Mathematics

Pick up Daron Acemoglu’s outstanding textbook “Introduction to Modern Growth” and open it randomly to any page.  There before you will be a few lines of text scattered amongst a variety of mathematical equations of varying density, complexity, and inscrutability.  It really is a wonderful book and pulls together all the wisdom existing in economics concerning the causes of that most intriguing of all questions: why and how does the economy grow?

Along the way you can be exhilarated.  You can discover the font of eternality in the notion of perpetual youth. You can see the future stretch to infinite horizons.  You can mingle with your ancestors in overlapping generations.  And you can wallow in theorems, proofs, and sundry other entertaining and sometimes difficult flora and fauna of modern economics.  

Amazing stuff.

And not only exhilarating but solidly logical.  The purpose of the pages of mathematics is to extinguish sloppy thinking from mere narrative.  It is to expose the subtleties and connections that elude us in simple speech.  It surfaces those vague notions that clutter and make ambiguous what might appear to the less mathematical as acceptable explanations of the phenomena of growth.  

This is the triumph of the mathematization of economics.  No sloppy thinking is allowed.  The various models presented in Acemoglu’s book represent a complete tour through the subject.  They are a complete odyssey.  They begin with the iconic first steps of Solow, and move through everything that has followed.  The technical progress of the discipline is astonishing.  Model after model is presented and explained in a sequence that draws us through decades of intense discussion and argument.  The elegance and pure logic on display is a testimony the those decades and to the never ending quest to produce explanations for growth that suffer from none of the failings of a merely verbal exegesis of the subject.

I tip my hat to the effort.  It’s a breathtaking achievement.

Now.  

One more thing.

That “L”.

Labor?

I always thought that “L” was for lumberjack.  All these years I have been wrong.  Those amazing models are including “labor” not “lumberjacks”.  How wrong I was!

But labor it is.  

That’s clear enough.  I mean we wouldn’t want to specify what we mean by labor would we?  It might be lumberjacks.  It might also be brain surgeons.  Or gardeners.  Or machinists.  Or artists.  Or economists [no, not that one!].  Or … well just about anything.  

That doesn’t matter though.  Who needs precision?  Who needs to be clear when all that modeling logic offsets any vagueness in the thought process?  The point is to eliminate mistakes in logic.  The point to to elucidate hidden connections and threads of thought.  The fact that the very raw material being modeled is vague doesn’t matter.

Does it?

I think it does.

I wouldn’t allow such an element of vagueness to infest a story I wrote.  Not at least if I wanted to be clear.  If I wanted to hide my uncertainty, however, I might just lull the reader with an ambiguity of specification.  I might, for instance, use the word “labor” and let the reader decide whether the object being described or analyzed was a lumberjack.  Or a brain surgeon. Or a gardener.  After all they’re all the same.  No?

Anyway, it’s nice to see the humility of economists.  All that hard earned and expensive skill.  Especially the mathematics.  And they’re all so humble that they don’t mind being confused with lumberjacks.  Not at all.  They’re all the same.  No?  All labor is the same.  It must be.  Or at least it must be to economists.

With a simple all-inclusive “L” we can substitute anyone for anyone else.  We could, for example, hear a lumberjack opine on a real business cycles or watch an economist climb that one hundred foot red oak in my backyard and prune away all those dead branches.  Labor is all the same.  No?  A lumberjack would laugh at the absurdity of it all.  Why don’t economists?

No amount of mathematical wizardry can eliminate the fog if the objects being modeled are allowed to remain foggy.  Modeling fog, however sophisticated the mathematics, still produces fog.

Allow me to introduce you to Total Factor Productivity.  Some people call it a measure of our ignorance.  I prefer to think of it as a quantity of fog.

Q.E.D.

As they say.