I was skeptical but now I’m convinced: Math matters

Without a grasp of math, how good is an economist?
Without a grasp of math, how good is an economist?
Image: AP Photo / Alexander F. Yuan
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To be a successful economist, you need lots of math. The Nobel Prize in economics went to Lloyd Shapley, whose PhD is in math, and Alvin Roth, whose research includes many equations. Before the Oct. 15 announcement, Quartz’s Ritchie King marveled at how quantitative economics has become. Yet I often hear rants like this (usually from non-economists) suggesting math is ruining economics. The argument goes something like this: Equations over-simplify human behavior. Or, as in this case, that economics should have fewer equations so everyone can understand and criticize it.

I don’t know enough math to understand a theoretical physics paper. I find physics interesting and experience gravity, but I have no business telling physicists how to do their work. The scope of economic, academic research is to push the knowledge frontier forward and, from this, offer policy solutions, not appeal to lay people.

Regarding over-simplification, I’d argue the opposite. Economic models are stylized abstractions of reality; designing them is an art and a science. I once had a professor who’d compare economic models to maps. If you include every tree and back road, the map is intractable. The same is true for economic models. You choose what’s important to include in order to understand how certain factors relate to each other. Even then, the math gets very complicated. Equations help economists see subtle points, higher order effects, changes in incentives, and how their ideas relate to earlier work. It also helps them to test their theories on data.

Great economists like Paul Krugman and Greg Mankiw (on the same side for once) each eloquently defended the role of mathematics in economic research. Before I went to graduate school, I was skeptical of how much math economists used. I also quoted Alfred Marshall and cited Adam Smith as examples. I tried to read papers in top journals and believed I understood them from the introduction.

Then I enrolled in an economics PhD program that required me to learn all the techniques economists actually use. I was borderline innumerate when I started (unlike most economists, I am not a natural quant) and I don’t recommend anyone learn as much math as I did in a single year.  I still spent most of that time maintaining it was unnecessary; that the hours I spent finding sigma-algebras was merely sadistic hazing.  I pushed on because I wanted to be an economist and figured I could only credibly claim that all math was bunk if I actually understood it.

But once I learned the skills, I changed my mind. I can’t overstate how much it made me a better economist. The ability to think mathematically made me much smarter. I could hold my own in seminars because the equations clarified my thoughts and enabled me to spot logical inconsistencies in other people’s arguments. Those equations I used to ignore in papers gave me a deeper understanding of the work. Mathematics is the language economists use to communicate with each other.  It is merely a tool to describe the economy.  Is advanced math necessary to understand the economy? Of course not, but it makes it much easier.

With the exception of the most esoteric, analytic papers, the scope of most academic macroeconomic research relates to important policy questions. Papers that don’t address interesting questions aren’t published in top journals. Economists who don’t have good ideas and use math for math’s sake are usually not successful. Even the most articulate economists, who regularly come up with elegant, brilliant ideas, use math as a powerful tool. The new Nobelists are two examples of this. With challenges we face now, we need the best tools at our disposal.