over this destructive love affair with mathiness is a fresh injection of “clarity, precision, and rigor.” This is like telling a group of criminal graffiti artists to use stencils when they’re defacing buildings.
The real problem is much deeper than Romer realizes. Economics is the science of human action. It deals with motivated human choice. As such, there are no strict quantitative relationships like the ones in the hard sciences. Objects don’t choose to fall at a certain speed, or choose to react to other objects in certain ways. Humans choose. Our choices are based on preferences which change unpredictably in an infinite number of ways over equally unpredictable and infinite varieties of circumstances.
The details of human action are unpredictable and not conducive to strict quantitative rules, but the logic of action provides a rich framework for doing economics.
Humans act in every conscious, perceptible moment. As we proceed through time, always forward, we are constantly selecting and employing means at our disposal toward the satisfaction of some end. This means that every action is costly: the means we used for our satisfaction could have been used in a different way to satisfy a different end, or we could have used a different set of means entirely to satisfy some different end. The next highest ranked alternative is the opportunity cost of any action. Because action always takes place in the present, but is forward-looking, and because we cannot revisit or retry an action in the past, there is a time cost for every action as well. Given a set of means suitable for want-satisfaction, we can mentally distribute, allocate, or plan the use of those means for a certain time or in a certain order based on our current expectations of future valuations/preference rankings. This type of action may be called a temporal allocation of means.
In production or lending or borrowing, however, we do not simply temporally allocate a given set of means toward want-satisfaction at various times, we substitute, or trade, a satisfaction of one time for a satisfaction of a different time. I may give up a present satisfaction so that I may have a future satisfaction, or I may forego a future satisfaction by presently employing some means to satisfy an end. This type of action may be called an intertemporal exchange of satisfactions. All present consumption reveals a systematic preference for present consumption over future consumption because all present consumption has the opportunity cost of delaying or postponing the consumption of the same means for later. An intertemporal exchange of present satisfaction for a future satisfaction can only happen if the future satisfaction is (presently considered) more highly ranked than the present one foregone. As such, all future satisfactions carry a present discount in relation to present satisfactions. This feature of human action is called time preference.