On Precise Mathematical Models

Mathematics is the key and the gateway to the sciences.  Roger Bacon said these words some 750 years ago.  They are as true today as they were then.  But what is also important is wisdom: knowing what you don’t know and knowing the characteristics of what you are studying.

A few days ago, I was at the horse barn for my weekly horseback riding lesson.  My trainer and I were discussing different cues among horses (some horses are more responsive to human physical commands, some more so to voice commands.  Some will lope on a small command, and some need a hard command, etc).  She said that there is no book on how to rise a horse, no formula one can follow, it can only be learned though practice and it differs from horse to horse.

There is a certain science to riding a horse.  There are techniques and training methods.  There is experimentation.  But it is hardly as precise as, say, chemistry or biology (aka the hard sciences).

Horseback riding, like economics, is a social science.  We are dealing with living, breathing, creatures with free will.  There’s an element of randomness that comes into play.

Recognizing this randomness is what separates a good economist from a bad one, a good social scientist from a bad one.  Unfortunately, many economists forget this lesson.  They’re focused on their “precise mathematical models” (to use Noah Smith’s term), and forget the logic of thinking like an economist.

Models and experiments are very important.  They help shape our thoughts, and theories must be rigorously tested time and time again.  But social sciences, especially economics, is about looking for the unknown.  How many people who would have gotten jobs now can’t because of a minimum wage hike?  How much slower is economic growth because of new regulations?  How else would have funds been used if World War 2 not occurred?  Evaluating things while looking through the “broken window fallacy” lens is important.  That is why opportunity cost is one of the first things young economists are taught (and seemingly the first thing they forget).

This is not a right-wing-left wing thing, or a free market-command market thing, or an Austrian-Keynesian thing.  Economists on both sides make the mistake of becoming obsessed with models and mathematics and forgetting the basic economic lessons.

There’s a difference between knowing mathematics and knowing economics.  Many economists are competent with the former and not the latter.

5 thoughts on “On Precise Mathematical Models

  1. One more: How much more would our standard of living (SOL) have risen without the inflationary policies of central banks (esp The Fed) over the last 40+ years?

    So much of the productivity gains of the modern economy have been stealthily siphoned off to the crony class (esp thru the finance sector) and it goes largely undetected because we still have had large SOL gains and there has low price inflation (for the most part) so they can profess that it hasn’t hurt us. Damn lies.

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  2. First off you’re asserting free will and randomness are the same thing. That isn’t true, you’re committing a fallacy of equivocation. You’re asserting randomness and free will within the same context of your premise and using them interchangeably. Randomness is a quantifiable and verifiable in mathematical models, free will can be, but is often a underpinning of other systems which don’t exist in applications of how things run. You assert that it isn’t as well. You don’t understand how mathematics are used in modeling of data to how they underpin them with the p-values in the data used. You assert that models have to be “precise mathematical models” that is purely false. Precision in the model has errors stated, otherwise you’ll just be asserting a perfect trend of anything in the data that has no underpinning of real data, to reality. You never stated that here though, you went on this talk about how data itself is this contrived system where those or all of them get lost in it. If it is the fault of anything it’s to how economics is contrived to how economists function or are trained.

    Predictive analytics is a very real thing that has and does get applied in many social aspects of understanding individuals are a group behavior to the individual of how they function in needs to wants. You don’t assert this in your premise, but rather say it’s contrived or throw “free will” as it means shutdown any talk.

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