I Do the Maths

This semester I'm teaching Intermediate Macroeconomics for the first time. It's a tough course to teach, since I'm trying to present some of the key ideas in my field of research without (a) overwhelming the students with details they won't understand, or (b) lying to them about what real economists think and do.

I devoted a bit over half an hour of class time last week to explaining why we use so much algebra (and a little calculus, although we don't call it that) in the course. Rather than rhapsodize over the beauty and power of systems of non-linear difference equations, I decided to have them read a couple blog posts by one of the most famous development economists to grace the blogosphere, Dani Rodrik. In his first post, Rodrik uses a simple anecdote to illustrate the central reason economists translate the real world into the toy world of mathematics:

The moral of the story is that if you are smart enough to be a Nobel-prize winning economist maybe you can do without the math, but the rest of us mere mortals cannot. We need the math to make sure that we think straight--to ensure that our conclusions follow from our premises and that we haven't left loose ends hanging in our argument.

Of course, there are still points in our reasoning when economists are still vulnerable to bad logic. In particular, economists can make major blunders when identifying the most relevant parts of the real world--the parts that need to be included in the model--and when translating the implications of the models back into real world terms.  But this system is still much better than simply describing arguments in way that leaves room for sloppiness throughout the process. While we're in the mathematics of the model, we know that every result must certainly follow from the premises.

A key question I wanted my students to think about was this: Philosophers, Literary Analysts, and Journalists all make their living by presenting arguments. So why aren't they concerned about bad logic and loose ends? One student suggested the key was one of Rodrik's statements:

In explaining our extensive and demanding curriculum, I emphasize that development is too important to be left to mushy thinking.

 Essentially, the student said, economics matters more than those others. While I would disagree with this to a certain extent--journalism certainly matters because it influences public opinion, and philosophy matters because it influences future economists*--I do think there is a sense in which the consequences of bad economic policy, the inevitable result of sloppy thinking, are more costly and immediate than the consequences of bad thinking in many other disciplines.

*I don't mention literary analysts here because I don't know enough about them to know who they influence and how bad thinking in literary criticism matters. I assume it's got to matter to someone at least... right?

The second of Rodrik's posts essentially answers some criticisms of the first. Being an empirical macroeconomist, I was pleased to see Rodrik mention how much cooler we are than pure theorists; that's how I chose to read that particular comment, anyway. I also think he sums up pretty well the technical demands that are really at play when we do mathematical economics:

What matters most is a certain habit of mind--of being able and willing to break a complicated problem into its constituent parts and then put it back together. 

These are the skills I'm really trying to teach my students. Finally, I have to mention the commenter Rodrik quotes who wants to see some more humility in mathematical economic theory:

I am not supportive of economists who then forget that they have a "model", an abstraction of the world, and begin to believe that their model is the world. I find very few economists that are humble enough to admit that about their analysis.

Like Rodrik, I hope I am always humble enough to distinguish what models are helpful for and what they are not. If our interest is to help the people of less developed countries, formal economic analysis is only one component in the complex process of promoting growth. It's an important one, at least I think it is. But a sense of professional perspective is indispensable.

(Since this is an important topic to understanding how I do this, I'm going to cross post it at that other blog I contribute to. They probably won't mind.)