Straddling the Siren Song

Last night during my Austrian economics class I argued that some of the mathematics in neoclassical economics is useful for a few things, a sentiment some (all perhaps?) of my classmates did not share. Jason Briggeman challenged me to note one insight the Cobb-Douglas production function (one example I offered that could be useful to economics) but the conversation went in another direction and I was too tired to backtrack to his inquiry so I could address it. After class I promised to answer his question in a blog post so here it is.

The C-D production function is a pretty uninteresting claim: GDP depends on how much labor and how much capital a country has. However, if we combine it with the Solow growth model we can use it to prove the existence of convergence (poor countries grow faster than rich countries). In the real world, absolute convergence (all countries converge) is a myth however conditional convergence (countries with similar institutions converge) is quite real.

We do not need C-D or Solow to learn this--we can simply look at the data--but it does help explain why this happens in a clean but still useful way. Similarly, we could use pure math to explain or demonstrate conditional convergence but that would be of little use; words are much more appropriate for that. In my defense of math in economics, I ask that Austrians recognize something they've always asserted: people are heterogenous. One person may instantly grasp the intitution of convergence while another may be assisted in the calculus. To dismiss all of mathematics in economics is to deny a potential tool economists can use to demonstrate how the world works. To embrace it completely is also a mistake for it nullifies the most important questions. Mathematics misses the point in some ways, but is appropriate in others.

Math in economics is a siren song. It is beautiful and pure, but also dangerous if we focus too much on it. Yet if we completely avoid the music we will deny ourselves valuable knowledge and drastically limit where we can go (Odysseus had to travel past the sirens' island in order to continue his journey). Economists must learn to straddle this siren song: to hear it but not to succumb to it. If we can force ourselves to stay grounded, like the hero The Odyssey who tied himself to the mast of his ship, we won't miss what can be learned from mathematics nor will we drown in a barren attempt to worship this dirge.